Table of spherical codes

Maintained by Henry Cohn

This data is archived at https://hdl.handle.net/1721.1/153543. If you cite the table, please refer to that data set, not this web page.

A spherical code is a configuration of points on the surface of a sphere, with the goal of maximizing the minimal angle between the points. The following table lists numerically optimized codes, with cases that are known to be optimal marked with *. Each entry links to coordinates for the code. Along with references, in some cases the table lists the minimal polynomial of the cosine of the minimal angle, in which case a code with this exact angle has been proved to exist.

The table is limited to 32 dimensions and 1024 points, with a few exceptions. It omits cases that have been systematically solved, namely dimensions below three and n-dimensional codes with at most 2n points (see R. A. Rankin, The closest packing of spherical caps in n dimensions, Proc. Glasgow Math. Assoc. 2 (1955), 139–144, doi:10.1017/S2040618500033219). The entries labeled “needs more optimization” have not fully converged to a local optimum, while most of the others probably have. There are two records listed in Ericson and Zinoviev's book (Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001) that I have not included below: for 80 points in 7 dimensions, their construction describes only 78 points, and for 1024 points in 16 dimensions, I am unable to get their construction to work.

You can access a plain text table here, which includes some polynomials too large to fit below, and upload additions or improvements here.

Dimension Number of points Cosine of minimal angle References and notes
3 7* 0.210138312731 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
3⁢x3−9⁢x2−3⁢x+1
3 8* 0.261203874964 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
7⁢x2+2⁢x−1
3 9* 0.333333333334 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
3⁢x−1
3 10* 0.404394325217 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
7⁢x3−4⁢x2−2⁢x+1
3 11* 0.447213595500 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
5⁢x2−1
3 12* 0.447213595500 L. Fejes [Tóth], Über eine Abschätzung des kürzesten Abstandes zweier Punkte eines auf einer Kugelfläche liegenden Punktsystems, Jber. Deutsch. Math.-Verein. 53 (1943), 66–68.
5⁢x2−1
3 13* 0.542636486830 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The strong thirteen spheres problem, Discrete Comput. Geom. 48 (2012), 128–141, doi:10.1007/s00454-011-9392-2.
x8−24⁢x7−12⁢x6+8⁢x5+38⁢x4+24⁢x3−12⁢x2−8⁢x+1
3 14* 0.563950300361 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; O. R. Musin and A. S. Tarasov, The Tammes problem for N=14, Exp. Math. 24 (2015), 460–468, doi:10.1080/10586458.2015.1022842.
4⁢x4−2⁢x3+3⁢x2−1
3 15 0.592605902926 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944; D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
13⁢x5−x4+6⁢x3+2⁢x2−3⁢x−1
3 16 0.612294616483 K. Schütte and B. L. van der Waerden, Auf welcher Kugel haben 5, 6, 7, 8 oder 9 Punkte mit Mindestabstand Eins Platz?, Math. Ann. 123 (1951), 96–124, doi:10.1007/BF02054944.
23⁢x6+6⁢x5+5⁢x4+4⁢x3−3⁢x2−2⁢x−1
3 17 0.628094415071 L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
4⁢x10−92⁢x9+24⁢x8+128⁢x7−58⁢x6−78⁢x5+35⁢x4+32⁢x3−4⁢x2−6⁢x−1
3 18 0.648695832224 T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485.
216⁢x11+108⁢x10+118⁢x9+209⁢x8−100⁢x7−160⁢x6+40⁢x5+46⁢x4−20⁢x3−12⁢x2+2⁢x+1
3 19 0.673116887561 D. E. Lazić, V. Šenk, and I. Šeškar, Arrangements of points on a sphere which maximize the least distance, Bull. Appl. Math. (Technical University Budapest) 47 (1987), 7–21.
Minimal polynomial listed in plain text data
3 20 0.676477138130 B. L. van der Waerden, Punkte auf der Kugel. Drei Zusätze, Math. Ann. 125 (1952), 213–222, doi:10.1007/BF01343118.
21⁢x3−9⁢x2−5⁢x+1
3 21 0.699498431067 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 22 0.710306258580 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 23 0.722846984869 T. Tarnai and Zs. Gáspár, Arrangement of 23 points on a sphere (on a conjecture of R. M. Robinson), Proc. Roy. Soc. London Ser. A 433 (1991), 257–267, doi:10.1098/rspa.1991.0046.
3 24* 0.723078468334 R. M. Robinson, Arrangements of 24 points on a sphere, Math. Ann. 144 (1961), 17–48, doi:10.1007/BF01396539.
7⁢x3+x2−3⁢x−1
3 25 0.747398628578 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 26 0.754278177121 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 27 0.758389210777 T. Tarnai and Zs. Gáspár, Improved packing of equal circles on a sphere and rigidity of its graph, Math. Proc. Cambridge Philos. Soc. 93 (1983), 191–218, doi:10.1017/S0305004100060485.
Minimal polynomial listed in plain text data
3 28 0.773230262338 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 29 0.780281415949 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 30 0.781551875095 B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056.
Minimal polynomial listed in plain text data
3 31 0.791118613299 J. Strohmajer, Über die Verteilung von Punkten auf der Kugel, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 6 (1963), 49–53.
Minimal polynomial listed in plain text data
3 32 0.793616614872 L. Danzer, Finite point-sets on S2 with minimum distance as large as possible, Discrete Math. 60 (1986), 3–66, doi:10.1016/0012-365X(86)90002-6.
Minimal polynomial listed in plain text data
3 33 0.806397613648 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 34 0.810984337204 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 35 0.815937771500 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 36 0.817248185290 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 37 0.824892480240 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 38 0.826583259422 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
363⁢x14+7685⁢x12+34299⁢x10−77139⁢x8+68985⁢x6−31833⁢x4+6561⁢x2−729
3 39 0.833991322411 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 40 0.837162072474 B. W. Clare and D. L. Kepert, The closest packing of equal circles on a sphere, Proc. Roy. Soc. London Ser. A 405 (1986), 329–344, doi:10.1098/rspa.1986.0056.
3 41 0.841236343029 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 42 0.843331551639 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
Minimal polynomial listed in plain text data
3 43 0.847208865437 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 44 0.848201378305 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 45 0.854249474082 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 46 0.857534166865 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 47 0.859122361410 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 48 0.859292295076 R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775.
34⁢x5+15⁢x4−12⁢x3−14⁢x2−6⁢x−1
3 49 0.866691479049 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 50 0.868173209127 E. Székely, Sur le problème de Tammes, Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae 17 (1974), 157–175, http://annalesm.elte.hu/annales17-1974/Annales_1974_T-XVII.pdf.
Minimal polynomial listed in plain text data
3 51 0.871484364931 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 52 0.872966708781 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
Minimal polynomial listed in plain text data
3 53 0.876189803956 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 54 0.877004306358 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 55 0.880785046525 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 56 0.881731578410 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 57 0.884363737604 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 58 0.886555745177 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 59 0.887855737148 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 60 0.889473567590 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 61 0.892008443283 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 62 0.893496850569 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 63 0.895036180815 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 64 0.896988167538 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 65 0.898259108584 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 66 0.899195777484 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 67 0.901198227760 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 68 0.902856921522 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 69 0.903831506358 James Buddenhagen and D. A. Kottwitz, 1997.
3 70 0.905043036803 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 71 0.906396736776 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 72 0.906849285445 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 73 0.909571628656 James Buddenhagen and D. A. Kottwitz, 1997.
3 74 0.910532623502 D. A. Kottwitz, 1997.
3 75 0.911390904652 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 76 0.912633133084 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 77 0.913536344688 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3 78 0.914034438768 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 79 0.916195009441 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 80 0.916690360742 James Buddenhagen, 1997.
3 81 0.918117193791 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 82 0.919172412416 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 83 0.919937881756 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 84 0.920151698890 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 85 0.922004026342 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 86 0.922710627798 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 87 0.923567597265 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 88 0.924093912593 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 89 0.925099726146 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 90 0.926173483336 D. A. Kottwitz, The densest packing of equal circles on a sphere, Acta Cryst. Sect. A 47 (1991), 158–165, doi:10.1107/S0108767390011370.
3 91 0.926844825210 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 92 0.927003416243 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 93 0.928418531906 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 94 0.928979461777 James Buddenhagen and D. A. Kottwitz, 1997.
3 95 0.929811497467 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 96 0.930285673249 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 97 0.931051674650 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 98 0.931239991046 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 99 0.932727363300 James Buddenhagen and D. A. Kottwitz, 1997.
3 100 0.933385128903 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 101 0.934025767057 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 102 0.934480088172 James Buddenhagen and D. A. Kottwitz, 1997.
3 103 0.935207723062 James Buddenhagen and D. A. Kottwitz, 1997.
3 104 0.935711381000 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 105 0.936434497689 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 106 0.937042014619 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 107 0.937517802204 James Buddenhagen and D. A. Kottwitz, 1997.
3 108 0.937862018289 James Buddenhagen and D. A. Kottwitz, 1997.
3 109 0.938798085650 James Buddenhagen and D. A. Kottwitz, 1997.
3 110 0.939026290863 James Buddenhagen and D. A. Kottwitz, 1997.
3 111 0.939729959842 Henry Cohn, 2024.
3 112 0.940339774660 James Buddenhagen and D. A. Kottwitz, 1997.
3 113 0.940847649045 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 114 0.941205445297 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 115 0.941916896842 James Buddenhagen and D. A. Kottwitz, 1997.
3 116 0.942351017116 James Buddenhagen and D. A. Kottwitz, 1997.
3 117 0.942866795114 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; J. Buddenhagen and D. A. Kottwitz, Multiplicity and symmetry breaking in (conjectured) densest packings of congruent circles on a circle, undated manuscript.
3 118 0.943283453359 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 119 0.943652307933 James Buddenhagen and D. A. Kottwitz, 1997.
3 120 0.943662307333 R. M. Robinson, Finite sets of points on a sphere with each nearest to five others, Math. Ann. 179 (1969), 296–318, doi:10.1007/BF01350775.
1364⁢x10+1230⁢x9−709⁢x8−1468⁢x7−688⁢x6+136⁢x5+286⁢x4+108⁢x3+4⁢x2−6⁢x−1
3 121 0.944678061273 Henry Cohn, 2024.
3 122 0.945086237318 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 123 0.945482265531 James Buddenhagen and D. A. Kottwitz, 1997.
3 124 0.945780154584 James Buddenhagen and D. A. Kottwitz, 1997.
3 125 0.946396812867 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 126 0.946752784732 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 127 0.947264465646 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 128 0.947573544865 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 129 0.947971561157 James Buddenhagen and D. A. Kottwitz, 1997.
3 130 0.948266309315 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3 131 0.948765511183 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 132 0.948962593971 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 133 0.949572658198 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 134 0.949971678353 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 135 0.950317557456 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 136 0.950634777737 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 137 0.951024783277 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 138 0.951358398188 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 139 0.951683443186 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 140 0.951979740880 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 141 0.952385754295 Henry Cohn, 2025.
3 142 0.952693726748 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 143 0.952998670435 Henry Cohn, 2024.
3 144 0.953228409663 Henry Cohn, 2025.
3 145 0.953609890346 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 146 0.953890527065 Henry Cohn, 2024.
3 147 0.954232032048 Henry Cohn, 2024.
3 148 0.954536757950 Henry Cohn, 2025.
3 149 0.954857978400 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 150 0.955020893900 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 151 0.955409384784 Henry Cohn, 2024.
3 152 0.955652691422 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 153 0.955934479813 Henry Cohn, 2025.
3 154 0.956200715693 Henry Cohn, 2024.
3 155 0.956523743427 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 156 0.956672320428 Henry Cohn, 2024.
3 157 0.957096132346 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 158 0.957339288658 Henry Cohn, 2024.
3 159 0.957588843682 Henry Cohn, 2024.
3 160 0.957856569962 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 161 0.958127175342 Henry Cohn, 2024.
3 162 0.958288809704 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 163 0.958615566728 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 164 0.958889976688 Henry Cohn, 2024.
3 165 0.959124889495 Henry Cohn, 2024.
3 166 0.959323846675 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 167 0.959625833713 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 168 0.959759331314 Henry Cohn, 2025.
3 169 0.960021869084 Henry Cohn, 2025.
3 170 0.960117137568 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121 (see footnote 1).
3 171 0.960456738161 Henry Cohn, 2025.
3 172 0.960629559055 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 173 0.960986467408 Henry Cohn, 2025.
3 174 0.961153945452 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 175 0.961330724045 Henry Cohn, 2024.
3 176 0.961593582498 Henry Cohn, 2024.
3 177 0.961828786663 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 178 0.961965173662 Henry Cohn, 2024.
3 179 0.962096013263 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 180 0.962128794086 T. Tarnai, Packing of 180 equal circles on a sphere, Elem. Math. 38 (1983), 119–122, doi:10.5169/seals-37194.
Minimal polynomial listed in plain text data
3 181 0.962508969964 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 182 0.962801835015 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 183 0.962987455061 Henry Cohn, 2024.
3 184 0.963227493195 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 185 0.963400251151 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 186 0.963602302299 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 187 0.963858096099 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 188 0.964002261472 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 189 0.964190407206 Henry Cohn, 2024.
3 190 0.964292984546 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 191 0.964504935278 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 192 0.964585751396 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 193 0.964893730830 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 194 0.965083352280 Henry Cohn, 2024.
3 195 0.965251036900 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 196 0.965468021791 Henry Cohn, 2024.
3 197 0.965671400310 Henry Cohn, 2025.
3 198 0.965829315374 Henry Cohn, 2024.
3 199 0.965916172795 Henry Cohn, 2024.
3 200 0.965942044452 Henry Cohn, 2025.
3 201 0.966306900791 Henry Cohn, 2024.
3 202 0.966420952188 Henry Cohn, 2025.
3 203 0.966622724376 Henry Cohn, 2024.
3 204 0.966712897537 Henry Cohn, 2024.
3 205 0.966826978769 Henry Cohn, 2025.
3 206 0.967078415732 Henry Cohn, 2024.
3 207 0.967258049747 Henry Cohn, 2024.
3 208 0.967362842483 Henry Cohn, 2024.
3 209 0.967547223611 Henry Cohn, 2024.
3 210 0.967630597679 Henry Cohn, 2024.
3 211 0.967822897132 Henry Cohn, 2024.
3 212 0.967927157323 Henry Cohn, 2024.
3 213 0.968163116144 Henry Cohn, 2024.
3 214 0.968277360489 Henry Cohn, 2025.
3 215 0.968453681521 Henry Cohn, 2024.
3 216 0.968596893733 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 217 0.968776493956 Henry Cohn, 2025.
3 218 0.968883394297 Henry Cohn, 2025.
3 219 0.969051617681 Henry Cohn, 2025.
3 220 0.969138855053 Henry Cohn, 2024.
3 221 0.969215831481 Henry Cohn, 2024.
3 222 0.969434787486 Henry Cohn, 2024.
3 223 0.969554841105 Henry Cohn, 2024.
3 224 0.969694397387 Henry Cohn, 2024.
3 225 0.969832486673 Henry Cohn, 2024.
3 226 0.969909293134 Henry Cohn, 2026.
3 227 0.970127376655 Henry Cohn, 2025.
3 228 0.970249147842 Henry Cohn, 2024.
3 229 0.970369120893 Henry Cohn, 2025.
3 230 0.970483445180 Henry Cohn, 2024.
3 231 0.970608829668 Henry Cohn, 2024.
3 232 0.970693980479 Henry Cohn, 2024.
3 233 0.970846696940 Henry Cohn, 2025.
3 234 0.970904333828 Henry Cohn, 2025.
3 235 0.971108669673 Henry Cohn, 2025.
3 236 0.971194820033 Henry Cohn, 2024.
3 237 0.971302463818 Henry Cohn, 2024.
3 238 0.971452268582 Henry Cohn, 2025.
3 239 0.971571256039 Henry Cohn, 2024.
3 240 0.971657594484 Henry Cohn, 2024.
3 241 0.971802213952 Henry Cohn, 2024.
3 242 0.971893361216 Henry Cohn, 2025.
3 243 0.971985441053 Henry Cohn, 2024.
3 244 0.972112111081 Henry Cohn, 2025.
3 245 0.972207255147 Henry Cohn, 2024.
3 246 0.972337795891 Henry Cohn, 2024.
3 247 0.972484516196 Henry Cohn, 2024.
3 248 0.972578579063 Henry Cohn, 2026.
3 249 0.972727698402 Henry Cohn, 2024.
3 250 0.972808023884 Henry Cohn, 2025.
3 251 0.972878488641 Henry Cohn, 2025.
3 252 0.973005270899 Henry Cohn, 2024.
3 253 0.973112111220 Henry Cohn, 2024.
3 254 0.973166303401 Henry Cohn, 2026.
3 255 0.973336098901 Henry Cohn, 2025.
3 256 0.973419418775 Henry Cohn, 2024.
3 257 0.973518713646 Henry Cohn, 2024.
3 258 0.973601287197 Henry Cohn, 2024.
3 259 0.973687576212 Henry Cohn, 2024.
3 260 0.973743009714 Henry Cohn, 2024.
3 261 0.973920735044 Henry Cohn, 2025.
3 262 0.974027125019 Henry Cohn, 2024.
3 263 0.974151459437 Henry Cohn, 2024.
3 264 0.974246723175 Henry Cohn, 2026, needs more optimization.
3 265 0.974330655728 Henry Cohn, 2024.
3 266 0.974398321697 Henry Cohn, 2024.
3 267 0.974465984042 Henry Cohn, 2025.
3 268 0.974543890479 Henry Cohn, 2024.
3 269 0.974603593005 Henry Cohn, 2024.
3 270 0.974616849625 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
Minimal polynomial listed in plain text data
3 271 0.974808781632 Henry Cohn, 2024.
3 272 0.974950342892 Henry Cohn, 2024.
3 273 0.975065447378 Henry Cohn, 2024.
3 274 0.975124578016 Henry Cohn, 2024.
3 275 0.975240636386 Henry Cohn, 2024.
3 276 0.975320045419 Henry Cohn, 2024.
3 277 0.975403410833 Henry Cohn, 2026.
3 278 0.975464347279 Henry Cohn, 2024.
3 279 0.975521244170 Henry Cohn, 2024.
3 280 0.975556159117 Henry Cohn, 2024.
3 281 0.975696078155 Henry Cohn, 2024.
3 282 0.975817103894 X. Lai, D. Yue, J.-K. Hao, F. Glover, and Z. Lü, Iterated dynamic neighborhood search for packing equal circles on a sphere, Comput. Oper. Res. 151 (2023), Paper No. 106121, 17 pp., doi:10.1016/j.cor.2022.106121.
3 283 0.975926949120 Henry Cohn, 2024.
3 284 0.976026277162 Henry Cohn, 2024.
3 285 0.976129872554 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 286 0.976190218722 Henry Cohn, 2026, needs more optimization.
3 287 0.976292535597 Henry Cohn, 2024.
3 288 0.976363801867 Henry Cohn, 2026.
3 289 0.976439859800 Henry Cohn, 2024.
3 290 0.976500970455 Henry Cohn, 2024.
3 291 0.976554952830 Henry Cohn, 2024.
3 292 0.976605729892 Henry Cohn, 2024.
3 293 0.976711107353 Henry Cohn, 2024.
3 294 0.976800057925 Henry Cohn, 2024.
3 295 0.976890767574 Henry Cohn, 2024.
3 296 0.976945912178 Henry Cohn, 2024.
3 297 0.977073329897 Henry Cohn, 2024.
3 298 0.977138858396 Henry Cohn, 2026, needs more optimization.
3 299 0.977212486453 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 300 0.977219217071 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
Minimal polynomial listed in plain text data
3 301 0.977392313268 Henry Cohn, 2024.
3 302 0.977456955232 Henry Cohn, 2026.
3 303 0.977523371220 Henry Cohn, 2024.
3 304 0.977583884150 Henry Cohn, 2024.
3 305 0.977632490985 Henry Cohn, 2024.
3 306 0.977704022662 Henry Cohn, 2026, needs more optimization.
3 307 0.977813909097 Henry Cohn, 2026.
3 308 0.977892051736 Henry Cohn, 2024.
3 309 0.977961312021 Henry Cohn, 2024.
3 310 0.978013425289 Henry Cohn, 2024.
3 311 0.978090634292 Henry Cohn, 2024.
3 312 0.978120344725 Henry Cohn, 2026, needs more optimization.
3 313 0.978224715180 Henry Cohn, 2026, needs more optimization.
3 314 0.978264330414 Henry Cohn, 2026.
3 315 0.978359778769 Henry Cohn, 2024.
3 316 0.978410524035 Henry Cohn, 2026, needs more optimization.
3 317 0.978487475787 Henry Cohn, 2024.
3 318 0.978544321333 Henry Cohn, 2026.
3 319 0.978603060123 Henry Cohn, 2024.
3 320 0.978663267012 Henry Cohn, 2024.
3 321 0.978701173891 Henry Cohn, 2026, needs more optimization.
3 322 0.978822184431 Henry Cohn, 2026.
3 323 0.978911588007 Henry Cohn, 2024.
3 324 0.978994028886 Henry Cohn, 2026, needs more optimization.
3 325 0.979042391577 Henry Cohn, 2026, needs more optimization.
3 326 0.979095664122 Henry Cohn, 2026, needs more optimization.
3 327 0.979174283158 Henry Cohn, 2026.
3 328 0.979218771893 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 329 0.979277586775 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 330 0.979324628117 Henry Cohn, 2026, needs more optimization.
3 331 0.979372870264 Henry Cohn, 2026, needs more optimization.
3 332 0.979423824372 Henry Cohn, 2024.
3 333 0.979489583411 Uploaded by anonymous internet user, 2026.
3 334 0.979582034493 Henry Cohn, 2024.
3 335 0.979642932989 Henry Cohn, 2024.
3 336 0.979686468464 Henry Cohn, 2026.
3 337 0.979751882491 Henry Cohn, 2026.
3 338 0.979838818714 Henry Cohn, 2024.
3 339 0.979904919491 Henry Cohn, 2024.
3 340 0.979943850373 Henry Cohn, 2026.
3 341 0.979999270037 Henry Cohn, 2026.
3 342 0.980044047715 Henry Cohn, 2024.
3 343 0.980089600940 Henry Cohn, 2026.
3 344 0.980135977822 Henry Cohn, 2024.
3 345 0.980197727452 Henry Cohn, 2026, needs more optimization.
3 346 0.980275208082 Henry Cohn, 2024.
3 347 0.980349152228 Henry Cohn, 2024.
3 348 0.980406993197 Henry Cohn, 2024.
3 349 0.980459797495 Henry Cohn, 2026.
3 350 0.980513222800 Henry Cohn, 2026, needs more optimization.
3 351 0.980569841643 Henry Cohn, 2026, needs more optimization.
3 352 0.980619398778 Henry Cohn, 2024.
3 353 0.980684289246 Henry Cohn, 2026, needs more optimization.
3 354 0.980732120240 Henry Cohn, 2026, needs more optimization.
3 355 0.980776958770 Henry Cohn, 2024.
3 356 0.980821413544 Henry Cohn, 2026, needs more optimization.
3 357 0.980865743540 Henry Cohn, 2026.
3 358 0.980900885582 Henry Cohn, 2026.
3 359 0.980938721612 Henry Cohn, 2024.
3 360 0.980946761337 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
3 361 0.981091247737 Henry Cohn, 2026.
3 362 0.981168174853 Henry Cohn, 2026, needs more optimization.
3 363 0.981225268927 Henry Cohn, 2024.
3 364 0.981274673313 Henry Cohn, 2026, needs more optimization.
3 365 0.981316235560 Henry Cohn, 2026, needs more optimization.
3 366 0.981370227579 Henry Cohn, 2026.
3 367 0.981413141131 Henry Cohn, 2026.
3 368 0.981467030026 Henry Cohn, 2024.
3 369 0.981501369093 Henry Cohn, 2024.
3 370 0.981559453185 Henry Cohn, 2024.
3 371 0.981613640563 Henry Cohn, 2024.
3 372 0.981659202089 Henry Cohn, 2024.
3 373 0.981715627838 Henry Cohn, 2024.
3 374 0.981743695439 Henry Cohn, 2024.
3 375 0.981792889902 Henry Cohn, 2024.
3 376 0.981825598990 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 377 0.981882570132 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 378 0.981926575478 Henry Cohn, 2024.
3 379 0.981950820416 Henry Cohn, 2026, needs more optimization.
3 380 0.981966079866 Henry Cohn, 2025.
3 381 0.982053259897 Henry Cohn, 2026.
3 382 0.982151506158 Henry Cohn, 2026.
3 383 0.982191165481 Henry Cohn, 2024.
3 384 0.982231012956 Henry Cohn, 2026.
3 385 0.982281435205 Henry Cohn, 2024.
3 386 0.982306281079 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 387 0.982346497568 Henry Cohn, 2024.
3 388 0.982373183313 Henry Cohn, 2024.
3 389 0.982413940425 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 390 0.982438912809 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 391 0.982527810044 Henry Cohn, 2026, needs more optimization.
3 392 0.982588475638 Henry Cohn, 2026.
3 393 0.982649357699 Henry Cohn, 2024.
3 394 0.982692375827 Henry Cohn, 2024.
3 395 0.982725448100 Henry Cohn, 2026.
3 396 0.982765123660 Henry Cohn, 2026, needs more optimization.
3 397 0.982798694889 Henry Cohn, 2026.
3 398 0.982818286825 Henry Cohn, 2026, needs more optimization.
3 399 0.982856003493 Henry Cohn, 2026.
3 400 0.982906066576 Henry Cohn, 2026.
3 401 0.982947111243 Henry Cohn, 2026.
3 402 0.982978704486 Henry Cohn, 2026.
3 403 0.983047226508 Henry Cohn, 2026, needs more optimization.
3 404 0.983109826036 Henry Cohn, 2026, needs more optimization.
3 405 0.983167971716 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 406 0.983206265163 Henry Cohn, 2024.
3 407 0.983245189251 Henry Cohn, 2026.
3 408 0.983288123210 Henry Cohn, 2024.
3 409 0.983324857501 Henry Cohn, 2024.
3 410 0.983353344472 Henry Cohn, 2026.
3 411 0.983397760620 Henry Cohn, 2024.
3 412 0.983427715393 Henry Cohn, 2026.
3 413 0.983461427167 Henry Cohn, 2024.
3 414 0.983495155996 Henry Cohn, 2024.
3 415 0.983543364662 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 416 0.983572356049 Henry Cohn, 2024.
3 417 0.983606337391 Henry Cohn, 2026.
3 418 0.983665321041 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 419 0.983706936316 Henry Cohn, 2026.
3 420 0.983735076323 Henry Cohn, 2026, needs more optimization.
3 421 0.983801876824 Henry Cohn, 2024.
3 422 0.983830218357 Henry Cohn, 2026, needs more optimization.
3 423 0.983865935748 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 424 0.983899706345 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 425 0.983936732284 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 426 0.983967656850 Henry Cohn, 2024.
3 427 0.984017759902 Henry Cohn, 2024.
3 428 0.984058613099 Henry Cohn, 2026.
3 429 0.984081497349 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 430 0.984128863955 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 431 0.984165514392 Henry Cohn, 2024.
3 432 0.984201636678 Henry Cohn, 2024.
3 433 0.984245053116 Henry Cohn, 2026, needs more optimization.
3 434 0.984271594586 Henry Cohn, 2026, needs more optimization.
3 435 0.984318874079 Henry Cohn, 2026.
3 436 0.984359381087 Henry Cohn, 2024.
3 437 0.984376596212 Henry Cohn, 2024.
3 438 0.984419779873 Henry Cohn, 2024.
3 439 0.984454579489 Henry Cohn, 2026, needs more optimization.
3 440 0.984472421765 Henry Cohn, 2024.
3 441 0.984527980944 Henry Cohn, 2024.
3 442 0.984558411966 Henry Cohn, 2026, needs more optimization.
3 443 0.984592266668 Henry Cohn, 2024.
3 444 0.984628415926 Henry Cohn, 2024.
3 445 0.984660232607 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 446 0.984702068844 Henry Cohn, 2024.
3 447 0.984730509217 Henry Cohn, 2024.
3 448 0.984778913431 Henry Cohn, 2024.
3 449 0.984798090520 Henry Cohn, 2026, needs more optimization.
3 450 0.984834221710 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 451 0.984869418821 Henry Cohn, 2026.
3 452 0.984911000119 Henry Cohn, 2024.
3 453 0.984942286924 Henry Cohn, 2024.
3 454 0.984966228755 Henry Cohn, 2026, needs more optimization.
3 455 0.984994478749 Henry Cohn, 2024.
3 456 0.985031017295 Henry Cohn, 2024.
3 457 0.985064695326 Henry Cohn, 2024.
3 458 0.985097884587 Henry Cohn, 2024.
3 459 0.985125472667 Henry Cohn, 2026, needs more optimization.
3 460 0.985147680862 Henry Cohn, 2026.
3 461 0.985183865100 Henry Cohn, 2026, needs more optimization.
3 462 0.985218304940 Henry Cohn, 2026.
3 463 0.985261069429 Henry Cohn, 2026.
3 464 0.985297019485 Henry Cohn, 2024.
3 465 0.985320807146 Henry Cohn, 2026.
3 466 0.985359575651 Henry Cohn, 2026, needs more optimization.
3 467 0.985386081788 Henry Cohn, 2024.
3 468 0.985411837325 Henry Cohn, 2024.
3 469 0.985444627723 Henry Cohn, 2024.
3 470 0.985482640963 Henry Cohn, 2024.
3 471 0.985509915678 Henry Cohn, 2024.
3 472 0.985523730012 Henry Cohn, 2026.
3 473 0.985558412595 Henry Cohn, 2024.
3 475 0.985596616344 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 476 0.985629966650 Henry Cohn, 2026.
3 477 0.985650812703 Henry Cohn, 2026.
3 478 0.985679876222 Henry Cohn, 2026.
3 479 0.985699836279 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 480 0.985721861452 T. Tarnai and Zs. Gáspár, Multi-symmetric close packings of equal spheres on the spherical surface, Acta Cryst. Sect. A 43 (1987), 612–616, doi:10.1107/S0108767387098842.
3 481 0.985794622844 Henry Cohn, 2026.
3 482 0.985841177159 Henry Cohn, 2026, needs more optimization.
3 483 0.985869964684 Henry Cohn, 2026.
3 484 0.985899970950 Henry Cohn, 2026, needs more optimization.
3 485 0.985916387073 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 486 0.985950768752 Henry Cohn, 2024.
3 487 0.985985004243 Henry Cohn, 2024.
3 488 0.986009149228 Henry Cohn, 2024.
3 489 0.986026483781 Henry Cohn, 2024.
3 490 0.986059626300 Henry Cohn, 2026, needs more optimization.
3 491 0.986099610800 Henry Cohn, 2024.
3 492 0.986121929372 Henry Cohn, 2024.
3 493 0.986156039294 Henry Cohn, 2026, needs more optimization.
3 494 0.986181802784 Henry Cohn, 2026, needs more optimization.
3 495 0.986212504789 Henry Cohn, 2026.
3 496 0.986246272307 Henry Cohn, 2024.
3 497 0.986267131233 Henry Cohn, 2024.
3 498 0.986298103712 Henry Cohn, 2024.
3 499 0.986323180888 Henry Cohn, 2024.
3 500 0.986340444099 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 501 0.986368725989 Henry Cohn, 2026.
3 502 0.986395118302 Henry Cohn, 2026, needs more optimization.
3 503 0.986428428291 Henry Cohn, 2024.
3 504 0.986455469484 Henry Cohn, 2024.
3 505 0.986472546669 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 506 0.986501726579 Henry Cohn, 2026.
3 507 0.986527855040 Henry Cohn, 2024.
3 508 0.986549751783 Henry Cohn, 2026, needs more optimization.
3 509 0.986555665406 Henry Cohn, 2026, needs more optimization.
3 510 0.986562950498 Henry Cohn, 2025.
3 511 0.986616701042 Henry Cohn, 2026.
3 512 0.986666793363 Henry Cohn, 2026.
3 513 0.986700077118 Henry Cohn, 2024.
3 514 0.986720532797 Henry Cohn, 2024.
3 515 0.986747912527 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 516 0.986772800882 Henry Cohn, 2026.
3 517 0.986799492641 Henry Cohn, 2024.
3 518 0.986819181629 Henry Cohn, 2026.
3 519 0.986843855828 Henry Cohn, 2026, needs more optimization.
3 520 0.986876145782 Henry Cohn, 2024.
3 521 0.986900278325 Henry Cohn, 2024.
3 522 0.986922042800 Henry Cohn, 2026, needs more optimization.
3 523 0.986949812576 Henry Cohn, 2026, needs more optimization.
3 524 0.986971259359 Henry Cohn, 2026, needs more optimization.
3 525 0.986995192288 Henry Cohn, 2026.
3 526 0.987019236077 Henry Cohn, 2024.
3 527 0.987045953386 Henry Cohn, 2026.
3 528 0.987069504316 Henry Cohn, 2024.
3 529 0.987089590281 Henry Cohn, 2024.
3 530 0.987121524163 Henry Cohn, 2024.
3 531 0.987141738237 Henry Cohn, 2024.
3 532 0.987165596115 Henry Cohn, 2024.
3 533 0.987185368627 Henry Cohn, 2024.
3 534 0.987215557894 Henry Cohn, 2024.
3 535 0.987233678537 Henry Cohn, 2026, needs more optimization.
3 536 0.987259191622 Henry Cohn, 2024.
3 537 0.987271183218 Henry Cohn, 2024.
3 538 0.987299580832 Henry Cohn, 2026.
3 539 0.987336486625 Henry Cohn, 2024.
3 540 0.987351430022 Henry Cohn, 2024.
3 541 0.987374329775 Henry Cohn, 2026.
3 542 0.987388996662 Henry Cohn, 2024.
3 543 0.987423671103 Henry Cohn, 2026.
3 544 0.987447704608 Henry Cohn, 2024.
3 545 0.987469058651 Henry Cohn, 2024.
3 546 0.987491594825 Henry Cohn, 2024.
3 547 0.987512470728 Henry Cohn, 2024.
3 548 0.987533400403 Henry Cohn, 2024.
3 549 0.987547178474 Henry Cohn, 2024.
3 550 0.987583651579 Henry Cohn, 2026.
3 551 0.987606449640 Henry Cohn, 2024.
3 552 0.987622107541 Henry Cohn, 2026, needs more optimization.
3 553 0.987648249263 Henry Cohn, 2024.
3 554 0.987670281304 Henry Cohn, 2024.
3 555 0.987693259384 Henry Cohn, 2024.
3 556 0.987718378190 Henry Cohn, 2024.
3 557 0.987733482064 Henry Cohn, 2026.
3 558 0.987758227820 Henry Cohn, 2026, needs more optimization.
3 559 0.987780703660 Henry Cohn, 2026.
3 560 0.987804065628 Henry Cohn, 2024.
3 561 0.987825037070 Henry Cohn, 2024.
3 562 0.987840456566 Henry Cohn, 2026.
3 563 0.987867088796 Henry Cohn, 2024.
3 564 0.987882106063 Henry Cohn, 2026, needs more optimization.
3 565 0.987909929449 Henry Cohn, 2026.
3 566 0.987930679295 Henry Cohn, 2024.
3 567 0.987952567335 Henry Cohn, 2024.
3 568 0.987974408939 Henry Cohn, 2024.
3 569 0.987994333054 Henry Cohn, 2024.
3 570 0.988009696089 Henry Cohn, 2026.
3 571 0.988036994032 Henry Cohn, 2024.
3 572 0.988045143812 Henry Cohn, 2025.
3 573 0.988071110674 Henry Cohn, 2026.
3 574 0.988099427052 Henry Cohn, 2024.
3 575 0.988116092887 Henry Cohn, 2024.
3 576 0.988134624929 Henry Cohn, 2024.
3 577 0.988155543378 Henry Cohn, 2024.
3 578 0.988175563350 Henry Cohn, 2024.
3 579 0.988199193100 Henry Cohn, 2024.
3 580 0.988214394071 Henry Cohn, 2024.
3 581 0.988236302808 Henry Cohn, 2024.
3 582 0.988258915209 Henry Cohn, 2024.
3 583 0.988278440743 Henry Cohn, 2024.
3 584 0.988296373611 Henry Cohn, 2024.
3 585 0.988316187693 Henry Cohn, 2024.
3 586 0.988336136398 Henry Cohn, 2024.
3 587 0.988354165587 Henry Cohn, 2024.
3 588 0.988367697736 Henry Cohn, 2026.
3 589 0.988390327285 Henry Cohn, 2024.
3 590 0.988413417033 Henry Cohn, 2024.
3 591 0.988426313006 Henry Cohn, 2026.
3 592 0.988448203051 Henry Cohn, 2026, needs more optimization.
3 593 0.988465092827 Henry Cohn, 2026, needs more optimization.
3 594 0.988487490044 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 595 0.988509243514 Henry Cohn, 2024.
3 596 0.988525644295 Henry Cohn, 2026.
3 597 0.988541943633 Henry Cohn, 2026.
3 598 0.988562584541 Henry Cohn, 2026.
3 599 0.988581647683 Henry Cohn, 2024.
3 600 0.988601034993 Henry Cohn, 2024.
3 601 0.988621946438 Henry Cohn, 2024.
3 602 0.988636181250 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 603 0.988656705182 Henry Cohn, 2026.
3 604 0.988675027867 Henry Cohn, 2024.
3 605 0.988698898761 Henry Cohn, 2026.
3 606 0.988712847782 Henry Cohn, 2024.
3 607 0.988726120928 Henry Cohn, 2026, needs more optimization.
3 608 0.988753049193 Henry Cohn, 2026, needs more optimization.
3 609 0.988760157529 Henry Cohn, 2024.
3 610 0.988786015398 Henry Cohn, 2026, needs more optimization.
3 611 0.988800912579 Henry Cohn, 2026, needs more optimization.
3 612 0.988821722164 Henry Cohn, 2026.
3 613 0.988842455232 Henry Cohn, 2024.
3 614 0.988857096430 Henry Cohn, 2024.
3 615 0.988871501752 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 616 0.988892714835 Henry Cohn, 2024.
3 617 0.988912783824 Henry Cohn, 2024.
3 618 0.988927807992 Henry Cohn, 2024.
3 619 0.988948201134 Henry Cohn, 2025.
3 620 0.988948235960 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 621 0.988984109802 Henry Cohn, 2024.
3 622 0.989000035626 Henry Cohn, 2026.
3 623 0.989012818314 Henry Cohn, 2024.
3 624 0.989034528790 Henry Cohn, 2024.
3 625 0.989047039560 Henry Cohn, 2026.
3 626 0.989070144515 Henry Cohn, 2026.
3 627 0.989088135354 Henry Cohn, 2024.
3 628 0.989102260063 Henry Cohn, 2026, needs more optimization.
3 629 0.989121123248 Henry Cohn, 2024.
3 630 0.989134691942 Henry Cohn, 2024.
3 631 0.989155822068 Henry Cohn, 2024.
3 632 0.989172993109 Henry Cohn, 2024.
3 633 0.989188471837 Henry Cohn, 2024.
3 634 0.989201672520 Henry Cohn, 2026, needs more optimization.
3 635 0.989217714617 Henry Cohn, 2026.
3 636 0.989241817788 Henry Cohn, 2026, needs more optimization.
3 637 0.989258652996 Henry Cohn, 2026, needs more optimization.
3 638 0.989267204518 Henry Cohn, 2024.
3 639 0.989289999844 Henry Cohn, 2026.
3 640 0.989301986015 Henry Cohn, 2024.
3 641 0.989321411266 Henry Cohn, 2024.
3 642 0.989332573182 Henry Cohn, 2024.
3 643 0.989348424838 Henry Cohn, 2026.
3 644 0.989370321417 Henry Cohn, 2026, needs more optimization.
3 645 0.989382211173 Henry Cohn, 2026.
3 646 0.989398690989 Henry Cohn, 2024.
3 647 0.989412931660 Henry Cohn, 2026.
3 648 0.989432732650 Henry Cohn, 2026, needs more optimization.
3 649 0.989449788067 Henry Cohn, 2026, needs more optimization.
3 650 0.989461679845 Henry Cohn, 2026.
3 651 0.989485039605 Henry Cohn, 2024.
3 652 0.989499769582 Henry Cohn, 2026, needs more optimization.
3 653 0.989517659733 Henry Cohn, 2024.
3 654 0.989528389272 Henry Cohn, 2024.
3 655 0.989544914621 Henry Cohn, 2026.
3 656 0.989563787961 Henry Cohn, 2024.
3 657 0.989576352164 Henry Cohn, 2024.
3 658 0.989590441670 Henry Cohn, 2024.
3 659 0.989608602208 Henry Cohn, 2024.
3 660 0.989620099017 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 661 0.989637856948 Henry Cohn, 2026.
3 662 0.989658469367 Henry Cohn, 2024.
3 663 0.989668542979 Henry Cohn, 2024.
3 664 0.989679965913 Henry Cohn, 2026.
3 665 0.989692795314 Henry Cohn, 2026, needs more optimization.
3 666 0.989717351243 Henry Cohn, 2026.
3 667 0.989730982552 Henry Cohn, 2026.
3 668 0.989745107483 Henry Cohn, 2026, needs more optimization.
3 669 0.989759503144 Henry Cohn, 2026, needs more optimization.
3 670 0.989765777159 Henry Cohn, 2024.
3 671 0.989789044042 Henry Cohn, 2026.
3 672 0.989793192154 Henry Cohn, 2026.
3 673 0.989818330488 Henry Cohn, 2024.
3 674 0.989830195771 Henry Cohn, 2026.
3 675 0.989846916474 Henry Cohn, 2026, needs more optimization.
3 676 0.989861529212 Henry Cohn, 2024.
3 677 0.989873040790 Henry Cohn, 2026.
3 678 0.989879779829 Henry Cohn, 2024.
3 679 0.989905658846 Henry Cohn, 2026.
3 680 0.989918641431 Henry Cohn, 2026, needs more optimization.
3 681 0.989936920244 Henry Cohn, 2024.
3 682 0.989953273780 Henry Cohn, 2026.
3 683 0.989967898456 Henry Cohn, 2026, needs more optimization.
3 684 0.989976775468 Henry Cohn, 2026.
3 685 0.990001194661 Henry Cohn, 2026, needs more optimization.
3 686 0.990006418271 Henry Cohn, 2024.
3 687 0.990018591365 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 688 0.990037853003 Henry Cohn, 2024.
3 689 0.990050270939 Henry Cohn, 2026.
3 692 0.990060116362 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 693 0.990078939985 Henry Cohn, 2026, needs more optimization.
3 694 0.990103743087 Henry Cohn, 2026, needs more optimization.
3 695 0.990114989762 Henry Cohn, 2026.
3 696 0.990138293016 Henry Cohn, 2026.
3 697 0.990163001875 Henry Cohn, 2026.
3 698 0.990178131415 Henry Cohn, 2024.
3 700 0.990178902285 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 701 0.990202422862 Henry Cohn, 2026, needs more optimization.
3 702 0.990207507930 Henry Cohn, 2025.
3 703 0.990226501892 Henry Cohn, 2026.
3 704 0.990247522104 Henry Cohn, 2026, needs more optimization.
3 705 0.990263988750 Henry Cohn, 2026, needs more optimization.
3 706 0.990280269273 Henry Cohn, 2026.
3 707 0.990307749113 Henry Cohn, 2024.
3 708 0.990308161139 Henry Cohn, 2026, needs more optimization.
3 709 0.990323405334 Henry Cohn, 2026.
3 710 0.990330662130 Henry Cohn, 2026.
3 711 0.990344030199 Henry Cohn, 2026.
3 712 0.990367295324 Henry Cohn, 2026.
3 713 0.990383183483 Henry Cohn, 2026, needs more optimization.
3 714 0.990387021113 Henry Cohn, 2026, needs more optimization.
3 715 0.990399232380 Henry Cohn, 2026, needs more optimization.
3 716 0.990424201178 Henry Cohn, 2024.
3 717 0.990435741748 Henry Cohn, 2026, needs more optimization.
3 718 0.990448237688 Henry Cohn, 2024.
3 719 0.990461529899 Henry Cohn, 2024.
3 720 0.990474919274 Henry Cohn, 2024.
3 721 0.990485931183 Henry Cohn, 2026.
3 722 0.990499809958 Henry Cohn, 2024.
3 723 0.990511130438 Henry Cohn, 2026, needs more optimization.
3 724 0.990532198847 Henry Cohn, 2024.
3 725 0.990534529638 Henry Cohn, 2024.
3 726 0.990551400323 Henry Cohn, 2026, needs more optimization.
3 727 0.990566965324 Henry Cohn, 2024.
3 728 0.990571170733 Henry Cohn, 2026, needs more optimization.
3 729 0.990582447225 Henry Cohn, 2026.
3 730 0.990603287439 Henry Cohn, 2024.
3 731 0.990612626443 Henry Cohn, 2024.
3 732 0.990621413211 Henry Cohn, 2025.
3 733 0.990635126076 Henry Cohn, 2026, needs more optimization.
3 734 0.990652693534 Henry Cohn, 2026, needs more optimization.
3 735 0.990663442704 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 736 0.990680033860 Henry Cohn, 2026.
3 737 0.990695306177 Henry Cohn, 2024.
3 738 0.990704677084 Henry Cohn, 2024.
3 739 0.990712804225 Henry Cohn, 2026, needs more optimization.
3 740 0.990728865941 Henry Cohn, 2024.
3 741 0.990738820030 Henry Cohn, 2026.
3 742 0.990755361153 Henry Cohn, 2024.
3 743 0.990760199525 Henry Cohn, 2026.
3 744 0.990775592495 Henry Cohn, 2026.
3 745 0.990786255617 Henry Cohn, 2026, needs more optimization.
3 746 0.990800147694 Henry Cohn, 2026, needs more optimization.
3 747 0.990816878553 Henry Cohn, 2024.
3 748 0.990825554002 Henry Cohn, 2026, needs more optimization.
3 749 0.990837968357 Henry Cohn, 2026.
3 750 0.990841277672 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 751 0.990857663690 Henry Cohn, 2024.
3 752 0.990870655114 Henry Cohn, 2026.
3 753 0.990883514545 Henry Cohn, 2024.
3 754 0.990896951324 Henry Cohn, 2026.
3 755 0.990899134605 Henry Cohn, 2026, needs more optimization.
3 756 0.990921465227 Henry Cohn, 2026, needs more optimization.
3 757 0.990937812953 Henry Cohn, 2024.
3 758 0.990946005792 Henry Cohn, 2024.
3 759 0.990954743746 Henry Cohn, 2024.
3 760 0.990970877087 Henry Cohn, 2024.
3 761 0.990975674468 Henry Cohn, 2026.
3 762 0.990993252010 Henry Cohn, 2024.
3 763 0.991002546962 Henry Cohn, 2024.
3 764 0.991020014033 Henry Cohn, 2026, needs more optimization.
3 765 0.991024981687 Henry Cohn, 2026.
3 766 0.991034226787 Henry Cohn, 2026.
3 767 0.991054850991 Henry Cohn, 2024.
3 768 0.991061683327 Henry Cohn, 2026.
3 769 0.991073054499 Henry Cohn, 2024.
3 770 0.991085755280 Henry Cohn, 2024.
3 771 0.991091108034 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 772 0.991107834438 Henry Cohn, 2024.
3 773 0.991119133097 Henry Cohn, 2026.
3 774 0.991132071939 Henry Cohn, 2024.
3 775 0.991142879959 Henry Cohn, 2026, needs more optimization.
3 776 0.991154326067 Henry Cohn, 2026, needs more optimization.
3 777 0.991161697853 Henry Cohn, 2024.
3 778 0.991176106801 Henry Cohn, 2026, needs more optimization.
3 779 0.991186101604 Henry Cohn, 2026.
3 780 0.991195467101 Henry Cohn, 2024.
3 781 0.991212495316 Henry Cohn, 2024.
3 782 0.991215176194 Henry Cohn, 2026, needs more optimization.
3 783 0.991224996115 Henry Cohn, 2026, needs more optimization.
3 784 0.991237581418 Henry Cohn, 2024.
3 785 0.991246019903 Henry Cohn, 2026, needs more optimization.
3 786 0.991261576581 Henry Cohn, 2026.
3 787 0.991274863578 Henry Cohn, 2026, needs more optimization.
3 788 0.991285577631 Henry Cohn, 2026.
3 789 0.991288795806 Henry Cohn, 2026, needs more optimization.
3 790 0.991311108786 Henry Cohn, 2024.
3 791 0.991319397658 Henry Cohn, 2024.
3 792 0.991327970122 Henry Cohn, 2024.
3 793 0.991336046420 Henry Cohn, 2026, needs more optimization.
3 794 0.991351979569 Henry Cohn, 2026, needs more optimization.
3 795 0.991358758545 Henry Cohn, 2026, needs more optimization.
3 796 0.991373620973 Henry Cohn, 2024.
3 797 0.991382382844 Henry Cohn, 2024.
3 798 0.991393707648 Henry Cohn, 2026.
3 799 0.991404670338 Henry Cohn, 2026, needs more optimization.
3 800 0.991414851715 Henry Cohn, 2024.
3 801 0.991423315526 Henry Cohn, 2026, needs more optimization.
3 802 0.991434092719 Henry Cohn, 2026, needs more optimization.
3 803 0.991449666567 Henry Cohn, 2026.
3 804 0.991459924550 Henry Cohn, 2024.
3 805 0.991468080347 Henry Cohn, 2024.
3 806 0.991477473360 Henry Cohn, 2026, needs more optimization.
3 807 0.991488929993 Henry Cohn, 2024.
3 808 0.991499113412 Henry Cohn, 2026.
3 809 0.991512053057 Henry Cohn, 2026, needs more optimization.
3 810 0.991520665687 Henry Cohn, 2024.
3 811 0.991528398760 Henry Cohn, 2026.
3 812 0.991540671325 Henry Cohn, 2026.
3 813 0.991547822510 Henry Cohn, 2024.
3 814 0.991561413238 Henry Cohn, 2026.
3 815 0.991566961515 Henry Cohn, 2026, needs more optimization.
3 816 0.991580342934 Henry Cohn, 2024.
3 817 0.991591011326 Henry Cohn, 2024.
3 818 0.991597088261 Henry Cohn, 2026, needs more optimization.
3 819 0.991609552334 Henry Cohn, 2026, needs more optimization.
3 820 0.991624044122 Henry Cohn, 2024.
3 821 0.991630141544 Henry Cohn, 2026, needs more optimization.
3 822 0.991639297576 Henry Cohn, 2026.
3 823 0.991650165081 Henry Cohn, 2024.
3 824 0.991660076581 Henry Cohn, 2024.
3 825 0.991668700691 Henry Cohn, 2026, needs more optimization.
3 826 0.991679202359 Henry Cohn, 2026, needs more optimization.
3 827 0.991687079882 Henry Cohn, 2026, needs more optimization.
3 828 0.991700756929 Henry Cohn, 2024.
3 829 0.991713398461 Henry Cohn, 2024.
3 830 0.991721621394 Henry Cohn, 2024.
3 831 0.991727034826 Henry Cohn, 2026.
3 832 0.991733957066 Henry Cohn, 2026.
3 833 0.991746497052 Henry Cohn, 2026, needs more optimization.
3 834 0.991758792862 Henry Cohn, 2026.
3 835 0.991760361201 Henry Cohn, 2026, needs more optimization.
3 836 0.991770170970 Henry Cohn, 2026, needs more optimization.
3 837 0.991780503947 Henry Cohn, 2026.
3 838 0.991796901190 Henry Cohn, 2026, needs more optimization.
3 839 0.991804757710 Henry Cohn, 2026, needs more optimization.
3 840 0.991804766911 Henry Cohn, 2026, needs more optimization.
3 841 0.991814443294 Henry Cohn, 2026, needs more optimization.
3 842 0.991823488659 Henry Cohn, 2026, needs more optimization.
3 843 0.991831838468 Henry Cohn, 2026, needs more optimization.
3 844 0.991847904603 Henry Cohn, 2026, needs more optimization.
3 845 0.991854773658 Henry Cohn, 2026.
3 846 0.991861923064 Henry Cohn, 2026, needs more optimization.
3 847 0.991869552615 Henry Cohn, 2026.
3 848 0.991876988506 Henry Cohn, 2026.
3 849 0.991884604711 Henry Cohn, 2026.
3 850 0.991888540783 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 851 0.991898113840 Henry Cohn, 2026.
3 852 0.991904249523 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 853 0.991917992635 Henry Cohn, 2026, needs more optimization.
3 854 0.991934892199 Henry Cohn, 2026, needs more optimization.
3 855 0.991948423912 Henry Cohn, 2026.
3 856 0.991959729671 Henry Cohn, 2026, needs more optimization.
3 857 0.991976230701 Henry Cohn, 2026, needs more optimization.
3 858 0.991987713948 Henry Cohn, 2026.
3 859 0.991994869581 Henry Cohn, 2026, needs more optimization.
3 860 0.992000220754 Henry Cohn, 2026.
3 861 0.992009500278 Henry Cohn, 2026, needs more optimization.
3 862 0.992019497768 Henry Cohn, 2026, needs more optimization.
3 863 0.992030941840 Henry Cohn, 2026, needs more optimization.
3 864 0.992045910827 Henry Cohn, 2025.
3 865 0.992049202700 Henry Cohn, 2026.
3 866 0.992059688359 Henry Cohn, 2026.
3 867 0.992072381754 Henry Cohn, 2025.
3 868 0.992079944623 Henry Cohn, 2026, needs more optimization.
3 869 0.992081498110 Henry Cohn, 2026, needs more optimization.
3 870 0.992086777323 Henry Cohn, 2026.
3 871 0.992092487763 Henry Cohn, 2026.
3 872 0.992098850920 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 873 0.992109762118 Henry Cohn, 2026.
3 874 0.992124798888 Henry Cohn, 2026, needs more optimization.
3 875 0.992137558500 Henry Cohn, 2026.
3 876 0.992144390399 Henry Cohn, 2026, needs more optimization.
3 877 0.992154329715 Henry Cohn, 2025.
3 878 0.992163492985 Henry Cohn, 2026, needs more optimization.
3 879 0.992169044878 Henry Cohn, 2026, needs more optimization.
3 880 0.992185909971 Henry Cohn, 2025.
3 881 0.992192486886 Henry Cohn, 2025.
3 882 0.992198371680 Henry Cohn, 2025.
3 883 0.992205241611 Henry Cohn, 2026, needs more optimization.
3 884 0.992213790273 Henry Cohn, 2026, needs more optimization.
3 885 0.992223428918 Henry Cohn, 2026, needs more optimization.
3 886 0.992236374298 Henry Cohn, 2026.
3 887 0.992242382220 Henry Cohn, 2025.
3 888 0.992254762001 Henry Cohn, 2026, needs more optimization.
3 889 0.992263156986 Henry Cohn, 2026, needs more optimization.
3 890 0.992270276715 Henry Cohn, 2026, needs more optimization.
3 891 0.992282227835 Henry Cohn, 2026, needs more optimization.
3 892 0.992285856055 Henry Cohn, 2026.
3 893 0.992295938057 Henry Cohn, 2026, needs more optimization.
3 894 0.992309459744 Henry Cohn, 2025.
3 895 0.992316358484 Henry Cohn, 2025.
3 896 0.992316827394 Henry Cohn, 2026.
3 897 0.992332110080 Henry Cohn, 2025.
3 898 0.992338696092 Henry Cohn, 2025.
3 899 0.992345607640 Henry Cohn, 2026.
3 900 0.992355674372 Henry Cohn, 2026.
3 901 0.992359379297 Henry Cohn, 2026, needs more optimization.
3 902 0.992371987754 Henry Cohn, 2026, needs more optimization.
3 903 0.992381166748 Henry Cohn, 2026, needs more optimization.
3 904 0.992389880049 Henry Cohn, 2026, needs more optimization.
3 905 0.992399597008 Henry Cohn, 2026, needs more optimization.
3 906 0.992403005721 Henry Cohn, 2026, needs more optimization.
3 907 0.992414669143 Henry Cohn, 2026, needs more optimization.
3 908 0.992421146623 Henry Cohn, 2026, needs more optimization.
3 909 0.992427416986 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 910 0.992437123795 Henry Cohn, 2025.
3 911 0.992442944074 Henry Cohn, 2026.
3 912 0.992454600852 Henry Cohn, 2025.
3 913 0.992469408976 Henry Cohn, 2026, needs more optimization.
3 914 0.992471207708 Henry Cohn, 2025.
3 915 0.992480688576 Henry Cohn, 2026.
3 916 0.992487103876 Henry Cohn, 2026.
3 917 0.992497063301 Henry Cohn, 2026.
3 918 0.992505582224 Henry Cohn, 2026, needs more optimization.
3 919 0.992512397512 Henry Cohn, 2026.
3 920 0.992517498611 Henry Cohn, 2026.
3 921 0.992531086582 Henry Cohn, 2026, needs more optimization.
3 922 0.992534989878 Henry Cohn, 2026, needs more optimization.
3 923 0.992545962026 Henry Cohn, 2026.
3 924 0.992553990146 Henry Cohn, 2025.
3 925 0.992561907552 Henry Cohn, 2026.
3 926 0.992564856890 Henry Cohn, 2026.
3 927 0.992576719918 Henry Cohn, 2026, needs more optimization.
3 928 0.992580182120 Henry Cohn, 2026.
3 929 0.992588276926 Henry Cohn, 2026.
3 930 0.992594659009 Henry Cohn, 2026.
3 931 0.992603050921 Henry Cohn, 2026.
3 932 0.992611560837 Henry Cohn, 2026, needs more optimization.
3 933 0.992624602034 Henry Cohn, 2025.
3 934 0.992625562166 Henry Cohn, 2026, needs more optimization.
3 935 0.992636958816 Henry Cohn, 2026, needs more optimization.
3 936 0.992645524924 Henry Cohn, 2026, needs more optimization.
3 937 0.992652128678 Henry Cohn, 2026, needs more optimization.
3 938 0.992665682904 Henry Cohn, 2025.
3 939 0.992672947443 Henry Cohn, 2025.
3 940 0.992677472433 Henry Cohn, 2026.
3 941 0.992684585898 Henry Cohn, 2026.
3 942 0.992696579115 Henry Cohn, 2025.
3 943 0.992698781018 Henry Cohn, 2026, needs more optimization.
3 944 0.992710970106 Henry Cohn, 2026, needs more optimization.
3 945 0.992717631580 Henry Cohn, 2025.
3 946 0.992721615967 Henry Cohn, 2026, needs more optimization.
3 947 0.992726855397 Henry Cohn, 2026.
3 948 0.992731846336 Henry Cohn, 2026, needs more optimization.
3 950 0.992747537865 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 951 0.992759834272 Henry Cohn, 2026.
3 952 0.992771438024 Henry Cohn, 2025.
3 953 0.992777278705 Henry Cohn, 2026, needs more optimization.
3 954 0.992782538892 Henry Cohn, 2026, needs more optimization.
3 955 0.992790097506 Henry Cohn, 2026, needs more optimization.
3 956 0.992801093482 Henry Cohn, 2025.
3 957 0.992810004476 Henry Cohn, 2025.
3 958 0.992816897464 Henry Cohn, 2026, needs more optimization.
3 959 0.992823549807 Henry Cohn, 2026.
3 960 0.992829045249 Henry Cohn, 2026, needs more optimization.
3 961 0.992838773549 Henry Cohn, 2025.
3 962 0.992842996151 Henry Cohn, 2026.
3 963 0.992851430685 Henry Cohn, 2026.
3 964 0.992860398135 Henry Cohn, 2025.
3 965 0.992867446456 Henry Cohn, 2026, needs more optimization.
3 966 0.992873726071 Henry Cohn, 2026.
3 967 0.992879664516 Henry Cohn, 2026.
3 968 0.992886923604 Henry Cohn, 2025.
3 969 0.992894684947 Henry Cohn, 2026.
3 970 0.992900101767 Henry Cohn, 2026, needs more optimization.
3 971 0.992910234827 Henry Cohn, 2025.
3 973 0.992912611281 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 974 0.992924646469 Henry Cohn, 2026.
3 975 0.992931434432 Henry Cohn, 2026.
3 976 0.992939131361 Henry Cohn, 2026, needs more optimization.
3 977 0.992953433939 Henry Cohn, 2025.
3 978 0.992956413001 Henry Cohn, 2026, needs more optimization.
3 979 0.992964322394 Henry Cohn, 2026.
3 980 0.992974636259 Henry Cohn, 2024.
3 981 0.992980975086 Henry Cohn, 2026, needs more optimization.
3 982 0.992986020491 Henry Cohn, 2026.
3 983 0.992998353831 Henry Cohn, 2025.
3 984 0.993003417762 Henry Cohn, 2025.
3 985 0.993011691492 Henry Cohn, 2025.
3 986 0.993014102217 Henry Cohn, 2026.
3 987 0.993015794704 Henry Cohn, 2026, needs more optimization.
3 988 0.993022620792 Henry Cohn, 2026.
3 989 0.993037184620 Henry Cohn, 2025.
3 990 0.993037809287 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
3 991 0.993048484035 Henry Cohn, 2026, needs more optimization.
3 992 0.993056519614 Henry Cohn, 2026, needs more optimization.
3 993 0.993060184436 Henry Cohn, 2026, needs more optimization.
3 994 0.993068317141 Henry Cohn, 2026.
3 995 0.993077408987 Henry Cohn, 2026.
3 996 0.993082345308 Henry Cohn, 2026, needs more optimization.
3 997 0.993095069137 Henry Cohn, 2026, needs more optimization.
3 998 0.993095695908 Henry Cohn, 2026, needs more optimization.
3 999 0.993104404829 Henry Cohn, 2026, needs more optimization.
3 1000 0.993108149353 Henry Cohn, 2026.
3 1001 0.993116770143 Henry Cohn, 2026.
3 1002 0.993125357511 Henry Cohn, 2026.
3 1003 0.993132170420 Henry Cohn, 2025.
3 1004 0.993135717753 Henry Cohn, 2026, needs more optimization.
3 1005 0.993147564003 Henry Cohn, 2026.
3 1006 0.993151568176 Henry Cohn, 2026.
3 1007 0.993154938662 Henry Cohn, 2026.
3 1008 0.993159005478 Henry Cohn, 2025.
3 1009 0.993168697866 Henry Cohn, 2026, needs more optimization.
3 1010 0.993175003357 Henry Cohn, 2026, needs more optimization.
3 1011 0.993182198559 Henry Cohn, 2026, needs more optimization.
3 1012 0.993189191007 Henry Cohn, 2026, needs more optimization.
3 1013 0.993196507117 Henry Cohn, 2026, needs more optimization.
3 1014 0.993201603787 Henry Cohn, 2026, needs more optimization.
3 1015 0.993208460986 Henry Cohn, 2026, needs more optimization.
3 1016 0.993214864340 Henry Cohn, 2026, needs more optimization.
3 1017 0.993221388472 Henry Cohn, 2026, needs more optimization.
3 1018 0.993228963851 Henry Cohn, 2026, needs more optimization.
3 1019 0.993235373182 Henry Cohn, 2026.
3 1020 0.993235373238 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1021 0.993243005692 Henry Cohn, 2026, needs more optimization.
3 1022 0.993250016173 Henry Cohn, 2026, needs more optimization.
3 1023 0.993256159904 Henry Cohn, 2026, needs more optimization.
3 1024 0.993262743051 Henry Cohn, 2026, needs more optimization.
4 9 0.162015199612 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
16⁢x3−16⁢x2−4⁢x+1
4 10* 0.166666666667 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011; C. Bachoc and F. Vallentin, Optimality and uniqueness of the (4,10,1/6) spherical code, J. Combin. Theory Ser. A 116 (2009), 195–204, doi:10.1016/j.jcta.2008.05.001.
6⁢x−1
4 11 0.230405563595 L. T. Wille, Close packing in curved space by simulated annealing, Journal of Physics A: Mathematical and General 20 (1987), L1211–L1218, doi:10.1088/0305-4470/20/17/014.
8⁢x3−12⁢x2−2⁢x+1
4 12 0.25 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011.
4⁢x−1
4 13 0.307295653982 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5632⁢x9+9472⁢x8−3072⁢x7−5888⁢x6+544⁢x5+944⁢x4+152⁢x3−44⁢x2−14⁢x−1
4 14 0.319518594213 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
58⁢x7+174⁢x6+140⁢x5−16⁢x4−54⁢x3−10⁢x2+4⁢x+1
4 15 0.350992175946 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
36⁢x4−18⁢x3+10⁢x2−1
4 16 0.387628177123 A. L. Mackay, The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere, J. Phys. A 13 (1980), 3373–3379, doi:10.1088/0305-4470/13/11/011.
256⁢x10+1024⁢x9+256⁢x8−1152⁢x7+160⁢x6+176⁢x5−144⁢x4+36⁢x3+37⁢x2−6⁢x−3
4 17 0.412259362694 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 18 0.422819414074 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
4 19 0.434258545911 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3⁢x2+x−1
4 20 0.434258545911 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3⁢x2+x−1
4 21 0.471380858508 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
16⁢x8−128⁢x7−64⁢x6+32⁢x5+72⁢x4+32⁢x3−16⁢x2−8⁢x+1
4 22 0.497884130844 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 23 0.5 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
2⁢x−1
4 24* 0.5 L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; D. de Laat, N. Leijenhorst, and W. H. H. de Muinck Keizer, Optimality and uniqueness of the D4 root system, preprint, 2024, arXiv:2404.18794.
2⁢x−1
4 25 0.537316056656 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 26 0.540789617698 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
3392⁢x6+2112⁢x5−496⁢x4−656⁢x3−132⁢x2+6⁢x−1
4 27 0.557591351181 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
794⁢x5+393⁢x4−344⁢x3−82⁢x2+6⁢x+1
4 28 0.567338804075 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 29 0.573148530449 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
4 30 0.584232813931 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 31 0.590765838581 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
4 32 0.595720149236 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 33 0.600755407756 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 34 0.610128556790 Henry Cohn, 2024.
4 35 0.621523986641 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 36 0.628309089475 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 37 0.630368722499 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 38 0.640732732793 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 39 0.646928247960 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 40 0.650497801063 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4 41 0.655274051124 Henry Cohn, 2024.
4 42 0.658420878517 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 43 0.662667198430 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
4 44 0.668804906276 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
36⁢x8−60⁢x7+481⁢x6+166⁢x5−205⁢x4−116⁢x3+11⁢x2+10⁢x+1
4 45 0.676924957837 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 46 0.682325866078 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 47 0.685400852293 Henry Cohn, 2025.
4 48 0.689831186714 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 49 0.693413660571 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 50 0.693726127145 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
4 51 0.701375493264 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 52 0.703627792371 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 53 0.707671488219 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 54 0.709714380727 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 55 0.715661893754 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 56 0.719201427062 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 57 0.722366203194 Henry Cohn, 2025.
4 58 0.724963759986 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 59 0.726684594037 Henry Cohn, 2025.
4 60 0.728768479335 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 61 0.731517689032 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 62 0.733882910506 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 63 0.738725371284 Henry Cohn, 2025.
4 64 0.739558032728 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 65 0.742483255369 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 66 0.745996162085 Henry Cohn, 2025.
4 67 0.748966563154 Henry Cohn, 2025.
4 68 0.751044149551 Henry Cohn, 2025.
4 69 0.752628993819 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 70 0.753734038368 Henry Cohn, 2025.
4 71 0.756373364760 Henry Cohn, 2025.
4 72 0.758022144348 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 73 0.759191014470 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 74 0.759545691353 Henry Cohn, 2025.
4 75 0.760558878464 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 76 0.761064664765 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
4 77 0.765202546890 Henry Cohn, 2025.
4 78 0.768765601292 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 79 0.773060404397 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 80 0.775691894892 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 81 0.777799033764 Henry Cohn, 2025.
4 82 0.779753559198 Henry Cohn, 2025.
4 83 0.781053544402 Henry Cohn, 2025.
4 84 0.782373204314 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 85 0.783715044186 Henry Cohn, 2024.
4 86 0.784899010819 Henry Cohn, 2026.
4 87 0.785487328991 Henry Cohn, 2025.
4 88 0.785927649195 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 89 0.788520093069 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 90 0.790391197000 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 91 0.791393154383 Henry Cohn, 2025.
4 92 0.792211293351 Henry Cohn, 2025.
4 93 0.793047017514 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 94 0.793553793569 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 95 0.796982807052 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 96 0.797980534415 Henry Cohn, 2025.
4 97 0.799480375605 Henry Cohn, 2023.
4 98 0.800765983579 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 99 0.801793100994 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4 100 0.803178722499 Henry Cohn, 2025.
4 101 0.803884649087 Henry Cohn, 2025.
4 102 0.804699654814 Henry Cohn, 2025.
4 103 0.805093331367 Henry Cohn, 2025.
4 104 0.806308735044 Henry Cohn, 2025.
4 105 0.807104881635 Henry Cohn, 2026.
4 106 0.807600771583 Henry Cohn, 2025.
4 107 0.808031793624 Henry Cohn, 2025.
4 108 0.808488610194 Henry Cohn, 2025.
4 109 0.808686924144 Henry Cohn, 2026.
4 110 0.808927278464 Henry Cohn, 2026.
4 111 0.808991157916 Henry Cohn, 2025.
4 112 0.809016055614 Henry Cohn, 2025.
4 113 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 114 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 115 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 116 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 117 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 118 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 119 0.809016994375 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
4⁢x2−2⁢x−1
4 120* 0.809016994375 L. Schläfli, Theorie der vielfachen Kontinuität [1852], Denkschriften der Schweizerischen naturforschenden Gesellschaft, vol. 38, J. H. Graf, Bern, 1901; K. Böröczky, Packing of spheres in spaces of constant curvature, Acta Mathematica Academiae Scientiarum Hungarica 32 (1978), 243–261, doi:10.1007/BF01902361.
4⁢x2−2⁢x−1
4 121 0.824637993171 Henry Cohn, 2026.
4 122 0.826371363846 Henry Cohn, 2026.
4 123 0.827331732524 Henry Cohn, 2025.
4 124 0.829076814196 Henry Cohn, 2025.
4 125 0.830275122838 Henry Cohn, 2025.
4 126 0.831265978577 Henry Cohn, 2025.
4 127 0.832258295757 Henry Cohn, 2025.
4 128 0.833179172458 Henry Cohn, 2026.
4 129 0.833853106202 Henry Cohn, 2025.
4 130 0.834729130389 Henry Cohn, 2025.
4 131 0.835454616797 Henry Cohn, 2025.
4 132 0.835826242592 Henry Cohn, 2025.
4 133 0.836970287069 Henry Cohn, 2025.
4 134 0.837549857120 Henry Cohn, 2025.
4 135 0.838174290974 Henry Cohn, 2025.
4 136 0.838408035762 Henry Cohn, 2025.
4 137 0.838792717376 Henry Cohn, 2025.
4 138 0.839094608099 Henry Cohn, 2025.
4 139 0.839507413737 Henry Cohn, 2024.
4 140 0.839796230234 Henry Cohn, 2025.
4 141 0.840152855333 Henry Cohn, 2024.
4 142 0.840928789319 Henry Cohn, 2025.
4 143 0.842625863066 Henry Cohn, 2025.
4 144 0.843226230314 Henry Cohn, 2026.
4 145 0.845004703395 Henry Cohn, 2025.
4 146 0.846045189902 Henry Cohn, 2024.
4 147 0.846906008500 Henry Cohn, 2025.
4 148 0.847320837337 Henry Cohn, 2025.
4 149 0.847701351395 Henry Cohn, 2025.
4 150 0.848007962348 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 151 0.848395999617 Henry Cohn, 2025.
4 152 0.848746833410 Henry Cohn, 2024.
4 153 0.849106783811 Henry Cohn, 2025.
4 154 0.849448181031 Henry Cohn, 2024.
4 155 0.850528693851 Henry Cohn, 2025.
4 156 0.852364181174 Henry Cohn, 2025.
4 157 0.853098036527 Henry Cohn, 2025.
4 158 0.853541001367 Henry Cohn, 2025.
4 159 0.853851387665 Henry Cohn, 2025.
4 160 0.854015402705 Henry Cohn, 2025.
4 161 0.855036011488 Henry Cohn, 2025.
4 162 0.856011990176 Henry Cohn, 2025.
4 163 0.856420172916 Henry Cohn, 2026, needs more optimization.
4 164 0.856668082967 Henry Cohn, 2025.
4 165 0.856908324217 Henry Cohn, 2024.
4 166 0.857225219240 Henry Cohn, 2025.
4 167 0.857623781724 Henry Cohn, 2025.
4 168 0.859313317303 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 169 0.860417510162 Henry Cohn, 2025.
4 170 0.861171923129 Henry Cohn, 2026, needs more optimization.
4 171 0.861877205800 Henry Cohn, 2025.
4 172 0.862347277695 Henry Cohn, 2026, needs more optimization.
4 173 0.862725307388 Henry Cohn, 2025.
4 174 0.863170417348 Henry Cohn, 2026.
4 175 0.863367463185 Henry Cohn, 2025.
4 176 0.863624102971 Henry Cohn, 2025.
4 177 0.863764381494 Henry Cohn, 2025.
4 178 0.863928834672 Henry Cohn, 2025.
4 179 0.864723195011 Henry Cohn, 2025.
4 180 0.865782670861 Henry Cohn, 2025.
4 181 0.866598382577 Henry Cohn, 2025.
4 182 0.867007940139 Henry Cohn, 2026, needs more optimization.
4 183 0.867335807322 Henry Cohn, 2025.
4 184 0.867763055785 Henry Cohn, 2025.
4 185 0.868215850425 Henry Cohn, 2026.
4 186 0.868511699240 Henry Cohn, 2026, needs more optimization.
4 187 0.868813031570 Henry Cohn, 2026, needs more optimization.
4 188 0.869207825431 Henry Cohn, 2025.
4 189 0.869491543071 Henry Cohn, 2025.
4 190 0.870050972636 Henry Cohn, 2025.
4 191 0.870814241870 Henry Cohn, 2025.
4 192 0.871301083435 Henry Cohn, 2026, needs more optimization.
4 193 0.871545546243 Henry Cohn, 2025.
4 194 0.871792013221 Henry Cohn, 2025.
4 195 0.872105415403 Henry Cohn, 2026, needs more optimization.
4 196 0.872623379660 Henry Cohn, 2026.
4 197 0.873487426793 Henry Cohn, 2025.
4 198 0.874156501901 Henry Cohn, 2025.
4 199 0.874984411725 Henry Cohn, 2026, needs more optimization.
4 200 0.875612598379 Henry Cohn, 2026, needs more optimization.
4 201 0.876095772023 Henry Cohn, 2026, needs more optimization.
4 202 0.876488116733 Henry Cohn, 2026, needs more optimization.
4 203 0.876805551538 Henry Cohn, 2026, needs more optimization.
4 204 0.877193219688 Henry Cohn, 2026.
4 205 0.877534211883 Henry Cohn, 2025.
4 206 0.877759299475 Henry Cohn, 2026, needs more optimization.
4 207 0.877983074153 Henry Cohn, 2026.
4 208 0.878215104089 Henry Cohn, 2025.
4 209 0.878614728692 Henry Cohn, 2026.
4 210 0.879213799752 Henry Cohn, 2025.
4 211 0.879509739381 Henry Cohn, 2026, needs more optimization.
4 212 0.879653371881 Henry Cohn, 2026.
4 213 0.879785709458 Henry Cohn, 2026, needs more optimization.
4 214 0.879945724274 Henry Cohn, 2025.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880901244364 Henry Cohn, 2026, needs more optimization.
4 217 0.881484651958 Henry Cohn, 2026, needs more optimization.
4 218 0.881821797282 Henry Cohn, 2026, needs more optimization.
4 219 0.881957670465 Henry Cohn, 2025.
4 220 0.882547029792 Henry Cohn, 2025.
4 221 0.883034324004 Henry Cohn, 2026.
4 222 0.883456069925 Henry Cohn, 2025.
4 223 0.884138189446 Henry Cohn, 2025.
4 224 0.884684734191 Henry Cohn, 2025.
4 225 0.885119168015 Henry Cohn, 2026.
4 226 0.885291300019 Henry Cohn, 2026, needs more optimization.
4 227 0.885541386047 Henry Cohn, 2025.
4 228 0.885824040293 Henry Cohn, 2025.
4 229 0.886054618847 Henry Cohn, 2026, needs more optimization.
4 230 0.886372063295 Henry Cohn, 2025.
4 231 0.886803795527 Henry Cohn, 2026, needs more optimization.
4 232 0.887100396043 Henry Cohn, 2026.
4 233 0.887339463629 Henry Cohn, 2025.
4 234 0.887586535331 Henry Cohn, 2025.
4 235 0.887898565845 Henry Cohn, 2026, needs more optimization.
4 236 0.888076450831 Henry Cohn, 2025.
4 237 0.888444553045 Henry Cohn, 2025.
4 238 0.888895172867 Henry Cohn, 2025.
4 239 0.889105362853 Henry Cohn, 2026.
4 240 0.889490756122 Henry Cohn, 2026, needs more optimization.
4 241 0.889823774494 Henry Cohn, 2026, needs more optimization.
4 242 0.890126399703 Henry Cohn, 2026, needs more optimization.
4 243 0.890327494714 Henry Cohn, 2025.
4 244 0.890724603786 Henry Cohn, 2026.
4 245 0.890944532473 Henry Cohn, 2026, needs more optimization.
4 246 0.891230987587 Henry Cohn, 2025.
4 247 0.891664123274 Henry Cohn, 2026.
4 248 0.891998662279 Henry Cohn, 2026, needs more optimization.
4 249 0.892287393255 Henry Cohn, 2026, needs more optimization.
4 250 0.892630822839 Henry Cohn, 2026, needs more optimization.
4 251 0.892960353406 Henry Cohn, 2026, needs more optimization.
4 252 0.893161098750 Henry Cohn, 2026, needs more optimization.
4 253 0.893448664411 Henry Cohn, 2026, needs more optimization.
4 254 0.893685910560 Henry Cohn, 2026, needs more optimization.
4 255 0.893997549375 Henry Cohn, 2026.
4 256 0.894519020596 Henry Cohn, 2026, needs more optimization.
4 257 0.894704108549 Henry Cohn, 2026.
4 258 0.894983024298 Henry Cohn, 2026, needs more optimization.
4 259 0.895406017327 Henry Cohn, 2026, needs more optimization.
4 260 0.895577214593 Henry Cohn, 2026, needs more optimization.
4 261 0.895824546881 Henry Cohn, 2026, needs more optimization.
4 262 0.896146221992 Henry Cohn, 2026, needs more optimization.
4 263 0.896399514582 Henry Cohn, 2026, needs more optimization.
4 264 0.896601239305 Henry Cohn, 2026, needs more optimization.
4 265 0.896744363478 Henry Cohn, 2026, needs more optimization.
4 266 0.896945851288 Henry Cohn, 2026, needs more optimization.
4 267 0.897202167324 Henry Cohn, 2026, needs more optimization.
4 268 0.897338995363 Henry Cohn, 2026, needs more optimization.
4 269 0.897583832374 Henry Cohn, 2026, needs more optimization.
4 270 0.897712971292 Henry Cohn, 2026, needs more optimization.
4 271 0.897978047494 Henry Cohn, 2026, needs more optimization.
4 272 0.898184936311 Henry Cohn, 2026, needs more optimization.
4 273 0.898338560157 Henry Cohn, 2026, needs more optimization.
4 274 0.898505331338 Henry Cohn, 2026, needs more optimization.
4 275 0.898703283722 Henry Cohn, 2026, needs more optimization.
4 276 0.898990508307 Henry Cohn, 2026, needs more optimization.
4 277 0.899249687396 Henry Cohn, 2026, needs more optimization.
4 278 0.899398021271 Henry Cohn, 2026, needs more optimization.
4 279 0.899550133880 Henry Cohn, 2026, needs more optimization.
4 280 0.899640967995 Henry Cohn, 2026, needs more optimization.
4 281 0.900127314981 Henry Cohn, 2026.
4 282 0.900628397128 Henry Cohn, 2026, needs more optimization.
4 283 0.900999811191 Henry Cohn, 2026, needs more optimization.
4 284 0.901160897936 Henry Cohn, 2026, needs more optimization.
4 285 0.901207601315 Henry Cohn, 2026, needs more optimization.
4 286 0.901352035495 Henry Cohn, 2026, needs more optimization.
4 287 0.901407925373 Henry Cohn, 2026, needs more optimization.
4 288 0.901415628383 Henry Cohn, 2026, needs more optimization.
4 289 0.902147462122 Henry Cohn, 2026, needs more optimization.
4 290 0.902647323284 Henry Cohn, 2026, needs more optimization.
4 291 0.903108216948 Henry Cohn, 2026, needs more optimization.
4 292 0.903476439366 Henry Cohn, 2026, needs more optimization.
4 293 0.903745557533 Henry Cohn, 2026, needs more optimization.
4 294 0.903947278395 Henry Cohn, 2026, needs more optimization.
4 295 0.904225079202 Henry Cohn, 2026, needs more optimization.
4 296 0.904538570202 Henry Cohn, 2026, needs more optimization.
4 297 0.904733465765 Henry Cohn, 2026, needs more optimization.
4 298 0.904877266479 Henry Cohn, 2026, needs more optimization.
4 299 0.905146611996 Henry Cohn, 2026, needs more optimization.
4 300 0.905312123871 Henry Cohn, 2026, needs more optimization.
4 301 0.905597318680 Henry Cohn, 2026, needs more optimization.
4 302 0.905738098264 Henry Cohn, 2026, needs more optimization.
4 303 0.906066938468 Henry Cohn, 2026, needs more optimization.
4 304 0.906254637567 Henry Cohn, 2026, needs more optimization.
4 305 0.906320387023 Henry Cohn, 2026, needs more optimization.
4 306 0.906511544495 Henry Cohn, 2026, needs more optimization.
4 307 0.906769020187 Henry Cohn, 2026, needs more optimization.
4 308 0.906981079246 Henry Cohn, 2026, needs more optimization.
4 309 0.907297386610 Henry Cohn, 2026, needs more optimization.
4 310 0.907345163074 Henry Cohn, 2026, needs more optimization.
4 311 0.907479010087 Henry Cohn, 2026, needs more optimization.
4 312 0.907797918050 Henry Cohn, 2026, needs more optimization.
4 313 0.907999397269 Henry Cohn, 2026, needs more optimization.
4 314 0.908137005840 Henry Cohn, 2026, needs more optimization.
4 315 0.908334408866 Henry Cohn, 2026, needs more optimization.
4 316 0.908439132055 Henry Cohn, 2026, needs more optimization.
4 317 0.908713928386 Henry Cohn, 2026, needs more optimization.
4 318 0.908941299492 Henry Cohn, 2026, needs more optimization.
4 319 0.909145405307 Henry Cohn, 2026, needs more optimization.
4 320 0.909320854901 Henry Cohn, 2026, needs more optimization.
4 321 0.909491369498 Henry Cohn, 2026, needs more optimization.
4 322 0.909572924191 Henry Cohn, 2026, needs more optimization.
4 323 0.909664277020 Henry Cohn, 2026, needs more optimization.
4 324 0.909833171539 Henry Cohn, 2026, needs more optimization.
4 325 0.910040662440 Henry Cohn, 2026, needs more optimization.
4 326 0.910201960133 Henry Cohn, 2026, needs more optimization.
4 327 0.910288142665 Henry Cohn, 2026, needs more optimization.
4 328 0.910395023215 Henry Cohn, 2026, needs more optimization.
4 329 0.910665712623 Henry Cohn, 2026, needs more optimization.
4 330 0.910911540300 Henry Cohn, 2026, needs more optimization.
4 331 0.911137010713 Henry Cohn, 2026, needs more optimization.
4 332 0.911288710603 Henry Cohn, 2026, needs more optimization.
4 333 0.911520999341 Henry Cohn, 2026, needs more optimization.
4 334 0.911635352404 Henry Cohn, 2026, needs more optimization.
4 335 0.911928209819 Henry Cohn, 2026, needs more optimization.
4 336 0.912142693612 Henry Cohn, 2026, needs more optimization.
4 337 0.912392283319 Henry Cohn, 2026, needs more optimization.
4 338 0.912622753554 Henry Cohn, 2026, needs more optimization.
4 339 0.912849496394 Henry Cohn, 2026, needs more optimization.
4 340 0.913082210088 Henry Cohn, 2026, needs more optimization.
4 341 0.913350204421 Henry Cohn, 2026, needs more optimization.
4 342 0.913448740922 Henry Cohn, 2026, needs more optimization.
4 343 0.913632488568 Henry Cohn, 2026, needs more optimization.
4 344 0.913824325681 Henry Cohn, 2026, needs more optimization.
4 345 0.914105247595 Henry Cohn, 2026, needs more optimization.
4 346 0.914199615014 Henry Cohn, 2026, needs more optimization.
4 347 0.914370745668 Henry Cohn, 2026, needs more optimization.
4 348 0.914597659316 Henry Cohn, 2026, needs more optimization.
4 349 0.914787147751 Henry Cohn, 2026, needs more optimization.
4 350 0.914826499941 Henry Cohn, 2026, needs more optimization.
4 351 0.915003300656 Henry Cohn, 2026, needs more optimization.
4 352 0.915195438247 Henry Cohn, 2026, needs more optimization.
4 353 0.915241483582 Henry Cohn, 2026, needs more optimization.
4 354 0.915422024189 Henry Cohn, 2026, needs more optimization.
4 355 0.915510186992 Henry Cohn, 2026, needs more optimization.
4 356 0.915645206942 Henry Cohn, 2026, needs more optimization.
4 357 0.915773139125 Henry Cohn, 2026, needs more optimization.
4 358 0.915932571848 Henry Cohn, 2026, needs more optimization.
4 359 0.916064146263 Henry Cohn, 2026, needs more optimization.
4 360 0.916227016893 Henry Cohn, 2026, needs more optimization.
4 361 0.916275616951 Henry Cohn, 2026, needs more optimization.
4 362 0.916284241069 Henry Cohn, 2026, needs more optimization.
4 363 0.916449857138 Henry Cohn, 2026, needs more optimization.
4 364 0.916566270835 Henry Cohn, 2026, needs more optimization.
4 365 0.916732127641 Henry Cohn, 2026, needs more optimization.
4 366 0.916828437041 Henry Cohn, 2026, needs more optimization.
4 367 0.917138975218 Henry Cohn, 2026, needs more optimization.
4 368 0.917194982988 Henry Cohn, 2026, needs more optimization.
4 369 0.917249817356 Henry Cohn, 2026, needs more optimization.
4 370 0.917312758518 Henry Cohn, 2026, needs more optimization.
4 371 0.917449371611 Henry Cohn, 2026, needs more optimization.
4 372 0.917595341351 Henry Cohn, 2026, needs more optimization.
4 373 0.917877174623 Henry Cohn, 2026, needs more optimization.
4 374 0.918147785233 Henry Cohn, 2026, needs more optimization.
4 375 0.918338724046 Henry Cohn, 2026, needs more optimization.
4 376 0.918496193596 Henry Cohn, 2026, needs more optimization.
4 377 0.918569680183 Henry Cohn, 2026, needs more optimization.
4 378 0.918649548034 Henry Cohn, 2026, needs more optimization.
4 379 0.918855228427 Henry Cohn, 2026, needs more optimization.
4 380 0.918968688895 Henry Cohn, 2026, needs more optimization.
4 381 0.919137746629 Henry Cohn, 2026, needs more optimization.
4 382 0.919183440988 Henry Cohn, 2026, needs more optimization.
4 383 0.919269387804 Henry Cohn, 2026, needs more optimization.
4 384 0.919332504152 Henry Cohn, 2026, needs more optimization.
4 385 0.919374373395 Henry Cohn, 2026, needs more optimization.
4 386 0.919462080655 Henry Cohn, 2026, needs more optimization.
4 387 0.919485767372 Henry Cohn, 2026, needs more optimization.
4 388 0.919680409497 Henry Cohn, 2026, needs more optimization.
4 389 0.919722706966 Henry Cohn, 2026, needs more optimization.
4 390 0.919936179660 Henry Cohn, 2026, needs more optimization.
4 391 0.920140555756 Henry Cohn, 2026, needs more optimization.
4 392 0.920311946197 Henry Cohn, 2026, needs more optimization.
4 393 0.920430103140 Henry Cohn, 2026, needs more optimization.
4 394 0.920471448895 Henry Cohn, 2026, needs more optimization.
4 395 0.920571069762 Henry Cohn, 2026, needs more optimization.
4 396 0.920783591868 Henry Cohn, 2026, needs more optimization.
4 397 0.921004408625 Henry Cohn, 2026, needs more optimization.
4 398 0.921112962607 Henry Cohn, 2026, needs more optimization.
4 399 0.921169631743 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 400 0.921281154098 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 401 0.921449432364 Henry Cohn, 2026, needs more optimization.
4 402 0.921691128153 Henry Cohn, 2026, needs more optimization.
4 403 0.921777133855 Henry Cohn, 2026, needs more optimization.
4 404 0.921826297598 Henry Cohn, 2026, needs more optimization.
4 405 0.921860539955 Henry Cohn, 2026, needs more optimization.
4 406 0.921891687192 Henry Cohn, 2026, needs more optimization.
4 407 0.921971401665 Henry Cohn, 2026, needs more optimization.
4 408 0.921997660815 Henry Cohn, 2026, needs more optimization.
4 409 0.922339066157 Henry Cohn, 2026, needs more optimization.
4 410 0.922637784830 Henry Cohn, 2026, needs more optimization.
4 411 0.922708081549 Henry Cohn, 2026, needs more optimization.
4 412 0.922993794176 Henry Cohn, 2026, needs more optimization.
4 413 0.923215104838 Henry Cohn, 2026, needs more optimization.
4 414 0.923243303012 Henry Cohn, 2026, needs more optimization.
4 415 0.923432188322 Henry Cohn, 2026, needs more optimization.
4 416 0.923453699868 Henry Cohn, 2026, needs more optimization.
4 417 0.923513439158 Henry Cohn, 2026, needs more optimization.
4 418 0.923595435844 Henry Cohn, 2026, needs more optimization.
4 419 0.923725698350 Henry Cohn, 2026, needs more optimization.
4 420 0.923894048591 Henry Cohn, 2026, needs more optimization.
4 421 0.923980593106 Henry Cohn, 2026, needs more optimization.
4 422 0.924134530060 Henry Cohn, 2026, needs more optimization.
4 423 0.924286175725 Henry Cohn, 2026, needs more optimization.
4 424 0.924500348082 Henry Cohn, 2026, needs more optimization.
4 425 0.924700614054 Henry Cohn, 2026, needs more optimization.
4 426 0.924907486541 Henry Cohn, 2026, needs more optimization.
4 427 0.925096734289 Henry Cohn, 2026, needs more optimization.
4 428 0.925214426385 Henry Cohn, 2026, needs more optimization.
4 429 0.925413131787 Henry Cohn, 2026, needs more optimization.
4 430 0.925532810634 Henry Cohn, 2026, needs more optimization.
4 431 0.925691510827 Henry Cohn, 2026, needs more optimization.
4 432 0.925804465285 Henry Cohn, 2026, needs more optimization.
4 433 0.925930539663 Henry Cohn, 2026, needs more optimization.
4 434 0.925998197102 Henry Cohn, 2026, needs more optimization.
4 435 0.926183308535 Henry Cohn, 2026, needs more optimization.
4 436 0.926256081358 Henry Cohn, 2026, needs more optimization.
4 437 0.926442603154 Henry Cohn, 2026, needs more optimization.
4 438 0.926608240701 Henry Cohn, 2026, needs more optimization.
4 439 0.926759637027 Henry Cohn, 2026, needs more optimization.
4 440 0.926887365155 Henry Cohn, 2026, needs more optimization.
4 441 0.927036892630 Henry Cohn, 2026, needs more optimization.
4 442 0.927161288181 Henry Cohn, 2026, needs more optimization.
4 443 0.927211478016 Henry Cohn, 2026, needs more optimization.
4 444 0.927332275626 Henry Cohn, 2026, needs more optimization.
4 445 0.927430179902 Henry Cohn, 2026, needs more optimization.
4 446 0.927512259568 Henry Cohn, 2026, needs more optimization.
4 447 0.927594443776 Henry Cohn, 2026, needs more optimization.
4 448 0.927691710837 Henry Cohn, 2026, needs more optimization.
4 449 0.927843987913 Henry Cohn, 2026, needs more optimization.
4 450 0.928010204812 Henry Cohn, 2026, needs more optimization.
4 451 0.928081665169 Henry Cohn, 2026, needs more optimization.
4 452 0.928144362779 Henry Cohn, 2026, needs more optimization.
4 453 0.928186977030 Henry Cohn, 2026, needs more optimization.
4 454 0.928308531512 Henry Cohn, 2026, needs more optimization.
4 455 0.928327645700 Henry Cohn, 2026, needs more optimization.
4 456 0.928426727334 Henry Cohn, 2026, needs more optimization.
4 457 0.928541688922 Henry Cohn, 2026, needs more optimization.
4 458 0.928587629933 Henry Cohn, 2026, needs more optimization.
4 459 0.928668383431 Henry Cohn, 2026, needs more optimization.
4 460 0.928755859680 Henry Cohn, 2026, needs more optimization.
4 461 0.928916303242 Henry Cohn, 2026, needs more optimization.
4 462 0.929026761128 Henry Cohn, 2026, needs more optimization.
4 463 0.929124192900 Henry Cohn, 2026, needs more optimization.
4 464 0.929225837018 Henry Cohn, 2026, needs more optimization.
4 465 0.929338086871 Henry Cohn, 2026, needs more optimization.
4 466 0.929493611202 Henry Cohn, 2026, needs more optimization.
4 467 0.929652460745 Henry Cohn, 2026, needs more optimization.
4 468 0.929731607409 Henry Cohn, 2026, needs more optimization.
4 469 0.929858667670 Henry Cohn, 2026, needs more optimization.
4 470 0.929964722242 Henry Cohn, 2026, needs more optimization.
4 471 0.930087402486 Henry Cohn, 2026, needs more optimization.
4 472 0.930284440643 Henry Cohn, 2026, needs more optimization.
4 473 0.930409696786 Henry Cohn, 2026, needs more optimization.
4 474 0.930540845163 Henry Cohn, 2026, needs more optimization.
4 475 0.930658845161 Henry Cohn, 2026, needs more optimization.
4 476 0.930696686791 Henry Cohn, 2026, needs more optimization.
4 477 0.930791534273 Henry Cohn, 2026, needs more optimization.
4 478 0.930948232259 Henry Cohn, 2026, needs more optimization.
4 479 0.930994386934 Henry Cohn, 2026, needs more optimization.
4 480 0.931045112948 Henry Cohn, 2026, needs more optimization.
4 481 0.931140491211 Henry Cohn, 2026, needs more optimization.
4 482 0.931247547162 Henry Cohn, 2026, needs more optimization.
4 483 0.931360305402 Henry Cohn, 2026, needs more optimization.
4 484 0.931463358810 Henry Cohn, 2026, needs more optimization.
4 485 0.931577737344 Henry Cohn, 2026, needs more optimization.
4 486 0.931621017509 Henry Cohn, 2026, needs more optimization.
4 487 0.931675713173 Henry Cohn, 2026, needs more optimization.
4 488 0.931783092912 Henry Cohn, 2026, needs more optimization.
4 489 0.931863767270 Henry Cohn, 2026, needs more optimization.
4 490 0.931967844529 Henry Cohn, 2026, needs more optimization.
4 491 0.932017412115 Henry Cohn, 2026, needs more optimization.
4 492 0.932072621558 Henry Cohn, 2026, needs more optimization.
4 493 0.932141798752 Henry Cohn, 2026, needs more optimization.
4 494 0.932206145008 Henry Cohn, 2026, needs more optimization.
4 495 0.932282644994 Henry Cohn, 2026, needs more optimization.
4 496 0.932380050469 Henry Cohn, 2026, needs more optimization.
4 497 0.932486122371 Henry Cohn, 2026, needs more optimization.
4 498 0.932566496857 Henry Cohn, 2026, needs more optimization.
4 499 0.932634491005 Henry Cohn, 2026, needs more optimization.
4 500 0.932698594062 Henry Cohn, 2026, needs more optimization.
4 501 0.932738996207 Henry Cohn, 2026, needs more optimization.
4 502 0.932845323970 Henry Cohn, 2026, needs more optimization.
4 503 0.932924437333 Henry Cohn, 2026, needs more optimization.
4 504 0.933024669559 Henry Cohn, 2026, needs more optimization.
4 505 0.933093459762 Henry Cohn, 2026, needs more optimization.
4 506 0.933166070470 Henry Cohn, 2026, needs more optimization.
4 507 0.933261671104 Henry Cohn, 2026, needs more optimization.
4 508 0.933350520591 Henry Cohn, 2026, needs more optimization.
4 509 0.933456439500 Henry Cohn, 2026, needs more optimization.
4 510 0.933530697443 Henry Cohn, 2026, needs more optimization.
4 511 0.933642077565 Henry Cohn, 2026, needs more optimization.
4 512 0.933740816341 Henry Cohn, 2026, needs more optimization.
4 513 0.933891024620 Henry Cohn, 2026, needs more optimization.
4 514 0.933943028256 Henry Cohn, 2026, needs more optimization.
4 515 0.934029685643 Henry Cohn, 2026, needs more optimization.
4 516 0.934175399142 Henry Cohn, 2026, needs more optimization.
4 517 0.934193620696 Henry Cohn, 2026, needs more optimization.
4 518 0.934305876211 Henry Cohn, 2026, needs more optimization.
4 519 0.934446704656 Henry Cohn, 2026, needs more optimization.
4 520 0.934503800337 Henry Cohn, 2026, needs more optimization.
4 521 0.934587988035 Henry Cohn, 2026, needs more optimization.
4 522 0.934731876858 Henry Cohn, 2026, needs more optimization.
4 523 0.934786346012 Henry Cohn, 2026, needs more optimization.
4 524 0.934876190131 Henry Cohn, 2026, needs more optimization.
4 525 0.934988351825 Henry Cohn, 2026, needs more optimization.
4 526 0.935084865551 Henry Cohn, 2026, needs more optimization.
4 527 0.935178432944 Henry Cohn, 2026, needs more optimization.
4 528 0.935245846539 Henry Cohn, 2026, needs more optimization.
4 529 0.935293054321 Henry Cohn, 2026, needs more optimization.
4 530 0.935327093948 Henry Cohn, 2026, needs more optimization.
4 531 0.935457813866 Henry Cohn, 2026, needs more optimization.
4 532 0.935522953512 Henry Cohn, 2026, needs more optimization.
4 533 0.935592679913 Henry Cohn, 2026, needs more optimization.
4 534 0.935715440732 Henry Cohn, 2026, needs more optimization.
4 535 0.935747983892 Henry Cohn, 2026, needs more optimization.
4 536 0.935764712370 Henry Cohn, 2026, needs more optimization.
4 537 0.935851827637 Henry Cohn, 2026, needs more optimization.
4 538 0.936004672466 Henry Cohn, 2026, needs more optimization.
4 539 0.936070025277 Henry Cohn, 2026, needs more optimization.
4 540 0.936168399322 Henry Cohn, 2026, needs more optimization.
4 541 0.936204654771 Henry Cohn, 2026, needs more optimization.
4 542 0.936272956077 Henry Cohn, 2026, needs more optimization.
4 543 0.936387377450 Henry Cohn, 2026, needs more optimization.
4 544 0.936452956991 Henry Cohn, 2026, needs more optimization.
4 545 0.936524512250 Henry Cohn, 2026, needs more optimization.
4 546 0.936527304089 Henry Cohn, 2026, needs more optimization.
4 547 0.936600720841 Henry Cohn, 2026, needs more optimization.
4 548 0.936670541881 Henry Cohn, 2026, needs more optimization.
4 549 0.936739800041 Henry Cohn, 2026, needs more optimization.
4 550 0.936830691034 Henry Cohn, 2026, needs more optimization.
4 551 0.936860348618 Henry Cohn, 2026, needs more optimization.
4 552 0.936982415329 Henry Cohn, 2026, needs more optimization.
4 553 0.937066764746 Henry Cohn, 2026, needs more optimization.
4 554 0.937186204064 Henry Cohn, 2026, needs more optimization.
4 555 0.937288038089 Henry Cohn, 2026, needs more optimization.
4 556 0.937342624323 Henry Cohn, 2026, needs more optimization.
4 557 0.937410521847 Henry Cohn, 2026, needs more optimization.
4 558 0.937462551951 Henry Cohn, 2026, needs more optimization.
4 559 0.937608425869 Henry Cohn, 2026, needs more optimization.
4 560 0.937687909331 Henry Cohn, 2026, needs more optimization.
4 561 0.937741390008 Henry Cohn, 2026, needs more optimization.
4 562 0.937800135929 Henry Cohn, 2026, needs more optimization.
4 563 0.937854616216 Henry Cohn, 2026, needs more optimization.
4 564 0.937946958280 Henry Cohn, 2026, needs more optimization.
4 565 0.938001484234 Henry Cohn, 2026, needs more optimization.
4 566 0.938108773196 Henry Cohn, 2026, needs more optimization.
4 567 0.938170296793 Henry Cohn, 2026, needs more optimization.
4 568 0.938268908027 Henry Cohn, 2026, needs more optimization.
4 569 0.938344588548 Henry Cohn, 2026, needs more optimization.
4 570 0.938349141920 Henry Cohn, 2026, needs more optimization.
4 571 0.938420308040 Henry Cohn, 2026, needs more optimization.
4 572 0.938479558933 Henry Cohn, 2026, needs more optimization.
4 573 0.938551975281 Henry Cohn, 2026, needs more optimization.
4 574 0.938608701133 Henry Cohn, 2026, needs more optimization.
4 575 0.938717380795 Henry Cohn, 2026, needs more optimization.
4 576 0.938784833589 Henry Cohn, 2026, needs more optimization.
4 577 0.938907343673 Henry Cohn, 2026, needs more optimization.
4 578 0.938953322082 Henry Cohn, 2026, needs more optimization.
4 579 0.939048499509 Henry Cohn, 2026, needs more optimization.
4 580 0.939141179227 Henry Cohn, 2026, needs more optimization.
4 581 0.939204108810 Henry Cohn, 2026, needs more optimization.
4 582 0.939262537386 Henry Cohn, 2026, needs more optimization.
4 583 0.939307111089 Henry Cohn, 2026, needs more optimization.
4 584 0.939329798612 Henry Cohn, 2026, needs more optimization.
4 585 0.939432773359 Henry Cohn, 2026, needs more optimization.
4 586 0.939487297605 Henry Cohn, 2026, needs more optimization.
4 587 0.939550383261 Henry Cohn, 2026, needs more optimization.
4 588 0.939559793000 Henry Cohn, 2026, needs more optimization.
4 589 0.939637566969 Henry Cohn, 2026, needs more optimization.
4 590 0.939651040423 Henry Cohn, 2026, needs more optimization.
4 591 0.939776027077 Henry Cohn, 2026, needs more optimization.
4 592 0.939828349564 Henry Cohn, 2026, needs more optimization.
4 593 0.939829380710 Henry Cohn, 2026, needs more optimization.
4 594 0.939848575178 Henry Cohn, 2026, needs more optimization.
4 595 0.939917387324 Henry Cohn, 2026, needs more optimization.
4 596 0.939973475439 Henry Cohn, 2026, needs more optimization.
4 597 0.939992326265 Henry Cohn, 2026, needs more optimization.
4 598 0.940086160207 Henry Cohn, 2026, needs more optimization.
4 600 0.940100886633 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 601 0.940232544017 Henry Cohn, 2026, needs more optimization.
4 602 0.940339273728 Henry Cohn, 2026, needs more optimization.
4 603 0.940407811131 Henry Cohn, 2026, needs more optimization.
4 604 0.940530241663 Henry Cohn, 2026, needs more optimization.
4 605 0.940595897672 Henry Cohn, 2026, needs more optimization.
4 606 0.940629332993 Henry Cohn, 2026, needs more optimization.
4 607 0.940690407187 Henry Cohn, 2026, needs more optimization.
4 608 0.940763737888 Henry Cohn, 2026, needs more optimization.
4 609 0.940823032137 Henry Cohn, 2026, needs more optimization.
4 610 0.940912709564 Henry Cohn, 2026, needs more optimization.
4 611 0.940947295787 Henry Cohn, 2026, needs more optimization.
4 612 0.940999234162 Henry Cohn, 2026, needs more optimization.
4 613 0.941058479695 Henry Cohn, 2026, needs more optimization.
4 614 0.941160930995 Henry Cohn, 2026, needs more optimization.
4 615 0.941237606521 Henry Cohn, 2026, needs more optimization.
4 616 0.941276608542 Henry Cohn, 2026, needs more optimization.
4 617 0.941339328104 Henry Cohn, 2026, needs more optimization.
4 618 0.941401968416 Henry Cohn, 2026, needs more optimization.
4 619 0.941445542755 Henry Cohn, 2026, needs more optimization.
4 620 0.941512427051 Henry Cohn, 2026, needs more optimization.
4 621 0.941548194183 Henry Cohn, 2026, needs more optimization.
4 622 0.941656526092 Henry Cohn, 2026, needs more optimization.
4 623 0.941696457719 Henry Cohn, 2026, needs more optimization.
4 624 0.941766559592 Henry Cohn, 2026, needs more optimization.
4 625 0.941838431002 Henry Cohn, 2026, needs more optimization.
4 626 0.941955443279 Henry Cohn, 2026, needs more optimization.
4 627 0.941998018942 Henry Cohn, 2026, needs more optimization.
4 628 0.942077697649 Henry Cohn, 2026, needs more optimization.
4 629 0.942133201968 Henry Cohn, 2026, needs more optimization.
4 630 0.942218535915 Henry Cohn, 2026, needs more optimization.
4 631 0.942289209513 Henry Cohn, 2026, needs more optimization.
4 632 0.942316211327 Henry Cohn, 2026, needs more optimization.
4 633 0.942417363986 Henry Cohn, 2026, needs more optimization.
4 634 0.942493383645 Henry Cohn, 2026, needs more optimization.
4 635 0.942529575089 Henry Cohn, 2026, needs more optimization.
4 636 0.942596119081 Henry Cohn, 2026, needs more optimization.
4 637 0.942614444546 Henry Cohn, 2026, needs more optimization.
4 638 0.942691700756 Henry Cohn, 2026, needs more optimization.
4 639 0.942756347541 Henry Cohn, 2026, needs more optimization.
4 640 0.942772999882 Henry Cohn, 2026, needs more optimization.
4 641 0.942876039843 Henry Cohn, 2026, needs more optimization.
4 642 0.942969051020 Henry Cohn, 2026, needs more optimization.
4 643 0.943068391833 Henry Cohn, 2026, needs more optimization.
4 644 0.943073892703 Henry Cohn, 2026, needs more optimization.
4 645 0.943118989496 Henry Cohn, 2026, needs more optimization.
4 646 0.943159621002 Henry Cohn, 2026, needs more optimization.
4 647 0.943207668875 Henry Cohn, 2026, needs more optimization.
4 648 0.943218851964 Henry Cohn, 2026, needs more optimization.
4 649 0.943257780687 Henry Cohn, 2026, needs more optimization.
4 650 0.943274345246 Henry Cohn, 2026, needs more optimization.
4 651 0.943339245664 Henry Cohn, 2026, needs more optimization.
4 652 0.943364587933 Henry Cohn, 2026, needs more optimization.
4 653 0.943379121445 Henry Cohn, 2026, needs more optimization.
4 654 0.943389655961 Henry Cohn, 2026, needs more optimization.
4 655 0.943451720020 Henry Cohn, 2026, needs more optimization.
4 656 0.943484447577 Henry Cohn, 2026, needs more optimization.
4 657 0.943546241712 Henry Cohn, 2026, needs more optimization.
4 658 0.943547354188 Henry Cohn, 2026, needs more optimization.
4 659 0.943561735522 Henry Cohn, 2026, needs more optimization.
4 660 0.943594661847 Henry Cohn, 2026, needs more optimization.
4 661 0.943623943567 Henry Cohn, 2026, needs more optimization.
4 662 0.943665038239 Henry Cohn, 2026, needs more optimization.
4 663 0.943709855467 Henry Cohn, 2026, needs more optimization.
4 664 0.943744033307 Henry Cohn, 2026, needs more optimization.
4 665 0.943779039775 Henry Cohn, 2026, needs more optimization.
4 666 0.943797504575 Henry Cohn, 2026, needs more optimization.
4 667 0.943828183852 Henry Cohn, 2026, needs more optimization.
4 668 0.943865438647 Henry Cohn, 2026, needs more optimization.
4 669 0.943891706519 Henry Cohn, 2026, needs more optimization.
4 670 0.943960439578 Henry Cohn, 2026, needs more optimization.
4 671 0.943997210820 Henry Cohn, 2026, needs more optimization.
4 672 0.944039779123 Henry Cohn, 2026, needs more optimization.
4 673 0.944115095092 Henry Cohn, 2026, needs more optimization.
4 674 0.944214356306 Henry Cohn, 2026, needs more optimization.
4 675 0.944323146535 Henry Cohn, 2026, needs more optimization.
4 676 0.944350962751 Henry Cohn, 2026, needs more optimization.
4 677 0.944399984729 Henry Cohn, 2026, needs more optimization.
4 678 0.944513116444 Henry Cohn, 2026, needs more optimization.
4 679 0.944589356043 Henry Cohn, 2026, needs more optimization.
4 680 0.944648718475 Henry Cohn, 2026, needs more optimization.
4 681 0.944719250904 Henry Cohn, 2026, needs more optimization.
4 682 0.944803443663 Henry Cohn, 2026, needs more optimization.
4 683 0.944832790327 Henry Cohn, 2026, needs more optimization.
4 684 0.944916555327 Henry Cohn, 2026, needs more optimization.
4 685 0.944976313583 Henry Cohn, 2026, needs more optimization.
4 686 0.945013618972 Henry Cohn, 2026, needs more optimization.
4 687 0.945149580143 Henry Cohn, 2026, needs more optimization.
4 688 0.945215812794 Henry Cohn, 2026, needs more optimization.
4 689 0.945292022564 Henry Cohn, 2026, needs more optimization.
4 690 0.945359225444 Henry Cohn, 2026, needs more optimization.
4 691 0.945455645291 Henry Cohn, 2026, needs more optimization.
4 692 0.945502802428 Henry Cohn, 2026, needs more optimization.
4 693 0.945612640744 Henry Cohn, 2026, needs more optimization.
4 694 0.945656651681 Henry Cohn, 2026, needs more optimization.
4 695 0.945721169263 Henry Cohn, 2026, needs more optimization.
4 696 0.945812264278 Henry Cohn, 2026, needs more optimization.
4 697 0.945831918935 Henry Cohn, 2026, needs more optimization.
4 698 0.945878915234 Henry Cohn, 2026, needs more optimization.
4 699 0.945995802950 Henry Cohn, 2026, needs more optimization.
4 700 0.946035096171 Henry Cohn, 2026, needs more optimization.
4 701 0.946101841884 Henry Cohn, 2026, needs more optimization.
4 702 0.946186074127 Henry Cohn, 2026, needs more optimization.
4 703 0.946201979994 Henry Cohn, 2026, needs more optimization.
4 704 0.946305095175 Henry Cohn, 2026, needs more optimization.
4 705 0.946324753546 Henry Cohn, 2026, needs more optimization.
4 706 0.946379355957 Henry Cohn, 2026, needs more optimization.
4 707 0.946432730609 Henry Cohn, 2026, needs more optimization.
4 708 0.946486897981 Henry Cohn, 2026, needs more optimization.
4 709 0.946515983215 Henry Cohn, 2026, needs more optimization.
4 710 0.946555332286 Henry Cohn, 2026, needs more optimization.
4 711 0.946597907309 Henry Cohn, 2026, needs more optimization.
4 712 0.946659590171 Henry Cohn, 2026, needs more optimization.
4 713 0.946723980784 Henry Cohn, 2026, needs more optimization.
4 714 0.946788540707 Henry Cohn, 2026, needs more optimization.
4 715 0.946814487460 Henry Cohn, 2026, needs more optimization.
4 716 0.946822189414 Henry Cohn, 2026, needs more optimization.
4 717 0.946896917788 Henry Cohn, 2026, needs more optimization.
4 718 0.946925379119 Henry Cohn, 2026, needs more optimization.
4 719 0.946958238862 Henry Cohn, 2026, needs more optimization.
4 720 0.947002376751 Henry Cohn, 2026, needs more optimization.
4 721 0.947056821065 Henry Cohn, 2026, needs more optimization.
4 722 0.947101538417 Henry Cohn, 2026, needs more optimization.
4 723 0.947125051685 Henry Cohn, 2026, needs more optimization.
4 724 0.947177898860 Henry Cohn, 2026, needs more optimization.
4 725 0.947192105518 Henry Cohn, 2026, needs more optimization.
4 726 0.947204767357 Henry Cohn, 2026, needs more optimization.
4 727 0.947252653863 Henry Cohn, 2026, needs more optimization.
4 728 0.947309102686 Henry Cohn, 2026, needs more optimization.
4 729 0.947341086493 Henry Cohn, 2026, needs more optimization.
4 730 0.947425281913 Henry Cohn, 2026, needs more optimization.
4 731 0.947460344003 Henry Cohn, 2026, needs more optimization.
4 732 0.947505682538 Henry Cohn, 2026, needs more optimization.
4 733 0.947547537480 Henry Cohn, 2026, needs more optimization.
4 734 0.947552094365 Henry Cohn, 2026, needs more optimization.
4 735 0.947575524392 Henry Cohn, 2026, needs more optimization.
4 736 0.947610887612 Henry Cohn, 2026, needs more optimization.
4 737 0.947663870175 Henry Cohn, 2026, needs more optimization.
4 738 0.947676701069 Henry Cohn, 2026, needs more optimization.
4 739 0.947707474168 Henry Cohn, 2026, needs more optimization.
4 740 0.947738125273 Henry Cohn, 2026, needs more optimization.
4 741 0.947822680450 Henry Cohn, 2026, needs more optimization.
4 742 0.947838577178 Henry Cohn, 2026, needs more optimization.
4 743 0.947863885928 Henry Cohn, 2026, needs more optimization.
4 744 0.947943071994 Henry Cohn, 2026, needs more optimization.
4 745 0.947997722477 Henry Cohn, 2026, needs more optimization.
4 746 0.948055031823 Henry Cohn, 2026, needs more optimization.
4 747 0.948098704012 Henry Cohn, 2026, needs more optimization.
4 748 0.948118892737 Henry Cohn, 2026, needs more optimization.
4 749 0.948180885101 Henry Cohn, 2026, needs more optimization.
4 750 0.948240856020 Henry Cohn, 2026, needs more optimization.
4 751 0.948281404659 Henry Cohn, 2026, needs more optimization.
4 752 0.948317585132 Henry Cohn, 2026, needs more optimization.
4 753 0.948343890897 Henry Cohn, 2026, needs more optimization.
4 754 0.948359329966 Henry Cohn, 2026, needs more optimization.
4 755 0.948384190179 Henry Cohn, 2026, needs more optimization.
4 756 0.948420321405 Henry Cohn, 2026, needs more optimization.
4 757 0.948469627019 Henry Cohn, 2026, needs more optimization.
4 758 0.948528431153 Henry Cohn, 2026, needs more optimization.
4 759 0.948556608949 Henry Cohn, 2026, needs more optimization.
4 760 0.948640906312 Henry Cohn, 2026, needs more optimization.
4 761 0.948682833839 Henry Cohn, 2026, needs more optimization.
4 762 0.948762048366 Henry Cohn, 2026, needs more optimization.
4 763 0.948802168315 Henry Cohn, 2026, needs more optimization.
4 764 0.948840710698 Henry Cohn, 2026, needs more optimization.
4 765 0.948849327855 Henry Cohn, 2026, needs more optimization.
4 766 0.948910026012 Henry Cohn, 2026, needs more optimization.
4 767 0.948941762706 Henry Cohn, 2026, needs more optimization.
4 768 0.948970708524 Henry Cohn, 2026, needs more optimization.
4 769 0.949050202954 Henry Cohn, 2026, needs more optimization.
4 770 0.949098904875 Henry Cohn, 2026, needs more optimization.
4 771 0.949104948719 Henry Cohn, 2026, needs more optimization.
4 772 0.949147699629 Henry Cohn, 2026, needs more optimization.
4 773 0.949228896199 Henry Cohn, 2026, needs more optimization.
4 774 0.949298593935 Henry Cohn, 2026, needs more optimization.
4 775 0.949335151775 Henry Cohn, 2026, needs more optimization.
4 776 0.949366076287 Henry Cohn, 2026, needs more optimization.
4 777 0.949404673333 Henry Cohn, 2026, needs more optimization.
4 778 0.949415759420 Henry Cohn, 2026, needs more optimization.
4 779 0.949499040358 Henry Cohn, 2026, needs more optimization.
4 780 0.949516477888 Henry Cohn, 2026, needs more optimization.
4 781 0.949534403975 Henry Cohn, 2026, needs more optimization.
4 782 0.949545757926 Henry Cohn, 2026, needs more optimization.
4 783 0.949603080321 Henry Cohn, 2026, needs more optimization.
4 784 0.949656855516 Henry Cohn, 2026, needs more optimization.
4 785 0.949673315235 Henry Cohn, 2026, needs more optimization.
4 786 0.949734411157 Henry Cohn, 2026, needs more optimization.
4 787 0.949764074703 Henry Cohn, 2026, needs more optimization.
4 788 0.949807330057 Henry Cohn, 2026, needs more optimization.
4 789 0.949821931397 Henry Cohn, 2026, needs more optimization.
4 790 0.949865413790 Henry Cohn, 2026, needs more optimization.
4 791 0.949888387027 Henry Cohn, 2026, needs more optimization.
4 792 0.949937432180 Henry Cohn, 2026, needs more optimization.
4 793 0.949989750186 Henry Cohn, 2026, needs more optimization.
4 794 0.949990993092 Henry Cohn, 2026, needs more optimization.
4 795 0.950018073295 Henry Cohn, 2026, needs more optimization.
4 796 0.950052272705 Henry Cohn, 2026, needs more optimization.
4 797 0.950071951333 Henry Cohn, 2026, needs more optimization.
4 798 0.950090331327 Henry Cohn, 2026, needs more optimization.
4 800 0.950110636208 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 801 0.950164848881 Henry Cohn, 2026, needs more optimization.
4 802 0.950168450827 Henry Cohn, 2026, needs more optimization.
4 803 0.950212237262 Henry Cohn, 2026, needs more optimization.
4 804 0.950237930908 Henry Cohn, 2026, needs more optimization.
4 805 0.950268730085 Henry Cohn, 2026, needs more optimization.
4 806 0.950296520661 Henry Cohn, 2026, needs more optimization.
4 807 0.950314393457 Henry Cohn, 2026, needs more optimization.
4 808 0.950365112566 Henry Cohn, 2026, needs more optimization.
4 809 0.950366408762 Henry Cohn, 2026, needs more optimization.
4 810 0.950415317973 Henry Cohn, 2026, needs more optimization.
4 811 0.950418590746 Henry Cohn, 2026, needs more optimization.
4 812 0.950466092596 Henry Cohn, 2026, needs more optimization.
4 813 0.950486441674 Henry Cohn, 2026, needs more optimization.
4 814 0.950519506083 Henry Cohn, 2026, needs more optimization.
4 815 0.950522920069 Henry Cohn, 2026, needs more optimization.
4 816 0.950548368615 Henry Cohn, 2026, needs more optimization.
4 817 0.950562540063 Henry Cohn, 2026, needs more optimization.
4 818 0.950567853025 Henry Cohn, 2026, needs more optimization.
4 819 0.950571141763 Henry Cohn, 2026, needs more optimization.
4 820 0.950600375158 Henry Cohn, 2026, needs more optimization.
4 821 0.950613123719 Henry Cohn, 2026, needs more optimization.
4 822 0.950616133350 Henry Cohn, 2026, needs more optimization.
4 823 0.950618083866 Henry Cohn, 2026, needs more optimization.
4 824 0.950783670413 Henry Cohn, 2026, needs more optimization.
4 825 0.950784233007 Henry Cohn, 2026, needs more optimization.
4 826 0.950785036066 Henry Cohn, 2026, needs more optimization.
4 827 0.950785986839 Henry Cohn, 2026, needs more optimization.
4 828 0.950786495939 Henry Cohn, 2026, needs more optimization.
4 829 0.950787403925 Henry Cohn, 2026, needs more optimization.
4 830 0.950788858885 Henry Cohn, 2026, needs more optimization.
4 831 0.950790825653 Henry Cohn, 2026, needs more optimization.
4 832 0.950791770003 Henry Cohn, 2026, needs more optimization.
4 833 0.950791848284 Henry Cohn, 2026, needs more optimization.
4 834 0.950793544008 Henry Cohn, 2026, needs more optimization.
4 835 0.950794392795 Henry Cohn, 2026, needs more optimization.
4 836 0.950795410034 Henry Cohn, 2026, needs more optimization.
4 837 0.950795639960 Henry Cohn, 2026, needs more optimization.
4 838 0.950796987616 Henry Cohn, 2026, needs more optimization.
4 840 0.950797547280 Henry Cohn, 2025, needs more optimization.
4 841 0.950955646343 Henry Cohn, 2026, needs more optimization.
4 842 0.951052055583 Henry Cohn, 2026, needs more optimization.
4 843 0.951118473976 Henry Cohn, 2026, needs more optimization.
4 844 0.951235521794 Henry Cohn, 2026, needs more optimization.
4 845 0.951287705549 Henry Cohn, 2026, needs more optimization.
4 846 0.951404188928 Henry Cohn, 2026, needs more optimization.
4 847 0.951467813406 Henry Cohn, 2026, needs more optimization.
4 848 0.951552114074 Henry Cohn, 2026, needs more optimization.
4 849 0.951612708396 Henry Cohn, 2026, needs more optimization.
4 850 0.951689369104 Henry Cohn, 2026, needs more optimization.
4 851 0.951797679501 Henry Cohn, 2026, needs more optimization.
4 852 0.951836722297 Henry Cohn, 2026, needs more optimization.
4 853 0.951908220624 Henry Cohn, 2026, needs more optimization.
4 854 0.951987047224 Henry Cohn, 2026, needs more optimization.
4 855 0.952036929162 Henry Cohn, 2026, needs more optimization.
4 856 0.952135299987 Henry Cohn, 2026, needs more optimization.
4 857 0.952191602758 Henry Cohn, 2026, needs more optimization.
4 858 0.952232393250 Henry Cohn, 2026, needs more optimization.
4 859 0.952304988341 Henry Cohn, 2026, needs more optimization.
4 860 0.952374304034 Henry Cohn, 2026, needs more optimization.
4 861 0.952476139491 Henry Cohn, 2026, needs more optimization.
4 862 0.952489025963 Henry Cohn, 2026, needs more optimization.
4 863 0.952569813448 Henry Cohn, 2026, needs more optimization.
4 864 0.952616759093 Henry Cohn, 2026, needs more optimization.
4 865 0.952690546018 Henry Cohn, 2026, needs more optimization.
4 866 0.952773092049 Henry Cohn, 2026, needs more optimization.
4 867 0.952837078417 Henry Cohn, 2026, needs more optimization.
4 868 0.952844074284 Henry Cohn, 2026, needs more optimization.
4 869 0.952844879988 Henry Cohn, 2026, needs more optimization.
4 870 0.952848992490 Henry Cohn, 2026, needs more optimization.
4 871 0.952872331370 Henry Cohn, 2026, needs more optimization.
4 872 0.952917906206 Henry Cohn, 2026, needs more optimization.
4 873 0.952950752252 Henry Cohn, 2026, needs more optimization.
4 874 0.952962425831 Henry Cohn, 2026, needs more optimization.
4 875 0.953000515882 Henry Cohn, 2026, needs more optimization.
4 876 0.953014222361 Henry Cohn, 2026, needs more optimization.
4 877 0.953069169290 Henry Cohn, 2026, needs more optimization.
4 878 0.953112686679 Henry Cohn, 2026, needs more optimization.
4 879 0.953154673886 Henry Cohn, 2026, needs more optimization.
4 880 0.953172064263 Henry Cohn, 2026, needs more optimization.
4 881 0.953218919758 Henry Cohn, 2026, needs more optimization.
4 882 0.953261990509 Henry Cohn, 2026, needs more optimization.
4 883 0.953292381315 Henry Cohn, 2026, needs more optimization.
4 884 0.953301928914 Henry Cohn, 2026, needs more optimization.
4 885 0.953337187258 Henry Cohn, 2026, needs more optimization.
4 886 0.953394148009 Henry Cohn, 2026, needs more optimization.
4 887 0.953416878841 Henry Cohn, 2026, needs more optimization.
4 888 0.953422226027 Henry Cohn, 2026, needs more optimization.
4 889 0.953473070085 Henry Cohn, 2026, needs more optimization.
4 890 0.953542157805 Henry Cohn, 2026, needs more optimization.
4 891 0.953577459762 Henry Cohn, 2026, needs more optimization.
4 892 0.953594174369 Henry Cohn, 2026, needs more optimization.
4 893 0.953641778340 Henry Cohn, 2026, needs more optimization.
4 894 0.953641862636 Henry Cohn, 2026, needs more optimization.
4 895 0.953696460634 Henry Cohn, 2026, needs more optimization.
4 896 0.953697561733 Henry Cohn, 2026, needs more optimization.
4 897 0.953714080121 Henry Cohn, 2026, needs more optimization.
4 900 0.953772277048 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 901 0.953855632936 Henry Cohn, 2026, needs more optimization.
4 902 0.953892078161 Henry Cohn, 2026, needs more optimization.
4 903 0.953932291069 Henry Cohn, 2026, needs more optimization.
4 904 0.953972640501 Henry Cohn, 2026, needs more optimization.
4 905 0.954046514093 Henry Cohn, 2026, needs more optimization.
4 906 0.954083671032 Henry Cohn, 2026, needs more optimization.
4 907 0.954116981720 Henry Cohn, 2026, needs more optimization.
4 908 0.954119149597 Henry Cohn, 2026, needs more optimization.
4 909 0.954120165093 Henry Cohn, 2026, needs more optimization.
4 910 0.954139386016 Henry Cohn, 2026, needs more optimization.
4 911 0.954148120119 Henry Cohn, 2026, needs more optimization.
4 912 0.954156183803 Henry Cohn, 2026, needs more optimization.
4 913 0.954158071957 Henry Cohn, 2026, needs more optimization.
4 914 0.954189275759 Henry Cohn, 2026, needs more optimization.
4 915 0.954211926197 Henry Cohn, 2026, needs more optimization.
4 916 0.954241463459 Henry Cohn, 2026, needs more optimization.
4 917 0.954300035723 Henry Cohn, 2026, needs more optimization.
4 918 0.954336111719 Henry Cohn, 2026, needs more optimization.
4 919 0.954387119858 Henry Cohn, 2026, needs more optimization.
4 920 0.954429716378 Henry Cohn, 2026, needs more optimization.
4 921 0.954439546783 Henry Cohn, 2026, needs more optimization.
4 922 0.954485722763 Henry Cohn, 2026, needs more optimization.
4 923 0.954545844934 Henry Cohn, 2026, needs more optimization.
4 924 0.954586489953 Henry Cohn, 2026, needs more optimization.
4 925 0.954611969674 Henry Cohn, 2026, needs more optimization.
4 926 0.954615840237 Henry Cohn, 2026, needs more optimization.
4 927 0.954675196445 Henry Cohn, 2026, needs more optimization.
4 928 0.954733747668 Henry Cohn, 2026, needs more optimization.
4 929 0.954784417614 Henry Cohn, 2026, needs more optimization.
4 930 0.954827002641 Henry Cohn, 2026, needs more optimization.
4 931 0.954892630966 Henry Cohn, 2026, needs more optimization.
4 932 0.954920621506 Henry Cohn, 2026, needs more optimization.
4 933 0.955008682083 Henry Cohn, 2026, needs more optimization.
4 934 0.955010485535 Henry Cohn, 2026, needs more optimization.
4 935 0.955019206788 Henry Cohn, 2026, needs more optimization.
4 936 0.955077651638 Henry Cohn, 2026, needs more optimization.
4 937 0.955098596609 Henry Cohn, 2026, needs more optimization.
4 938 0.955131384032 Henry Cohn, 2026, needs more optimization.
4 939 0.955145136091 Henry Cohn, 2026, needs more optimization.
4 940 0.955164669480 Henry Cohn, 2026, needs more optimization.
4 941 0.955208533343 Henry Cohn, 2026, needs more optimization.
4 942 0.955247910141 Henry Cohn, 2026, needs more optimization.
4 943 0.955275659317 Henry Cohn, 2026, needs more optimization.
4 944 0.955321283474 Henry Cohn, 2026, needs more optimization.
4 945 0.955348983223 Henry Cohn, 2026, needs more optimization.
4 946 0.955389200991 Henry Cohn, 2026, needs more optimization.
4 947 0.955396682650 Henry Cohn, 2026, needs more optimization.
4 948 0.955463995553 Henry Cohn, 2026, needs more optimization.
4 949 0.955495979773 Henry Cohn, 2026, needs more optimization.
4 950 0.955541457491 Henry Cohn, 2026, needs more optimization.
4 951 0.955545105051 Henry Cohn, 2026, needs more optimization.
4 952 0.955547724742 Henry Cohn, 2026, needs more optimization.
4 954 0.955568065538 Henry Cohn, 2026, needs more optimization.
4 955 0.955597837119 Henry Cohn, 2026, needs more optimization.
4 956 0.955645729343 Henry Cohn, 2026, needs more optimization.
4 957 0.955649490439 Henry Cohn, 2026, needs more optimization.
4 958 0.955683929157 Henry Cohn, 2026, needs more optimization.
4 959 0.955725686034 Henry Cohn, 2026, needs more optimization.
4 960 0.955787000120 Henry Cohn, 2026, needs more optimization.
4 961 0.955903013884 Henry Cohn, 2026, needs more optimization.
4 962 0.955915216877 Henry Cohn, 2026, needs more optimization.
4 963 0.955922049091 Henry Cohn, 2026, needs more optimization.
4 964 0.956031048578 Henry Cohn, 2026, needs more optimization.
4 965 0.956049296748 Henry Cohn, 2026, needs more optimization.
4 966 0.956072723743 Henry Cohn, 2026, needs more optimization.
4 967 0.956078868062 Henry Cohn, 2026, needs more optimization.
4 968 0.956088549067 Henry Cohn, 2026, needs more optimization.
4 969 0.956105221877 Henry Cohn, 2026, needs more optimization.
4 970 0.956120519679 Henry Cohn, 2026, needs more optimization.
4 971 0.956127786366 Henry Cohn, 2026, needs more optimization.
4 972 0.956149311875 Henry Cohn, 2026, needs more optimization.
4 973 0.956164223824 Henry Cohn, 2026, needs more optimization.
4 974 0.956173147582 Henry Cohn, 2026, needs more optimization.
4 975 0.956188064323 Henry Cohn, 2026, needs more optimization.
4 976 0.956227009408 Henry Cohn, 2026, needs more optimization.
4 977 0.956298548232 Henry Cohn, 2026, needs more optimization.
4 978 0.956306186233 Henry Cohn, 2026, needs more optimization.
4 979 0.956335652394 Henry Cohn, 2026, needs more optimization.
4 980 0.956379507689 Henry Cohn, 2026, needs more optimization.
4 981 0.956447899295 Henry Cohn, 2026, needs more optimization.
4 982 0.956447918955 Henry Cohn, 2026, needs more optimization.
4 983 0.956519060895 Henry Cohn, 2026, needs more optimization.
4 984 0.956638657350 Henry Cohn, 2026, needs more optimization.
4 985 0.956642058938 Henry Cohn, 2026, needs more optimization.
4 986 0.956657921018 Henry Cohn, 2026, needs more optimization.
4 987 0.956658899986 Henry Cohn, 2026, needs more optimization.
4 988 0.956664668751 Henry Cohn, 2026, needs more optimization.
4 989 0.956718203486 Henry Cohn, 2026, needs more optimization.
4 990 0.956774884708 Henry Cohn, 2026, needs more optimization.
4 991 0.956833934865 Henry Cohn, 2026, needs more optimization.
4 992 0.956878271857 Henry Cohn, 2026, needs more optimization.
4 993 0.956950286327 Henry Cohn, 2026, needs more optimization.
4 994 0.956981007702 Henry Cohn, 2026, needs more optimization.
4 995 0.957034656591 Henry Cohn, 2026, needs more optimization.
4 996 0.957060051341 Henry Cohn, 2026, needs more optimization.
4 997 0.957126463037 Henry Cohn, 2026, needs more optimization.
4 1000 0.957131117239 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
4 1001 0.957259283408 Henry Cohn, 2026, needs more optimization.
4 1002 0.957293581646 Henry Cohn, 2026, needs more optimization.
4 1003 0.957338798658 Henry Cohn, 2026, needs more optimization.
4 1004 0.957354808448 Henry Cohn, 2026, needs more optimization.
4 1005 0.957373559388 Henry Cohn, 2026, needs more optimization.
4 1006 0.957379480196 Henry Cohn, 2026, needs more optimization.
4 1007 0.957395769750 Henry Cohn, 2026, needs more optimization.
4 1008 0.957445945067 Henry Cohn, 2026, needs more optimization.
4 1009 0.957468074292 Henry Cohn, 2026, needs more optimization.
4 1011 0.957476045519 Henry Cohn, 2026, needs more optimization.
4 1012 0.957516963160 Henry Cohn, 2026, needs more optimization.
4 1013 0.957580697245 Henry Cohn, 2026, needs more optimization.
4 1014 0.957608910554 Henry Cohn, 2026, needs more optimization.
4 1015 0.957635676859 Henry Cohn, 2026, needs more optimization.
4 1016 0.957663303708 Henry Cohn, 2026, needs more optimization.
4 1017 0.957673523072 Henry Cohn, 2026, needs more optimization.
4 1018 0.957717244077 Henry Cohn, 2026, needs more optimization.
4 1019 0.957740836906 Henry Cohn, 2026, needs more optimization.
4 1020 0.957756557370 Henry Cohn, 2026, needs more optimization.
4 1021 0.957779229357 Henry Cohn, 2026, needs more optimization.
4 1022 0.957786476882 Henry Cohn, 2026, needs more optimization.
4 1023 0.957843421434 Henry Cohn, 2026, needs more optimization.
4 1024 0.957881987659 Henry Cohn, 2026, needs more optimization.
5 11 0.132853542599 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
45⁢x3−25⁢x2−5⁢x+1
5 12 0.153931605034 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
25⁢x4+30⁢x3+24⁢x2+2⁢x−1
5 13 0.187259851883 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
17⁢x3−5⁢x2−5⁢x+1
5 14 0.2 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x−1
5 15 0.2 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x−1
5 16* 0.2 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
5⁢x−1
5 17 0.270475835269 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
9⁢x4−16⁢x3−10⁢x2+1
5 18 0.275501741660 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
484⁢x5−488⁢x4+97⁢x3+17⁢x2−x−1
5 19 0.291822399025 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
57⁢x6−38⁢x5−109⁢x4+32⁢x3+23⁢x2−10⁢x+1
5 20 0.299385692900 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5⁢x3+13⁢x2−x−1
5 21 0.314916957176 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
5 22 0.354995034167 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 23 0.369772696944 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 24 0.374232982466 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
1620⁢x10+5508⁢x9−5751⁢x8−2406⁢x7+2055⁢x6+276⁢x5+559⁢x4−210⁢x3−127⁢x2+48⁢x−4
5 25 0.379621025394 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5 26 0.390240659505 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
5 27 0.401659264277 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
5 28 0.408169699093 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 29 0.411034435092 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
Minimal polynomial listed in plain text data
5 30 0.413029776123 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
269⁢x7−1419⁢x6−283⁢x5+405⁢x4+15⁢x3−9⁢x2−x−1
5 31 0.433911863960 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
Minimal polynomial listed in plain text data
5 32 0.441830743928 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8⁢x10−40⁢x9+74⁢x8−78⁢x7+73⁢x6−10⁢x5−3⁢x4+18⁢x3−9⁢x2−2⁢x+1
5 33 0.460004535963 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; K. J. Nurmela, Constructing spherical codes by global optimization methods, Research Report A32, Digital Systems Laboratory, Helsinki University of Technology, 1995, https://research.ics.aalto.fi/publications/info/bibdb.HUT-TCS-A32.shtml.
5 34 0.470482910392 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 35 0.478437929066 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 36 0.483999000231 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
49⁢x6−6⁢x5−53⁢x4+12⁢x3+13⁢x2−2⁢x−1
5 37 0.493828518526 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 38 0.496243746648 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 39 0.499971927191 Henry Cohn, 2025.
5 40 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Five dimensional non-lattice sphere packings, Canad. Math. Bull. 10 (1967), 387–393, doi:10.4153/CMB-1967-037-5; F. Szöllősi, A note on five dimensional kissing arrangements, Math. Res. Lett. 30 (2023), no. 5, 1609–1615, doi:10.4310/MRL.2023.v30.n5.a13, arXiv:2301.08272; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937.
2⁢x−1
5 41 0.514994652513 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 42 0.518241155863 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 43 0.524709601830 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 44 0.527457712324 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 45 0.535068808289 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 46 0.538291308677 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 47 0.540668770936 Henry Cohn, 2025.
5 48 0.545112501822 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 49 0.546918160679 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
7⁢x2−2⁢x−1
5 50 0.546918160679 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x2−2⁢x−1
5 51 0.554740414282 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 52 0.560107395820 Henry Cohn, 2025.
5 53 0.566883217391 Henry Cohn, 2025.
5 54 0.571075948469 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 55 0.574604319465 Henry Cohn, 2025.
5 56 0.577211861101 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 57 0.577350269190 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
3⁢x2−1
5 58 0.581466614772 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 59 0.586915485192 Henry Cohn, 2025.
5 60 0.593346597794 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 61 0.596251134208 Henry Cohn, 2025.
5 62 0.599005179291 Henry Cohn, 2023.
5 63 0.603554375176 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 64 0.605837370318 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 65 0.608465017856 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 66 0.608980005147 Henry Cohn, 2025.
5 67 0.611900403428 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 68 0.615240038880 Henry Cohn, 2025.
5 69 0.616793716634 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 70 0.617072261706 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 71 0.617972684614 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 72 0.617972684614 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 73 0.618033988750 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
x2+x−1
5 74 0.618033988750 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
x2+x−1
5 75 0.624659315083 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 76 0.631404527694 Henry Cohn, 2025.
5 77 0.636485570257 Henry Cohn, 2025.
5 78 0.640236043820 Henry Cohn, 2025.
5 79 0.643657523051 Henry Cohn, 2025.
5 80 0.646960184204 Henry Cohn, 2025.
5 81 0.648893901838 Henry Cohn, 2025.
5 82 0.651451517528 Henry Cohn, 2025.
5 83 0.655404165086 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 84 0.657612544747 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 85 0.659252981910 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 86 0.660931731561 Henry Cohn, 2025.
5 87 0.662618952049 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 88 0.664476994912 Henry Cohn, 2025.
5 89 0.666241382508 Henry Cohn, 2025.
5 90 0.666666666667 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996; T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−2
5 91 0.670415108805 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 92 0.672086633602 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 93 0.673630757747 Henry Cohn, 2026.
5 94 0.674852154382 Henry Cohn, 2026.
5 95 0.676048879094 Henry Cohn, 2026.
5 96 0.677473018556 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 97 0.679241845577 Henry Cohn, 2025.
5 98 0.680270697922 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 99 0.681881045310 Henry Cohn, 2025.
5 100 0.683153263764 Henry Cohn, 2025.
5 101 0.685186090412 Henry Cohn, 2025.
5 102 0.687443384073 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 103 0.688689846172 Henry Cohn, 2026.
5 104 0.689316429043 Henry Cohn, 2026.
5 105 0.690713450603 Henry Cohn, 2026.
5 106 0.692005491905 Henry Cohn, 2025.
5 107 0.693863512900 Henry Cohn, 2025.
5 108 0.695352225600 Henry Cohn, 2026.
5 109 0.696434500115 Henry Cohn, 2025.
5 110 0.698102767792 Henry Cohn, 2025.
5 111 0.699314980427 Henry Cohn, 2026.
5 112 0.700443897808 Henry Cohn, 2025.
5 113 0.701786576995 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 114 0.703016293850 Henry Cohn, 2026.
5 115 0.704057149283 Henry Cohn, 2025.
5 116 0.705292505873 Henry Cohn, 2025.
5 117 0.706879377909 Henry Cohn, 2025.
5 118 0.708028481260 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 119 0.709175837480 Henry Cohn, 2026.
5 120 0.710406057156 Henry Cohn, 2025.
5 121 0.711530217808 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 122 0.712249276837 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 123 0.713918633096 Henry Cohn, 2025.
5 124 0.715011517303 Henry Cohn, 2026.
5 125 0.716344500109 Henry Cohn, 2026.
5 126 0.717125377103 Henry Cohn, 2026.
5 127 0.718593587420 Henry Cohn, 2026.
5 128 0.719621301444 Henry Cohn, 2025.
5 129 0.720947646950 Henry Cohn, 2025.
5 130 0.721711816020 Henry Cohn, 2025.
5 131 0.723014786916 Henry Cohn, 2026, needs more optimization.
5 132 0.724187140657 Henry Cohn, 2026, needs more optimization.
5 133 0.725083698449 Henry Cohn, 2026, needs more optimization.
5 134 0.726366009074 Henry Cohn, 2026, needs more optimization.
5 135 0.727580411253 Henry Cohn, 2026, needs more optimization.
5 136 0.728518305111 Henry Cohn, 2026, needs more optimization.
5 137 0.729817089071 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 138 0.730143082796 Henry Cohn, 2025.
5 139 0.730768285544 Henry Cohn, 2026, needs more optimization.
5 140 0.731654612332 Henry Cohn, 2026, needs more optimization.
5 141 0.732554198222 Henry Cohn, 2026, needs more optimization.
5 142 0.733643357382 Henry Cohn, 2026, needs more optimization.
5 143 0.734506087652 Henry Cohn, 2025.
5 144 0.734979576626 Henry Cohn, 2026, needs more optimization.
5 145 0.735813646953 Henry Cohn, 2026, needs more optimization.
5 146 0.736183322946 Henry Cohn, 2026, needs more optimization.
5 147 0.736967148066 Henry Cohn, 2025.
5 148 0.737200174837 Henry Cohn, 2025.
5 149 0.737884019958 Henry Cohn, 2025.
5 150 0.738295981996 Henry Cohn, 2025.
5 151 0.739166634932 Henry Cohn, 2026, needs more optimization.
5 152 0.739744299669 Henry Cohn, 2026, needs more optimization.
5 153 0.740575866367 Henry Cohn, 2026, needs more optimization.
5 154 0.741221187032 Henry Cohn, 2026, needs more optimization.
5 155 0.742161234709 Henry Cohn, 2025.
5 156 0.742808811623 Henry Cohn, 2025.
5 157 0.743231311843 Henry Cohn, 2026, needs more optimization.
5 158 0.743483872286 Henry Cohn, 2026, needs more optimization.
5 159 0.743819326703 Henry Cohn, 2026, needs more optimization.
5 160 0.744143092099 Henry Cohn, 2025.
5 161 0.747768123526 Henry Cohn, 2025.
5 162 0.748843925322 Henry Cohn, 2025.
5 163 0.750218552457 Henry Cohn, 2025.
5 164 0.750876806783 Henry Cohn, 2025.
5 165 0.751992378586 Henry Cohn, 2026, needs more optimization.
5 166 0.752534073395 Henry Cohn, 2025.
5 167 0.753532673949 Henry Cohn, 2025.
5 168 0.754218675211 Henry Cohn, 2025.
5 169 0.755267409761 Henry Cohn, 2026, needs more optimization.
5 170 0.755993792807 Henry Cohn, 2025.
5 171 0.756603786557 Henry Cohn, 2026, needs more optimization.
5 172 0.757288355849 Henry Cohn, 2025.
5 173 0.758571738268 Henry Cohn, 2026, needs more optimization.
5 174 0.759690412033 Henry Cohn, 2025.
5 175 0.760597483271 Henry Cohn, 2025.
5 176 0.761278064091 Henry Cohn, 2025.
5 177 0.762048677174 Henry Cohn, 2026, needs more optimization.
5 178 0.762588876155 Henry Cohn, 2026, needs more optimization.
5 179 0.763200785343 Henry Cohn, 2026, needs more optimization.
5 180 0.763782659007 Henry Cohn, 2026, needs more optimization.
5 181 0.764357517196 Henry Cohn, 2026, needs more optimization.
5 182 0.764805574387 Henry Cohn, 2026, needs more optimization.
5 183 0.765391354290 Henry Cohn, 2026, needs more optimization.
5 184 0.766028627355 Henry Cohn, 2026, needs more optimization.
5 185 0.766453259311 Henry Cohn, 2026, needs more optimization.
5 186 0.766932960638 Henry Cohn, 2026, needs more optimization.
5 187 0.767582491098 Henry Cohn, 2026, needs more optimization.
5 188 0.768218265620 Henry Cohn, 2026, needs more optimization.
5 189 0.768781533643 Henry Cohn, 2026, needs more optimization.
5 190 0.769147855433 Henry Cohn, 2026, needs more optimization.
5 191 0.769623857454 Henry Cohn, 2026, needs more optimization.
5 192 0.769966409551 Henry Cohn, 2026, needs more optimization.
5 193 0.770551586865 Henry Cohn, 2026, needs more optimization.
5 194 0.771470333954 Henry Cohn, 2026, needs more optimization.
5 195 0.771805769165 Henry Cohn, 2026, needs more optimization.
5 196 0.772565596586 Henry Cohn, 2026, needs more optimization.
5 197 0.773284124288 Henry Cohn, 2026, needs more optimization.
5 198 0.773739010899 Henry Cohn, 2026, needs more optimization.
5 199 0.774495083742 Henry Cohn, 2026, needs more optimization.
5 200 0.775207277562 Henry Cohn, 2026, needs more optimization.
5 201 0.775761798246 Henry Cohn, 2026, needs more optimization.
5 202 0.776403953367 Henry Cohn, 2026, needs more optimization.
5 203 0.777004020555 Henry Cohn, 2026, needs more optimization.
5 204 0.777651049818 Henry Cohn, 2026, needs more optimization.
5 205 0.778174047446 Henry Cohn, 2026, needs more optimization.
5 206 0.778538826805 Henry Cohn, 2026, needs more optimization.
5 207 0.779326219380 Henry Cohn, 2026, needs more optimization.
5 208 0.779850145586 Henry Cohn, 2026, needs more optimization.
5 209 0.780432495488 Henry Cohn, 2026, needs more optimization.
5 210 0.780935154172 Henry Cohn, 2026, needs more optimization.
5 211 0.781570167143 Henry Cohn, 2026, needs more optimization.
5 212 0.782083103017 Henry Cohn, 2026, needs more optimization.
5 213 0.782722690189 Henry Cohn, 2026, needs more optimization.
5 214 0.783176238997 Henry Cohn, 2026, needs more optimization.
5 215 0.783725431983 Henry Cohn, 2026, needs more optimization.
5 216 0.784294485724 Henry Cohn, 2026, needs more optimization.
5 217 0.784890947958 Henry Cohn, 2026, needs more optimization.
5 218 0.785309143418 Henry Cohn, 2026, needs more optimization.
5 219 0.785774054261 Henry Cohn, 2026, needs more optimization.
5 220 0.786124971075 Henry Cohn, 2026, needs more optimization.
5 221 0.786547456316 Henry Cohn, 2026, needs more optimization.
5 222 0.787009382463 Henry Cohn, 2026, needs more optimization.
5 223 0.787504159397 Henry Cohn, 2026, needs more optimization.
5 224 0.788087915811 Henry Cohn, 2026, needs more optimization.
5 225 0.788465721339 Henry Cohn, 2026, needs more optimization.
5 226 0.789018541783 Henry Cohn, 2026, needs more optimization.
5 227 0.789377676691 Henry Cohn, 2026, needs more optimization.
5 228 0.789967524513 Henry Cohn, 2026, needs more optimization.
5 229 0.790515587864 Henry Cohn, 2026, needs more optimization.
5 230 0.790852111671 Henry Cohn, 2026, needs more optimization.
5 231 0.791392627705 Henry Cohn, 2026, needs more optimization.
5 232 0.791762932881 Henry Cohn, 2026, needs more optimization.
5 233 0.792229623895 Henry Cohn, 2026, needs more optimization.
5 234 0.792670887458 Henry Cohn, 2026, needs more optimization.
5 235 0.793353491575 Henry Cohn, 2026, needs more optimization.
5 236 0.793997898020 Henry Cohn, 2026, needs more optimization.
5 237 0.794422977064 Henry Cohn, 2026, needs more optimization.
5 238 0.795014640201 Henry Cohn, 2025.
5 239 0.795425406950 Henry Cohn, 2025.
5 240 0.795938099707 Henry Cohn, 2025.
5 241 0.796065311911 Henry Cohn, 2025.
5 242 0.796344808534 Henry Cohn, 2026, needs more optimization.
5 243 0.796601630926 Henry Cohn, 2026, needs more optimization.
5 244 0.796884386411 Henry Cohn, 2026, needs more optimization.
5 245 0.797264977293 Henry Cohn, 2026, needs more optimization.
5 246 0.797740685154 Henry Cohn, 2026, needs more optimization.
5 247 0.797959926296 Henry Cohn, 2026, needs more optimization.
5 248 0.798542538167 Henry Cohn, 2026, needs more optimization.
5 249 0.798774889917 Henry Cohn, 2026, needs more optimization.
5 250 0.798942701929 Henry Cohn, 2026, needs more optimization.
5 251 0.799347717803 Henry Cohn, 2026, needs more optimization.
5 252 0.799654642385 Henry Cohn, 2026, needs more optimization.
5 253 0.800146780510 Henry Cohn, 2026, needs more optimization.
5 254 0.800357927193 Henry Cohn, 2026, needs more optimization.
5 255 0.800620115103 Henry Cohn, 2026, needs more optimization.
5 256 0.801086621022 Henry Cohn, 2026, needs more optimization.
5 257 0.801501980170 Henry Cohn, 2026, needs more optimization.
5 258 0.801963530121 Henry Cohn, 2026, needs more optimization.
5 259 0.802392534699 Henry Cohn, 2026, needs more optimization.
5 260 0.802811281075 Henry Cohn, 2026, needs more optimization.
5 261 0.803199820448 Henry Cohn, 2026, needs more optimization.
5 262 0.803528360555 Henry Cohn, 2026, needs more optimization.
5 263 0.803880217610 Henry Cohn, 2026, needs more optimization.
5 264 0.804073828152 Henry Cohn, 2026, needs more optimization.
5 265 0.804460905001 Henry Cohn, 2026, needs more optimization.
5 266 0.804570276506 Henry Cohn, 2026, needs more optimization.
5 267 0.804868330317 Henry Cohn, 2026, needs more optimization.
5 268 0.805063639580 Henry Cohn, 2026, needs more optimization.
5 269 0.805322193555 Henry Cohn, 2026, needs more optimization.
5 270 0.805492056139 Henry Cohn, 2026, needs more optimization.
5 271 0.805732295362 Henry Cohn, 2026, needs more optimization.
5 272 0.805950739077 Henry Cohn, 2026, needs more optimization.
5 273 0.806012290215 Henry Cohn, 2026, needs more optimization.
5 274 0.806066322390 Henry Cohn, 2026, needs more optimization.
5 275 0.806245022408 Henry Cohn, 2026, needs more optimization.
5 276 0.806327554943 Henry Cohn, 2026, needs more optimization.
5 277 0.806496990318 Henry Cohn, 2026, needs more optimization.
5 278 0.806685014319 Henry Cohn, 2026, needs more optimization.
5 279 0.806773457806 Henry Cohn, 2026, needs more optimization.
5 280 0.807051762694 Henry Cohn, 2026, needs more optimization.
5 281 0.807116872906 Henry Cohn, 2026, needs more optimization.
5 282 0.807147257783 Henry Cohn, 2026, needs more optimization.
5 283 0.807741772749 Henry Cohn, 2026, needs more optimization.
5 284 0.808229708350 Henry Cohn, 2026, needs more optimization.
5 285 0.808651808766 Henry Cohn, 2026, needs more optimization.
5 286 0.809174640016 Henry Cohn, 2026, needs more optimization.
5 287 0.809590215178 Henry Cohn, 2026, needs more optimization.
5 288 0.810237082050 Henry Cohn, 2026, needs more optimization.
5 289 0.810466063488 Henry Cohn, 2026, needs more optimization.
5 290 0.811069537110 Henry Cohn, 2026, needs more optimization.
5 291 0.811567080793 Henry Cohn, 2026, needs more optimization.
5 292 0.812093911996 Henry Cohn, 2026, needs more optimization.
5 293 0.812702082856 Henry Cohn, 2026, needs more optimization.
5 294 0.813136856954 Henry Cohn, 2026, needs more optimization.
5 295 0.813530708418 Henry Cohn, 2026, needs more optimization.
5 296 0.813997556042 Henry Cohn, 2026, needs more optimization.
5 297 0.814424573729 Henry Cohn, 2026, needs more optimization.
5 298 0.815064385481 Henry Cohn, 2026, needs more optimization.
5 299 0.815433700290 Henry Cohn, 2026, needs more optimization.
5 300 0.815847945049 Henry Cohn, 2026, needs more optimization.
5 301 0.816404044325 Henry Cohn, 2026, needs more optimization.
5 302 0.817000628229 Henry Cohn, 2026, needs more optimization.
5 303 0.817467399235 Henry Cohn, 2026, needs more optimization.
5 304 0.817785714689 Henry Cohn, 2026, needs more optimization.
5 305 0.818194019506 Henry Cohn, 2026, needs more optimization.
5 306 0.818530939462 Henry Cohn, 2026, needs more optimization.
5 307 0.818934851712 Henry Cohn, 2026, needs more optimization.
5 308 0.819271321405 Henry Cohn, 2026, needs more optimization.
5 309 0.819565479957 Henry Cohn, 2026, needs more optimization.
5 310 0.819748110540 Henry Cohn, 2026, needs more optimization.
5 311 0.819765316449 Henry Cohn, 2026, needs more optimization.
5 312 0.819813710039 Henry Cohn, 2026, needs more optimization.
5 313 0.819873570321 Henry Cohn, 2026, needs more optimization.
5 314 0.819882211053 Henry Cohn, 2026, needs more optimization.
5 315 0.819896863509 Henry Cohn, 2026, needs more optimization.
5 316 0.819948818516 Henry Cohn, 2026, needs more optimization.
5 317 0.820204250461 Henry Cohn, 2026, needs more optimization.
5 318 0.820654852438 Henry Cohn, 2026, needs more optimization.
5 319 0.820661955221 Henry Cohn, 2026, needs more optimization.
5 320 0.820677046620 Henry Cohn, 2026, needs more optimization.
5 321 0.820938627112 Henry Cohn, 2026, needs more optimization.
5 322 0.821203295795 Henry Cohn, 2026, needs more optimization.
5 323 0.821646558865 Henry Cohn, 2026, needs more optimization.
5 324 0.822153055262 Henry Cohn, 2026, needs more optimization.
5 325 0.822382085802 Henry Cohn, 2026, needs more optimization.
5 326 0.822986247537 Henry Cohn, 2026, needs more optimization.
5 327 0.823129093709 Henry Cohn, 2026, needs more optimization.
5 328 0.823345347812 Henry Cohn, 2026, needs more optimization.
5 329 0.823604364966 Henry Cohn, 2026, needs more optimization.
5 330 0.823733029802 Henry Cohn, 2026, needs more optimization.
5 331 0.823956961350 Henry Cohn, 2026, needs more optimization.
5 332 0.824259692949 Henry Cohn, 2026, needs more optimization.
5 333 0.824462498614 Henry Cohn, 2026, needs more optimization.
5 334 0.824959302712 Henry Cohn, 2026, needs more optimization.
5 335 0.825216772441 Henry Cohn, 2026, needs more optimization.
5 336 0.825245541668 Henry Cohn, 2026, needs more optimization.
5 337 0.825621439673 Henry Cohn, 2026, needs more optimization.
5 338 0.826033000851 Henry Cohn, 2026, needs more optimization.
5 339 0.826186125719 Henry Cohn, 2026, needs more optimization.
5 340 0.826612099133 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 341 0.827020672419 Henry Cohn, 2026, needs more optimization.
5 342 0.827285586110 Henry Cohn, 2026, needs more optimization.
5 343 0.827468005343 Henry Cohn, 2026, needs more optimization.
5 344 0.827698286916 Henry Cohn, 2026, needs more optimization.
5 345 0.827998189114 Henry Cohn, 2026, needs more optimization.
5 346 0.828228758265 Henry Cohn, 2026, needs more optimization.
5 347 0.828522871637 Henry Cohn, 2026, needs more optimization.
5 348 0.828641460249 Henry Cohn, 2026, needs more optimization.
5 349 0.828829375108 Henry Cohn, 2026, needs more optimization.
5 350 0.829094197400 Henry Cohn, 2026, needs more optimization.
5 351 0.829588104704 Henry Cohn, 2026, needs more optimization.
5 352 0.830094624139 Henry Cohn, 2026, needs more optimization.
5 353 0.830243179811 Henry Cohn, 2026, needs more optimization.
5 354 0.830490623713 Henry Cohn, 2026, needs more optimization.
5 355 0.830838425397 Henry Cohn, 2026, needs more optimization.
5 356 0.831105524214 Henry Cohn, 2026, needs more optimization.
5 357 0.831422779809 Henry Cohn, 2026, needs more optimization.
5 358 0.831857412500 Henry Cohn, 2026, needs more optimization.
5 359 0.831980432967 Henry Cohn, 2026, needs more optimization.
5 360 0.832227083673 Henry Cohn, 2026, needs more optimization.
5 361 0.832554394585 Henry Cohn, 2026, needs more optimization.
5 362 0.832968324138 Henry Cohn, 2026, needs more optimization.
5 363 0.833310585883 Henry Cohn, 2026, needs more optimization.
5 364 0.833567660034 Henry Cohn, 2026, needs more optimization.
5 365 0.833833326546 Henry Cohn, 2026, needs more optimization.
5 366 0.833945786325 Henry Cohn, 2026, needs more optimization.
5 367 0.834333532495 Henry Cohn, 2026, needs more optimization.
5 368 0.834498641447 Henry Cohn, 2026, needs more optimization.
5 369 0.835029796106 Henry Cohn, 2026, needs more optimization.
5 370 0.835194566500 Henry Cohn, 2026, needs more optimization.
5 371 0.835265822758 Henry Cohn, 2026, needs more optimization.
5 372 0.835715199755 Henry Cohn, 2026, needs more optimization.
5 373 0.835839469037 Henry Cohn, 2026, needs more optimization.
5 374 0.836250821008 Henry Cohn, 2026, needs more optimization.
5 375 0.836438411222 Henry Cohn, 2026, needs more optimization.
5 376 0.836870378889 Henry Cohn, 2026, needs more optimization.
5 377 0.837241095833 Henry Cohn, 2026, needs more optimization.
5 378 0.837290772525 Henry Cohn, 2026, needs more optimization.
5 379 0.837503793563 Henry Cohn, 2026, needs more optimization.
5 380 0.837634838538 Henry Cohn, 2026, needs more optimization.
5 381 0.838342651937 Henry Cohn, 2026, needs more optimization.
5 382 0.838645238996 Henry Cohn, 2026, needs more optimization.
5 383 0.838819074272 Henry Cohn, 2026, needs more optimization.
5 384 0.839041535672 Henry Cohn, 2026, needs more optimization.
5 385 0.839334048467 Henry Cohn, 2026, needs more optimization.
5 386 0.839436622765 Henry Cohn, 2026, needs more optimization.
5 387 0.839745660723 Henry Cohn, 2026, needs more optimization.
5 388 0.839882872536 Henry Cohn, 2026, needs more optimization.
5 389 0.840101744876 Henry Cohn, 2026, needs more optimization.
5 390 0.840409883682 Henry Cohn, 2026, needs more optimization.
5 391 0.840653398916 Henry Cohn, 2026, needs more optimization.
5 392 0.840781839903 Henry Cohn, 2026, needs more optimization.
5 393 0.841199877309 Henry Cohn, 2026, needs more optimization.
5 394 0.841350742422 Henry Cohn, 2026, needs more optimization.
5 395 0.841405005255 Henry Cohn, 2026, needs more optimization.
5 396 0.841691388451 Henry Cohn, 2026, needs more optimization.
5 397 0.841775049045 Henry Cohn, 2026, needs more optimization.
5 398 0.841989761948 Henry Cohn, 2026, needs more optimization.
5 399 0.842166314677 Henry Cohn, 2026, needs more optimization.
5 400 0.842323813381 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 401 0.842721650182 Henry Cohn, 2026, needs more optimization.
5 402 0.842843985854 Henry Cohn, 2026, needs more optimization.
5 403 0.842955674639 Henry Cohn, 2026, needs more optimization.
5 404 0.843113970123 Henry Cohn, 2026, needs more optimization.
5 405 0.843307431720 Henry Cohn, 2026, needs more optimization.
5 406 0.843603205683 Henry Cohn, 2026, needs more optimization.
5 407 0.843759018076 Henry Cohn, 2026, needs more optimization.
5 408 0.843898313457 Henry Cohn, 2026, needs more optimization.
5 409 0.843944117687 Henry Cohn, 2026, needs more optimization.
5 410 0.844092013171 Henry Cohn, 2026, needs more optimization.
5 411 0.844384326319 Henry Cohn, 2026, needs more optimization.
5 412 0.844512773440 Henry Cohn, 2026, needs more optimization.
5 413 0.844804885963 Henry Cohn, 2026, needs more optimization.
5 414 0.844818390866 Henry Cohn, 2026, needs more optimization.
5 415 0.845182359228 Henry Cohn, 2026, needs more optimization.
5 416 0.845414857191 Henry Cohn, 2026, needs more optimization.
5 417 0.845502742662 Henry Cohn, 2026, needs more optimization.
5 418 0.845700492726 Henry Cohn, 2026, needs more optimization.
5 419 0.845785037012 Henry Cohn, 2026, needs more optimization.
5 420 0.845954019216 Henry Cohn, 2026, needs more optimization.
5 421 0.846095965144 Henry Cohn, 2026, needs more optimization.
5 422 0.846394176275 Henry Cohn, 2026, needs more optimization.
5 423 0.846451463553 Henry Cohn, 2026, needs more optimization.
5 424 0.846737416042 Henry Cohn, 2026, needs more optimization.
5 425 0.846953828024 Henry Cohn, 2026, needs more optimization.
5 426 0.847133702805 Henry Cohn, 2026, needs more optimization.
5 427 0.847324575820 Henry Cohn, 2026, needs more optimization.
5 428 0.847527900538 Henry Cohn, 2026, needs more optimization.
5 429 0.847673005702 Henry Cohn, 2026, needs more optimization.
5 430 0.847921905944 Henry Cohn, 2026, needs more optimization.
5 431 0.848159382486 Henry Cohn, 2026, needs more optimization.
5 432 0.848172505170 Henry Cohn, 2026, needs more optimization.
5 433 0.848465703664 Henry Cohn, 2026, needs more optimization.
5 434 0.848685346154 Henry Cohn, 2026, needs more optimization.
5 435 0.848869517996 Henry Cohn, 2026, needs more optimization.
5 436 0.848969937914 Henry Cohn, 2026, needs more optimization.
5 437 0.849134024172 Henry Cohn, 2026, needs more optimization.
5 438 0.849416287869 Henry Cohn, 2026, needs more optimization.
5 439 0.849619803394 Henry Cohn, 2026, needs more optimization.
5 440 0.849658377768 Henry Cohn, 2026, needs more optimization.
5 441 0.849850955353 Henry Cohn, 2026, needs more optimization.
5 442 0.849965017491 Henry Cohn, 2026, needs more optimization.
5 443 0.850121451511 Henry Cohn, 2026, needs more optimization.
5 444 0.850398707640 Henry Cohn, 2026, needs more optimization.
5 445 0.850633592900 Henry Cohn, 2026, needs more optimization.
5 446 0.850843076587 Henry Cohn, 2026, needs more optimization.
5 447 0.850997319525 Henry Cohn, 2026, needs more optimization.
5 448 0.851072892540 Henry Cohn, 2026, needs more optimization.
5 449 0.851136594878 Henry Cohn, 2026, needs more optimization.
5 450 0.851508210244 Henry Cohn, 2026, needs more optimization.
5 451 0.851708515687 Henry Cohn, 2026, needs more optimization.
5 452 0.851797628155 Henry Cohn, 2026, needs more optimization.
5 453 0.851809135356 Henry Cohn, 2026, needs more optimization.
5 454 0.852030004551 Henry Cohn, 2026, needs more optimization.
5 455 0.852309415242 Henry Cohn, 2026, needs more optimization.
5 456 0.852370436069 Henry Cohn, 2026, needs more optimization.
5 457 0.852574363575 Henry Cohn, 2026, needs more optimization.
5 458 0.852737519380 Henry Cohn, 2026, needs more optimization.
5 459 0.852813820235 Henry Cohn, 2026, needs more optimization.
5 460 0.853035239655 Henry Cohn, 2026, needs more optimization.
5 461 0.853250800827 Henry Cohn, 2026, needs more optimization.
5 462 0.853452247297 Henry Cohn, 2026, needs more optimization.
5 463 0.853536329123 Henry Cohn, 2026, needs more optimization.
5 464 0.853626004225 Henry Cohn, 2026, needs more optimization.
5 465 0.853853846230 Henry Cohn, 2026, needs more optimization.
5 466 0.854012762433 Henry Cohn, 2026, needs more optimization.
5 467 0.854070932073 Henry Cohn, 2026, needs more optimization.
5 468 0.854359590981 Henry Cohn, 2026, needs more optimization.
5 469 0.854473913815 Henry Cohn, 2026, needs more optimization.
5 470 0.854639232912 Henry Cohn, 2026, needs more optimization.
5 471 0.854694670864 Henry Cohn, 2026, needs more optimization.
5 472 0.854786207555 Henry Cohn, 2026, needs more optimization.
5 473 0.854970814638 Henry Cohn, 2026, needs more optimization.
5 474 0.855266799970 Henry Cohn, 2026, needs more optimization.
5 475 0.855291746173 Henry Cohn, 2026, needs more optimization.
5 476 0.855431104944 Henry Cohn, 2026, needs more optimization.
5 477 0.855636044252 Henry Cohn, 2026, needs more optimization.
5 478 0.855799085152 Henry Cohn, 2026, needs more optimization.
5 479 0.855908330312 Henry Cohn, 2026, needs more optimization.
5 480 0.856091361478 Henry Cohn, 2026, needs more optimization.
5 481 0.856261643777 Henry Cohn, 2026, needs more optimization.
5 482 0.856446289047 Henry Cohn, 2026, needs more optimization.
5 483 0.856663277713 Henry Cohn, 2026, needs more optimization.
5 484 0.856699846839 Henry Cohn, 2026, needs more optimization.
5 485 0.856722158023 Henry Cohn, 2026, needs more optimization.
5 486 0.856883833912 Henry Cohn, 2026, needs more optimization.
5 487 0.857088136661 Henry Cohn, 2026, needs more optimization.
5 488 0.857248448220 Henry Cohn, 2026, needs more optimization.
5 489 0.857360976818 Henry Cohn, 2026, needs more optimization.
5 490 0.857427559011 Henry Cohn, 2026, needs more optimization.
5 491 0.857603266625 Henry Cohn, 2026, needs more optimization.
5 492 0.857832941341 Henry Cohn, 2026, needs more optimization.
5 493 0.857880114548 Henry Cohn, 2026, needs more optimization.
5 494 0.857958770928 Henry Cohn, 2026, needs more optimization.
5 495 0.858156941815 Henry Cohn, 2026, needs more optimization.
5 496 0.858495831186 Henry Cohn, 2026, needs more optimization.
5 497 0.858636315714 Henry Cohn, 2026, needs more optimization.
5 498 0.858740147710 Henry Cohn, 2026, needs more optimization.
5 499 0.858852017683 Henry Cohn, 2026, needs more optimization.
5 500 0.859113792366 Henry Cohn, 2026, needs more optimization.
5 501 0.859270658587 Henry Cohn, 2026, needs more optimization.
5 502 0.859506675569 Henry Cohn, 2026, needs more optimization.
5 503 0.859513109838 Henry Cohn, 2026, needs more optimization.
5 504 0.859622067767 Henry Cohn, 2026, needs more optimization.
5 505 0.859743295253 Henry Cohn, 2026, needs more optimization.
5 506 0.859866426789 Henry Cohn, 2026, needs more optimization.
5 507 0.860047380502 Henry Cohn, 2026, needs more optimization.
5 508 0.860120641541 Henry Cohn, 2026, needs more optimization.
5 509 0.860259706698 Henry Cohn, 2026, needs more optimization.
5 510 0.860468121401 Henry Cohn, 2026, needs more optimization.
5 511 0.860636956296 Henry Cohn, 2026, needs more optimization.
5 512 0.860673886892 Henry Cohn, 2026, needs more optimization.
5 513 0.860737065673 Henry Cohn, 2026, needs more optimization.
5 514 0.860855589807 Henry Cohn, 2026, needs more optimization.
5 515 0.860999057133 Henry Cohn, 2026, needs more optimization.
5 516 0.861222460872 Henry Cohn, 2026, needs more optimization.
5 517 0.861327460479 Henry Cohn, 2026, needs more optimization.
5 518 0.861466572643 Henry Cohn, 2026, needs more optimization.
5 519 0.861608771353 Henry Cohn, 2026, needs more optimization.
5 520 0.861723548746 Henry Cohn, 2026, needs more optimization.
5 521 0.861738716105 Henry Cohn, 2026, needs more optimization.
5 522 0.861956001249 Henry Cohn, 2026, needs more optimization.
5 523 0.862167868780 Henry Cohn, 2026, needs more optimization.
5 524 0.862240511012 Henry Cohn, 2026, needs more optimization.
5 525 0.862461051856 Henry Cohn, 2026, needs more optimization.
5 526 0.862648821814 Henry Cohn, 2026, needs more optimization.
5 527 0.862658333486 Henry Cohn, 2026, needs more optimization.
5 528 0.862757704068 Henry Cohn, 2026, needs more optimization.
5 529 0.862969097844 Henry Cohn, 2026, needs more optimization.
5 530 0.863033047305 Henry Cohn, 2026, needs more optimization.
5 531 0.863195187887 Henry Cohn, 2026, needs more optimization.
5 532 0.863294709382 Henry Cohn, 2026, needs more optimization.
5 533 0.863511391071 Henry Cohn, 2026, needs more optimization.
5 534 0.863651384996 Henry Cohn, 2026, needs more optimization.
5 535 0.863750784320 Henry Cohn, 2026, needs more optimization.
5 536 0.863914564022 Henry Cohn, 2026, needs more optimization.
5 537 0.863992967024 Henry Cohn, 2026, needs more optimization.
5 538 0.864134034137 Henry Cohn, 2026, needs more optimization.
5 539 0.864268157062 Henry Cohn, 2026, needs more optimization.
5 540 0.864339906405 Henry Cohn, 2026, needs more optimization.
5 541 0.864607029568 Henry Cohn, 2026, needs more optimization.
5 542 0.864719040204 Henry Cohn, 2026, needs more optimization.
5 543 0.864791202577 Henry Cohn, 2026, needs more optimization.
5 544 0.864935120574 Henry Cohn, 2026, needs more optimization.
5 545 0.865014308603 Henry Cohn, 2026, needs more optimization.
5 546 0.865110927487 Henry Cohn, 2026, needs more optimization.
5 547 0.865276087558 Henry Cohn, 2026, needs more optimization.
5 548 0.865413154275 Henry Cohn, 2026, needs more optimization.
5 549 0.865492385935 Henry Cohn, 2026, needs more optimization.
5 550 0.865542373006 Henry Cohn, 2026, needs more optimization.
5 551 0.865756432444 Henry Cohn, 2026, needs more optimization.
5 552 0.865803881137 Henry Cohn, 2026, needs more optimization.
5 553 0.865974319346 Henry Cohn, 2026, needs more optimization.
5 554 0.866165810142 Henry Cohn, 2026, needs more optimization.
5 555 0.866199293079 Henry Cohn, 2026, needs more optimization.
5 556 0.866233484159 Henry Cohn, 2026, needs more optimization.
5 557 0.866439788630 Henry Cohn, 2026, needs more optimization.
5 558 0.866540264809 Henry Cohn, 2026, needs more optimization.
5 559 0.866794107397 Henry Cohn, 2026, needs more optimization.
5 560 0.867009559009 Henry Cohn, 2026, needs more optimization.
5 561 0.867015298355 Henry Cohn, 2026, needs more optimization.
5 562 0.867287334462 Henry Cohn, 2026, needs more optimization.
5 563 0.867387516743 Henry Cohn, 2026, needs more optimization.
5 564 0.867441564403 Henry Cohn, 2026, needs more optimization.
5 565 0.867443080337 Henry Cohn, 2026, needs more optimization.
5 566 0.867567423383 Henry Cohn, 2026, needs more optimization.
5 567 0.867771199891 Henry Cohn, 2026, needs more optimization.
5 568 0.867869608757 Henry Cohn, 2026, needs more optimization.
5 569 0.867958382846 Henry Cohn, 2026, needs more optimization.
5 570 0.868116110895 Henry Cohn, 2026, needs more optimization.
5 571 0.868294301180 Henry Cohn, 2026, needs more optimization.
5 572 0.868370381611 Henry Cohn, 2026, needs more optimization.
5 573 0.868451056584 Henry Cohn, 2026, needs more optimization.
5 574 0.868666791316 Henry Cohn, 2026, needs more optimization.
5 575 0.868669185272 Henry Cohn, 2026, needs more optimization.
5 576 0.868800872127 Henry Cohn, 2026, needs more optimization.
5 577 0.868901734456 Henry Cohn, 2026, needs more optimization.
5 578 0.868964149469 Henry Cohn, 2026, needs more optimization.
5 579 0.869108272585 Henry Cohn, 2026, needs more optimization.
5 580 0.869303939159 Henry Cohn, 2026, needs more optimization.
5 581 0.869444873481 Henry Cohn, 2026, needs more optimization.
5 582 0.869504322759 Henry Cohn, 2026, needs more optimization.
5 583 0.869619311507 Henry Cohn, 2026, needs more optimization.
5 584 0.869694163816 Henry Cohn, 2026, needs more optimization.
5 585 0.869882930852 Henry Cohn, 2026, needs more optimization.
5 586 0.870012441905 Henry Cohn, 2026, needs more optimization.
5 587 0.870087390645 Henry Cohn, 2026, needs more optimization.
5 588 0.870089237104 Henry Cohn, 2026, needs more optimization.
5 589 0.870174572273 Henry Cohn, 2026, needs more optimization.
5 590 0.870344360141 Henry Cohn, 2026, needs more optimization.
5 591 0.870372210675 Henry Cohn, 2026, needs more optimization.
5 592 0.870421093852 Henry Cohn, 2026, needs more optimization.
5 593 0.870576290268 Henry Cohn, 2026, needs more optimization.
5 594 0.870725741425 Henry Cohn, 2026, needs more optimization.
5 595 0.870811006656 Henry Cohn, 2026, needs more optimization.
5 596 0.870901167359 Henry Cohn, 2026, needs more optimization.
5 597 0.871007990849 Henry Cohn, 2026, needs more optimization.
5 598 0.871204563121 Henry Cohn, 2026, needs more optimization.
5 600 0.871259398472 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5 601 0.871564015322 Henry Cohn, 2026, needs more optimization.
5 602 0.871570952256 Henry Cohn, 2026, needs more optimization.
5 603 0.871657740933 Henry Cohn, 2026, needs more optimization.
5 604 0.871749566934 Henry Cohn, 2026, needs more optimization.
5 605 0.871760304019 Henry Cohn, 2026, needs more optimization.
5 606 0.871839378886 Henry Cohn, 2026, needs more optimization.
5 607 0.871971878644 Henry Cohn, 2026, needs more optimization.
5 608 0.872051497414 Henry Cohn, 2026, needs more optimization.
5 609 0.872237072303 Henry Cohn, 2026, needs more optimization.
5 610 0.872324987498 Henry Cohn, 2026, needs more optimization.
5 611 0.872401388126 Henry Cohn, 2026, needs more optimization.
5 612 0.872538756674 Henry Cohn, 2026, needs more optimization.
5 613 0.872628910734 Henry Cohn, 2026, needs more optimization.
5 614 0.872796229134 Henry Cohn, 2026, needs more optimization.
5 615 0.872874450733 Henry Cohn, 2026, needs more optimization.
5 616 0.873038823664 Henry Cohn, 2026, needs more optimization.
5 617 0.873150762149 Henry Cohn, 2026, needs more optimization.
5 618 0.873298620656 Henry Cohn, 2026, needs more optimization.
5 619 0.873410371837 Henry Cohn, 2026, needs more optimization.
5 620 0.873492093314 Henry Cohn, 2026, needs more optimization.
5 621 0.873597877607 Henry Cohn, 2026, needs more optimization.
5 622 0.873688364178 Henry Cohn, 2026, needs more optimization.
5 623 0.873776310108 Henry Cohn, 2026, needs more optimization.
5 624 0.873922917740 Henry Cohn, 2026, needs more optimization.
5 625 0.874065819161 Henry Cohn, 2026, needs more optimization.
5 626 0.874128817035 Henry Cohn, 2026, needs more optimization.
5 627 0.874158249692 Henry Cohn, 2026, needs more optimization.
5 628 0.874259146555 Henry Cohn, 2026, needs more optimization.
5 629 0.874405130543 Henry Cohn, 2026, needs more optimization.
5 630 0.874562936645 Henry Cohn, 2026, needs more optimization.
5 631 0.874614017711 Henry Cohn, 2026, needs more optimization.
5 632 0.874756358765 Henry Cohn, 2026, needs more optimization.
5 633 0.874890832229 Henry Cohn, 2026, needs more optimization.
5 634 0.874980276351 Henry Cohn, 2026, needs more optimization.
5 635 0.875107531071 Henry Cohn, 2026, needs more optimization.
5 636 0.875214858231 Henry Cohn, 2026, needs more optimization.
5 637 0.875295414514 Henry Cohn, 2026, needs more optimization.
5 638 0.875321481654 Henry Cohn, 2026, needs more optimization.
5 639 0.875385736491 Henry Cohn, 2026, needs more optimization.
5 640 0.875568864324 Henry Cohn, 2026, needs more optimization.
5 641 0.875583936234 Henry Cohn, 2026, needs more optimization.
5 642 0.875648194236 Henry Cohn, 2026, needs more optimization.
5 643 0.875768584431 Henry Cohn, 2026, needs more optimization.
5 644 0.875772538255 Henry Cohn, 2026, needs more optimization.
5 645 0.876024665253 Henry Cohn, 2026, needs more optimization.
5 646 0.876098426814 Henry Cohn, 2026, needs more optimization.
5 647 0.876268685546 Henry Cohn, 2026, needs more optimization.
5 648 0.876310735352 Henry Cohn, 2026, needs more optimization.
5 649 0.876432021890 Henry Cohn, 2026, needs more optimization.
5 650 0.876493124963 Henry Cohn, 2026, needs more optimization.
5 651 0.876592562186 Henry Cohn, 2026, needs more optimization.
5 652 0.876638892868 Henry Cohn, 2026, needs more optimization.
5 653 0.876675935625 Henry Cohn, 2026, needs more optimization.
5 654 0.876775581419 Henry Cohn, 2026, needs more optimization.
5 655 0.876906999525 Henry Cohn, 2026, needs more optimization.
5 656 0.876991539620 Henry Cohn, 2026, needs more optimization.
5 657 0.877133985243 Henry Cohn, 2026, needs more optimization.
5 658 0.877257146443 Henry Cohn, 2026, needs more optimization.
5 659 0.877332143675 Henry Cohn, 2026, needs more optimization.
5 660 0.877435126829 Henry Cohn, 2026, needs more optimization.
5 661 0.877449073823 Henry Cohn, 2026, needs more optimization.
5 662 0.877545058549 Henry Cohn, 2026, needs more optimization.
5 663 0.877640466725 Henry Cohn, 2026, needs more optimization.
5 664 0.877775659839 Henry Cohn, 2026, needs more optimization.
5 665 0.877781201301 Henry Cohn, 2026, needs more optimization.
5 666 0.877864123125 Henry Cohn, 2026, needs more optimization.
5 667 0.877924354152 Henry Cohn, 2026, needs more optimization.
5 668 0.877994271216 Henry Cohn, 2026, needs more optimization.
5 669 0.878174452533 Henry Cohn, 2026, needs more optimization.
5 670 0.878186914222 Henry Cohn, 2026, needs more optimization.
5 671 0.878368547861 Henry Cohn, 2026, needs more optimization.
5 672 0.878443101828 Henry Cohn, 2026, needs more optimization.
5 673 0.878534099642 Henry Cohn, 2026, needs more optimization.
5 674 0.878647973053 Henry Cohn, 2026, needs more optimization.
5 675 0.878671865592 Henry Cohn, 2026, needs more optimization.
5 676 0.878772190863 Henry Cohn, 2026, needs more optimization.
5 677 0.878901191881 Henry Cohn, 2026, needs more optimization.
5 678 0.879037609126 Henry Cohn, 2026, needs more optimization.
5 679 0.879081140773 Henry Cohn, 2026, needs more optimization.
5 680 0.879121363288 Henry Cohn, 2026, needs more optimization.
5 681 0.879261113099 Henry Cohn, 2026, needs more optimization.
5 682 0.879349348269 Henry Cohn, 2026, needs more optimization.
5 683 0.879413658928 Henry Cohn, 2026, needs more optimization.
5 684 0.879531314024 Henry Cohn, 2026, needs more optimization.
5 685 0.879567542027 Henry Cohn, 2026, needs more optimization.
5 686 0.879607043385 Henry Cohn, 2026, needs more optimization.
5 687 0.879826163571 Henry Cohn, 2026, needs more optimization.
5 688 0.879923455125 Henry Cohn, 2026, needs more optimization.
5 689 0.880002007566 Henry Cohn, 2026, needs more optimization.
5 690 0.880053142103 Henry Cohn, 2026, needs more optimization.
5 691 0.880163616416 Henry Cohn, 2026, needs more optimization.
5 692 0.880261588144 Henry Cohn, 2026, needs more optimization.
5 693 0.880323346834 Henry Cohn, 2026, needs more optimization.
5 694 0.880416713946 Henry Cohn, 2026, needs more optimization.
5 695 0.880471524630 Henry Cohn, 2026, needs more optimization.
5 696 0.880547758507 Henry Cohn, 2026, needs more optimization.
5 697 0.880621630536 Henry Cohn, 2026, needs more optimization.
5 698 0.880700251476 Henry Cohn, 2026, needs more optimization.
5 699 0.880810240809 Henry Cohn, 2026, needs more optimization.
5 700 0.880833578702 Henry Cohn, 2026, needs more optimization.
5 701 0.880992769024 Henry Cohn, 2026, needs more optimization.
5 702 0.881068237432 Henry Cohn, 2026, needs more optimization.
5 703 0.881074945298 Henry Cohn, 2026, needs more optimization.
5 704 0.881198499985 Henry Cohn, 2026, needs more optimization.
5 705 0.881228831974 Henry Cohn, 2026, needs more optimization.
5 706 0.881337068637 Henry Cohn, 2026, needs more optimization.
5 707 0.881445238390 Henry Cohn, 2026, needs more optimization.
5 708 0.881597892341 Henry Cohn, 2026, needs more optimization.
5 709 0.881726591333 Henry Cohn, 2026, needs more optimization.
5 710 0.881730054287 Henry Cohn, 2026, needs more optimization.
5 711 0.881787594442 Henry Cohn, 2026, needs more optimization.
5 712 0.881857747971 Henry Cohn, 2026, needs more optimization.
5 713 0.881947445322 Henry Cohn, 2026, needs more optimization.
5 714 0.882026618898 Henry Cohn, 2026, needs more optimization.
5 715 0.882125182368 Henry Cohn, 2026, needs more optimization.
5 716 0.882203768563 Henry Cohn, 2026, needs more optimization.
5 717 0.882308606465 Henry Cohn, 2026, needs more optimization.
5 718 0.882423200591 Henry Cohn, 2026, needs more optimization.
5 719 0.882439070315 Henry Cohn, 2026, needs more optimization.
5 720 0.882559623196 Henry Cohn, 2026, needs more optimization.
5 721 0.882614598626 Henry Cohn, 2026, needs more optimization.
5 722 0.882717119377 Henry Cohn, 2026, needs more optimization.
5 723 0.882809088468 Henry Cohn, 2026, needs more optimization.
5 724 0.882891834657 Henry Cohn, 2026, needs more optimization.
5 725 0.882970832072 Henry Cohn, 2026, needs more optimization.
5 726 0.883099891913 Henry Cohn, 2026, needs more optimization.
5 727 0.883129683230 Henry Cohn, 2026, needs more optimization.
5 728 0.883248056349 Henry Cohn, 2026, needs more optimization.
5 729 0.883298458774 Henry Cohn, 2026, needs more optimization.
5 730 0.883341785088 Henry Cohn, 2026, needs more optimization.
5 731 0.883429383882 Henry Cohn, 2026, needs more optimization.
5 732 0.883518226266 Henry Cohn, 2026, needs more optimization.
5 733 0.883592767819 Henry Cohn, 2026, needs more optimization.
5 734 0.883680718527 Henry Cohn, 2026, needs more optimization.
5 735 0.883725334486 Henry Cohn, 2026, needs more optimization.
5 736 0.883801917895 Henry Cohn, 2026, needs more optimization.
5 737 0.883864196251 Henry Cohn, 2026, needs more optimization.
5 738 0.883968646140 Henry Cohn, 2026, needs more optimization.
5 739 0.884044157702 Henry Cohn, 2026, needs more optimization.
5 740 0.884126997442 Henry Cohn, 2026, needs more optimization.
5 741 0.884310752205 Henry Cohn, 2026, needs more optimization.
5 742 0.884395831306 Henry Cohn, 2026, needs more optimization.
5 743 0.884509308399 Henry Cohn, 2026, needs more optimization.
5 744 0.884613154581 Henry Cohn, 2026, needs more optimization.
5 745 0.884660850828 Henry Cohn, 2026, needs more optimization.
5 746 0.884751071422 Henry Cohn, 2026, needs more optimization.
5 747 0.884824192906 Henry Cohn, 2026, needs more optimization.
5 748 0.884911852468 Henry Cohn, 2026, needs more optimization.
5 749 0.884967052549 Henry Cohn, 2026, needs more optimization.
5 750 0.885020637899 Henry Cohn, 2026, needs more optimization.
5 751 0.885121974514 Henry Cohn, 2026, needs more optimization.
5 752 0.885182841179 Henry Cohn, 2026, needs more optimization.
5 753 0.885219978660 Henry Cohn, 2026, needs more optimization.
5 754 0.885313687281 Henry Cohn, 2026, needs more optimization.
5 755 0.885361454575 Henry Cohn, 2026, needs more optimization.
5 756 0.885405920690 Henry Cohn, 2026, needs more optimization.
5 757 0.885482311501 Henry Cohn, 2026, needs more optimization.
5 758 0.885579571776 Henry Cohn, 2026, needs more optimization.
5 759 0.885619066819 Henry Cohn, 2026, needs more optimization.
5 760 0.885674196384 Henry Cohn, 2026, needs more optimization.
5 761 0.885792286080 Henry Cohn, 2026, needs more optimization.
5 762 0.885852276259 Henry Cohn, 2026, needs more optimization.
5 763 0.885935010585 Henry Cohn, 2026, needs more optimization.
5 764 0.886054884111 Henry Cohn, 2026, needs more optimization.
5 765 0.886147678316 Henry Cohn, 2026, needs more optimization.
5 766 0.886224622139 Henry Cohn, 2026, needs more optimization.
5 767 0.886257305017 Henry Cohn, 2026, needs more optimization.
5 768 0.886276876345 Henry Cohn, 2026, needs more optimization.
5 769 0.886326447651 Henry Cohn, 2026, needs more optimization.
5 770 0.886396277346 Henry Cohn, 2026, needs more optimization.
5 771 0.886478144545 Henry Cohn, 2026, needs more optimization.
5 772 0.886552860977 Henry Cohn, 2026, needs more optimization.
5 773 0.886629344480 Henry Cohn, 2026, needs more optimization.
5 774 0.886728885820 Henry Cohn, 2026, needs more optimization.
5 775 0.886817030311 Henry Cohn, 2026, needs more optimization.
5 776 0.886926404330 Henry Cohn, 2026, needs more optimization.
5 777 0.886938120078 Henry Cohn, 2026, needs more optimization.
5 778 0.887039200274 Henry Cohn, 2026, needs more optimization.
5 779 0.887106607191 Henry Cohn, 2026, needs more optimization.
5 780 0.887255923798 Henry Cohn, 2026, needs more optimization.
5 781 0.887271802004 Henry Cohn, 2026, needs more optimization.
5 782 0.887277849076 Henry Cohn, 2026, needs more optimization.
5 783 0.887327397561 Henry Cohn, 2026, needs more optimization.
5 784 0.887399638692 Henry Cohn, 2026, needs more optimization.
5 785 0.887468628560 Henry Cohn, 2026, needs more optimization.
5 786 0.887523755388 Henry Cohn, 2026, needs more optimization.
5 787 0.887642139685 Henry Cohn, 2026, needs more optimization.
5 788 0.887720673802 Henry Cohn, 2026, needs more optimization.
5 789 0.887793312073 Henry Cohn, 2026, needs more optimization.
5 790 0.887892094433 Henry Cohn, 2026, needs more optimization.
5 791 0.887897948695 Henry Cohn, 2026, needs more optimization.
5 792 0.887989360711 Henry Cohn, 2026, needs more optimization.
5 793 0.888048179819 Henry Cohn, 2026, needs more optimization.
5 794 0.888128529802 Henry Cohn, 2026, needs more optimization.
5 795 0.888172587627 Henry Cohn, 2026, needs more optimization.
5 796 0.888229638610 Henry Cohn, 2026, needs more optimization.
5 797 0.888306668193 Henry Cohn, 2026, needs more optimization.
5 798 0.888387744022 Henry Cohn, 2026, needs more optimization.
5 799 0.888471300909 Henry Cohn, 2026, needs more optimization.
5 800 0.888518568776 Henry Cohn, 2026, needs more optimization.
5 801 0.888549251879 Henry Cohn, 2026, needs more optimization.
5 802 0.888647892669 Henry Cohn, 2026, needs more optimization.
5 803 0.888778576586 Henry Cohn, 2026, needs more optimization.
5 804 0.888897556897 Henry Cohn, 2026, needs more optimization.
5 805 0.888913689089 Henry Cohn, 2026, needs more optimization.
5 806 0.888950423008 Henry Cohn, 2026, needs more optimization.
5 807 0.889002750030 Henry Cohn, 2026, needs more optimization.
5 808 0.889097917401 Henry Cohn, 2026, needs more optimization.
5 809 0.889220359267 Henry Cohn, 2026, needs more optimization.
5 810 0.889234419889 Henry Cohn, 2026, needs more optimization.
5 811 0.889369824816 Henry Cohn, 2026, needs more optimization.
5 812 0.889455683318 Henry Cohn, 2026, needs more optimization.
5 813 0.889527693045 Henry Cohn, 2026, needs more optimization.
5 814 0.889656915853 Henry Cohn, 2026, needs more optimization.
5 815 0.889691461566 Henry Cohn, 2026, needs more optimization.
5 816 0.889694325426 Henry Cohn, 2026, needs more optimization.
5 817 0.889711616962 Henry Cohn, 2026, needs more optimization.
5 818 0.889819090954 Henry Cohn, 2026, needs more optimization.
5 819 0.889855729273 Henry Cohn, 2026, needs more optimization.
5 820 0.889878877469 Henry Cohn, 2026, needs more optimization.
5 821 0.889981781290 Henry Cohn, 2026, needs more optimization.
5 822 0.890017549561 Henry Cohn, 2026, needs more optimization.
5 823 0.890104096656 Henry Cohn, 2026, needs more optimization.
5 824 0.890248015288 Henry Cohn, 2026, needs more optimization.
5 825 0.890339989793 Henry Cohn, 2026, needs more optimization.
5 826 0.890340059783 Henry Cohn, 2026, needs more optimization.
5 827 0.890419308531 Henry Cohn, 2026, needs more optimization.
5 828 0.890537732990 Henry Cohn, 2026, needs more optimization.
5 829 0.890543854299 Henry Cohn, 2026, needs more optimization.
5 830 0.890626125633 Henry Cohn, 2026, needs more optimization.
5 831 0.890713046271 Henry Cohn, 2026, needs more optimization.
5 832 0.890713048660 Henry Cohn, 2026, needs more optimization.
5 833 0.890723598948 Henry Cohn, 2026, needs more optimization.
5 834 0.890779852377 Henry Cohn, 2026, needs more optimization.
5 835 0.890866964485 Henry Cohn, 2026, needs more optimization.
5 836 0.891001833253 Henry Cohn, 2026, needs more optimization.
5 837 0.891081536921 Henry Cohn, 2026, needs more optimization.
5 838 0.891157138605 Henry Cohn, 2026, needs more optimization.
5 839 0.891220549691 Henry Cohn, 2026, needs more optimization.
5 840 0.891290129781 Henry Cohn, 2026, needs more optimization.
5 841 0.891365370433 Henry Cohn, 2026, needs more optimization.
5 842 0.891413151855 Henry Cohn, 2026, needs more optimization.
5 843 0.891497073691 Henry Cohn, 2026, needs more optimization.
5 844 0.891523497587 Henry Cohn, 2026, needs more optimization.
5 845 0.891546044543 Henry Cohn, 2026, needs more optimization.
5 846 0.891653661189 Henry Cohn, 2026, needs more optimization.
5 847 0.891720810747 Henry Cohn, 2026, needs more optimization.
5 848 0.891803162804 Henry Cohn, 2026, needs more optimization.
5 849 0.891858926786 Henry Cohn, 2026, needs more optimization.
5 850 0.891897651104 Henry Cohn, 2026, needs more optimization.
5 851 0.891944238751 Henry Cohn, 2026, needs more optimization.
5 852 0.892047096173 Henry Cohn, 2026, needs more optimization.
5 853 0.892101734839 Henry Cohn, 2026, needs more optimization.
5 854 0.892148800710 Henry Cohn, 2026, needs more optimization.
5 855 0.892172117498 Henry Cohn, 2026, needs more optimization.
5 856 0.892353781871 Henry Cohn, 2026, needs more optimization.
5 857 0.892354615720 Henry Cohn, 2026, needs more optimization.
5 858 0.892395435493 Henry Cohn, 2026, needs more optimization.
5 859 0.892503639736 Henry Cohn, 2026, needs more optimization.
5 860 0.892574658013 Henry Cohn, 2026, needs more optimization.
5 861 0.892591242195 Henry Cohn, 2026, needs more optimization.
5 862 0.892625219532 Henry Cohn, 2026, needs more optimization.
5 863 0.892692712129 Henry Cohn, 2026, needs more optimization.
5 864 0.892754849096 Henry Cohn, 2026, needs more optimization.
5 865 0.892870371877 Henry Cohn, 2026, needs more optimization.
5 866 0.892879683130 Henry Cohn, 2026, needs more optimization.
5 867 0.892993817223 Henry Cohn, 2026, needs more optimization.
5 868 0.893077768210 Henry Cohn, 2026, needs more optimization.
5 869 0.893080274414 Henry Cohn, 2026, needs more optimization.
5 870 0.893169776807 Henry Cohn, 2026, needs more optimization.
5 871 0.893248990839 Henry Cohn, 2026, needs more optimization.
5 872 0.893300085965 Henry Cohn, 2026, needs more optimization.
5 873 0.893318831652 Henry Cohn, 2026, needs more optimization.
5 874 0.893377700593 Henry Cohn, 2026, needs more optimization.
5 875 0.893472048072 Henry Cohn, 2026, needs more optimization.
5 876 0.893522011094 Henry Cohn, 2026, needs more optimization.
5 877 0.893612488655 Henry Cohn, 2026, needs more optimization.
5 878 0.893661530473 Henry Cohn, 2026, needs more optimization.
5 879 0.893723100851 Henry Cohn, 2026, needs more optimization.
5 880 0.893796570283 Henry Cohn, 2026, needs more optimization.
5 881 0.893799299194 Henry Cohn, 2026, needs more optimization.
5 882 0.893815338597 Henry Cohn, 2026, needs more optimization.
5 883 0.893944805798 Henry Cohn, 2026, needs more optimization.
5 884 0.894001559460 Henry Cohn, 2026, needs more optimization.
5 885 0.894070236790 Henry Cohn, 2026, needs more optimization.
5 886 0.894123945764 Henry Cohn, 2026, needs more optimization.
5 887 0.894210670120 Henry Cohn, 2026, needs more optimization.
5 888 0.894287656729 Henry Cohn, 2026, needs more optimization.
5 889 0.894298040274 Henry Cohn, 2026, needs more optimization.
5 890 0.894353367184 Henry Cohn, 2026, needs more optimization.
5 891 0.894388341453 Henry Cohn, 2026, needs more optimization.
5 892 0.894525283581 Henry Cohn, 2026, needs more optimization.
5 893 0.894577358596 Henry Cohn, 2026, needs more optimization.
5 894 0.894638659678 Henry Cohn, 2026, needs more optimization.
5 895 0.894640812238 Henry Cohn, 2026, needs more optimization.
5 896 0.894725756715 Henry Cohn, 2026, needs more optimization.
5 897 0.894729240354 Henry Cohn, 2026, needs more optimization.
5 898 0.894815524213 Henry Cohn, 2026, needs more optimization.
5 899 0.894872707878 Henry Cohn, 2026, needs more optimization.
5 900 0.894893155689 Henry Cohn, 2026, needs more optimization.
5 901 0.894966847426 Henry Cohn, 2026, needs more optimization.
5 902 0.895045246874 Henry Cohn, 2026, needs more optimization.
5 903 0.895142788436 Henry Cohn, 2026, needs more optimization.
5 904 0.895208806870 Henry Cohn, 2026, needs more optimization.
5 905 0.895273778005 Henry Cohn, 2026, needs more optimization.
5 906 0.895385293374 Henry Cohn, 2026, needs more optimization.
5 907 0.895386920324 Henry Cohn, 2026, needs more optimization.
5 908 0.895469772870 Henry Cohn, 2026, needs more optimization.
5 909 0.895494031616 Henry Cohn, 2026, needs more optimization.
5 910 0.895554480235 Henry Cohn, 2026, needs more optimization.
5 911 0.895661808989 Henry Cohn, 2026, needs more optimization.
5 912 0.895697148297 Henry Cohn, 2026, needs more optimization.
5 913 0.895773344569 Henry Cohn, 2026, needs more optimization.
5 914 0.895817030417 Henry Cohn, 2026, needs more optimization.
5 915 0.895835606451 Henry Cohn, 2026, needs more optimization.
5 916 0.895926760507 Henry Cohn, 2026, needs more optimization.
5 917 0.895958062609 Henry Cohn, 2026, needs more optimization.
5 918 0.896046302790 Henry Cohn, 2026, needs more optimization.
5 919 0.896056310848 Henry Cohn, 2026, needs more optimization.
5 920 0.896155726013 Henry Cohn, 2026, needs more optimization.
5 921 0.896172475604 Henry Cohn, 2026, needs more optimization.
5 922 0.896266400715 Henry Cohn, 2026, needs more optimization.
5 923 0.896287886483 Henry Cohn, 2026, needs more optimization.
5 924 0.896375614751 Henry Cohn, 2026, needs more optimization.
5 925 0.896392588139 Henry Cohn, 2026, needs more optimization.
5 926 0.896458097187 Henry Cohn, 2026, needs more optimization.
5 927 0.896478589385 Henry Cohn, 2026, needs more optimization.
5 928 0.896559392712 Henry Cohn, 2026, needs more optimization.
5 929 0.896621386274 Henry Cohn, 2026, needs more optimization.
5 930 0.896692759321 Henry Cohn, 2026, needs more optimization.
5 931 0.896763168187 Henry Cohn, 2026, needs more optimization.
5 932 0.896824613493 Henry Cohn, 2026, needs more optimization.
5 933 0.896864904483 Henry Cohn, 2026, needs more optimization.
5 934 0.896922241565 Henry Cohn, 2026, needs more optimization.
5 935 0.896990528358 Henry Cohn, 2026, needs more optimization.
5 936 0.897003765218 Henry Cohn, 2026, needs more optimization.
5 937 0.897071987117 Henry Cohn, 2026, needs more optimization.
5 938 0.897152896088 Henry Cohn, 2026, needs more optimization.
5 939 0.897167672490 Henry Cohn, 2026, needs more optimization.
5 940 0.897209844567 Henry Cohn, 2026, needs more optimization.
5 941 0.897251648789 Henry Cohn, 2026, needs more optimization.
5 942 0.897324483215 Henry Cohn, 2026, needs more optimization.
5 943 0.897426436927 Henry Cohn, 2026, needs more optimization.
5 944 0.897502807607 Henry Cohn, 2026, needs more optimization.
5 945 0.897522793297 Henry Cohn, 2026, needs more optimization.
5 946 0.897574130997 Henry Cohn, 2026, needs more optimization.
5 947 0.897647738880 Henry Cohn, 2026, needs more optimization.
5 948 0.897720417870 Henry Cohn, 2026, needs more optimization.
5 949 0.897796247631 Henry Cohn, 2026, needs more optimization.
5 950 0.897847114900 Henry Cohn, 2026, needs more optimization.
5 951 0.897900850448 Henry Cohn, 2026, needs more optimization.
5 952 0.897949347162 Henry Cohn, 2026, needs more optimization.
5 953 0.897974680630 Henry Cohn, 2026, needs more optimization.
5 954 0.897989940978 Henry Cohn, 2026, needs more optimization.
5 955 0.897993635507 Henry Cohn, 2026, needs more optimization.
5 956 0.898012901826 Henry Cohn, 2026, needs more optimization.
5 957 0.898092790221 Henry Cohn, 2026, needs more optimization.
5 958 0.898194970402 Henry Cohn, 2026, needs more optimization.
5 959 0.898241488168 Henry Cohn, 2026, needs more optimization.
5 960 0.898258964071 Henry Cohn, 2026, needs more optimization.
5 961 0.898350966490 Henry Cohn, 2026, needs more optimization.
5 962 0.898394543411 Henry Cohn, 2026, needs more optimization.
5 963 0.898410557948 Henry Cohn, 2026, needs more optimization.
5 964 0.898493375370 Henry Cohn, 2026, needs more optimization.
5 965 0.898526503381 Henry Cohn, 2026, needs more optimization.
5 966 0.898572373830 Henry Cohn, 2026, needs more optimization.
5 967 0.898582679467 Henry Cohn, 2026, needs more optimization.
5 968 0.898723614323 Henry Cohn, 2026, needs more optimization.
5 969 0.898809120914 Henry Cohn, 2026, needs more optimization.
5 970 0.898829085812 Henry Cohn, 2026, needs more optimization.
5 971 0.898874519816 Henry Cohn, 2026, needs more optimization.
5 972 0.898895415940 Henry Cohn, 2026, needs more optimization.
5 973 0.898933453713 Henry Cohn, 2026, needs more optimization.
5 974 0.899017050967 Henry Cohn, 2026, needs more optimization.
5 975 0.899093969453 Henry Cohn, 2026, needs more optimization.
5 976 0.899120228455 Henry Cohn, 2026, needs more optimization.
5 977 0.899142208433 Henry Cohn, 2026, needs more optimization.
5 978 0.899221177670 Henry Cohn, 2026, needs more optimization.
5 979 0.899224484048 Henry Cohn, 2026, needs more optimization.
5 980 0.899328275939 Henry Cohn, 2026, needs more optimization.
5 981 0.899360537507 Henry Cohn, 2026, needs more optimization.
5 982 0.899422567270 Henry Cohn, 2026, needs more optimization.
5 983 0.899480922599 Henry Cohn, 2026, needs more optimization.
5 984 0.899493833932 Henry Cohn, 2026, needs more optimization.
5 985 0.899617401395 Henry Cohn, 2026, needs more optimization.
5 986 0.899696794359 Henry Cohn, 2026, needs more optimization.
5 987 0.899712591738 Henry Cohn, 2026, needs more optimization.
5 988 0.899770017692 Henry Cohn, 2026, needs more optimization.
5 989 0.899856296790 Henry Cohn, 2026, needs more optimization.
5 990 0.899871312482 Henry Cohn, 2026, needs more optimization.
5 991 0.899894525371 Henry Cohn, 2026, needs more optimization.
5 992 0.899922902319 Henry Cohn, 2026, needs more optimization.
5 993 0.899992738877 Henry Cohn, 2026, needs more optimization.
5 994 0.900048202274 Henry Cohn, 2026, needs more optimization.
5 995 0.900104087348 Henry Cohn, 2026, needs more optimization.
5 996 0.900203331113 Henry Cohn, 2026, needs more optimization.
5 997 0.900241063201 Henry Cohn, 2026, needs more optimization.
5 998 0.900318225154 Henry Cohn, 2026, needs more optimization.
5 999 0.900393975792 Henry Cohn, 2026, needs more optimization.
5 1000 0.900398098170 Henry Cohn, 2026, needs more optimization.
5 1001 0.900454400022 Henry Cohn, 2026, needs more optimization.
5 1002 0.900500741478 Henry Cohn, 2026, needs more optimization.
5 1003 0.900551034675 Henry Cohn, 2026, needs more optimization.
5 1004 0.900558188081 Henry Cohn, 2026, needs more optimization.
5 1005 0.900623105809 Henry Cohn, 2026, needs more optimization.
5 1006 0.900676966348 Henry Cohn, 2026, needs more optimization.
5 1007 0.900684707902 Henry Cohn, 2026, needs more optimization.
5 1008 0.900831049584 Henry Cohn, 2026, needs more optimization.
5 1009 0.900844315314 Henry Cohn, 2026, needs more optimization.
5 1010 0.900906170815 Henry Cohn, 2026, needs more optimization.
5 1011 0.900956375095 Henry Cohn, 2026, needs more optimization.
5 1012 0.900966735994 Henry Cohn, 2026, needs more optimization.
5 1013 0.901008966679 Henry Cohn, 2026, needs more optimization.
5 1014 0.901094695647 Henry Cohn, 2026, needs more optimization.
5 1015 0.901105098529 Henry Cohn, 2026, needs more optimization.
5 1016 0.901109512132 Henry Cohn, 2026, needs more optimization.
5 1017 0.901151735953 Henry Cohn, 2026, needs more optimization.
5 1018 0.901203296102 Henry Cohn, 2026, needs more optimization.
5 1019 0.901292873060 Henry Cohn, 2026, needs more optimization.
5 1020 0.901302608303 Henry Cohn, 2026, needs more optimization.
5 1021 0.901386627556 Henry Cohn, 2026, needs more optimization.
5 1022 0.901434586515 Henry Cohn, 2026, needs more optimization.
5 1023 0.901472127211 Henry Cohn, 2026, needs more optimization.
5 1024 0.901474900590 Henry Cohn, 2026, needs more optimization.
6 13 0.113079752148 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
96⁢x3−36⁢x2−6⁢x+1
6 14 0.132490920324 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
6 15 0.144948974279 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
20⁢x2+4⁢x−1
6 16 0.171071421043 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6400⁢x5+960⁢x4−1024⁢x3−32⁢x2+31⁢x−1
6 17 0.183274337024 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
400⁢x4+240⁢x3+16⁢x2−8⁢x−1
6 18 0.197812188602 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
784⁢x8−280⁢x7−1191⁢x6+120⁢x5+218⁢x4−62⁢x3−31⁢x2+2⁢x+1
6 19 0.200226025892 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 20 0.214285714286 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
14⁢x−3
6 21 0.242852848014 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 22 0.248865699460 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 23 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 24 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 25 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 26 0.25 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x−1
6 27* 0.25 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
4⁢x−1
6 28 0.3 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−3
6 29 0.327844830882 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 30 0.333157886299 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
6 31 0.333333333334 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
3⁢x−1
6 32 0.333333333334 J. H. van Lint and J. J. Seidel, Equilateral point sets in elliptic geometry, Indag. Math. 28 (1966), 335–348, https://research.tue.nl/en/publications/equilateral-point-sets-in-elliptic-geometry.
3⁢x−1
6 33 0.344948974279 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
20⁢x2−4⁢x−1
6 34 0.346451336111 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
64⁢x5+64⁢x4−76⁢x3+7⁢x2+6⁢x−1
6 35 0.358257569496 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
5⁢x2+x−1
6 36 0.358257569496 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x2+x−1
6 37 0.366623377687 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
64⁢x4+96⁢x3−80⁢x2+16⁢x−1
6 38 0.367688450451 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7424⁢x8+1280⁢x7−3904⁢x6−768⁢x5+448⁢x4+80⁢x3−1
6 39 0.384936289161 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
6 40 0.386096677606 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
31⁢x4−12⁢x3−14⁢x2+8⁢x−1
6 41 0.389434811673 Henry Cohn, 2023.
6 42 0.390388203203 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x2+x−1
6 43 0.399773924374 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
1024⁢x9−4096⁢x8−1536⁢x7+1024⁢x6+704⁢x5+64⁢x4−96⁢x3−16⁢x2+4⁢x−1
6 44 0.405666616164 Henry Cohn, 2023.
6 45 0.426943864061 Henry Cohn, 2025.
6 46 0.435705030667 Henry Cohn, 2025.
6 47 0.441020734927 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 48 0.443609864234 Henry Cohn, 2025.
6 49 0.446060501890 Henry Cohn, 2023.
6 50 0.446739131277 Henry Cohn, 2023.
58⁢x3−50⁢x2+13⁢x−1
6 51 0.456479386398 Henry Cohn, 2025.
6 52 0.458253528717 Henry Cohn, 2023.
6 53 0.459145031877 Henry Cohn, 2025.
6 54 0.462714285892 Henry Cohn, 2023.
4104⁢x4−216⁢x3−3654⁢x2+1955⁢x−289
6 55 0.472467412878 Henry Cohn, 2024.
6 56 0.475645784548 Henry Cohn, 2023.
33024⁢x6+14848⁢x5−45568⁢x4+5832⁢x3+12257⁢x2−4922⁢x+529
6 57 0.479790821500 Henry Cohn, 2025.
6 58 0.482548584905 Henry Cohn, 2024.
20⁢x2+9⁢x−9
6 59 0.485942488798 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 60 0.486876290376 Henry Cohn, 2025.
6 61 0.491730182082 Henry Cohn, 2025.
6 62 0.495376595904 Henry Cohn, 2023.
6 63 0.498122491823 Henry Cohn, 2023.
6 64 0.498522963739 Henry Cohn, 2025.
6 65 0.499974913357 Henry Cohn, 2025.
6 66 0.499976896430 Henry Cohn, 2026.
6 67 0.499991659867 Henry Cohn, 2026.
6 72 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155, doi:10.4153/CMB-1969-014-1; J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383–403, doi:10.1007/BF02574051; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060.
2⁢x−1
6 73 0.513985952311 Henry Cohn, 2025.
6 74 0.521539568537 Henry Cohn, 2025.
6 75 0.524373608780 Henry Cohn, 2026.
6 76 0.524881252881 Henry Cohn, 2026.
6 77 0.527287929827 Henry Cohn, 2025.
6 78 0.528662896579 Henry Cohn, 2025.
6 79 0.533648501058 Henry Cohn, 2025.
6 80 0.536468893038 Henry Cohn, 2025.
6 81 0.538396586915 Henry Cohn, 2026.
6 82 0.539382071135 Henry Cohn, 2026.
6 83 0.543248902467 Henry Cohn, 2026.
6 84 0.545957959230 Henry Cohn, 2026, needs more optimization.
6 85 0.546038397748 Henry Cohn, 2026.
6 86 0.548916479202 Matevž Kovačič, 2026, https://github.com/matevz-kovacic/active-model.
6 87 0.550379697504 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 88 0.552456735670 Henry Cohn, 2025.
6 89 0.555561660912 Henry Cohn, 2025, needs more optimization.
6 90 0.557506870643 Henry Cohn, 2026, needs more optimization.
6 91 0.557588802583 Henry Cohn, 2026.
6 92 0.560971622256 Henry Cohn, 2025.
6 93 0.563013323310 Henry Cohn, 2023.
6 94 0.565350375903 Henry Cohn, 2024.
6 95 0.565789396150 Henry Cohn, 2023.
6 96 0.565950871118 Henry Cohn, 2023.
6 97 0.568133461901 Henry Cohn, 2025.
6 98 0.571037776392 Matevž Kovačič, 2026, https://github.com/matevz-kovacic/active-model.
6 99 0.573881665753 Henry Cohn, 2023.
6 100 0.574916276575 Henry Cohn, 2024.
6 101 0.578318097782 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 102 0.580736682189 Henry Cohn, 2023, needs more optimization.
6 103 0.581239830251 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 104 0.582504372840 Henry Cohn, 2026.
6 105 0.583291339461 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 107 0.583371498649 Henry Cohn, 2026.
6 108 0.584228700283 Henry Cohn, 2026.
6 109 0.585348750770 Henry Cohn, 2026.
6 110 0.585555924412 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 111 0.585638229827 Henry Cohn, 2026.
6 112 0.585693130025 Henry Cohn, 2026.
6 113 0.586622932873 Henry Cohn, 2025.
6 114 0.588109690133 Henry Cohn, 2023.
6 115 0.596004657476 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 116 0.596413035821 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 117 0.596421584132 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 118 0.596439417428 Henry Cohn, 2026, needs more optimization.
6 119 0.598424113264 Henry Cohn, 2026.
6 120 0.599016149465 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 121 0.603688760597 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 122 0.605232558247 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 123 0.606415945860 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 125 0.607973280228 Henry Cohn, 2026.
6 126 0.610385708469 Henry Cohn, 2026.
6 127 0.616412771721 Henry Cohn, 2026.
6 128 0.618886682387 Henry Cohn, 2026.
6 129 0.620224367829 Henry Cohn, 2025.
6 130 0.623410242886 Henry Cohn, 2026, needs more optimization.
6 132 0.624698586308 Henry Cohn, 2026, needs more optimization.
6 133 0.626200564251 Henry Cohn, 2026, needs more optimization.
6 134 0.628619229268 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 135 0.630530656158 Henry Cohn, 2026, needs more optimization.
6 136 0.631774376880 Henry Cohn, 2026, needs more optimization.
6 137 0.633402294823 Henry Cohn, 2025.
6 138 0.634581514230 Henry Cohn, 2026, needs more optimization.
6 139 0.636150040514 Henry Cohn, 2026, needs more optimization.
6 140 0.637374263264 Henry Cohn, 2026, needs more optimization.
6 141 0.639286013806 Henry Cohn, 2026, needs more optimization.
6 142 0.639907719383 Henry Cohn, 2026, needs more optimization.
6 143 0.641418520213 Henry Cohn, 2026, needs more optimization.
6 144 0.642197635304 Henry Cohn, 2026, needs more optimization.
6 145 0.643715797598 Henry Cohn, 2026, needs more optimization.
6 146 0.644834686297 Henry Cohn, 2026, needs more optimization.
6 147 0.645786741328 Henry Cohn, 2026, needs more optimization.
6 148 0.646694158541 Henry Cohn, 2026, needs more optimization.
6 149 0.647930950529 Henry Cohn, 2026, needs more optimization.
6 150 0.649234363496 Henry Cohn, 2026, needs more optimization.
6 151 0.649894104895 Henry Cohn, 2026, needs more optimization.
6 152 0.650971226891 Henry Cohn, 2026, needs more optimization.
6 153 0.651424838401 Henry Cohn, 2026, needs more optimization.
6 154 0.651891074500 Henry Cohn, 2026, needs more optimization.
6 155 0.652674198752 Henry Cohn, 2026, needs more optimization.
6 156 0.653218824470 Henry Cohn, 2026, needs more optimization.
6 157 0.653539050196 Henry Cohn, 2026, needs more optimization.
6 158 0.654174169895 Henry Cohn, 2026, needs more optimization.
6 159 0.654917496412 Henry Cohn, 2026, needs more optimization.
6 160 0.655640275548 Henry Cohn, 2026, needs more optimization.
6 161 0.656167449429 Henry Cohn, 2026, needs more optimization.
6 162 0.656793961711 Henry Cohn, 2026, needs more optimization.
6 163 0.657616903752 Henry Cohn, 2026, needs more optimization.
6 164 0.658347046765 Henry Cohn, 2026, needs more optimization.
6 165 0.659084509520 Henry Cohn, 2026, needs more optimization.
6 166 0.659930832598 Henry Cohn, 2026, needs more optimization.
6 167 0.660355875176 Henry Cohn, 2026, needs more optimization.
6 168 0.660627525311 Henry Cohn, 2026, needs more optimization.
6 169 0.661754050760 Henry Cohn, 2026, needs more optimization.
6 170 0.662663966597 Henry Cohn, 2026, needs more optimization.
6 171 0.663635354345 Henry Cohn, 2026, needs more optimization.
6 172 0.664135030350 Henry Cohn, 2026, needs more optimization.
6 173 0.664451438570 Henry Cohn, 2026, needs more optimization.
6 174 0.664870945435 Henry Cohn, 2026, needs more optimization.
6 175 0.665443411314 Henry Cohn, 2026, needs more optimization.
6 176 0.666108306675 Henry Cohn, 2026, needs more optimization.
6 177 0.667548831820 Henry Cohn, 2026, needs more optimization.
6 178 0.668378835639 Henry Cohn, 2026, needs more optimization.
6 179 0.669945126872 Henry Cohn, 2026, needs more optimization.
6 180 0.671097066749 Henry Cohn, 2026, needs more optimization.
6 181 0.671959625888 Henry Cohn, 2026, needs more optimization.
6 182 0.672541539736 Henry Cohn, 2026, needs more optimization.
6 183 0.673119295847 Henry Cohn, 2026, needs more optimization.
6 184 0.673469020772 Henry Cohn, 2026, needs more optimization.
6 185 0.674050677338 Henry Cohn, 2026, needs more optimization.
6 186 0.674289189660 Henry Cohn, 2026, needs more optimization.
6 187 0.674602707689 Henry Cohn, 2026, needs more optimization.
6 188 0.675445915684 Henry Cohn, 2026, needs more optimization.
6 189 0.676161369766 Henry Cohn, 2026, needs more optimization.
6 190 0.677062787920 Henry Cohn, 2026, needs more optimization.
6 191 0.677999166695 Henry Cohn, 2026, needs more optimization.
6 192 0.678394529953 Henry Cohn, 2026, needs more optimization.
6 193 0.678970907542 Henry Cohn, 2026, needs more optimization.
6 194 0.679778275659 Henry Cohn, 2026, needs more optimization.
6 195 0.679949085740 Henry Cohn, 2026, needs more optimization.
6 196 0.680560342651 Henry Cohn, 2026, needs more optimization.
6 197 0.681014487091 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 198 0.681810178806 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 199 0.682835623072 Henry Cohn, 2026, needs more optimization.
6 200 0.683419079431 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 201 0.684423960591 Henry Cohn, 2026, needs more optimization.
6 202 0.684695807095 Henry Cohn, 2026, needs more optimization.
6 203 0.685464316067 Henry Cohn, 2026, needs more optimization.
6 204 0.685817406613 Henry Cohn, 2026, needs more optimization.
6 205 0.686209806248 Henry Cohn, 2026, needs more optimization.
6 206 0.686760535878 Henry Cohn, 2026, needs more optimization.
6 207 0.687792664686 Henry Cohn, 2026, needs more optimization.
6 208 0.688112333873 Henry Cohn, 2026, needs more optimization.
6 209 0.688639236219 Henry Cohn, 2026, needs more optimization.
6 210 0.689051018258 Henry Cohn, 2026, needs more optimization.
6 211 0.689771821428 Henry Cohn, 2026, needs more optimization.
6 212 0.690367071709 Henry Cohn, 2026, needs more optimization.
6 213 0.691143697727 Henry Cohn, 2026, needs more optimization.
6 214 0.691928421847 Henry Cohn, 2026, needs more optimization.
6 215 0.692810407054 Henry Cohn, 2026, needs more optimization.
6 216 0.693149727059 Henry Cohn, 2026, needs more optimization.
6 217 0.694030764970 Henry Cohn, 2026, needs more optimization.
6 218 0.694428132423 Henry Cohn, 2026, needs more optimization.
6 219 0.694876487855 Henry Cohn, 2026, needs more optimization.
6 220 0.694995629064 Henry Cohn, 2026, needs more optimization.
6 221 0.695418366142 Henry Cohn, 2026, needs more optimization.
6 222 0.695867575619 Henry Cohn, 2026, needs more optimization.
6 223 0.696218094268 Henry Cohn, 2026, needs more optimization.
6 224 0.697123573666 Henry Cohn, 2026, needs more optimization.
6 225 0.697415667599 Henry Cohn, 2026, needs more optimization.
6 226 0.697939337586 Henry Cohn, 2026, needs more optimization.
6 227 0.698312547914 Henry Cohn, 2026, needs more optimization.
6 228 0.698896218015 Henry Cohn, 2026, needs more optimization.
6 229 0.699200496392 Henry Cohn, 2026, needs more optimization.
6 230 0.699618562179 Henry Cohn, 2026, needs more optimization.
6 243 0.7 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−7
6 244 0.703650683928 Henry Cohn, 2026, needs more optimization.
6 245 0.703739768473 Henry Cohn, 2026, needs more optimization.
6 246 0.704003315580 Henry Cohn, 2026, needs more optimization.
6 247 0.704049579225 Henry Cohn, 2026, needs more optimization.
6 248 0.704235335577 Henry Cohn, 2026, needs more optimization.
6 249 0.704292042044 Henry Cohn, 2026, needs more optimization.
6 250 0.704404138161 Henry Cohn, 2026, needs more optimization.
6 251 0.704633060513 Henry Cohn, 2026, needs more optimization.
6 252 0.704719860238 Henry Cohn, 2026, needs more optimization.
6 253 0.704943057084 Henry Cohn, 2026, needs more optimization.
6 254 0.705090515386 Henry Cohn, 2026, needs more optimization.
6 255 0.705176035928 Henry Cohn, 2026, needs more optimization.
6 256 0.705180371185 Henry Cohn, 2026, needs more optimization.
6 257 0.705416704139 Henry Cohn, 2026, needs more optimization.
6 258 0.706001250576 Henry Cohn, 2026, needs more optimization.
6 259 0.706716718619 Henry Cohn, 2026, needs more optimization.
6 260 0.707187161621 Henry Cohn, 2026, needs more optimization.
6 261 0.707854912555 Henry Cohn, 2026, needs more optimization.
6 262 0.708781132131 Henry Cohn, 2026, needs more optimization.
6 263 0.709263462525 Henry Cohn, 2026, needs more optimization.
6 264 0.709771364775 Henry Cohn, 2026, needs more optimization.
6 265 0.711035551868 Henry Cohn, 2026, needs more optimization.
6 266 0.712056158101 Henry Cohn, 2026, needs more optimization.
6 267 0.712797549094 Henry Cohn, 2026, needs more optimization.
6 268 0.713054804511 Henry Cohn, 2026, needs more optimization.
6 269 0.713552615264 Henry Cohn, 2026, needs more optimization.
6 270 0.714480033580 Henry Cohn, 2026, needs more optimization.
6 271 0.715178667916 Henry Cohn, 2026, needs more optimization.
6 272 0.716089085279 Henry Cohn, 2026, needs more optimization.
6 273 0.716666380575 Henry Cohn, 2026, needs more optimization.
6 274 0.717513736093 Henry Cohn, 2026, needs more optimization.
6 275 0.718325541152 Henry Cohn, 2026, needs more optimization.
6 276 0.718916346207 Henry Cohn, 2026, needs more optimization.
6 277 0.719526311640 Henry Cohn, 2026, needs more optimization.
6 278 0.720038364195 Henry Cohn, 2026, needs more optimization.
6 279 0.720797154147 Henry Cohn, 2026, needs more optimization.
6 280 0.721343297863 Henry Cohn, 2026, needs more optimization.
6 281 0.722063348058 Henry Cohn, 2026, needs more optimization.
6 282 0.722535743921 Henry Cohn, 2026, needs more optimization.
6 283 0.723161896922 Henry Cohn, 2026, needs more optimization.
6 284 0.723871953648 Henry Cohn, 2026, needs more optimization.
6 285 0.724560497991 Henry Cohn, 2026, needs more optimization.
6 286 0.725079942440 Henry Cohn, 2026, needs more optimization.
6 287 0.725207519580 Henry Cohn, 2026, needs more optimization.
6 288 0.725551966579 Henry Cohn, 2026, needs more optimization.
6 289 0.725553517119 Henry Cohn, 2026, needs more optimization.
6 290 0.726303490253 Henry Cohn, 2026, needs more optimization.
6 291 0.726997243048 Henry Cohn, 2026, needs more optimization.
6 292 0.727966382875 Henry Cohn, 2026, needs more optimization.
6 293 0.728393704045 Henry Cohn, 2026, needs more optimization.
6 294 0.728865960556 Henry Cohn, 2026, needs more optimization.
6 295 0.729386418527 Henry Cohn, 2026, needs more optimization.
6 296 0.729924070292 Henry Cohn, 2026, needs more optimization.
6 297 0.730334874930 Henry Cohn, 2026, needs more optimization.
6 298 0.730725406784 Henry Cohn, 2026, needs more optimization.
6 299 0.731065269229 Henry Cohn, 2026, needs more optimization.
6 300 0.731430718908 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 301 0.731928769556 Henry Cohn, 2026, needs more optimization.
6 302 0.732399733895 Henry Cohn, 2026, needs more optimization.
6 303 0.732798654621 Henry Cohn, 2026, needs more optimization.
6 304 0.732993374900 Henry Cohn, 2026, needs more optimization.
6 305 0.733453239030 Henry Cohn, 2026, needs more optimization.
6 306 0.733827988185 Henry Cohn, 2026, needs more optimization.
6 307 0.734108253126 Henry Cohn, 2026, needs more optimization.
6 308 0.734489715727 Henry Cohn, 2026, needs more optimization.
6 309 0.734655274463 Henry Cohn, 2026, needs more optimization.
6 310 0.734886388184 Henry Cohn, 2026, needs more optimization.
6 311 0.735450031640 Henry Cohn, 2026, needs more optimization.
6 312 0.735994320272 Henry Cohn, 2026, needs more optimization.
6 313 0.736422265463 Henry Cohn, 2026, needs more optimization.
6 314 0.736839569970 Henry Cohn, 2026, needs more optimization.
6 315 0.737261229302 Henry Cohn, 2026, needs more optimization.
6 316 0.737689866143 Henry Cohn, 2026, needs more optimization.
6 317 0.738034492924 Henry Cohn, 2026, needs more optimization.
6 318 0.738517004595 Henry Cohn, 2026, needs more optimization.
6 319 0.738981174917 Henry Cohn, 2026, needs more optimization.
6 320 0.739360669446 Henry Cohn, 2026, needs more optimization.
6 321 0.740392507328 Henry Cohn, 2026, needs more optimization.
6 322 0.740718623472 Henry Cohn, 2026, needs more optimization.
6 323 0.741210649064 Henry Cohn, 2026, needs more optimization.
6 324 0.741472277385 Henry Cohn, 2026, needs more optimization.
6 325 0.742100535452 Henry Cohn, 2026, needs more optimization.
6 326 0.742386151341 Henry Cohn, 2026, needs more optimization.
6 327 0.742830477483 Henry Cohn, 2026, needs more optimization.
6 328 0.742903969411 Henry Cohn, 2026, needs more optimization.
6 329 0.743336911920 Henry Cohn, 2026, needs more optimization.
6 330 0.743703583645 Henry Cohn, 2026, needs more optimization.
6 331 0.744121710687 Henry Cohn, 2026, needs more optimization.
6 332 0.744375581136 Henry Cohn, 2026, needs more optimization.
6 333 0.744404080573 Henry Cohn, 2026, needs more optimization.
6 334 0.744692647756 Henry Cohn, 2026, needs more optimization.
6 335 0.745155499023 Henry Cohn, 2026, needs more optimization.
6 336 0.745795172280 Henry Cohn, 2026, needs more optimization.
6 337 0.746050970072 Henry Cohn, 2026, needs more optimization.
6 338 0.746536810251 Henry Cohn, 2026, needs more optimization.
6 339 0.746541484650 Henry Cohn, 2026, needs more optimization.
6 340 0.746547327615 Henry Cohn, 2026, needs more optimization.
6 341 0.746549800600 Henry Cohn, 2026, needs more optimization.
6 342 0.746555037918 Henry Cohn, 2026, needs more optimization.
6 343 0.748201872568 Henry Cohn, 2026, needs more optimization.
6 344 0.748891333107 Henry Cohn, 2026, needs more optimization.
6 345 0.749168886017 Henry Cohn, 2026, needs more optimization.
6 346 0.749361533116 Henry Cohn, 2026, needs more optimization.
6 347 0.749672574610 Henry Cohn, 2026, needs more optimization.
6 348 0.750060948395 Henry Cohn, 2026, needs more optimization.
6 349 0.750323250801 Henry Cohn, 2026, needs more optimization.
6 350 0.750535324476 Henry Cohn, 2026, needs more optimization.
6 351 0.750816019938 Henry Cohn, 2026, needs more optimization.
6 352 0.751167366847 Henry Cohn, 2026, needs more optimization.
6 353 0.751504887645 Henry Cohn, 2026, needs more optimization.
6 354 0.751707781559 Henry Cohn, 2026, needs more optimization.
6 355 0.751875015808 Henry Cohn, 2026, needs more optimization.
6 356 0.752154535514 Henry Cohn, 2026, needs more optimization.
6 357 0.752448097554 Henry Cohn, 2026, needs more optimization.
6 358 0.752900568948 Henry Cohn, 2026, needs more optimization.
6 359 0.753214276804 Henry Cohn, 2026, needs more optimization.
6 360 0.753274216061 Henry Cohn, 2026, needs more optimization.
6 361 0.753631114511 Henry Cohn, 2026, needs more optimization.
6 362 0.754025228210 Henry Cohn, 2026, needs more optimization.
6 363 0.754158167199 Henry Cohn, 2026, needs more optimization.
6 364 0.754546850909 Henry Cohn, 2026, needs more optimization.
6 365 0.754688774749 Henry Cohn, 2026, needs more optimization.
6 366 0.755029583027 Henry Cohn, 2026, needs more optimization.
6 367 0.755301213009 Henry Cohn, 2026, needs more optimization.
6 368 0.755542124057 Henry Cohn, 2026, needs more optimization.
6 369 0.755894584699 Henry Cohn, 2026, needs more optimization.
6 370 0.756118715648 Henry Cohn, 2026, needs more optimization.
6 371 0.756591999949 Henry Cohn, 2026, needs more optimization.
6 372 0.756694702296 Henry Cohn, 2026, needs more optimization.
6 373 0.757058978386 Henry Cohn, 2026, needs more optimization.
6 374 0.757260927893 Henry Cohn, 2026, needs more optimization.
6 375 0.757512930404 Henry Cohn, 2026, needs more optimization.
6 376 0.757928584430 Henry Cohn, 2026, needs more optimization.
6 377 0.758154656885 Henry Cohn, 2026, needs more optimization.
6 378 0.758496973623 Henry Cohn, 2026, needs more optimization.
6 379 0.758921958365 Henry Cohn, 2026, needs more optimization.
6 380 0.759281532699 Henry Cohn, 2026, needs more optimization.
6 381 0.759287188836 Henry Cohn, 2026, needs more optimization.
6 382 0.759553828960 Henry Cohn, 2026, needs more optimization.
6 383 0.759651144367 Henry Cohn, 2026, needs more optimization.
6 384 0.759895034414 Henry Cohn, 2026, needs more optimization.
6 385 0.760293490745 Henry Cohn, 2026, needs more optimization.
6 386 0.760400152116 Henry Cohn, 2026, needs more optimization.
6 387 0.760665940114 Henry Cohn, 2026, needs more optimization.
6 388 0.761094843796 Henry Cohn, 2026, needs more optimization.
6 389 0.761277408237 Henry Cohn, 2026, needs more optimization.
6 390 0.761719412074 Henry Cohn, 2026, needs more optimization.
6 391 0.761743903441 Henry Cohn, 2026, needs more optimization.
6 392 0.762056837313 Henry Cohn, 2026, needs more optimization.
6 393 0.762147020533 Henry Cohn, 2026, needs more optimization.
6 394 0.762396033611 Henry Cohn, 2026, needs more optimization.
6 395 0.762808555436 Henry Cohn, 2026, needs more optimization.
6 396 0.763162430869 Henry Cohn, 2026, needs more optimization.
6 397 0.763205345818 Henry Cohn, 2026, needs more optimization.
6 400 0.763461948905 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 401 0.764132137583 Henry Cohn, 2026, needs more optimization.
6 402 0.764333777135 Henry Cohn, 2026, needs more optimization.
6 403 0.764553451385 Henry Cohn, 2026, needs more optimization.
6 404 0.764898868902 Henry Cohn, 2026, needs more optimization.
6 405 0.765049126009 Henry Cohn, 2026, needs more optimization.
6 406 0.765251881874 Henry Cohn, 2026, needs more optimization.
6 407 0.765554760762 Henry Cohn, 2026, needs more optimization.
6 408 0.765775905542 Henry Cohn, 2026, needs more optimization.
6 409 0.765829596901 Henry Cohn, 2026, needs more optimization.
6 410 0.766020547392 Henry Cohn, 2026, needs more optimization.
6 411 0.766324786941 Henry Cohn, 2026, needs more optimization.
6 412 0.766583398021 Henry Cohn, 2026, needs more optimization.
6 413 0.766729780804 Henry Cohn, 2026, needs more optimization.
6 414 0.767055465298 Henry Cohn, 2026, needs more optimization.
6 415 0.767434170300 Henry Cohn, 2026, needs more optimization.
6 416 0.767448222137 Henry Cohn, 2026, needs more optimization.
6 417 0.768007147668 Henry Cohn, 2026, needs more optimization.
6 418 0.768185944537 Henry Cohn, 2026, needs more optimization.
6 419 0.768267219762 Henry Cohn, 2026, needs more optimization.
6 420 0.768681426369 Henry Cohn, 2026, needs more optimization.
6 421 0.768858491706 Henry Cohn, 2026, needs more optimization.
6 422 0.769113280656 Henry Cohn, 2026, needs more optimization.
6 423 0.769297208100 Henry Cohn, 2026, needs more optimization.
6 424 0.769565411744 Henry Cohn, 2026, needs more optimization.
6 425 0.769819834776 Henry Cohn, 2026, needs more optimization.
6 426 0.770072640071 Henry Cohn, 2026, needs more optimization.
6 427 0.770112754737 Henry Cohn, 2026, needs more optimization.
6 428 0.770408862110 Henry Cohn, 2026, needs more optimization.
6 429 0.770523122177 Henry Cohn, 2026, needs more optimization.
6 430 0.770828186021 Henry Cohn, 2026, needs more optimization.
6 431 0.770920789190 Henry Cohn, 2026, needs more optimization.
6 432 0.771048530093 Henry Cohn, 2026, needs more optimization.
6 433 0.771341538295 Henry Cohn, 2026, needs more optimization.
6 434 0.771483828651 Henry Cohn, 2026, needs more optimization.
6 435 0.771776053637 Henry Cohn, 2026, needs more optimization.
6 436 0.771820556665 Henry Cohn, 2026, needs more optimization.
6 437 0.771948691950 Henry Cohn, 2026, needs more optimization.
6 438 0.772124005201 Henry Cohn, 2026, needs more optimization.
6 439 0.772515797546 Henry Cohn, 2026, needs more optimization.
6 440 0.772633502270 Henry Cohn, 2026, needs more optimization.
6 441 0.772898014379 Henry Cohn, 2026, needs more optimization.
6 442 0.773078267758 Henry Cohn, 2026, needs more optimization.
6 443 0.773241999150 Henry Cohn, 2026, needs more optimization.
6 444 0.773374860258 Henry Cohn, 2026, needs more optimization.
6 445 0.773765808863 Henry Cohn, 2026, needs more optimization.
6 446 0.774045335435 Henry Cohn, 2026, needs more optimization.
6 447 0.774215321356 Henry Cohn, 2026, needs more optimization.
6 448 0.774388239003 Henry Cohn, 2026, needs more optimization.
6 449 0.774712503032 Henry Cohn, 2026, needs more optimization.
6 450 0.774821207861 Henry Cohn, 2026, needs more optimization.
6 451 0.775055478001 Henry Cohn, 2026, needs more optimization.
6 452 0.775195265624 Henry Cohn, 2026, needs more optimization.
6 453 0.775424039881 Henry Cohn, 2026, needs more optimization.
6 454 0.775479034329 Henry Cohn, 2026, needs more optimization.
6 455 0.775844162997 Henry Cohn, 2026, needs more optimization.
6 456 0.776060647477 Henry Cohn, 2026, needs more optimization.
6 457 0.776313469909 Henry Cohn, 2026, needs more optimization.
6 458 0.776420378220 Henry Cohn, 2026, needs more optimization.
6 459 0.776648116094 Henry Cohn, 2026, needs more optimization.
6 460 0.776745024753 Henry Cohn, 2026, needs more optimization.
6 461 0.776780023563 Henry Cohn, 2026, needs more optimization.
6 462 0.777135317332 Henry Cohn, 2026, needs more optimization.
6 463 0.777364236562 Henry Cohn, 2026, needs more optimization.
6 464 0.777438678661 Henry Cohn, 2026, needs more optimization.
6 465 0.777662660066 Henry Cohn, 2026, needs more optimization.
6 466 0.777930710595 Henry Cohn, 2026, needs more optimization.
6 467 0.778019503277 Henry Cohn, 2026, needs more optimization.
6 468 0.778280099466 Henry Cohn, 2026, needs more optimization.
6 469 0.778330000874 Henry Cohn, 2026, needs more optimization.
6 470 0.778710697369 Henry Cohn, 2026, needs more optimization.
6 471 0.778902495149 Henry Cohn, 2026, needs more optimization.
6 472 0.779173675191 Henry Cohn, 2026, needs more optimization.
6 473 0.779465600609 Henry Cohn, 2026, needs more optimization.
6 474 0.779641642919 Henry Cohn, 2026, needs more optimization.
6 475 0.779678431603 Henry Cohn, 2026, needs more optimization.
6 476 0.779727697904 Henry Cohn, 2026, needs more optimization.
6 477 0.779843720094 Henry Cohn, 2026, needs more optimization.
6 478 0.780129330095 Henry Cohn, 2026, needs more optimization.
6 479 0.780334733069 Henry Cohn, 2026, needs more optimization.
6 480 0.780544516155 Henry Cohn, 2026, needs more optimization.
6 481 0.780686578591 Henry Cohn, 2026, needs more optimization.
6 482 0.780895222420 Henry Cohn, 2026, needs more optimization.
6 483 0.781069934649 Henry Cohn, 2026, needs more optimization.
6 484 0.781376662148 Henry Cohn, 2026, needs more optimization.
6 485 0.781541866561 Henry Cohn, 2026, needs more optimization.
6 486 0.781631963196 Henry Cohn, 2026, needs more optimization.
6 487 0.781955071902 Henry Cohn, 2026, needs more optimization.
6 488 0.782125042734 Henry Cohn, 2026, needs more optimization.
6 489 0.782377327952 Henry Cohn, 2026, needs more optimization.
6 490 0.782441705680 Henry Cohn, 2026, needs more optimization.
6 491 0.782691545546 Henry Cohn, 2026, needs more optimization.
6 492 0.782793796837 Henry Cohn, 2026, needs more optimization.
6 493 0.783008718486 Henry Cohn, 2026, needs more optimization.
6 494 0.783254239036 Henry Cohn, 2026, needs more optimization.
6 495 0.783276031244 Henry Cohn, 2026, needs more optimization.
6 496 0.783452416656 Henry Cohn, 2026, needs more optimization.
6 497 0.783649962127 Henry Cohn, 2026, needs more optimization.
6 500 0.783783509350 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 501 0.784438857427 Henry Cohn, 2026, needs more optimization.
6 502 0.784671697681 Henry Cohn, 2026, needs more optimization.
6 503 0.784865983420 Henry Cohn, 2026, needs more optimization.
6 504 0.785008081204 Henry Cohn, 2026, needs more optimization.
6 505 0.785164862007 Henry Cohn, 2026, needs more optimization.
6 506 0.785344328166 Henry Cohn, 2026, needs more optimization.
6 507 0.785472390025 Henry Cohn, 2026, needs more optimization.
6 508 0.785608688249 Henry Cohn, 2026, needs more optimization.
6 509 0.785861805161 Henry Cohn, 2026, needs more optimization.
6 510 0.786017726821 Henry Cohn, 2026, needs more optimization.
6 511 0.786276636903 Henry Cohn, 2026, needs more optimization.
6 512 0.786285940155 Henry Cohn, 2026, needs more optimization.
6 513 0.786400810490 Henry Cohn, 2026, needs more optimization.
6 514 0.786565931452 Henry Cohn, 2026, needs more optimization.
6 515 0.786632449053 Henry Cohn, 2026, needs more optimization.
6 516 0.786774046744 Henry Cohn, 2026, needs more optimization.
6 517 0.786913218623 Henry Cohn, 2026, needs more optimization.
6 518 0.787265128322 Henry Cohn, 2026, needs more optimization.
6 519 0.787280244188 Henry Cohn, 2026, needs more optimization.
6 520 0.787429234724 Henry Cohn, 2026, needs more optimization.
6 521 0.787664113667 Henry Cohn, 2026, needs more optimization.
6 522 0.787796345144 Henry Cohn, 2026, needs more optimization.
6 523 0.788007788108 Henry Cohn, 2026, needs more optimization.
6 524 0.788228758458 Henry Cohn, 2026, needs more optimization.
6 525 0.788430563366 Henry Cohn, 2026, needs more optimization.
6 526 0.788562976701 Henry Cohn, 2026, needs more optimization.
6 527 0.788866479091 Henry Cohn, 2026, needs more optimization.
6 528 0.788917288468 Henry Cohn, 2026, needs more optimization.
6 529 0.789113973369 Henry Cohn, 2026, needs more optimization.
6 530 0.789223575611 Henry Cohn, 2026, needs more optimization.
6 531 0.789405078604 Henry Cohn, 2026, needs more optimization.
6 532 0.789541623596 Henry Cohn, 2026, needs more optimization.
6 533 0.789657031902 Henry Cohn, 2026, needs more optimization.
6 534 0.789756436100 Henry Cohn, 2026, needs more optimization.
6 535 0.790016550881 Henry Cohn, 2026, needs more optimization.
6 536 0.790056138852 Henry Cohn, 2026, needs more optimization.
6 537 0.790290111821 Henry Cohn, 2026, needs more optimization.
6 538 0.790475590684 Henry Cohn, 2026, needs more optimization.
6 539 0.790492246764 Henry Cohn, 2026, needs more optimization.
6 540 0.790696072978 Henry Cohn, 2026, needs more optimization.
6 541 0.790876624855 Henry Cohn, 2026, needs more optimization.
6 542 0.790903544182 Henry Cohn, 2026, needs more optimization.
6 543 0.791091493569 Henry Cohn, 2026, needs more optimization.
6 544 0.791287066424 Henry Cohn, 2026, needs more optimization.
6 545 0.791480835767 Henry Cohn, 2026, needs more optimization.
6 546 0.791753496668 Henry Cohn, 2026, needs more optimization.
6 547 0.791796789560 Henry Cohn, 2026, needs more optimization.
6 548 0.791970414467 Henry Cohn, 2026, needs more optimization.
6 549 0.792112080575 Henry Cohn, 2026, needs more optimization.
6 550 0.792218655607 Henry Cohn, 2026, needs more optimization.
6 551 0.792440693388 Henry Cohn, 2026, needs more optimization.
6 552 0.792559337017 Henry Cohn, 2026, needs more optimization.
6 553 0.792703818265 Henry Cohn, 2026, needs more optimization.
6 554 0.792867520102 Henry Cohn, 2026, needs more optimization.
6 555 0.793005114076 Henry Cohn, 2026, needs more optimization.
6 556 0.793260479272 Henry Cohn, 2026, needs more optimization.
6 557 0.793312076980 Henry Cohn, 2026, needs more optimization.
6 558 0.793371005518 Henry Cohn, 2026, needs more optimization.
6 559 0.793487790612 Henry Cohn, 2026, needs more optimization.
6 560 0.793734837560 Henry Cohn, 2026, needs more optimization.
6 561 0.793990365233 Henry Cohn, 2026, needs more optimization.
6 562 0.793992789269 Henry Cohn, 2026, needs more optimization.
6 563 0.794209331668 Henry Cohn, 2026, needs more optimization.
6 564 0.794224195102 Henry Cohn, 2026, needs more optimization.
6 565 0.794448264563 Henry Cohn, 2026, needs more optimization.
6 566 0.794613028361 Henry Cohn, 2026, needs more optimization.
6 567 0.794774352417 Henry Cohn, 2026, needs more optimization.
6 568 0.795012944625 Henry Cohn, 2026, needs more optimization.
6 569 0.795031837171 Henry Cohn, 2026, needs more optimization.
6 570 0.795151284218 Henry Cohn, 2026, needs more optimization.
6 571 0.795223873506 Henry Cohn, 2026, needs more optimization.
6 572 0.795372708364 Henry Cohn, 2026, needs more optimization.
6 573 0.795571705498 Henry Cohn, 2026, needs more optimization.
6 574 0.795655125135 Henry Cohn, 2026, needs more optimization.
6 575 0.795873343956 Henry Cohn, 2026, needs more optimization.
6 576 0.796074504674 Henry Cohn, 2026, needs more optimization.
6 577 0.796191267467 Henry Cohn, 2026, needs more optimization.
6 578 0.796324950448 Henry Cohn, 2026, needs more optimization.
6 579 0.796570666878 Henry Cohn, 2026, needs more optimization.
6 580 0.796703884438 Henry Cohn, 2026, needs more optimization.
6 581 0.796751901714 Henry Cohn, 2026, needs more optimization.
6 582 0.796935198485 Henry Cohn, 2026, needs more optimization.
6 583 0.797063396844 Henry Cohn, 2026, needs more optimization.
6 584 0.797348157476 Henry Cohn, 2026, needs more optimization.
6 585 0.797375935229 Henry Cohn, 2026, needs more optimization.
6 586 0.797377705987 Henry Cohn, 2026, needs more optimization.
6 587 0.797506939477 Henry Cohn, 2026, needs more optimization.
6 588 0.797679508535 Henry Cohn, 2026, needs more optimization.
6 589 0.797817253791 Henry Cohn, 2026, needs more optimization.
6 590 0.797910928134 Henry Cohn, 2026, needs more optimization.
6 591 0.798112573037 Henry Cohn, 2026, needs more optimization.
6 592 0.798367973657 Henry Cohn, 2026, needs more optimization.
6 593 0.798457048321 Henry Cohn, 2026, needs more optimization.
6 594 0.798644425031 Henry Cohn, 2026, needs more optimization.
6 595 0.798783203486 Henry Cohn, 2026, needs more optimization.
6 596 0.798920532305 Henry Cohn, 2026, needs more optimization.
6 597 0.799043118941 Henry Cohn, 2026, needs more optimization.
6 598 0.799233568559 Henry Cohn, 2026, needs more optimization.
6 600 0.799263224349 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 601 0.799659012656 Henry Cohn, 2026, needs more optimization.
6 602 0.799772260172 Henry Cohn, 2026, needs more optimization.
6 603 0.799910052198 Henry Cohn, 2026, needs more optimization.
6 604 0.800057954648 Henry Cohn, 2026, needs more optimization.
6 605 0.800201376426 Henry Cohn, 2026, needs more optimization.
6 606 0.800211081333 Henry Cohn, 2026, needs more optimization.
6 607 0.800469454276 Henry Cohn, 2026, needs more optimization.
6 608 0.800480506369 Henry Cohn, 2026, needs more optimization.
6 609 0.800618933235 Henry Cohn, 2026, needs more optimization.
6 610 0.800759288393 Henry Cohn, 2026, needs more optimization.
6 611 0.800997617334 Henry Cohn, 2026, needs more optimization.
6 612 0.801125936396 Henry Cohn, 2026, needs more optimization.
6 613 0.801159472693 Henry Cohn, 2026, needs more optimization.
6 614 0.801441336786 Henry Cohn, 2026, needs more optimization.
6 615 0.801480505446 Henry Cohn, 2026, needs more optimization.
6 616 0.801642621139 Henry Cohn, 2026, needs more optimization.
6 617 0.801644772884 Henry Cohn, 2026, needs more optimization.
6 618 0.801781108797 Henry Cohn, 2026, needs more optimization.
6 619 0.801905257656 Henry Cohn, 2026, needs more optimization.
6 620 0.801962418739 Henry Cohn, 2026, needs more optimization.
6 621 0.802155949872 Henry Cohn, 2026, needs more optimization.
6 622 0.802418969194 Henry Cohn, 2026, needs more optimization.
6 623 0.802560377728 Henry Cohn, 2026, needs more optimization.
6 624 0.802573805029 Henry Cohn, 2026, needs more optimization.
6 625 0.802699803330 Henry Cohn, 2026, needs more optimization.
6 626 0.802893393204 Henry Cohn, 2026, needs more optimization.
6 627 0.802912374599 Henry Cohn, 2026, needs more optimization.
6 628 0.802993797425 Henry Cohn, 2026, needs more optimization.
6 629 0.803181949257 Henry Cohn, 2026, needs more optimization.
6 630 0.803288391010 Henry Cohn, 2026, needs more optimization.
6 631 0.803406859361 Henry Cohn, 2026, needs more optimization.
6 632 0.803551695288 Henry Cohn, 2026, needs more optimization.
6 633 0.803753269935 Henry Cohn, 2026, needs more optimization.
6 634 0.803972924051 Henry Cohn, 2026, needs more optimization.
6 635 0.803986640773 Henry Cohn, 2026, needs more optimization.
6 636 0.804077378267 Henry Cohn, 2026, needs more optimization.
6 637 0.804211991390 Henry Cohn, 2026, needs more optimization.
6 638 0.804378807116 Henry Cohn, 2026, needs more optimization.
6 639 0.804379865429 Henry Cohn, 2026, needs more optimization.
6 640 0.804586122395 Henry Cohn, 2026, needs more optimization.
6 641 0.804604405634 Henry Cohn, 2026, needs more optimization.
6 642 0.804663290794 Henry Cohn, 2026, needs more optimization.
6 643 0.804766598690 Henry Cohn, 2026, needs more optimization.
6 644 0.804939565399 Henry Cohn, 2026, needs more optimization.
6 645 0.805176979910 Henry Cohn, 2026, needs more optimization.
6 646 0.805254017940 Henry Cohn, 2026, needs more optimization.
6 647 0.805428561859 Henry Cohn, 2026, needs more optimization.
6 648 0.805449569725 Henry Cohn, 2026, needs more optimization.
6 649 0.805545745710 Henry Cohn, 2026, needs more optimization.
6 650 0.805651356929 Henry Cohn, 2026, needs more optimization.
6 651 0.805794215292 Henry Cohn, 2026, needs more optimization.
6 652 0.805921443896 Henry Cohn, 2026, needs more optimization.
6 653 0.806067249760 Henry Cohn, 2026, needs more optimization.
6 654 0.806182518572 Henry Cohn, 2026, needs more optimization.
6 655 0.806367634591 Henry Cohn, 2026, needs more optimization.
6 656 0.806396065308 Henry Cohn, 2026, needs more optimization.
6 657 0.806530893023 Henry Cohn, 2026, needs more optimization.
6 658 0.806594405409 Henry Cohn, 2026, needs more optimization.
6 659 0.806708903240 Henry Cohn, 2026, needs more optimization.
6 660 0.806749576576 Henry Cohn, 2026, needs more optimization.
6 661 0.806891206756 Henry Cohn, 2026, needs more optimization.
6 662 0.807082160083 Henry Cohn, 2026, needs more optimization.
6 663 0.807251285704 Henry Cohn, 2026, needs more optimization.
6 664 0.807282856762 Henry Cohn, 2026, needs more optimization.
6 665 0.807559501062 Henry Cohn, 2026, needs more optimization.
6 666 0.807578771832 Henry Cohn, 2026, needs more optimization.
6 667 0.807738868522 Henry Cohn, 2026, needs more optimization.
6 668 0.807776999619 Henry Cohn, 2026, needs more optimization.
6 669 0.807819621632 Henry Cohn, 2026, needs more optimization.
6 670 0.807890811180 Henry Cohn, 2026, needs more optimization.
6 671 0.808064172966 Henry Cohn, 2026, needs more optimization.
6 672 0.808129076706 Henry Cohn, 2026, needs more optimization.
6 673 0.808283853581 Henry Cohn, 2026, needs more optimization.
6 674 0.808454476202 Henry Cohn, 2026, needs more optimization.
6 675 0.808542431041 Henry Cohn, 2026, needs more optimization.
6 676 0.808750947477 Henry Cohn, 2026, needs more optimization.
6 677 0.808924470044 Henry Cohn, 2026, needs more optimization.
6 678 0.808977553361 Henry Cohn, 2026, needs more optimization.
6 679 0.809095643326 Henry Cohn, 2026, needs more optimization.
6 680 0.809197980219 Henry Cohn, 2026, needs more optimization.
6 681 0.809367571718 Henry Cohn, 2026, needs more optimization.
6 682 0.809508530974 Henry Cohn, 2026, needs more optimization.
6 683 0.809570364073 Henry Cohn, 2026, needs more optimization.
6 684 0.809704030004 Henry Cohn, 2026, needs more optimization.
6 685 0.809808019217 Henry Cohn, 2026, needs more optimization.
6 686 0.809901222873 Henry Cohn, 2026, needs more optimization.
6 687 0.809947533437 Henry Cohn, 2026, needs more optimization.
6 688 0.810112204993 Henry Cohn, 2026, needs more optimization.
6 689 0.810278351612 Henry Cohn, 2026, needs more optimization.
6 690 0.810364726817 Henry Cohn, 2026, needs more optimization.
6 691 0.810468489997 Henry Cohn, 2026, needs more optimization.
6 692 0.810571587534 Henry Cohn, 2026, needs more optimization.
6 693 0.810669399736 Henry Cohn, 2026, needs more optimization.
6 694 0.810820935573 Henry Cohn, 2026, needs more optimization.
6 695 0.810852892349 Henry Cohn, 2026, needs more optimization.
6 696 0.811063700698 Henry Cohn, 2026, needs more optimization.
6 697 0.811156182442 Henry Cohn, 2026, needs more optimization.
6 698 0.811429054132 Henry Cohn, 2026, needs more optimization.
6 699 0.811547349940 Henry Cohn, 2026, needs more optimization.
6 700 0.811670256223 Henry Cohn, 2026, needs more optimization.
6 701 0.811690484733 Henry Cohn, 2026, needs more optimization.
6 702 0.811744594927 Henry Cohn, 2026, needs more optimization.
6 703 0.811870674093 Henry Cohn, 2026, needs more optimization.
6 704 0.811886612955 Henry Cohn, 2026, needs more optimization.
6 705 0.811969655613 Henry Cohn, 2026, needs more optimization.
6 706 0.812131470610 Henry Cohn, 2026, needs more optimization.
6 707 0.812327589265 Henry Cohn, 2026, needs more optimization.
6 708 0.812445949309 Henry Cohn, 2026, needs more optimization.
6 709 0.812551940853 Henry Cohn, 2026, needs more optimization.
6 710 0.812661768206 Henry Cohn, 2026, needs more optimization.
6 711 0.812741482721 Henry Cohn, 2026, needs more optimization.
6 712 0.812903197014 Henry Cohn, 2026, needs more optimization.
6 713 0.813006451187 Henry Cohn, 2026, needs more optimization.
6 714 0.813147641450 Henry Cohn, 2026, needs more optimization.
6 715 0.813300021950 Henry Cohn, 2026, needs more optimization.
6 716 0.813304455482 Henry Cohn, 2026, needs more optimization.
6 717 0.813333681510 Henry Cohn, 2026, needs more optimization.
6 718 0.813476335360 Henry Cohn, 2026, needs more optimization.
6 719 0.813613497061 Henry Cohn, 2026, needs more optimization.
6 720 0.813657833920 Henry Cohn, 2026, needs more optimization.
6 721 0.813808670395 Henry Cohn, 2026, needs more optimization.
6 722 0.813939447363 Henry Cohn, 2026, needs more optimization.
6 723 0.813954548106 Henry Cohn, 2026, needs more optimization.
6 724 0.814054457105 Henry Cohn, 2026, needs more optimization.
6 725 0.814197622012 Henry Cohn, 2026, needs more optimization.
6 726 0.814314764597 Henry Cohn, 2026, needs more optimization.
6 727 0.814485491400 Henry Cohn, 2026, needs more optimization.
6 728 0.814493782586 Henry Cohn, 2026, needs more optimization.
6 729 0.814544056456 Henry Cohn, 2026, needs more optimization.
6 730 0.814683307387 Henry Cohn, 2026, needs more optimization.
6 731 0.814841433644 Henry Cohn, 2026, needs more optimization.
6 732 0.814846787035 Henry Cohn, 2026, needs more optimization.
6 733 0.814911279900 Henry Cohn, 2026, needs more optimization.
6 734 0.815064813430 Henry Cohn, 2026, needs more optimization.
6 735 0.815092864952 Henry Cohn, 2026, needs more optimization.
6 736 0.815200391041 Henry Cohn, 2026, needs more optimization.
6 737 0.815345836707 Henry Cohn, 2026, needs more optimization.
6 738 0.815534367177 Henry Cohn, 2026, needs more optimization.
6 739 0.815622378521 Henry Cohn, 2026, needs more optimization.
6 740 0.815757558957 Henry Cohn, 2026, needs more optimization.
6 741 0.815870256878 Henry Cohn, 2026, needs more optimization.
6 742 0.816007058739 Henry Cohn, 2026, needs more optimization.
6 743 0.816026819336 Henry Cohn, 2026, needs more optimization.
6 744 0.816066211430 Henry Cohn, 2026, needs more optimization.
6 745 0.816200150297 Henry Cohn, 2026, needs more optimization.
6 746 0.816297892618 Henry Cohn, 2026, needs more optimization.
6 747 0.816511764960 Henry Cohn, 2026, needs more optimization.
6 748 0.816582828001 Henry Cohn, 2026, needs more optimization.
6 749 0.816586844989 Henry Cohn, 2026, needs more optimization.
6 750 0.816802490454 Henry Cohn, 2026, needs more optimization.
6 751 0.816946411729 Henry Cohn, 2026, needs more optimization.
6 752 0.816968965204 Henry Cohn, 2026, needs more optimization.
6 753 0.817114361961 Henry Cohn, 2026, needs more optimization.
6 754 0.817235442460 Henry Cohn, 2026, needs more optimization.
6 755 0.817239161708 Henry Cohn, 2026, needs more optimization.
6 756 0.817374059799 Henry Cohn, 2026, needs more optimization.
6 757 0.817453307549 Henry Cohn, 2026, needs more optimization.
6 758 0.817487013584 Henry Cohn, 2026, needs more optimization.
6 759 0.817672634375 Henry Cohn, 2026, needs more optimization.
6 760 0.817687694650 Henry Cohn, 2026, needs more optimization.
6 761 0.817731640849 Henry Cohn, 2026, needs more optimization.
6 762 0.817911112809 Henry Cohn, 2026, needs more optimization.
6 763 0.818092790792 Henry Cohn, 2026, needs more optimization.
6 764 0.818166238423 Henry Cohn, 2026, needs more optimization.
6 765 0.818293383622 Henry Cohn, 2026, needs more optimization.
6 766 0.818338308200 Henry Cohn, 2026, needs more optimization.
6 767 0.818383112047 Henry Cohn, 2026, needs more optimization.
6 768 0.818551880520 Henry Cohn, 2026, needs more optimization.
6 769 0.818614454494 Henry Cohn, 2026, needs more optimization.
6 770 0.818796598006 Henry Cohn, 2026, needs more optimization.
6 771 0.818811503012 Henry Cohn, 2026, needs more optimization.
6 772 0.818895326430 Henry Cohn, 2026, needs more optimization.
6 773 0.818930884205 Henry Cohn, 2026, needs more optimization.
6 774 0.819065211553 Henry Cohn, 2026, needs more optimization.
6 775 0.819098459600 Henry Cohn, 2026, needs more optimization.
6 776 0.819215121970 Henry Cohn, 2026, needs more optimization.
6 777 0.819286037507 Henry Cohn, 2026, needs more optimization.
6 778 0.819460741072 Henry Cohn, 2026, needs more optimization.
6 779 0.819541387053 Henry Cohn, 2026, needs more optimization.
6 780 0.819640698237 Henry Cohn, 2026, needs more optimization.
6 781 0.819687914836 Henry Cohn, 2026, needs more optimization.
6 782 0.819716497603 Henry Cohn, 2026, needs more optimization.
6 783 0.819821698629 Henry Cohn, 2026, needs more optimization.
6 784 0.819931674385 Henry Cohn, 2026, needs more optimization.
6 785 0.819971456785 Henry Cohn, 2026, needs more optimization.
6 786 0.820156155004 Henry Cohn, 2026, needs more optimization.
6 787 0.820173498227 Henry Cohn, 2026, needs more optimization.
6 788 0.820325463318 Henry Cohn, 2026, needs more optimization.
6 789 0.820409705943 Henry Cohn, 2026, needs more optimization.
6 790 0.820514015199 Henry Cohn, 2026, needs more optimization.
6 791 0.820566765562 Henry Cohn, 2026, needs more optimization.
6 792 0.820774959252 Henry Cohn, 2026, needs more optimization.
6 793 0.820777160444 Henry Cohn, 2026, needs more optimization.
6 794 0.820977237420 Henry Cohn, 2026, needs more optimization.
6 795 0.820987145812 Henry Cohn, 2026, needs more optimization.
6 796 0.820994379692 Henry Cohn, 2026, needs more optimization.
6 797 0.821048819254 Henry Cohn, 2026, needs more optimization.
6 798 0.821150822242 Henry Cohn, 2026, needs more optimization.
6 799 0.821259776642 Henry Cohn, 2026, needs more optimization.
6 800 0.821415166639 Henry Cohn, 2026, needs more optimization.
6 801 0.821557829752 Henry Cohn, 2026, needs more optimization.
6 802 0.821660764809 Henry Cohn, 2026, needs more optimization.
6 803 0.821705117776 Henry Cohn, 2026, needs more optimization.
6 804 0.821734653150 Henry Cohn, 2026, needs more optimization.
6 805 0.821802008037 Henry Cohn, 2026, needs more optimization.
6 806 0.821881181819 Henry Cohn, 2026, needs more optimization.
6 807 0.821936251327 Henry Cohn, 2026, needs more optimization.
6 808 0.821972388030 Henry Cohn, 2026, needs more optimization.
6 809 0.822125464595 Henry Cohn, 2026, needs more optimization.
6 810 0.822289639842 Henry Cohn, 2026, needs more optimization.
6 811 0.822348381758 Henry Cohn, 2026, needs more optimization.
6 812 0.822486748226 Henry Cohn, 2026, needs more optimization.
6 813 0.822636217100 Henry Cohn, 2026, needs more optimization.
6 814 0.822684918522 Henry Cohn, 2026, needs more optimization.
6 815 0.822760205213 Henry Cohn, 2026, needs more optimization.
6 816 0.822790070726 Henry Cohn, 2026, needs more optimization.
6 817 0.822971798787 Henry Cohn, 2026, needs more optimization.
6 818 0.823013074141 Henry Cohn, 2026, needs more optimization.
6 819 0.823124103646 Henry Cohn, 2026, needs more optimization.
6 820 0.823158824943 Henry Cohn, 2026, needs more optimization.
6 821 0.823310923033 Henry Cohn, 2026, needs more optimization.
6 822 0.823425090375 Henry Cohn, 2026, needs more optimization.
6 823 0.823634587352 Henry Cohn, 2026, needs more optimization.
6 824 0.823638058822 Henry Cohn, 2026, needs more optimization.
6 825 0.823712356380 Henry Cohn, 2026, needs more optimization.
6 826 0.823851250302 Henry Cohn, 2026, needs more optimization.
6 827 0.823988829878 Henry Cohn, 2026, needs more optimization.
6 828 0.823990705173 Henry Cohn, 2026, needs more optimization.
6 829 0.824032466003 Henry Cohn, 2026, needs more optimization.
6 830 0.824122981659 Henry Cohn, 2026, needs more optimization.
6 831 0.824245078971 Henry Cohn, 2026, needs more optimization.
6 832 0.824306306328 Henry Cohn, 2026, needs more optimization.
6 833 0.824353370153 Henry Cohn, 2026, needs more optimization.
6 834 0.824455497835 Henry Cohn, 2026, needs more optimization.
6 835 0.824516925497 Henry Cohn, 2026, needs more optimization.
6 836 0.824526418973 Henry Cohn, 2026, needs more optimization.
6 837 0.824643413942 Henry Cohn, 2026, needs more optimization.
6 838 0.824725503845 Henry Cohn, 2026, needs more optimization.
6 839 0.824871498407 Henry Cohn, 2026, needs more optimization.
6 840 0.824901569224 Henry Cohn, 2026, needs more optimization.
6 841 0.824989468112 Henry Cohn, 2026, needs more optimization.
6 842 0.825097174283 Henry Cohn, 2026, needs more optimization.
6 843 0.825129362461 Henry Cohn, 2026, needs more optimization.
6 844 0.825310924324 Henry Cohn, 2026, needs more optimization.
6 845 0.825390412267 Henry Cohn, 2026, needs more optimization.
6 846 0.825550826577 Henry Cohn, 2026, needs more optimization.
6 847 0.825558662230 Henry Cohn, 2026, needs more optimization.
6 848 0.825579202869 Henry Cohn, 2026, needs more optimization.
6 849 0.825775520829 Henry Cohn, 2026, needs more optimization.
6 850 0.825856668415 Henry Cohn, 2026, needs more optimization.
6 851 0.825860667359 Henry Cohn, 2026, needs more optimization.
6 852 0.825999311876 Henry Cohn, 2026, needs more optimization.
6 853 0.826135640515 Henry Cohn, 2026, needs more optimization.
6 854 0.826225026093 Henry Cohn, 2026, needs more optimization.
6 855 0.826390192857 Henry Cohn, 2026, needs more optimization.
6 856 0.826404610519 Henry Cohn, 2026, needs more optimization.
6 857 0.826505417336 Henry Cohn, 2026, needs more optimization.
6 858 0.826623667311 Henry Cohn, 2026, needs more optimization.
6 859 0.826623667813 Henry Cohn, 2026, needs more optimization.
6 860 0.826623708685 Henry Cohn, 2026, needs more optimization.
6 861 0.826631854989 Henry Cohn, 2026, needs more optimization.
6 862 0.826709207836 Henry Cohn, 2026, needs more optimization.
6 863 0.826871651180 Henry Cohn, 2026, needs more optimization.
6 864 0.827005432265 Henry Cohn, 2026, needs more optimization.
6 865 0.827013665386 Henry Cohn, 2026, needs more optimization.
6 866 0.827183301889 Henry Cohn, 2026, needs more optimization.
6 867 0.827199664630 Henry Cohn, 2026, needs more optimization.
6 868 0.827212262869 Henry Cohn, 2026, needs more optimization.
6 869 0.827341766745 Henry Cohn, 2026, needs more optimization.
6 870 0.827544150881 Henry Cohn, 2026, needs more optimization.
6 871 0.827544277430 Henry Cohn, 2026, needs more optimization.
6 872 0.827545589800 Henry Cohn, 2026, needs more optimization.
6 873 0.827648852898 Henry Cohn, 2026, needs more optimization.
6 874 0.827652552079 Henry Cohn, 2026, needs more optimization.
6 875 0.827657187661 Henry Cohn, 2026, needs more optimization.
6 876 0.827667118499 Henry Cohn, 2026, needs more optimization.
6 877 0.827816443386 Henry Cohn, 2026, needs more optimization.
6 878 0.827859121165 Henry Cohn, 2026, needs more optimization.
6 879 0.827881515223 Henry Cohn, 2026, needs more optimization.
6 880 0.827914319052 Henry Cohn, 2026, needs more optimization.
6 881 0.827974312734 Henry Cohn, 2026, needs more optimization.
6 882 0.827998463981 Henry Cohn, 2026, needs more optimization.
6 883 0.828016952389 Henry Cohn, 2026, needs more optimization.
6 884 0.828082473813 Henry Cohn, 2026, needs more optimization.
6 885 0.828312089269 Henry Cohn, 2026, needs more optimization.
6 886 0.828351244842 Henry Cohn, 2026, needs more optimization.
6 887 0.828416636124 Henry Cohn, 2026, needs more optimization.
6 888 0.828455578537 Henry Cohn, 2026, needs more optimization.
6 889 0.828554317492 Henry Cohn, 2026, needs more optimization.
6 890 0.828586243803 Henry Cohn, 2026, needs more optimization.
6 891 0.828610170696 Henry Cohn, 2026, needs more optimization.
6 892 0.828746384478 Henry Cohn, 2026, needs more optimization.
6 893 0.828777224857 Henry Cohn, 2026, needs more optimization.
6 894 0.828848910866 Henry Cohn, 2026, needs more optimization.
6 895 0.828850211057 Henry Cohn, 2026, needs more optimization.
6 896 0.828933318388 Henry Cohn, 2026, needs more optimization.
6 897 0.828967185340 Henry Cohn, 2026, needs more optimization.
6 898 0.829076533996 Henry Cohn, 2026, needs more optimization.
6 899 0.829083397336 Henry Cohn, 2026, needs more optimization.
6 900 0.829104123567 Henry Cohn, 2026, needs more optimization.
6 901 0.829303804368 Henry Cohn, 2026, needs more optimization.
6 902 0.829320434404 Henry Cohn, 2026, needs more optimization.
6 903 0.829430625324 Henry Cohn, 2026, needs more optimization.
6 904 0.829515670034 Henry Cohn, 2026, needs more optimization.
6 905 0.829603744978 Henry Cohn, 2026, needs more optimization.
6 906 0.829652152803 Henry Cohn, 2026, needs more optimization.
6 908 0.829782218118 Henry Cohn, 2026, needs more optimization.
6 909 0.829895522811 Henry Cohn, 2026, needs more optimization.
6 910 0.829939863494 Henry Cohn, 2026, needs more optimization.
6 911 0.829947229144 Henry Cohn, 2026, needs more optimization.
6 912 0.830008436606 Henry Cohn, 2026, needs more optimization.
6 913 0.830068369100 Henry Cohn, 2026, needs more optimization.
6 914 0.830151238732 Henry Cohn, 2026, needs more optimization.
6 916 0.830450005187 Henry Cohn, 2026, needs more optimization.
6 917 0.830454212255 Henry Cohn, 2026, needs more optimization.
6 918 0.830462477633 Henry Cohn, 2026, needs more optimization.
6 919 0.830487391376 Henry Cohn, 2026, needs more optimization.
6 920 0.830600918728 Henry Cohn, 2026, needs more optimization.
6 921 0.830622511213 Henry Cohn, 2026, needs more optimization.
6 922 0.830625277828 Henry Cohn, 2026, needs more optimization.
6 923 0.830742371685 Henry Cohn, 2026, needs more optimization.
6 924 0.830748501535 Henry Cohn, 2026, needs more optimization.
6 925 0.830773344016 Henry Cohn, 2026, needs more optimization.
6 926 0.830844924772 Henry Cohn, 2026, needs more optimization.
6 927 0.831055806032 Henry Cohn, 2026, needs more optimization.
6 928 0.831081774451 Henry Cohn, 2026, needs more optimization.
6 929 0.831184126814 Henry Cohn, 2026, needs more optimization.
6 930 0.831220209696 Henry Cohn, 2026, needs more optimization.
6 931 0.831282139113 Henry Cohn, 2026, needs more optimization.
6 932 0.831282179952 Henry Cohn, 2026, needs more optimization.
6 933 0.831290748381 Henry Cohn, 2026, needs more optimization.
6 934 0.831292738611 Henry Cohn, 2026, needs more optimization.
6 935 0.831325462240 Henry Cohn, 2026, needs more optimization.
6 936 0.831343173816 Henry Cohn, 2026, needs more optimization.
6 937 0.831404499463 Henry Cohn, 2026, needs more optimization.
6 938 0.831435689497 Henry Cohn, 2026, needs more optimization.
6 939 0.831688923402 Henry Cohn, 2026, needs more optimization.
6 940 0.831692924879 Henry Cohn, 2026, needs more optimization.
6 941 0.831695914253 Henry Cohn, 2026, needs more optimization.
6 942 0.831750441961 Henry Cohn, 2026, needs more optimization.
6 943 0.831774868371 Henry Cohn, 2026, needs more optimization.
6 945 0.831884746005 Henry Cohn, 2026, needs more optimization.
6 946 0.831907142464 Henry Cohn, 2026, needs more optimization.
6 947 0.831954876896 Henry Cohn, 2026, needs more optimization.
6 948 0.832011511133 Henry Cohn, 2026, needs more optimization.
6 949 0.832044616629 Henry Cohn, 2026, needs more optimization.
6 950 0.832054481110 Henry Cohn, 2026, needs more optimization.
6 951 0.832158442628 Henry Cohn, 2026, needs more optimization.
6 952 0.832192818202 Henry Cohn, 2026, needs more optimization.
6 953 0.832204860726 Henry Cohn, 2026, needs more optimization.
6 954 0.832224858863 Henry Cohn, 2026, needs more optimization.
6 955 0.832297710802 Henry Cohn, 2026, needs more optimization.
6 956 0.832309609445 Henry Cohn, 2026, needs more optimization.
6 957 0.832309818213 Henry Cohn, 2026, needs more optimization.
6 958 0.832324022694 Henry Cohn, 2026, needs more optimization.
6 959 0.832421425792 Henry Cohn, 2026, needs more optimization.
6 960 0.832465471241 Henry Cohn, 2026, needs more optimization.
6 961 0.832483924494 Henry Cohn, 2026, needs more optimization.
6 962 0.832513439778 Henry Cohn, 2026, needs more optimization.
6 963 0.832563200828 Henry Cohn, 2026, needs more optimization.
6 964 0.832623626194 Henry Cohn, 2026, needs more optimization.
6 965 0.832696287678 Henry Cohn, 2026, needs more optimization.
6 966 0.832724251265 Henry Cohn, 2026, needs more optimization.
6 967 0.832755614485 Henry Cohn, 2026, needs more optimization.
6 968 0.832820079674 Henry Cohn, 2026, needs more optimization.
6 969 0.832835294199 Henry Cohn, 2026, needs more optimization.
6 970 0.832865935154 Henry Cohn, 2026, needs more optimization.
6 971 0.832878133382 Henry Cohn, 2026, needs more optimization.
6 973 0.832885494479 Henry Cohn, 2026, needs more optimization.
6 974 0.832900829354 Henry Cohn, 2026, needs more optimization.
6 975 0.832990278007 Henry Cohn, 2026, needs more optimization.
6 976 0.833013698817 Henry Cohn, 2026, needs more optimization.
6 990 0.833333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6⁢x−5
6 1002 0.833333333334 Henry Cohn, 2026.
6⁢x−5
6 1003 0.835109071652 Henry Cohn, 2026, needs more optimization.
6 1004 0.836164654932 Henry Cohn, 2026, needs more optimization.
6 1005 0.836786379559 Henry Cohn, 2026, needs more optimization.
6 1006 0.837252363644 Henry Cohn, 2026, needs more optimization.
6 1007 0.837322382573 Henry Cohn, 2026, needs more optimization.
6 1008 0.837375748468 Henry Cohn, 2026, needs more optimization.
6 1009 0.837498850984 Henry Cohn, 2026, needs more optimization.
6 1010 0.837618353371 Henry Cohn, 2026, needs more optimization.
6 1011 0.837637083673 Henry Cohn, 2026, needs more optimization.
6 1012 0.837643480085 Henry Cohn, 2026, needs more optimization.
6 1013 0.837783947073 Henry Cohn, 2026, needs more optimization.
6 1014 0.837795123965 Henry Cohn, 2026, needs more optimization.
6 1015 0.837903779721 Henry Cohn, 2026, needs more optimization.
6 1016 0.837919462497 Henry Cohn, 2026, needs more optimization.
6 1017 0.837931127725 Henry Cohn, 2026, needs more optimization.
6 1018 0.838084091189 Henry Cohn, 2026, needs more optimization.
6 1019 0.838121459282 Henry Cohn, 2026, needs more optimization.
6 1020 0.838321760565 Henry Cohn, 2026, needs more optimization.
6 1021 0.838333043621 Henry Cohn, 2026, needs more optimization.
6 1022 0.838387533518 Henry Cohn, 2026, needs more optimization.
6 1023 0.838390421149 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
6 1024 0.838615211588 Henry Cohn, 2026, needs more optimization.
7 15 0.098701776273 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
175⁢x3−49⁢x2−7⁢x+1
7 16 0.113320879601 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
7 17 0.124841583816 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
7 18 0.126131983623 P. G. Adams, A numerical approach to Tamme's problem in Euclidean n-space, Master of Science thesis, Oregon State University, 1997, https://hdl.handle.net/1957/33911.
47⁢x2+2⁢x−1
7 19 0.156597385418 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
1280⁢x6−352⁢x4−48⁢x3+37⁢x2+3⁢x−1
7 20 0.169520847199 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x2+2⁢x−1
7 21 0.181523960801 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 22 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 23 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 24 0.182743997632 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
19⁢x2+2⁢x−1
7 25 0.214737233855 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
31⁢x2−2⁢x−1
7 26 0.231331430372 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 27 0.240549382010 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 28 0.247356651208 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 29 0.248893779344 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 30 0.249468282003 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 31 0.254502767515 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 32 0.265595699432 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
7 33 0.270023386002 Henry Cohn, 2024.
7 34 0.277696496789 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 35 0.289773019868 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
7 36 0.299959896814 Henry Cohn, 2023.
7 37 0.310451288111 Henry Cohn, 2026.
7 39 0.316279494687 Henry Cohn, 2023.
71⁢x2+6⁢x−9
7 40 0.323843153340 Henry Cohn, 2023.
7 41 0.325408592469 Henry Cohn, 2023.
32⁢x4+40⁢x3−23⁢x2−4⁢x+2
7 42 0.329083455200 Henry Cohn, 2025.
7 43 0.329665776133 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
7 44 0.332131779753 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
7 45 0.333226297127 Henry Cohn, 2026.
7 46 0.333312302683 Henry Cohn, 2026.
7 47 0.333332883018 Henry Cohn, 2026.
7 56* 0.333333333334 T. Gosset, On the regular and semi-regular figures in space of n dimensions, Messenger Math. 29 (1900), 43–48; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
3⁢x−1
7 57 0.389612708410 Henry Cohn, 2025.
7 58 0.393749423280 Henry Cohn, 2023.
7 59 0.403217495108 Henry Cohn, 2025.
7 60 0.407983464085 Henry Cohn, 2025.
7 61 0.412356098716 Henry Cohn, 2024.
7 62 0.414165742036 Henry Cohn, 2026.
7 63 0.415390831033 Henry Cohn, 2025.
7 64 0.420197073744 Henry Cohn, 2025.
7 67 0.421258543571 Henry Cohn, 2024.
622⁢x3−771⁢x2+288⁢x−31
7 68 0.427637413233 Henry Cohn, 2026.
7 69 0.428316243154 Henry Cohn, 2026.
7 70 0.428552367482 Henry Cohn, 2026.
7 78 0.428571428572 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
7 79 0.452754163206 Henry Cohn, 2026.
7 80 0.453887992064 Henry Cohn, 2024.
7 81 0.458141121605 Henry Cohn, 2026.
7 82 0.459673068887 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 83 0.460413485151 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 84 0.464981341724 Henry Cohn, 2026, needs more optimization.
7 86 0.466580867327 Henry Cohn, 2025, needs more optimization.
7 87 0.469578821552 Henry Cohn, 2024.
7 88 0.471422440239 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 89 0.474245162133 Henry Cohn, 2026, needs more optimization.
7 90 0.475294477919 Henry Cohn, 2024.
7 91 0.477365257014 Henry Cohn, 2026.
7 92 0.480306853225 Henry Cohn, 2025.
7 93 0.481807408321 Henry Cohn, 2026.
7 95 0.482130625709 Henry Cohn, 2026, needs more optimization.
7 96 0.482651330945 Henry Cohn, 2026.
7 97 0.486842071201 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 98 0.489141129031 Henry Cohn, 2026.
7 99 0.493009411323 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 100 0.494295595722 Henry Cohn, 2026, needs more optimization.
7 101 0.495171315420 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 102 0.496162296397 Henry Cohn, 2026.
7 103 0.496772778705 Henry Cohn, 2026.
7 104 0.497383950140 Henry Cohn, 2026, needs more optimization.
7 105 0.497977782378 Henry Cohn, 2026, needs more optimization.
7 106 0.498675447305 Henry Cohn, 2026.
7 107 0.499010255474 Henry Cohn, 2026, needs more optimization.
7 108 0.499442704928 Henry Cohn, 2026, needs more optimization.
7 109 0.499927763140 Henry Cohn, 2026, needs more optimization.
7 110 0.499969610867 Henry Cohn, 2026, needs more optimization.
7 111 0.499998586781 Henry Cohn, 2026, needs more optimization.
7 112 0.499999829417 Henry Cohn, 2026, needs more optimization.
7 126 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; J. Leech, Six and seven dimensional non-lattice sphere packings, Canad. Math. Bull. 12 (1969), 151–155, doi:10.4153/CMB-1969-014-1; J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discrete Comput. Geom. 13 (1995), 383–403, doi:10.1007/BF02574051; H. Cohn, Y. Jiao, A. Kumar, and S. Torquato, Rigidity of spherical codes, Geom. Topol. 15 (2011), 2235–2273, doi:10.2140/gt.2011.15.2235, arXiv:1102.5060.
2⁢x−1
7 127 0.509952460664 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 128 0.513834831907 Henry Cohn, 2026.
7 129 0.518758185595 Henry Cohn, 2026.
7 130 0.518780653650 Henry Cohn, 2026, needs more optimization.
7 132 0.519150244778 Henry Cohn, 2026, needs more optimization.
7 133 0.519150244844 Henry Cohn, 2026, needs more optimization.
7 134 0.519150248699 Henry Cohn, 2026, needs more optimization.
7 135 0.519150255859 Henry Cohn, 2026, needs more optimization.
7 136 0.519153914324 Henry Cohn, 2026, needs more optimization.
7 137 0.519751518195 Henry Cohn, 2024.
7 138 0.527218738805 Henry Cohn, 2025.
7 139 0.530442893410 Henry Cohn, 2026, needs more optimization.
7 143 0.531592013892 Henry Cohn, 2026, needs more optimization.
7 144 0.531632269397 Henry Cohn, 2026, needs more optimization.
7 145 0.532532286627 Henry Cohn, 2026, needs more optimization.
7 146 0.532826481234 Henry Cohn, 2026, needs more optimization.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.533995828316 Henry Cohn, 2026.
7 149 0.545945792862 Henry Cohn, 2026, needs more optimization.
7 150 0.545968825950 Henry Cohn, 2026, needs more optimization.
7 151 0.545970677690 Henry Cohn, 2026, needs more optimization.
7 152 0.546227195436 Henry Cohn, 2026, needs more optimization.
7 153 0.546231398845 Henry Cohn, 2026, needs more optimization.
7 154 0.546280405029 Henry Cohn, 2026, needs more optimization.
7 155 0.546473188925 Henry Cohn, 2026, needs more optimization.
7 156 0.552232058090 Henry Cohn, 2026, needs more optimization.
7 157 0.557005224138 Henry Cohn, 2026, needs more optimization.
7 158 0.558176627047 Henry Cohn, 2026, needs more optimization.
7 159 0.559254865728 Henry Cohn, 2026, needs more optimization.
7 160 0.559629486619 Henry Cohn, 2026, needs more optimization.
7 161 0.559629486792 Henry Cohn, 2026, needs more optimization.
7 162 0.559630049114 Henry Cohn, 2026, needs more optimization.
7 165 0.561660700022 Henry Cohn, 2026, needs more optimization.
7 168 0.561688600449 Henry Cohn, 2026, needs more optimization.
7 169 0.562559500091 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 170 0.563591812721 Henry Cohn, 2026, needs more optimization.
7 171 0.568957906360 Henry Cohn, 2026, needs more optimization.
7 172 0.569967211762 Henry Cohn, 2026, needs more optimization.
7 173 0.569967214515 Henry Cohn, 2026, needs more optimization.
7 174 0.569967814452 Henry Cohn, 2026, needs more optimization.
7 175 0.569967819241 Henry Cohn, 2026, needs more optimization.
7 176 0.570443304627 Henry Cohn, 2026, needs more optimization.
7 177 0.570453557788 Henry Cohn, 2026, needs more optimization.
7 178 0.570455565027 Henry Cohn, 2026, needs more optimization.
7 179 0.570548589247 Henry Cohn, 2026, needs more optimization.
7 180 0.570548702282 Henry Cohn, 2026, needs more optimization.
7 181 0.573146386876 Henry Cohn, 2026, needs more optimization.
7 182 0.577350269190 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), 257–283, https://projecteuclid.org/euclid.em/1259158465.
3⁢x2−1
7 183 0.586838784263 Henry Cohn, 2026, needs more optimization.
7 184 0.589761553072 Henry Cohn, 2026, needs more optimization.
7 200 0.590112298788 Henry Cohn, 2026.
19⁢x3−9⁢x2−3⁢x+1
7 201 0.594922872974 Henry Cohn, 2026, needs more optimization.
7 202 0.598299387059 Henry Cohn, 2026, needs more optimization.
7 203 0.600502824165 Henry Cohn, 2026, needs more optimization.
7 204 0.601296346692 Henry Cohn, 2026, needs more optimization.
7 205 0.602637728554 Henry Cohn, 2026, needs more optimization.
7 206 0.603221068362 Henry Cohn, 2026, needs more optimization.
7 207 0.603909347266 Henry Cohn, 2026, needs more optimization.
7 208 0.606748582761 Henry Cohn, 2026, needs more optimization.
7 209 0.608544791844 Henry Cohn, 2026, needs more optimization.
7 210 0.610197900880 Henry Cohn, 2026, needs more optimization.
7 211 0.611215932753 Henry Cohn, 2026, needs more optimization.
7 212 0.612379041439 Henry Cohn, 2026, needs more optimization.
7 213 0.612915896753 Henry Cohn, 2026, needs more optimization.
7 214 0.613776585849 Henry Cohn, 2026, needs more optimization.
7 215 0.614860221404 Henry Cohn, 2026, needs more optimization.
7 216 0.615210533902 Henry Cohn, 2026, needs more optimization.
7 217 0.616414679122 Henry Cohn, 2026, needs more optimization.
7 218 0.617875237286 Henry Cohn, 2026, needs more optimization.
7 220 0.618749727687 Henry Cohn, 2026, needs more optimization.
7 221 0.619555695066 Henry Cohn, 2026, needs more optimization.
7 222 0.619875243136 Henry Cohn, 2026, needs more optimization.
7 223 0.620004427096 Henry Cohn, 2026, needs more optimization.
7 224 0.623014773167 Henry Cohn, 2026, needs more optimization.
7 225 0.623054540144 Henry Cohn, 2026, needs more optimization.
7 226 0.623137560942 Henry Cohn, 2026, needs more optimization.
7 227 0.625163018182 Henry Cohn, 2026, needs more optimization.
7 228 0.625191079188 Henry Cohn, 2026, needs more optimization.
7 229 0.625797283052 Henry Cohn, 2026, needs more optimization.
7 230 0.625971610636 Henry Cohn, 2026, needs more optimization.
7 231 0.626275199300 Henry Cohn, 2026, needs more optimization.
7 232 0.627133596723 Henry Cohn, 2026, needs more optimization.
7 233 0.627539963323 Henry Cohn, 2026, needs more optimization.
7 234 0.627591703677 Henry Cohn, 2026, needs more optimization.
7 235 0.627640180225 Henry Cohn, 2026, needs more optimization.
7 236 0.628401621472 Henry Cohn, 2026, needs more optimization.
7 237 0.629685567068 Henry Cohn, 2026, needs more optimization.
7 238 0.629695168638 Henry Cohn, 2026, needs more optimization.
7 239 0.630338109947 Henry Cohn, 2026, needs more optimization.
7 240 0.630932475579 Henry Cohn, 2026, needs more optimization.
7 241 0.631028163030 Henry Cohn, 2026, needs more optimization.
7 242 0.633309641395 Henry Cohn, 2026, needs more optimization.
7 243 0.633420729247 Henry Cohn, 2026, needs more optimization.
7 244 0.633929111924 Henry Cohn, 2026, needs more optimization.
7 245 0.634442988352 Henry Cohn, 2026, needs more optimization.
7 246 0.634566509293 Henry Cohn, 2026, needs more optimization.
7 247 0.634826322762 Henry Cohn, 2026, needs more optimization.
7 248 0.634856486377 Henry Cohn, 2026, needs more optimization.
7 249 0.636485607717 Henry Cohn, 2026, needs more optimization.
7 250 0.636567595509 Henry Cohn, 2026, needs more optimization.
7 251 0.636625390855 Henry Cohn, 2026, needs more optimization.
7 252 0.637091811866 Henry Cohn, 2026, needs more optimization.
7 253 0.638298683834 Henry Cohn, 2026, needs more optimization.
7 254 0.638939972430 Henry Cohn, 2026, needs more optimization.
7 255 0.638943990693 Henry Cohn, 2026, needs more optimization.
7 256 0.639080182636 Henry Cohn, 2026, needs more optimization.
7 257 0.639718828012 Henry Cohn, 2026, needs more optimization.
7 258 0.640780598619 Henry Cohn, 2026, needs more optimization.
7 259 0.641098349608 Henry Cohn, 2026, needs more optimization.
7 260 0.641255380879 Henry Cohn, 2026, needs more optimization.
7 261 0.641290774896 Henry Cohn, 2026, needs more optimization.
7 262 0.642501830207 Henry Cohn, 2026, needs more optimization.
7 263 0.644822286538 Henry Cohn, 2026, needs more optimization.
7 264 0.645646990041 Henry Cohn, 2026, needs more optimization.
7 265 0.645810545335 Henry Cohn, 2026, needs more optimization.
7 266 0.646303209812 Henry Cohn, 2026, needs more optimization.
7 267 0.646964941820 Henry Cohn, 2026, needs more optimization.
7 268 0.647232419036 Henry Cohn, 2026, needs more optimization.
7 269 0.647776769561 Henry Cohn, 2026, needs more optimization.
7 270 0.648431175033 Henry Cohn, 2026, needs more optimization.
7 271 0.648619125096 Henry Cohn, 2026, needs more optimization.
7 272 0.649000173028 Henry Cohn, 2026, needs more optimization.
7 273 0.649490684887 Henry Cohn, 2026, needs more optimization.
7 274 0.649774414375 Henry Cohn, 2026, needs more optimization.
7 275 0.650329853623 Henry Cohn, 2026, needs more optimization.
7 276 0.650555041085 Henry Cohn, 2026, needs more optimization.
7 277 0.651291948177 Henry Cohn, 2026, needs more optimization.
7 278 0.651802413344 Henry Cohn, 2026, needs more optimization.
7 279 0.652265811204 Henry Cohn, 2026, needs more optimization.
7 280 0.652736823889 Henry Cohn, 2026, needs more optimization.
7 281 0.653334330389 Henry Cohn, 2026, needs more optimization.
7 282 0.653583660374 Henry Cohn, 2026, needs more optimization.
7 283 0.654014056743 Henry Cohn, 2026, needs more optimization.
7 284 0.654523380568 Henry Cohn, 2026, needs more optimization.
7 285 0.655130546555 Henry Cohn, 2026, needs more optimization.
7 286 0.655476610146 Henry Cohn, 2026, needs more optimization.
7 287 0.655809014545 Henry Cohn, 2026, needs more optimization.
7 288 0.656403351315 Henry Cohn, 2026, needs more optimization.
7 289 0.656861609900 Henry Cohn, 2026, needs more optimization.
7 290 0.657189748108 Henry Cohn, 2026, needs more optimization.
7 291 0.657460114191 Henry Cohn, 2026, needs more optimization.
7 292 0.658026383143 Henry Cohn, 2026, needs more optimization.
7 293 0.658403205910 Henry Cohn, 2026, needs more optimization.
7 294 0.658940681401 Henry Cohn, 2026, needs more optimization.
7 295 0.659107624970 Henry Cohn, 2026, needs more optimization.
7 296 0.659590713857 Henry Cohn, 2026, needs more optimization.
7 297 0.660007998737 Henry Cohn, 2026, needs more optimization.
7 298 0.660379816221 Henry Cohn, 2026, needs more optimization.
7 299 0.660982403764 Henry Cohn, 2026, needs more optimization.
7 300 0.661146168560 Henry Cohn, 2026, needs more optimization.
7 301 0.661602477909 Henry Cohn, 2026, needs more optimization.
7 302 0.661953970037 Henry Cohn, 2026, needs more optimization.
7 303 0.662611760783 Henry Cohn, 2026, needs more optimization.
7 304 0.662774323890 Henry Cohn, 2026, needs more optimization.
7 306 0.662774567933 Henry Cohn, 2026, needs more optimization.
7 307 0.662776758521 Henry Cohn, 2026, needs more optimization.
7 308 0.662829303983 Henry Cohn, 2026, needs more optimization.
7 309 0.662905611337 Henry Cohn, 2026, needs more optimization.
7 310 0.662945084336 Henry Cohn, 2026, needs more optimization.
7 311 0.663635360280 Henry Cohn, 2026, needs more optimization.
7 312 0.663635872479 Henry Cohn, 2026, needs more optimization.
7 313 0.663636365400 Henry Cohn, 2026, needs more optimization.
7 314 0.663636840465 Henry Cohn, 2026, needs more optimization.
7 315 0.663637293722 Henry Cohn, 2026, needs more optimization.
7 316 0.663637749880 Henry Cohn, 2026, needs more optimization.
7 317 0.663638072456 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 318 0.663870889175 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 319 0.664473033765 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 320 0.664759032651 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 322 0.665066262862 Henry Cohn, 2026, needs more optimization.
7 323 0.665323708305 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 324 0.665597793364 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 325 0.665932360138 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 326 0.666159688581 Henry Cohn, 2026, needs more optimization.
7 327 0.666159732535 Henry Cohn, 2026, needs more optimization.
7 328 0.666159771975 Henry Cohn, 2026, needs more optimization.
7 329 0.666159812884 Henry Cohn, 2026, needs more optimization.
7 330 0.666159852155 Henry Cohn, 2026, needs more optimization.
7 331 0.666159884326 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 332 0.666179578706 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 333 0.666200026936 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 334 0.666330547244 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 335 0.666582817716 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 358 0.666666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−2
7 359 0.668524326903 Henry Cohn, 2026, needs more optimization.
7 360 0.669362934454 Henry Cohn, 2026, needs more optimization.
7 361 0.669633423534 Henry Cohn, 2026, needs more optimization.
7 362 0.670192266698 Henry Cohn, 2026, needs more optimization.
7 363 0.670750854808 Henry Cohn, 2026, needs more optimization.
7 364 0.671294151256 Henry Cohn, 2026, needs more optimization.
7 365 0.671887914819 Henry Cohn, 2026, needs more optimization.
7 366 0.671934467982 Henry Cohn, 2026, needs more optimization.
7 367 0.672593553132 Henry Cohn, 2026, needs more optimization.
7 368 0.673276431317 Henry Cohn, 2026, needs more optimization.
7 369 0.673356851237 Henry Cohn, 2026, needs more optimization.
7 370 0.673506275826 Henry Cohn, 2026, needs more optimization.
7 371 0.673673235376 Henry Cohn, 2026, needs more optimization.
7 372 0.673937352186 Henry Cohn, 2026, needs more optimization.
7 373 0.675200736321 Henry Cohn, 2026, needs more optimization.
7 374 0.675806886522 Henry Cohn, 2026, needs more optimization.
7 375 0.676163660398 Henry Cohn, 2026, needs more optimization.
7 376 0.676760592707 Henry Cohn, 2026, needs more optimization.
7 377 0.676809608599 Henry Cohn, 2026, needs more optimization.
7 378 0.676962650280 Henry Cohn, 2026, needs more optimization.
7 379 0.676977902382 Henry Cohn, 2026, needs more optimization.
7 380 0.676998252678 Henry Cohn, 2026, needs more optimization.
7 381 0.677298292136 Henry Cohn, 2026, needs more optimization.
7 382 0.677313961837 Henry Cohn, 2026, needs more optimization.
7 383 0.677793975325 Henry Cohn, 2026, needs more optimization.
7 384 0.678284117476 Henry Cohn, 2026, needs more optimization.
7 385 0.678930053296 Henry Cohn, 2026, needs more optimization.
7 386 0.678973104605 Henry Cohn, 2026, needs more optimization.
7 387 0.679089823851 Henry Cohn, 2026, needs more optimization.
7 388 0.679579343842 Henry Cohn, 2026, needs more optimization.
7 389 0.679582785099 Henry Cohn, 2026, needs more optimization.
7 390 0.679898697993 Henry Cohn, 2026, needs more optimization.
7 391 0.680012075497 Henry Cohn, 2026, needs more optimization.
7 392 0.680112251936 Henry Cohn, 2026, needs more optimization.
7 393 0.680133869715 Henry Cohn, 2026, needs more optimization.
7 394 0.680145976056 Henry Cohn, 2026, needs more optimization.
7 395 0.680181943762 Henry Cohn, 2026, needs more optimization.
7 396 0.680430985281 Henry Cohn, 2026, needs more optimization.
7 397 0.680478074788 Henry Cohn, 2026, needs more optimization.
7 398 0.680540592144 Henry Cohn, 2026, needs more optimization.
7 399 0.681184384065 Henry Cohn, 2026, needs more optimization.
7 400 0.681382835472 Henry Cohn, 2026, needs more optimization.
7 401 0.681531294911 Henry Cohn, 2026, needs more optimization.
7 402 0.681925709228 Henry Cohn, 2026, needs more optimization.
7 403 0.681942722757 Henry Cohn, 2026, needs more optimization.
7 404 0.681944576172 Henry Cohn, 2026, needs more optimization.
7 405 0.683014355076 Henry Cohn, 2026, needs more optimization.
7 406 0.683122911717 Henry Cohn, 2026, needs more optimization.
7 407 0.683131889767 Henry Cohn, 2026, needs more optimization.
7 408 0.683324558743 Henry Cohn, 2026, needs more optimization.
7 409 0.683522563849 Henry Cohn, 2026, needs more optimization.
7 410 0.683564453737 Henry Cohn, 2026, needs more optimization.
7 411 0.683850126867 Henry Cohn, 2026, needs more optimization.
7 412 0.683974398230 Henry Cohn, 2026, needs more optimization.
7 413 0.684194302985 Henry Cohn, 2026, needs more optimization.
7 414 0.684215379852 Henry Cohn, 2026, needs more optimization.
7 415 0.684386975602 Henry Cohn, 2026, needs more optimization.
7 416 0.684415644831 Henry Cohn, 2026, needs more optimization.
7 417 0.684607910519 Henry Cohn, 2026, needs more optimization.
7 418 0.685261415247 Henry Cohn, 2026, needs more optimization.
7 419 0.686233220403 Henry Cohn, 2026, needs more optimization.
7 420 0.686400987840 Henry Cohn, 2026, needs more optimization.
7 421 0.686718066076 Henry Cohn, 2026, needs more optimization.
7 422 0.686962430420 Henry Cohn, 2026, needs more optimization.
7 423 0.687037857651 Henry Cohn, 2026, needs more optimization.
7 424 0.687898696693 Henry Cohn, 2026, needs more optimization.
7 425 0.688098483065 Henry Cohn, 2026, needs more optimization.
7 426 0.688867189582 Henry Cohn, 2026, needs more optimization.
7 427 0.690228210548 Henry Cohn, 2026, needs more optimization.
7 428 0.690512498853 Henry Cohn, 2026, needs more optimization.
7 429 0.691157592897 Henry Cohn, 2026, needs more optimization.
7 430 0.691234875468 Henry Cohn, 2026, needs more optimization.
7 431 0.691622823482 Henry Cohn, 2026, needs more optimization.
7 432 0.692316013565 Henry Cohn, 2026, needs more optimization.
7 433 0.692785364192 Henry Cohn, 2026, needs more optimization.
7 434 0.693144095516 Henry Cohn, 2026, needs more optimization.
7 435 0.693317159696 Henry Cohn, 2026, needs more optimization.
7 436 0.693606068806 Henry Cohn, 2026, needs more optimization.
7 437 0.693780989751 Henry Cohn, 2026, needs more optimization.
7 438 0.694193869810 Henry Cohn, 2026, needs more optimization.
7 439 0.694708629234 Henry Cohn, 2026, needs more optimization.
7 440 0.694966341333 Henry Cohn, 2026, needs more optimization.
7 441 0.695497445485 Henry Cohn, 2026, needs more optimization.
7 442 0.695855269381 Henry Cohn, 2026, needs more optimization.
7 443 0.696444008646 Henry Cohn, 2026, needs more optimization.
7 444 0.696495505221 Henry Cohn, 2026, needs more optimization.
7 445 0.696698695314 Henry Cohn, 2026, needs more optimization.
7 446 0.697147792035 Henry Cohn, 2026, needs more optimization.
7 447 0.697640162255 Henry Cohn, 2026, needs more optimization.
7 448 0.697706430488 Henry Cohn, 2026, needs more optimization.
7 449 0.698098872397 Henry Cohn, 2026, needs more optimization.
7 450 0.698801985717 Henry Cohn, 2026, needs more optimization.
7 451 0.699251286895 Henry Cohn, 2026, needs more optimization.
7 452 0.699351971029 Henry Cohn, 2026, needs more optimization.
7 453 0.699857211535 Henry Cohn, 2026, needs more optimization.
7 454 0.700493465313 Henry Cohn, 2026, needs more optimization.
7 455 0.700558461835 Henry Cohn, 2026, needs more optimization.
7 456 0.700652153915 Henry Cohn, 2026, needs more optimization.
7 457 0.700916626194 Henry Cohn, 2026, needs more optimization.
7 458 0.701284612183 Henry Cohn, 2026, needs more optimization.
7 459 0.701931689363 Henry Cohn, 2026, needs more optimization.
7 460 0.701984570679 Henry Cohn, 2026, needs more optimization.
7 461 0.702808776088 Henry Cohn, 2026, needs more optimization.
7 462 0.703366256347 Henry Cohn, 2026, needs more optimization.
7 463 0.703465407761 Henry Cohn, 2026, needs more optimization.
7 464 0.703890297078 Henry Cohn, 2026, needs more optimization.
7 465 0.704390331801 Henry Cohn, 2026, needs more optimization.
7 466 0.705191396460 Henry Cohn, 2026, needs more optimization.
7 467 0.705384604671 Henry Cohn, 2026, needs more optimization.
7 468 0.705696405538 Henry Cohn, 2026, needs more optimization.
7 469 0.705782722313 Henry Cohn, 2026, needs more optimization.
7 470 0.705921295367 Henry Cohn, 2026, needs more optimization.
7 471 0.706004701882 Henry Cohn, 2026, needs more optimization.
7 472 0.706072943599 Henry Cohn, 2026, needs more optimization.
7 473 0.706244259870 Henry Cohn, 2026, needs more optimization.
7 474 0.706519616782 Henry Cohn, 2026, needs more optimization.
7 475 0.706528776780 Henry Cohn, 2026, needs more optimization.
7 476 0.706666821255 Henry Cohn, 2026, needs more optimization.
7 477 0.706795715477 Henry Cohn, 2026, needs more optimization.
7 478 0.706880230853 Henry Cohn, 2026, needs more optimization.
7 479 0.706936423153 Henry Cohn, 2026, needs more optimization.
7 480 0.707050865122 Henry Cohn, 2026, needs more optimization.
7 481 0.707570435981 Henry Cohn, 2026, needs more optimization.
7 482 0.707629643609 Henry Cohn, 2026, needs more optimization.
7 483 0.707634289530 Henry Cohn, 2026, needs more optimization.
7 484 0.707637005315 Henry Cohn, 2026, needs more optimization.
7 485 0.707661866907 Henry Cohn, 2026, needs more optimization.
7 486 0.707715887074 Henry Cohn, 2026, needs more optimization.
7 487 0.707747171821 Henry Cohn, 2026, needs more optimization.
7 488 0.707829956962 Henry Cohn, 2026, needs more optimization.
7 489 0.707993718920 Henry Cohn, 2026, needs more optimization.
7 490 0.708046573854 Henry Cohn, 2026, needs more optimization.
7 491 0.708186322374 Henry Cohn, 2026, needs more optimization.
7 492 0.708188834945 Henry Cohn, 2026, needs more optimization.
7 493 0.708432526370 Henry Cohn, 2026, needs more optimization.
7 494 0.708855033052 Henry Cohn, 2026, needs more optimization.
7 495 0.709113739608 Henry Cohn, 2026, needs more optimization.
7 496 0.709116102520 Henry Cohn, 2026, needs more optimization.
7 497 0.709157745575 Henry Cohn, 2026, needs more optimization.
7 498 0.709273334443 Henry Cohn, 2026, needs more optimization.
7 500 0.709935789111 Henry Cohn, 2026, needs more optimization.
7 501 0.709936940114 Henry Cohn, 2026, needs more optimization.
7 502 0.710429090175 Henry Cohn, 2026, needs more optimization.
7 503 0.710492579368 Henry Cohn, 2026, needs more optimization.
7 504 0.710930565964 Henry Cohn, 2026, needs more optimization.
7 505 0.710931621745 Henry Cohn, 2026, needs more optimization.
7 506 0.710981468568 Henry Cohn, 2026, needs more optimization.
7 507 0.711080748912 Henry Cohn, 2026, needs more optimization.
7 508 0.711106286765 Henry Cohn, 2026, needs more optimization.
7 509 0.711201193804 Henry Cohn, 2026, needs more optimization.
7 510 0.711293614481 Henry Cohn, 2026, needs more optimization.
7 511 0.711363138156 Henry Cohn, 2026, needs more optimization.
7 512 0.711454727654 Henry Cohn, 2026, needs more optimization.
7 513 0.712172148167 Henry Cohn, 2026, needs more optimization.
7 514 0.712172858516 Henry Cohn, 2026, needs more optimization.
7 515 0.712174332932 Henry Cohn, 2026, needs more optimization.
7 516 0.712187605666 Henry Cohn, 2026, needs more optimization.
7 517 0.712210894377 Henry Cohn, 2026, needs more optimization.
7 518 0.712340678491 Henry Cohn, 2026, needs more optimization.
7 519 0.712372645069 Henry Cohn, 2026, needs more optimization.
7 520 0.712553554036 Henry Cohn, 2026, needs more optimization.
7 521 0.713126624328 Henry Cohn, 2026, needs more optimization.
7 522 0.713132305300 Henry Cohn, 2026, needs more optimization.
7 524 0.713132896741 Henry Cohn, 2026, needs more optimization.
7 525 0.713134779217 Henry Cohn, 2026, needs more optimization.
7 526 0.713136835087 Henry Cohn, 2026, needs more optimization.
7 527 0.713137350184 Henry Cohn, 2026, needs more optimization.
7 528 0.713143950997 Henry Cohn, 2026, needs more optimization.
7 529 0.713152366595 Henry Cohn, 2026, needs more optimization.
7 530 0.713308933799 Henry Cohn, 2026, needs more optimization.
7 531 0.713362812455 Henry Cohn, 2026, needs more optimization.
7 532 0.713415571798 Henry Cohn, 2026, needs more optimization.
7 533 0.713447851179 Henry Cohn, 2026, needs more optimization.
7 534 0.713451763297 Henry Cohn, 2026, needs more optimization.
7 535 0.713464596245 Henry Cohn, 2026, needs more optimization.
7 536 0.713491164389 Henry Cohn, 2026, needs more optimization.
7 537 0.713746136935 Henry Cohn, 2026, needs more optimization.
7 539 0.713788843162 Henry Cohn, 2026, needs more optimization.
7 540 0.713839032940 Henry Cohn, 2026, needs more optimization.
7 541 0.713901625426 Henry Cohn, 2026, needs more optimization.
7 542 0.713936687068 Henry Cohn, 2026, needs more optimization.
7 543 0.713972306627 Henry Cohn, 2026, needs more optimization.
7 544 0.714029264164 Henry Cohn, 2026, needs more optimization.
7 545 0.714047757773 Henry Cohn, 2026, needs more optimization.
7 546 0.714051907740 Henry Cohn, 2026, needs more optimization.
7 547 0.714053466298 Henry Cohn, 2026, needs more optimization.
7 548 0.714092434012 Henry Cohn, 2026, needs more optimization.
7 549 0.714185064809 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
7 632 0.714285714286 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−5
7 633 0.718298267267 Henry Cohn, 2026, needs more optimization.
7 634 0.720002194640 Henry Cohn, 2026, needs more optimization.
7 635 0.721178149045 Henry Cohn, 2026, needs more optimization.
7 636 0.722117626408 Henry Cohn, 2026, needs more optimization.
7 637 0.722898512200 Henry Cohn, 2026, needs more optimization.
7 638 0.723678519644 Henry Cohn, 2026, needs more optimization.
7 639 0.724493652130 Henry Cohn, 2026, needs more optimization.
7 640 0.724992025713 Henry Cohn, 2026, needs more optimization.
7 641 0.725507826504 Henry Cohn, 2026, needs more optimization.
7 642 0.726057470508 Henry Cohn, 2026, needs more optimization.
7 643 0.726414312059 Henry Cohn, 2026, needs more optimization.
7 644 0.726762928341 Henry Cohn, 2026, needs more optimization.
7 645 0.727066162922 Henry Cohn, 2026, needs more optimization.
7 646 0.727511904849 Henry Cohn, 2026, needs more optimization.
7 647 0.727892790480 Henry Cohn, 2026, needs more optimization.
7 648 0.728306768036 Henry Cohn, 2026, needs more optimization.
7 649 0.728641424700 Henry Cohn, 2026, needs more optimization.
7 650 0.729053726374 Henry Cohn, 2026, needs more optimization.
7 651 0.729293279472 Henry Cohn, 2026, needs more optimization.
7 652 0.729541465834 Henry Cohn, 2026, needs more optimization.
7 653 0.729774953674 Henry Cohn, 2026, needs more optimization.
7 654 0.729975587823 Henry Cohn, 2026, needs more optimization.
7 655 0.730234384890 Henry Cohn, 2026, needs more optimization.
7 656 0.730552175845 Henry Cohn, 2026, needs more optimization.
7 657 0.730808192012 Henry Cohn, 2026, needs more optimization.
7 658 0.731114380586 Henry Cohn, 2026, needs more optimization.
7 659 0.731366901677 Henry Cohn, 2026, needs more optimization.
7 660 0.731486943091 Henry Cohn, 2026, needs more optimization.
7 661 0.731863795408 Henry Cohn, 2026, needs more optimization.
7 662 0.732087885385 Henry Cohn, 2026, needs more optimization.
7 663 0.732304881024 Henry Cohn, 2026, needs more optimization.
7 664 0.732496826007 Henry Cohn, 2026, needs more optimization.
7 665 0.732896018934 Henry Cohn, 2026, needs more optimization.
7 666 0.733212844652 Henry Cohn, 2026, needs more optimization.
7 667 0.733492068059 Henry Cohn, 2026, needs more optimization.
7 668 0.733758107338 Henry Cohn, 2026, needs more optimization.
7 669 0.734019356759 Henry Cohn, 2026, needs more optimization.
7 670 0.734308429942 Henry Cohn, 2026, needs more optimization.
7 671 0.734584900595 Henry Cohn, 2026, needs more optimization.
7 672 0.734847291378 Henry Cohn, 2026, needs more optimization.
7 673 0.735093123384 Henry Cohn, 2026, needs more optimization.
7 674 0.735512210931 Henry Cohn, 2026, needs more optimization.
7 675 0.735688744487 Henry Cohn, 2026, needs more optimization.
7 676 0.735874165328 Henry Cohn, 2026, needs more optimization.
7 677 0.736127927421 Henry Cohn, 2026, needs more optimization.
7 678 0.736345194313 Henry Cohn, 2026, needs more optimization.
7 679 0.736580898368 Henry Cohn, 2026, needs more optimization.
7 680 0.736864007338 Henry Cohn, 2026, needs more optimization.
7 681 0.737096364909 Henry Cohn, 2026, needs more optimization.
7 682 0.737348982491 Henry Cohn, 2026, needs more optimization.
7 683 0.737495410953 Henry Cohn, 2026, needs more optimization.
7 684 0.737632275903 Henry Cohn, 2026, needs more optimization.
7 685 0.737758286377 Henry Cohn, 2026, needs more optimization.
7 686 0.737989005733 Henry Cohn, 2026, needs more optimization.
7 687 0.737989906740 Henry Cohn, 2026, needs more optimization.
7 688 0.737989906772 Henry Cohn, 2026, needs more optimization.
7 689 0.737991936320 Henry Cohn, 2026, needs more optimization.
7 691 0.738395191654 Henry Cohn, 2026, needs more optimization.
7 693 0.738395349605 Henry Cohn, 2026, needs more optimization.
7 694 0.738395410782 Henry Cohn, 2026, needs more optimization.
7 695 0.738395600097 Henry Cohn, 2026, needs more optimization.
7 696 0.738395669162 Henry Cohn, 2026, needs more optimization.
7 697 0.738395843328 Henry Cohn, 2026, needs more optimization.
7 698 0.738456048958 Henry Cohn, 2026, needs more optimization.
7 699 0.738456048990 Henry Cohn, 2026, needs more optimization.
7 700 0.738653996455 Henry Cohn, 2026, needs more optimization.
7 701 0.739113552646 Henry Cohn, 2026, needs more optimization.
7 702 0.739266939361 Henry Cohn, 2026, needs more optimization.
7 703 0.739875084238 Henry Cohn, 2026, needs more optimization.
7 704 0.739899464770 Henry Cohn, 2026, needs more optimization.
7 705 0.739963678687 Henry Cohn, 2026, needs more optimization.
7 706 0.740009252772 Henry Cohn, 2026, needs more optimization.
7 707 0.740045458555 Henry Cohn, 2026, needs more optimization.
7 708 0.740059679628 Henry Cohn, 2026, needs more optimization.
7 709 0.740076912588 Henry Cohn, 2026, needs more optimization.
7 710 0.740181319585 Henry Cohn, 2026, needs more optimization.
7 711 0.740846268866 Henry Cohn, 2026, needs more optimization.
7 712 0.740846563839 Henry Cohn, 2026, needs more optimization.
7 713 0.740850227665 Henry Cohn, 2026, needs more optimization.
7 714 0.740855929839 Henry Cohn, 2026, needs more optimization.
7 733 0.744904412220 Henry Cohn, 2026, needs more optimization.
7 734 0.749190003802 Henry Cohn, 2026, needs more optimization.
7 735 0.749318287594 Henry Cohn, 2026, needs more optimization.
7 736 0.749503078526 Henry Cohn, 2026, needs more optimization.
7 737 0.749709016922 Henry Cohn, 2026, needs more optimization.
7 739 0.749838697083 Henry Cohn, 2026, needs more optimization.
7 740 0.749991793491 Henry Cohn, 2026, needs more optimization.
7 882 0.75 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−3
7 883 0.755753469054 Henry Cohn, 2026, needs more optimization.
7 884 0.766403664401 Henry Cohn, 2026, needs more optimization.
7 885 0.766503944441 Henry Cohn, 2026, needs more optimization.
7 886 0.766515781148 Henry Cohn, 2026, needs more optimization.
7 887 0.766833372562 Henry Cohn, 2026, needs more optimization.
7 888 0.766868174357 Henry Cohn, 2026, needs more optimization.
7 889 0.766869767211 Henry Cohn, 2026, needs more optimization.
7 890 0.766985342372 Henry Cohn, 2026, needs more optimization.
7 891 0.767019951944 Henry Cohn, 2026, needs more optimization.
7 892 0.767218284221 Henry Cohn, 2026, needs more optimization.
7 893 0.767218291361 Henry Cohn, 2026, needs more optimization.
7 894 0.767234114676 Henry Cohn, 2026, needs more optimization.
7 895 0.767377566868 Henry Cohn, 2026, needs more optimization.
7 896 0.767393000683 Henry Cohn, 2026, needs more optimization.
7 897 0.767655586886 Henry Cohn, 2026, needs more optimization.
7 898 0.767719566781 Henry Cohn, 2026, needs more optimization.
7 899 0.767726173549 Henry Cohn, 2026, needs more optimization.
7 900 0.767761344075 Henry Cohn, 2026, needs more optimization.
7 901 0.767950331610 Henry Cohn, 2026, needs more optimization.
7 902 0.767962771785 Henry Cohn, 2026, needs more optimization.
7 903 0.768082732576 Henry Cohn, 2026, needs more optimization.
7 904 0.768127068769 Henry Cohn, 2026, needs more optimization.
7 905 0.768334709058 Henry Cohn, 2026, needs more optimization.
7 906 0.768374983020 Henry Cohn, 2026, needs more optimization.
7 907 0.768506291371 Henry Cohn, 2026, needs more optimization.
7 908 0.768561220401 Henry Cohn, 2026, needs more optimization.
7 909 0.768678637809 Henry Cohn, 2026, needs more optimization.
7 910 0.768710959083 Henry Cohn, 2026, needs more optimization.
7 911 0.768759400021 Henry Cohn, 2026, needs more optimization.
7 912 0.768901350638 Henry Cohn, 2026, needs more optimization.
7 913 0.768910378544 Henry Cohn, 2026, needs more optimization.
7 914 0.768913170338 Henry Cohn, 2026, needs more optimization.
7 915 0.769134591037 Henry Cohn, 2026, needs more optimization.
7 916 0.769165871676 Henry Cohn, 2026, needs more optimization.
7 917 0.769169800758 Henry Cohn, 2026, needs more optimization.
7 918 0.769514533595 Henry Cohn, 2026, needs more optimization.
7 919 0.769519167637 Henry Cohn, 2026, needs more optimization.
7 920 0.769538247750 Henry Cohn, 2026, needs more optimization.
7 921 0.769683149605 Henry Cohn, 2026, needs more optimization.
7 922 0.769867857347 Henry Cohn, 2026, needs more optimization.
7 923 0.769884537463 Henry Cohn, 2026, needs more optimization.
7 924 0.769912599306 Henry Cohn, 2026, needs more optimization.
7 925 0.769951156526 Henry Cohn, 2026, needs more optimization.
7 926 0.769985813035 Henry Cohn, 2026, needs more optimization.
7 927 0.770111455955 Henry Cohn, 2026, needs more optimization.
7 928 0.770208643882 Henry Cohn, 2026, needs more optimization.
7 929 0.770212316653 Henry Cohn, 2026, needs more optimization.
7 930 0.770252435110 Henry Cohn, 2026, needs more optimization.
7 931 0.770529103090 Henry Cohn, 2026, needs more optimization.
7 932 0.770546430155 Henry Cohn, 2026, needs more optimization.
7 933 0.770569395126 Henry Cohn, 2026, needs more optimization.
7 934 0.770613847338 Henry Cohn, 2026, needs more optimization.
7 935 0.770749875625 Henry Cohn, 2026, needs more optimization.
7 937 0.770888344495 Henry Cohn, 2026, needs more optimization.
7 938 0.771106969933 Henry Cohn, 2026, needs more optimization.
7 939 0.771135671981 Henry Cohn, 2026, needs more optimization.
7 940 0.771176764040 Henry Cohn, 2026, needs more optimization.
7 941 0.771204247709 Henry Cohn, 2026, needs more optimization.
7 942 0.771345988645 Henry Cohn, 2026, needs more optimization.
7 943 0.771345989379 Henry Cohn, 2026, needs more optimization.
7 944 0.771489190365 Henry Cohn, 2026, needs more optimization.
7 945 0.771494345044 Henry Cohn, 2026, needs more optimization.
7 946 0.771683406849 Henry Cohn, 2026, needs more optimization.
7 947 0.771710745645 Henry Cohn, 2026, needs more optimization.
7 948 0.771737994806 Henry Cohn, 2026, needs more optimization.
7 949 0.771744259420 Henry Cohn, 2026, needs more optimization.
7 950 0.771847034973 Henry Cohn, 2026, needs more optimization.
7 951 0.772058120892 Henry Cohn, 2026, needs more optimization.
7 952 0.772196050234 Henry Cohn, 2026, needs more optimization.
7 953 0.772204875620 Henry Cohn, 2026, needs more optimization.
7 954 0.772220580711 Henry Cohn, 2026, needs more optimization.
7 955 0.772304263156 Henry Cohn, 2026, needs more optimization.
7 956 0.772574272944 Henry Cohn, 2026, needs more optimization.
7 957 0.772589294165 Henry Cohn, 2026, needs more optimization.
7 958 0.772688630903 Henry Cohn, 2026, needs more optimization.
7 959 0.772709977457 Henry Cohn, 2026, needs more optimization.
7 960 0.772787278858 Henry Cohn, 2026, needs more optimization.
7 961 0.772791666020 Henry Cohn, 2026, needs more optimization.
7 962 0.772892870825 Henry Cohn, 2026, needs more optimization.
7 963 0.773139638357 Henry Cohn, 2026, needs more optimization.
7 964 0.773163638384 Henry Cohn, 2026, needs more optimization.
7 965 0.773185197223 Henry Cohn, 2026, needs more optimization.
7 966 0.773198999836 Henry Cohn, 2026, needs more optimization.
7 967 0.773286580118 Henry Cohn, 2026, needs more optimization.
7 968 0.773504349089 Henry Cohn, 2026, needs more optimization.
7 969 0.773549173297 Henry Cohn, 2026, needs more optimization.
7 970 0.773568297959 Henry Cohn, 2026, needs more optimization.
7 971 0.773687433376 Henry Cohn, 2026, needs more optimization.
7 972 0.773806054343 Henry Cohn, 2026, needs more optimization.
7 973 0.773822111206 Henry Cohn, 2026, needs more optimization.
7 974 0.773892533595 Henry Cohn, 2026, needs more optimization.
7 975 0.774035856919 Henry Cohn, 2026, needs more optimization.
7 976 0.774155676390 Henry Cohn, 2026, needs more optimization.
7 977 0.774184990965 Henry Cohn, 2026, needs more optimization.
7 978 0.774191107511 Henry Cohn, 2026, needs more optimization.
7 979 0.774270216495 Henry Cohn, 2026, needs more optimization.
7 980 0.774281567443 Henry Cohn, 2026, needs more optimization.
7 981 0.774457302989 Henry Cohn, 2026, needs more optimization.
7 982 0.774479020835 Henry Cohn, 2026, needs more optimization.
7 983 0.774559369840 Henry Cohn, 2026, needs more optimization.
7 984 0.774731879183 Henry Cohn, 2026, needs more optimization.
7 985 0.774737534236 Henry Cohn, 2026, needs more optimization.
7 986 0.774764140035 Henry Cohn, 2026, needs more optimization.
7 987 0.774858389897 Henry Cohn, 2026, needs more optimization.
7 988 0.775025761261 Henry Cohn, 2026, needs more optimization.
7 989 0.775034801356 Henry Cohn, 2026, needs more optimization.
7 990 0.775211611310 Henry Cohn, 2026, needs more optimization.
7 991 0.775245091475 Henry Cohn, 2026, needs more optimization.
7 992 0.775406488113 Henry Cohn, 2026, needs more optimization.
7 993 0.775420437781 Henry Cohn, 2026, needs more optimization.
7 994 0.775433191642 Henry Cohn, 2026, needs more optimization.
7 995 0.775616788845 Henry Cohn, 2026, needs more optimization.
7 996 0.775653967879 Henry Cohn, 2026, needs more optimization.
7 997 0.775682704772 Henry Cohn, 2026, needs more optimization.
7 998 0.775734959961 Henry Cohn, 2026, needs more optimization.
7 999 0.775745937975 Henry Cohn, 2026, needs more optimization.
7 1000 0.775785139360 Henry Cohn, 2026, needs more optimization.
7 1001 0.775949143061 Henry Cohn, 2026, needs more optimization.
7 1002 0.775960208085 Henry Cohn, 2026, needs more optimization.
7 1003 0.776149980560 Henry Cohn, 2026, needs more optimization.
7 1004 0.776174934655 Henry Cohn, 2026, needs more optimization.
7 1005 0.776299662665 Henry Cohn, 2026, needs more optimization.
7 1006 0.776367863148 Henry Cohn, 2026, needs more optimization.
7 1007 0.776406436013 Henry Cohn, 2026, needs more optimization.
7 1008 0.776714633448 Henry Cohn, 2026, needs more optimization.
7 1009 0.776717102784 Henry Cohn, 2026, needs more optimization.
7 1010 0.776769672744 Henry Cohn, 2026, needs more optimization.
7 1011 0.776921230706 Henry Cohn, 2026, needs more optimization.
7 1012 0.776924476159 Henry Cohn, 2026, needs more optimization.
7 1013 0.777105309452 Henry Cohn, 2026, needs more optimization.
7 1014 0.777142277824 Henry Cohn, 2026, needs more optimization.
7 1015 0.777178038957 Henry Cohn, 2026, needs more optimization.
7 1016 0.777301079890 Henry Cohn, 2026, needs more optimization.
7 1017 0.777348324220 Henry Cohn, 2026, needs more optimization.
7 1018 0.777360687807 Henry Cohn, 2026, needs more optimization.
7 1019 0.777443842822 Henry Cohn, 2026, needs more optimization.
7 1020 0.777789872189 Henry Cohn, 2026, needs more optimization.
7 1021 0.777813612228 Henry Cohn, 2026, needs more optimization.
7 1022 0.777975406949 Henry Cohn, 2026, needs more optimization.
7 1023 0.777979038563 Henry Cohn, 2026, needs more optimization.
7 1024 0.777993767078 Henry Cohn, 2026, needs more optimization.
8 17 0.087733463324 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
288⁢x3−64⁢x2−8⁢x+1
8 18 0.099469572709 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
8 19 0.111409975027 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 20 0.119496866688 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
224⁢x3+60⁢x2−2⁢x−1
8 21 0.130601937482 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
28⁢x2+4⁢x−1
8 22 0.130601937482 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
28⁢x2+4⁢x−1
8 23 0.157169941990 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 24 0.157692144940 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x4−4⁢x3−27⁢x2−2⁢x+1
8 25 0.164334174126 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 26 0.172652095036 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 27 0.179856457059 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 28 0.181158420022 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
36⁢x4+24⁢x3−36⁢x2+1
8 29 0.187922490077 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 30 0.203916279404 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 31 0.219706528517 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 32 0.227325452024 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
95⁢x2−4⁢x−4
8 33 0.227325452024 Henry Cohn, 2023.
95⁢x2−4⁢x−4
8 34 0.233864616950 Henry Cohn, 2023.
26887680⁢x6+11003904⁢x5−444096⁢x4−594432⁢x3−55800⁢x2−480⁢x−1
8 35 0.236461100794 Henry Cohn, 2023.
4⁢x4+8⁢x3−20⁢x2+1
8 38 0.239920745566 Henry Cohn, 2023.
1088⁢x4−80⁢x2+1
8 39 0.243600150512 Henry Cohn, 2023.
1183744⁢x8+122880⁢x7−575488⁢x6−138240⁢x5+53632⁢x4+14976⁢x3−1568⁢x2−720⁢x+81
8 40 0.265121155593 Henry Cohn, 2025.
8 41 0.269588854450 Henry Cohn, 2025.
8 42 0.276791074187 Henry Cohn, 2023.
8 43 0.285155668748 Henry Cohn, 2025.
8 44 0.288883348745 Henry Cohn, 2026.
8 45 0.293504048474 Henry Cohn, 2025.
8 46 0.298271343353 Henry Cohn, 2025.
8 47 0.301070997037 Henry Cohn, 2025.
8 48 0.306796780995 Henry Cohn, 2025.
8 49 0.310558546149 Henry Cohn, 2025.
8 50 0.314033492890 Henry Cohn, 2026.
8 51 0.316443462389 Henry Cohn, 2026.
8 52 0.317147531407 Henry Cohn, 2025.
8 53 0.323010527708 Henry Cohn, 2025.
8 54 0.326002020004 Henry Cohn, 2025.
8 55 0.328647326389 Henry Cohn, 2025.
8 56 0.330635803908 Henry Cohn, 2024.
8 57 0.332158951387 Henry Cohn, 2025.
8 58 0.332676598414 Henry Cohn, 2025.
8 59 0.333047687244 Henry Cohn, 2025.
8 60 0.333177612425 Henry Cohn, 2025.
8 61 0.333249870325 Henry Cohn, 2025.
8 62 0.333256273907 Henry Cohn, 2025.
8 63 0.333327460019 Henry Cohn, 2025.
8 64 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
8 65 0.340292894900 Henry Cohn, 2025.
8 66 0.348776902230 Henry Cohn, 2025.
8 67 0.350755730045 Henry Cohn, 2025.
8 68 0.352461904199 Henry Cohn, 2025.
8 71 0.353553390594 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8⁢x2−1
8 72 0.357142857143 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645.
14⁢x−5
8 73 0.374351529308 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 74 0.375030122030 Henry Cohn, 2025.
8 75 0.380121614172 Henry Cohn, 2026.
8 76 0.383280469013 Henry Cohn, 2023.
8 77 0.386305789989 Henry Cohn, 2025.
8 78 0.387879817423 Henry Cohn, 2025.
8 79 0.395049510669 Henry Cohn, 2026.
8 80 0.396541503332 Henry Cohn, 2026.
8 83 0.4 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5⁢x−2
8 84 0.401846838467 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 85 0.404581540848 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 86 0.405334578003 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 87 0.409324629428 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 88 0.414496555473 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 89 0.418879541456 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 90 0.421656007643 Henry Cohn, 2026, needs more optimization.
8 91 0.422013535027 Henry Cohn, 2026.
8 92 0.422534257743 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 93 0.423439618648 Henry Cohn, 2026.
8 94 0.425228129624 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 95 0.426308373208 Henry Cohn, 2026.
8 96 0.426582964791 Henry Cohn, 2026.
8 97 0.427518816511 Henry Cohn, 2026.
8 98 0.428413697861 Henry Cohn, 2026.
8 99 0.428528982794 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 100 0.428556416307 Henry Cohn, 2026.
8 101 0.428570622361 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 114 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
8 115 0.447550493892 Henry Cohn, 2026.
8 116 0.448006674268 Henry Cohn, 2026.
8 117 0.451120553073 Henry Cohn, 2026, needs more optimization.
8 118 0.455245746618 Henry Cohn, 2026, needs more optimization.
8 119 0.460486478645 Henry Cohn, 2026.
8 120 0.461570019406 Henry Cohn, 2026.
8 121 0.461664940349 Henry Cohn, 2026, needs more optimization.
8 122 0.461856796769 Henry Cohn, 2026.
8 123 0.462006235320 Henry Cohn, 2026, needs more optimization.
8 124 0.462008783202 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
8 125 0.462359114837 Henry Cohn, 2026, needs more optimization.
8 136 0.462585942982 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
68⁢x2−12⁢x−9
8 137 0.466199226032 Henry Cohn, 2025.
8 138 0.467414923908 Henry Cohn, 2026, needs more optimization.
8 139 0.468643112616 Henry Cohn, 2026, needs more optimization.
8 140 0.470790126946 Henry Cohn, 2026, needs more optimization.
8 141 0.472524013736 Henry Cohn, 2026, needs more optimization.
8 142 0.475929571130 Henry Cohn, 2026, needs more optimization.
8 143 0.476461017089 Henry Cohn, 2026, needs more optimization.
8 144 0.482430973234 Henry Cohn, 2026, needs more optimization.
8 145 0.484039898695 Henry Cohn, 2026, needs more optimization.
8 146 0.484264095166 Henry Cohn, 2026, needs more optimization.
8 147 0.485613223083 Henry Cohn, 2026, needs more optimization.
8 148 0.487312517364 Henry Cohn, 2026, needs more optimization.
8 149 0.488359213032 Henry Cohn, 2026, needs more optimization.
8 150 0.489648773793 Henry Cohn, 2026, needs more optimization.
8 151 0.490247002641 Henry Cohn, 2026, needs more optimization.
8 152 0.490964655368 Henry Cohn, 2026, needs more optimization.
8 153 0.491309363964 Henry Cohn, 2026, needs more optimization.
8 154 0.492097880475 Henry Cohn, 2026, needs more optimization.
8 155 0.492487433819 Henry Cohn, 2026, needs more optimization.
8 156 0.493290119829 Henry Cohn, 2026, needs more optimization.
8 157 0.493563072734 Henry Cohn, 2026, needs more optimization.
8 158 0.493973022112 Henry Cohn, 2026, needs more optimization.
8 159 0.494043147924 Henry Cohn, 2026, needs more optimization.
8 160 0.494736825094 Henry Cohn, 2026, needs more optimization.
8 161 0.495447759872 Henry Cohn, 2026, needs more optimization.
8 162 0.495649764656 Henry Cohn, 2026, needs more optimization.
8 163 0.496196205414 Henry Cohn, 2026, needs more optimization.
8 164 0.496310081804 Henry Cohn, 2026, needs more optimization.
8 165 0.496913741490 Henry Cohn, 2026, needs more optimization.
8 166 0.497162203411 Henry Cohn, 2026, needs more optimization.
8 167 0.497721323270 Henry Cohn, 2026, needs more optimization.
8 168 0.498088462293 Henry Cohn, 2026, needs more optimization.
8 169 0.498223256213 Henry Cohn, 2026, needs more optimization.
8 170 0.498750262782 Henry Cohn, 2026, needs more optimization.
8 171 0.498801836128 Henry Cohn, 2026, needs more optimization.
8 172 0.498942484738 Henry Cohn, 2026, needs more optimization.
8 173 0.499375167240 Henry Cohn, 2026, needs more optimization.
8 174 0.499521021281 Henry Cohn, 2026, needs more optimization.
8 175 0.499798667294 Henry Cohn, 2026, needs more optimization.
8 176 0.499873526438 Henry Cohn, 2026, needs more optimization.
8 177 0.499886086851 Henry Cohn, 2026, needs more optimization.
8 178 0.499893162400 Henry Cohn, 2026, needs more optimization.
8 179 0.499906883997 Henry Cohn, 2026, needs more optimization.
8 240* 0.5 A. Korkine and G. Zolotareff, Sur les formes quadratiques, Math. Ann. 6 (1873), 366–389, doi:10.1007/BF01442795; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8.
2⁢x−1
8 241 0.539501901248 Henry Cohn, 2024, needs more optimization.
8 242 0.543994640115 Henry Cohn, 2026, needs more optimization.
8 243 0.547248534885 Henry Cohn, 2026, needs more optimization.
8 244 0.549350562361 Henry Cohn, 2026, needs more optimization.
8 245 0.551498746970 Henry Cohn, 2026, needs more optimization.
8 246 0.553394111251 Henry Cohn, 2026, needs more optimization.
8 247 0.555266090324 Henry Cohn, 2026, needs more optimization.
8 248 0.557093066761 Henry Cohn, 2026, needs more optimization.
8 249 0.559054604379 Henry Cohn, 2026, needs more optimization.
8 250 0.559946787329 Henry Cohn, 2026, needs more optimization.
8 251 0.561370572299 Henry Cohn, 2026, needs more optimization.
8 252 0.562684715689 Henry Cohn, 2026, needs more optimization.
8 253 0.563782356681 Henry Cohn, 2026, needs more optimization.
8 254 0.564205030092 Henry Cohn, 2026, needs more optimization.
8 255 0.564226621828 Henry Cohn, 2026, needs more optimization.
8 256 0.564523679432 Henry Cohn, 2026, needs more optimization.
8 257 0.564949574808 Henry Cohn, 2026, needs more optimization.
8 258 0.566625996690 Henry Cohn, 2026, needs more optimization.
8 259 0.568531251676 Henry Cohn, 2026, needs more optimization.
8 260 0.568554256790 Henry Cohn, 2026, needs more optimization.
8 261 0.569474412654 Henry Cohn, 2026, needs more optimization.
8 262 0.569972866617 Henry Cohn, 2026, needs more optimization.
8 263 0.571021139436 Henry Cohn, 2026, needs more optimization.
8 264 0.571384073760 Henry Cohn, 2026, needs more optimization.
8 265 0.571540695208 Henry Cohn, 2026, needs more optimization.
8 266 0.572402016029 Henry Cohn, 2026, needs more optimization.
8 267 0.572984228761 Henry Cohn, 2026, needs more optimization.
8 268 0.573583849050 Henry Cohn, 2026, needs more optimization.
8 269 0.573869124046 Henry Cohn, 2026, needs more optimization.
8 270 0.574627466701 Henry Cohn, 2026, needs more optimization.
8 271 0.575114636041 Henry Cohn, 2026, needs more optimization.
8 272 0.575648342627 Henry Cohn, 2026, needs more optimization.
8 273 0.576007103314 Henry Cohn, 2026, needs more optimization.
8 274 0.577082531094 Henry Cohn, 2026, needs more optimization.
8 275 0.577880232458 Henry Cohn, 2026, needs more optimization.
8 276 0.578428223692 Henry Cohn, 2026, needs more optimization.
8 277 0.578570947119 Henry Cohn, 2026, needs more optimization.
8 278 0.578694749573 Henry Cohn, 2026, needs more optimization.
8 279 0.578742880120 Henry Cohn, 2026, needs more optimization.
8 280 0.578805552496 Henry Cohn, 2026, needs more optimization.
8 281 0.578879104873 Henry Cohn, 2026, needs more optimization.
8 282 0.579253818884 Henry Cohn, 2026, needs more optimization.
8 283 0.579288609086 Henry Cohn, 2026, needs more optimization.
8 284 0.580520452955 Henry Cohn, 2026, needs more optimization.
8 285 0.580665580447 Henry Cohn, 2026, needs more optimization.
8 286 0.581788984538 Henry Cohn, 2026, needs more optimization.
8 287 0.582957005221 Henry Cohn, 2026, needs more optimization.
8 288 0.584429934452 Henry Cohn, 2026, needs more optimization.
8 289 0.584695646412 Henry Cohn, 2026, needs more optimization.
8 290 0.585214781867 Henry Cohn, 2026, needs more optimization.
8 291 0.585216121977 Henry Cohn, 2026, needs more optimization.
8 292 0.585614582664 Henry Cohn, 2026, needs more optimization.
8 293 0.585719973735 Henry Cohn, 2026, needs more optimization.
8 294 0.586431436366 Henry Cohn, 2026, needs more optimization.
8 295 0.586866330534 Henry Cohn, 2026, needs more optimization.
8 296 0.588178345271 Henry Cohn, 2026, needs more optimization.
8 299 0.588656341741 Henry Cohn, 2026, needs more optimization.
8 300 0.588659210589 Henry Cohn, 2026, needs more optimization.
8 301 0.588683815890 Henry Cohn, 2026, needs more optimization.
8 302 0.588684734262 Henry Cohn, 2026, needs more optimization.
8 303 0.590576764339 Henry Cohn, 2026, needs more optimization.
8 304 0.590590010414 Henry Cohn, 2026, needs more optimization.
8 305 0.590642335600 Henry Cohn, 2026, needs more optimization.
8 306 0.590690107237 Henry Cohn, 2026, needs more optimization.
8 307 0.590768910737 Henry Cohn, 2026, needs more optimization.
8 308 0.590975246189 Henry Cohn, 2026, needs more optimization.
8 309 0.590975835369 Henry Cohn, 2026, needs more optimization.
8 310 0.591748494092 Henry Cohn, 2026, needs more optimization.
8 311 0.592694080866 Henry Cohn, 2026, needs more optimization.
8 312 0.593711560108 Henry Cohn, 2026, needs more optimization.
8 313 0.594290936103 Henry Cohn, 2026, needs more optimization.
8 314 0.594416382510 Henry Cohn, 2026, needs more optimization.
8 315 0.594746132939 Henry Cohn, 2026, needs more optimization.
8 316 0.594774104343 Henry Cohn, 2026, needs more optimization.
8 317 0.595127698465 Henry Cohn, 2026, needs more optimization.
8 318 0.595158259597 Henry Cohn, 2026, needs more optimization.
8 319 0.595272996668 Henry Cohn, 2026, needs more optimization.
8 320 0.595799620137 Henry Cohn, 2026, needs more optimization.
8 321 0.596348376090 Henry Cohn, 2026, needs more optimization.
8 322 0.597009193983 Henry Cohn, 2026, needs more optimization.
8 323 0.597585521531 Henry Cohn, 2026, needs more optimization.
8 324 0.598032769529 Henry Cohn, 2026, needs more optimization.
8 325 0.598633111133 Henry Cohn, 2026, needs more optimization.
8 326 0.599027363368 Henry Cohn, 2026, needs more optimization.
8 327 0.599940934149 Henry Cohn, 2026, needs more optimization.
8 328 0.600347098495 Henry Cohn, 2026, needs more optimization.
8 329 0.600630007965 Henry Cohn, 2026, needs more optimization.
8 330 0.600673973046 Henry Cohn, 2026, needs more optimization.
8 331 0.600899142072 Henry Cohn, 2026, needs more optimization.
8 332 0.600914147794 Henry Cohn, 2026, needs more optimization.
8 333 0.601572958657 Henry Cohn, 2026, needs more optimization.
8 334 0.601881591264 Henry Cohn, 2026, needs more optimization.
8 335 0.602154266592 Henry Cohn, 2026, needs more optimization.
8 336 0.602595151547 Henry Cohn, 2026, needs more optimization.
8 337 0.602727139686 Henry Cohn, 2026, needs more optimization.
8 338 0.602862451292 Henry Cohn, 2026, needs more optimization.
8 339 0.602940137504 Henry Cohn, 2026, needs more optimization.
8 340 0.603052528786 Henry Cohn, 2026, needs more optimization.
8 341 0.603111043930 Henry Cohn, 2026, needs more optimization.
8 342 0.603120715559 Henry Cohn, 2026, needs more optimization.
8 343 0.604241183695 Henry Cohn, 2026, needs more optimization.
8 344 0.604315159720 Henry Cohn, 2026, needs more optimization.
8 345 0.604440074471 Henry Cohn, 2026, needs more optimization.
8 346 0.604486159249 Henry Cohn, 2026, needs more optimization.
8 347 0.604487730075 Henry Cohn, 2026, needs more optimization.
8 348 0.604496639421 Henry Cohn, 2026, needs more optimization.
8 349 0.604498128902 Henry Cohn, 2026, needs more optimization.
8 350 0.604516407588 Henry Cohn, 2026, needs more optimization.
8 351 0.604525373965 Henry Cohn, 2026, needs more optimization.
8 352 0.604543457256 Henry Cohn, 2026, needs more optimization.
8 353 0.604548727949 Henry Cohn, 2026, needs more optimization.
8 354 0.604552653988 Henry Cohn, 2026, needs more optimization.
8 355 0.604683509183 Henry Cohn, 2026, needs more optimization.
8 356 0.606373932200 Henry Cohn, 2026, needs more optimization.
8 357 0.606594124945 Henry Cohn, 2026, needs more optimization.
8 358 0.606814110203 Henry Cohn, 2026, needs more optimization.
8 359 0.606910189080 Henry Cohn, 2026, needs more optimization.
8 360 0.606975914964 Henry Cohn, 2026, needs more optimization.
8 361 0.611019509418 Henry Cohn, 2026, needs more optimization.
8 362 0.611378602037 Henry Cohn, 2026, needs more optimization.
8 363 0.611405093464 Henry Cohn, 2026, needs more optimization.
8 364 0.611604557073 Henry Cohn, 2026, needs more optimization.
8 365 0.611771036235 Henry Cohn, 2026, needs more optimization.
8 366 0.612111608158 Henry Cohn, 2026, needs more optimization.
8 367 0.612209884221 Henry Cohn, 2026, needs more optimization.
8 368 0.612272510343 Henry Cohn, 2026, needs more optimization.
8 369 0.612330742933 Henry Cohn, 2026, needs more optimization.
8 370 0.614280900915 Henry Cohn, 2026, needs more optimization.
8 371 0.614458177435 Henry Cohn, 2026, needs more optimization.
8 372 0.615194699728 Henry Cohn, 2026, needs more optimization.
8 373 0.616551329088 Henry Cohn, 2026, needs more optimization.
8 374 0.617361192966 Henry Cohn, 2026, needs more optimization.
8 375 0.618182537197 Henry Cohn, 2026, needs more optimization.
8 376 0.618243297642 Henry Cohn, 2026, needs more optimization.
8 377 0.618664711822 Henry Cohn, 2026, needs more optimization.
8 378 0.621609538450 Henry Cohn, 2026, needs more optimization.
8 379 0.622000809104 Henry Cohn, 2026, needs more optimization.
8 380 0.622736223453 Henry Cohn, 2026, needs more optimization.
8 381 0.624159639106 Henry Cohn, 2026, needs more optimization.
8 382 0.624716330804 Henry Cohn, 2026, needs more optimization.
8 383 0.624850620711 Henry Cohn, 2026, needs more optimization.
8 384 0.625022765875 Henry Cohn, 2026, needs more optimization.
8 385 0.625386020215 Henry Cohn, 2026, needs more optimization.
8 386 0.625607724160 Henry Cohn, 2026, needs more optimization.
8 387 0.625886189962 Henry Cohn, 2026, needs more optimization.
8 388 0.626417404197 Henry Cohn, 2026, needs more optimization.
8 389 0.626817955582 Henry Cohn, 2026, needs more optimization.
8 390 0.627040767692 Henry Cohn, 2026, needs more optimization.
8 391 0.627501874978 Henry Cohn, 2026, needs more optimization.
8 392 0.627762259159 Henry Cohn, 2026, needs more optimization.
8 393 0.628160397957 Henry Cohn, 2026, needs more optimization.
8 394 0.628311253987 Henry Cohn, 2026, needs more optimization.
8 395 0.628582779094 Henry Cohn, 2026, needs more optimization.
8 396 0.629014746040 Henry Cohn, 2026, needs more optimization.
8 397 0.629116972440 Henry Cohn, 2026, needs more optimization.
8 398 0.629495159125 Henry Cohn, 2026, needs more optimization.
8 399 0.629812766094 Henry Cohn, 2026, needs more optimization.
8 400 0.630147279093 Henry Cohn, 2026, needs more optimization.
8 401 0.630340517930 Henry Cohn, 2026, needs more optimization.
8 402 0.630556440744 Henry Cohn, 2026, needs more optimization.
8 403 0.630793914166 Henry Cohn, 2026, needs more optimization.
8 404 0.631433260905 Henry Cohn, 2026, needs more optimization.
8 405 0.631947907009 Henry Cohn, 2026, needs more optimization.
8 406 0.632027930958 Henry Cohn, 2026, needs more optimization.
8 407 0.632312669504 Henry Cohn, 2026, needs more optimization.
8 408 0.632576421518 Henry Cohn, 2026, needs more optimization.
8 409 0.632756923570 Henry Cohn, 2026, needs more optimization.
8 410 0.633016483791 Henry Cohn, 2026, needs more optimization.
8 411 0.633300020588 Henry Cohn, 2026, needs more optimization.
8 412 0.633610927946 Henry Cohn, 2026, needs more optimization.
8 413 0.633861390629 Henry Cohn, 2026, needs more optimization.
8 414 0.634118291067 Henry Cohn, 2026, needs more optimization.
8 415 0.634352865964 Henry Cohn, 2026, needs more optimization.
8 416 0.634657586482 Henry Cohn, 2026, needs more optimization.
8 417 0.634754352405 Henry Cohn, 2026, needs more optimization.
8 418 0.634825543223 Henry Cohn, 2026, needs more optimization.
8 419 0.634978866731 Henry Cohn, 2026, needs more optimization.
8 420 0.635004804157 Henry Cohn, 2026, needs more optimization.
8 421 0.635205684917 Henry Cohn, 2026, needs more optimization.
8 422 0.635656172055 Henry Cohn, 2026, needs more optimization.
8 423 0.635749833637 Henry Cohn, 2026, needs more optimization.
8 424 0.635846139455 Henry Cohn, 2026, needs more optimization.
8 425 0.635997987104 Henry Cohn, 2026, needs more optimization.
8 426 0.636148122798 Henry Cohn, 2026, needs more optimization.
8 427 0.636376429834 Henry Cohn, 2026, needs more optimization.
8 428 0.636521221198 Henry Cohn, 2026, needs more optimization.
8 429 0.636723681236 Henry Cohn, 2026, needs more optimization.
8 430 0.636855327515 Henry Cohn, 2026, needs more optimization.
8 431 0.637177044534 Henry Cohn, 2026, needs more optimization.
8 432 0.637254289873 Henry Cohn, 2026, needs more optimization.
8 433 0.637676318005 Henry Cohn, 2026, needs more optimization.
8 434 0.637832402830 Henry Cohn, 2026, needs more optimization.
8 435 0.637897129096 Henry Cohn, 2026, needs more optimization.
8 436 0.638123992510 Henry Cohn, 2026, needs more optimization.
8 437 0.638687588975 Henry Cohn, 2026, needs more optimization.
8 438 0.639251748850 Henry Cohn, 2026, needs more optimization.
8 439 0.639340834260 Henry Cohn, 2026, needs more optimization.
8 440 0.639454117309 Henry Cohn, 2026, needs more optimization.
8 441 0.639715860979 Henry Cohn, 2026, needs more optimization.
8 442 0.639896014065 Henry Cohn, 2026, needs more optimization.
8 443 0.639935194648 Henry Cohn, 2026, needs more optimization.
8 444 0.640165531313 Henry Cohn, 2026, needs more optimization.
8 445 0.640356193211 Henry Cohn, 2026, needs more optimization.
8 446 0.640583382881 Henry Cohn, 2026, needs more optimization.
8 447 0.640896137734 Henry Cohn, 2026, needs more optimization.
8 448 0.641210160572 Henry Cohn, 2026, needs more optimization.
8 449 0.641499640032 Henry Cohn, 2026, needs more optimization.
8 450 0.641527675003 Henry Cohn, 2026, needs more optimization.
8 451 0.641552810470 Henry Cohn, 2026, needs more optimization.
8 452 0.641572063588 Henry Cohn, 2026, needs more optimization.
8 453 0.641646626049 Henry Cohn, 2026, needs more optimization.
8 454 0.641685157118 Henry Cohn, 2026, needs more optimization.
8 455 0.641741845619 Henry Cohn, 2026, needs more optimization.
8 456 0.641840724778 Henry Cohn, 2026, needs more optimization.
8 457 0.641886239772 Henry Cohn, 2026, needs more optimization.
8 458 0.641915306504 Henry Cohn, 2026, needs more optimization.
8 459 0.641953900145 Henry Cohn, 2026, needs more optimization.
8 460 0.642073202655 Henry Cohn, 2026, needs more optimization.
8 461 0.642127883847 Henry Cohn, 2026, needs more optimization.
8 462 0.642155257569 Henry Cohn, 2026, needs more optimization.
8 463 0.642260833571 Henry Cohn, 2026, needs more optimization.
8 464 0.642306748644 Henry Cohn, 2026, needs more optimization.
8 465 0.642343098311 Henry Cohn, 2026, needs more optimization.
8 466 0.642539261523 Henry Cohn, 2026, needs more optimization.
8 467 0.642685864497 Henry Cohn, 2026, needs more optimization.
8 468 0.642926166545 Henry Cohn, 2026, needs more optimization.
8 469 0.643119590378 Henry Cohn, 2026, needs more optimization.
8 470 0.643284970025 Henry Cohn, 2026, needs more optimization.
8 471 0.643437800686 Henry Cohn, 2026, needs more optimization.
8 472 0.643636340848 Henry Cohn, 2026, needs more optimization.
8 473 0.643809792486 Henry Cohn, 2026, needs more optimization.
8 474 0.643833015183 Henry Cohn, 2026, needs more optimization.
8 475 0.644049748672 Henry Cohn, 2026, needs more optimization.
8 476 0.644194914296 Henry Cohn, 2026, needs more optimization.
8 477 0.644345506565 Henry Cohn, 2026, needs more optimization.
8 478 0.644642718331 Henry Cohn, 2026, needs more optimization.
8 479 0.644770751218 Henry Cohn, 2026, needs more optimization.
8 480 0.645222710568 Henry Cohn, 2026, needs more optimization.
8 481 0.645331843906 Henry Cohn, 2026, needs more optimization.
8 482 0.645545406289 Henry Cohn, 2026, needs more optimization.
8 483 0.645624493579 Henry Cohn, 2026, needs more optimization.
8 484 0.646158517891 Henry Cohn, 2026, needs more optimization.
8 485 0.646385618854 Henry Cohn, 2026, needs more optimization.
8 486 0.646805472923 Henry Cohn, 2026, needs more optimization.
8 487 0.647253216387 Henry Cohn, 2026, needs more optimization.
8 488 0.647379338535 Henry Cohn, 2026, needs more optimization.
8 489 0.647400679296 Henry Cohn, 2026, needs more optimization.
8 490 0.647720981105 Henry Cohn, 2026, needs more optimization.
8 491 0.647998952833 Henry Cohn, 2026, needs more optimization.
8 492 0.648389658438 Henry Cohn, 2026, needs more optimization.
8 493 0.648765659691 Henry Cohn, 2026, needs more optimization.
8 494 0.648972961260 Henry Cohn, 2026, needs more optimization.
8 495 0.649004586258 Henry Cohn, 2026, needs more optimization.
8 497 0.649040740965 Henry Cohn, 2026, needs more optimization.
8 498 0.649064175709 Henry Cohn, 2026, needs more optimization.
8 499 0.649368032779 Henry Cohn, 2026, needs more optimization.
8 500 0.649487709556 Henry Cohn, 2026, needs more optimization.
8 501 0.649605936279 Henry Cohn, 2026, needs more optimization.
8 502 0.649819491123 Henry Cohn, 2026, needs more optimization.
8 503 0.650148200757 Henry Cohn, 2026, needs more optimization.
8 504 0.650330034251 Henry Cohn, 2026, needs more optimization.
8 505 0.650401056278 Henry Cohn, 2026, needs more optimization.
8 506 0.651003373593 Henry Cohn, 2026, needs more optimization.
8 507 0.651467057197 Henry Cohn, 2026, needs more optimization.
8 508 0.651575893146 Henry Cohn, 2026, needs more optimization.
8 509 0.651787245357 Henry Cohn, 2026, needs more optimization.
8 511 0.651820883373 Henry Cohn, 2026, needs more optimization.
8 512 0.652030682983 Henry Cohn, 2026, needs more optimization.
8 513 0.652124600989 Henry Cohn, 2026, needs more optimization.
8 514 0.652358598050 Henry Cohn, 2026, needs more optimization.
8 515 0.652418790948 Henry Cohn, 2026, needs more optimization.
8 516 0.652683432965 Henry Cohn, 2026, needs more optimization.
8 517 0.652808631235 Henry Cohn, 2026, needs more optimization.
8 518 0.653034111533 Henry Cohn, 2026, needs more optimization.
8 519 0.653292746339 Henry Cohn, 2026, needs more optimization.
8 520 0.653649737522 Henry Cohn, 2026, needs more optimization.
8 521 0.653780271671 Henry Cohn, 2026, needs more optimization.
8 522 0.654165789117 Henry Cohn, 2026, needs more optimization.
8 523 0.654187229492 Henry Cohn, 2026, needs more optimization.
8 524 0.654281978209 Henry Cohn, 2026, needs more optimization.
8 525 0.654394234557 Henry Cohn, 2026, needs more optimization.
8 526 0.654540154067 Henry Cohn, 2026, needs more optimization.
8 527 0.654611224335 Henry Cohn, 2026, needs more optimization.
8 528 0.654701364815 Henry Cohn, 2026, needs more optimization.
8 529 0.655016689839 Henry Cohn, 2026, needs more optimization.
8 530 0.655235074306 Henry Cohn, 2026, needs more optimization.
8 531 0.655715168100 Henry Cohn, 2026, needs more optimization.
8 532 0.655791550465 Henry Cohn, 2026, needs more optimization.
8 533 0.655991758765 Henry Cohn, 2026, needs more optimization.
8 534 0.656154781207 Henry Cohn, 2026, needs more optimization.
8 535 0.656436251208 Henry Cohn, 2026, needs more optimization.
8 536 0.656701904170 Henry Cohn, 2026, needs more optimization.
8 537 0.657017394215 Henry Cohn, 2026, needs more optimization.
8 538 0.657333349433 Henry Cohn, 2026, needs more optimization.
8 539 0.657507500320 Henry Cohn, 2026, needs more optimization.
8 540 0.657688114882 Henry Cohn, 2026, needs more optimization.
8 541 0.657785711153 Henry Cohn, 2026, needs more optimization.
8 542 0.658020421766 Henry Cohn, 2026, needs more optimization.
8 543 0.658310390884 Henry Cohn, 2026, needs more optimization.
8 544 0.658636021775 Henry Cohn, 2026, needs more optimization.
8 545 0.658861083537 Henry Cohn, 2026, needs more optimization.
8 546 0.659011112284 Henry Cohn, 2026, needs more optimization.
8 547 0.659328901742 Henry Cohn, 2026, needs more optimization.
8 548 0.659530575421 Henry Cohn, 2026, needs more optimization.
8 549 0.659611195054 Henry Cohn, 2026, needs more optimization.
8 550 0.659625284758 Henry Cohn, 2026, needs more optimization.
8 551 0.659962734457 Henry Cohn, 2026, needs more optimization.
8 552 0.660489037402 Henry Cohn, 2026, needs more optimization.
8 553 0.660621126485 Henry Cohn, 2026, needs more optimization.
8 554 0.660757882440 Henry Cohn, 2026, needs more optimization.
8 555 0.660856752208 Henry Cohn, 2026, needs more optimization.
8 556 0.661108820951 Henry Cohn, 2026, needs more optimization.
8 557 0.661255072069 Henry Cohn, 2026, needs more optimization.
8 558 0.661399841649 Henry Cohn, 2026, needs more optimization.
8 559 0.661739680561 Henry Cohn, 2026, needs more optimization.
8 560 0.661903640075 Henry Cohn, 2026, needs more optimization.
8 561 0.662019635313 Henry Cohn, 2026, needs more optimization.
8 562 0.662288409714 Henry Cohn, 2026, needs more optimization.
8 563 0.662426944948 Henry Cohn, 2026, needs more optimization.
8 564 0.662575927155 Henry Cohn, 2026, needs more optimization.
8 565 0.662674253598 Henry Cohn, 2026, needs more optimization.
8 566 0.662749356508 Henry Cohn, 2026, needs more optimization.
8 567 0.662782643184 Henry Cohn, 2026, needs more optimization.
8 568 0.662911656880 Henry Cohn, 2026, needs more optimization.
8 569 0.663083008239 Henry Cohn, 2026, needs more optimization.
8 570 0.663126150144 Henry Cohn, 2026, needs more optimization.
8 571 0.663286775611 Henry Cohn, 2026, needs more optimization.
8 572 0.663464580774 Henry Cohn, 2026, needs more optimization.
8 573 0.663512036937 Henry Cohn, 2026, needs more optimization.
8 574 0.663793225874 Henry Cohn, 2026, needs more optimization.
8 575 0.663929025811 Henry Cohn, 2026, needs more optimization.
8 576 0.663997353859 Henry Cohn, 2026, needs more optimization.
8 577 0.664085130174 Henry Cohn, 2026, needs more optimization.
8 578 0.664190208749 Henry Cohn, 2026, needs more optimization.
8 579 0.664343371297 Henry Cohn, 2026, needs more optimization.
8 580 0.664397180570 Henry Cohn, 2026, needs more optimization.
8 581 0.664512511648 Henry Cohn, 2026, needs more optimization.
8 582 0.664533562585 Henry Cohn, 2026, needs more optimization.
8 583 0.664740748095 Henry Cohn, 2026, needs more optimization.
8 585 0.664754488702 Henry Cohn, 2026, needs more optimization.
8 586 0.664857539248 Henry Cohn, 2026, needs more optimization.
8 587 0.664937698692 Henry Cohn, 2026, needs more optimization.
8 588 0.665025984108 Henry Cohn, 2026, needs more optimization.
8 589 0.665199284068 Henry Cohn, 2026, needs more optimization.
8 590 0.665220838798 Henry Cohn, 2026, needs more optimization.
8 591 0.665221152767 Henry Cohn, 2026, needs more optimization.
8 592 0.665237954461 Henry Cohn, 2026, needs more optimization.
8 593 0.665250968338 Henry Cohn, 2026, needs more optimization.
8 594 0.665272329916 Henry Cohn, 2026, needs more optimization.
8 595 0.665281279696 Henry Cohn, 2026, needs more optimization.
8 596 0.665281279935 Henry Cohn, 2026, needs more optimization.
8 597 0.665314893567 Henry Cohn, 2026, needs more optimization.
8 598 0.665314893645 Henry Cohn, 2026, needs more optimization.
8 599 0.665326219588 Henry Cohn, 2026, needs more optimization.
8 600 0.665352468882 Henry Cohn, 2026, needs more optimization.
8 601 0.665357264564 Henry Cohn, 2026, needs more optimization.
8 602 0.665375981015 Henry Cohn, 2026, needs more optimization.
8 603 0.665423924032 Henry Cohn, 2026, needs more optimization.
8 604 0.665423924034 Henry Cohn, 2026, needs more optimization.
8 605 0.665446000371 Henry Cohn, 2026, needs more optimization.
8 606 0.665516147585 Henry Cohn, 2026, needs more optimization.
8 607 0.665530345015 Henry Cohn, 2026, needs more optimization.
8 608 0.665572854329 Henry Cohn, 2026, needs more optimization.
8 609 0.665607995189 Henry Cohn, 2026, needs more optimization.
8 610 0.665624368835 Henry Cohn, 2026, needs more optimization.
8 611 0.665634785867 Henry Cohn, 2026, needs more optimization.
8 612 0.665653993565 Henry Cohn, 2026, needs more optimization.
8 613 0.665659338557 Henry Cohn, 2026, needs more optimization.
8 614 0.665679316757 Henry Cohn, 2026, needs more optimization.
8 615 0.665717470528 Henry Cohn, 2026, needs more optimization.
8 617 0.665728216638 Henry Cohn, 2026, needs more optimization.
8 618 0.665750684637 Henry Cohn, 2026, needs more optimization.
8 619 0.665884608928 Henry Cohn, 2026, needs more optimization.
8 620 0.665945422806 Henry Cohn, 2026, needs more optimization.
8 621 0.665986955522 Henry Cohn, 2026, needs more optimization.
8 622 0.665997256548 Henry Cohn, 2026, needs more optimization.
8 623 0.666018176370 Henry Cohn, 2026, needs more optimization.
8 624 0.666021769867 Henry Cohn, 2026, needs more optimization.
8 628 0.666067050918 Henry Cohn, 2026, needs more optimization.
8 629 0.666080879178 Henry Cohn, 2026, needs more optimization.
8 630 0.666123699929 Henry Cohn, 2026, needs more optimization.
8 631 0.666168344207 Henry Cohn, 2026, needs more optimization.
8 632 0.666175572509 Henry Cohn, 2026, needs more optimization.
8 633 0.666198388460 Henry Cohn, 2026, needs more optimization.
8 634 0.666198396527 Henry Cohn, 2026, needs more optimization.
8 635 0.666205260104 Henry Cohn, 2026, needs more optimization.
8 636 0.666298695171 Henry Cohn, 2026, needs more optimization.
8 637 0.666308451325 Henry Cohn, 2026, needs more optimization.
8 638 0.666333107266 Henry Cohn, 2026, needs more optimization.
8 639 0.666347573305 Henry Cohn, 2026, needs more optimization.
8 640 0.666362757554 Henry Cohn, 2026, needs more optimization.
8 641 0.666452057952 Henry Cohn, 2026, needs more optimization.
8 644 0.666452115623 Henry Cohn, 2026, needs more optimization.
8 645 0.666472015238 Henry Cohn, 2026, needs more optimization.
8 646 0.666518605384 Henry Cohn, 2026, needs more optimization.
8 647 0.666520146109 Henry Cohn, 2026, needs more optimization.
8 648 0.666525089708 Henry Cohn, 2026, needs more optimization.
8 649 0.666530896821 Henry Cohn, 2026, needs more optimization.
8 650 0.666541462294 Henry Cohn, 2026, needs more optimization.
8 651 0.666558607482 Henry Cohn, 2026, needs more optimization.
8 652 0.666571874871 Henry Cohn, 2026, needs more optimization.
8 653 0.666586810255 Henry Cohn, 2026, needs more optimization.
8 654 0.666587546104 Henry Cohn, 2026, needs more optimization.
8 655 0.666587856494 Henry Cohn, 2026, needs more optimization.
8 656 0.666588243489 Henry Cohn, 2026, needs more optimization.
8 658 0.666589790275 Henry Cohn, 2026, needs more optimization.
8 659 0.666593485505 Henry Cohn, 2026, needs more optimization.
8 660 0.666734041256 Henry Cohn, 2026, needs more optimization.
8 661 0.667059535033 Henry Cohn, 2026, needs more optimization.
8 662 0.667266802214 Henry Cohn, 2026, needs more optimization.
8 663 0.668189402058 Henry Cohn, 2026, needs more optimization.
8 664 0.668388509942 Henry Cohn, 2026, needs more optimization.
8 665 0.668667306294 Henry Cohn, 2026, needs more optimization.
8 666 0.668685051123 Henry Cohn, 2026, needs more optimization.
8 667 0.668689342405 Henry Cohn, 2026, needs more optimization.
8 668 0.668755835856 Henry Cohn, 2026, needs more optimization.
8 669 0.668759815844 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
8 670 0.669180118824 Henry Cohn, 2026, needs more optimization.
8 671 0.669708221221 Henry Cohn, 2026, needs more optimization.
8 672 0.669884995181 Henry Cohn, 2026, needs more optimization.
8 673 0.670145633580 Henry Cohn, 2026, needs more optimization.
8 674 0.670497080089 Henry Cohn, 2026, needs more optimization.
8 675 0.670784213757 Henry Cohn, 2026, needs more optimization.
8 676 0.671136264999 Henry Cohn, 2026, needs more optimization.
8 677 0.671548362107 Henry Cohn, 2026, needs more optimization.
8 678 0.671995807549 Henry Cohn, 2026, needs more optimization.
8 679 0.673148775111 Henry Cohn, 2026, needs more optimization.
8 680 0.673409625028 Henry Cohn, 2026, needs more optimization.
8 681 0.673441590626 Henry Cohn, 2026, needs more optimization.
8 682 0.673479994225 Henry Cohn, 2026, needs more optimization.
8 683 0.673483258587 Henry Cohn, 2026, needs more optimization.
8 684 0.673537408049 Henry Cohn, 2026, needs more optimization.
8 685 0.674072276136 Henry Cohn, 2026, needs more optimization.
8 686 0.674212585969 Henry Cohn, 2026, needs more optimization.
8 687 0.674551317222 Henry Cohn, 2026, needs more optimization.
8 688 0.674938290362 Henry Cohn, 2026, needs more optimization.
8 689 0.675169791317 Henry Cohn, 2026, needs more optimization.
8 690 0.675522724203 Henry Cohn, 2026, needs more optimization.
8 691 0.676056176548 Henry Cohn, 2026, needs more optimization.
8 692 0.676435496792 Henry Cohn, 2026, needs more optimization.
8 693 0.676908414559 Henry Cohn, 2026, needs more optimization.
8 694 0.677369417718 Henry Cohn, 2026, needs more optimization.
8 695 0.677450043524 Henry Cohn, 2026, needs more optimization.
8 696 0.677681779752 Henry Cohn, 2026, needs more optimization.
8 697 0.677810009173 Henry Cohn, 2026, needs more optimization.
8 698 0.678219408151 Henry Cohn, 2026, needs more optimization.
8 699 0.678433611855 Henry Cohn, 2026, needs more optimization.
8 700 0.678621364252 Henry Cohn, 2026, needs more optimization.
8 701 0.679067365557 Henry Cohn, 2026, needs more optimization.
8 702 0.679291853395 Henry Cohn, 2026, needs more optimization.
8 703 0.679783554296 Henry Cohn, 2026, needs more optimization.
8 704 0.680144936276 Henry Cohn, 2026, needs more optimization.
8 705 0.680251246009 Henry Cohn, 2026, needs more optimization.
8 706 0.680421035610 Henry Cohn, 2026, needs more optimization.
8 707 0.680529373797 Henry Cohn, 2026, needs more optimization.
8 708 0.680603353264 Henry Cohn, 2026, needs more optimization.
8 709 0.680917640799 Henry Cohn, 2026, needs more optimization.
8 710 0.681407272589 Henry Cohn, 2026, needs more optimization.
8 711 0.681570128531 Henry Cohn, 2026, needs more optimization.
8 712 0.681898468914 Henry Cohn, 2026, needs more optimization.
8 713 0.682062582300 Henry Cohn, 2026, needs more optimization.
8 714 0.682450090109 Henry Cohn, 2026, needs more optimization.
8 715 0.682455967149 Henry Cohn, 2026, needs more optimization.
8 716 0.682927894979 Henry Cohn, 2026, needs more optimization.
8 717 0.683250994564 Henry Cohn, 2026, needs more optimization.
8 718 0.683505160052 Henry Cohn, 2026, needs more optimization.
8 719 0.683536181222 Henry Cohn, 2026, needs more optimization.
8 720 0.683900135499 Henry Cohn, 2026, needs more optimization.
8 721 0.683988553738 Henry Cohn, 2026, needs more optimization.
8 722 0.684082233662 Henry Cohn, 2026, needs more optimization.
8 723 0.684327519137 Henry Cohn, 2026, needs more optimization.
8 724 0.684572014441 Henry Cohn, 2026, needs more optimization.
8 725 0.684992629018 Henry Cohn, 2026, needs more optimization.
8 726 0.685139480657 Henry Cohn, 2026, needs more optimization.
8 727 0.685417157265 Henry Cohn, 2026, needs more optimization.
8 728 0.685493816281 Henry Cohn, 2026, needs more optimization.
8 729 0.685800733122 Henry Cohn, 2026, needs more optimization.
8 730 0.686122753466 Henry Cohn, 2026, needs more optimization.
8 731 0.686238276831 Henry Cohn, 2026, needs more optimization.
8 732 0.686363520458 Henry Cohn, 2026, needs more optimization.
8 733 0.686431730499 Henry Cohn, 2026, needs more optimization.
8 734 0.686768544652 Henry Cohn, 2026, needs more optimization.
8 735 0.686834288692 Henry Cohn, 2026, needs more optimization.
8 736 0.687498973563 Henry Cohn, 2026, needs more optimization.
8 737 0.687550849039 Henry Cohn, 2026, needs more optimization.
8 738 0.687683457031 Henry Cohn, 2026, needs more optimization.
8 739 0.687767513131 Henry Cohn, 2026, needs more optimization.
8 740 0.687921186451 Henry Cohn, 2026, needs more optimization.
8 741 0.688124255983 Henry Cohn, 2026, needs more optimization.
8 742 0.688248699774 Henry Cohn, 2026, needs more optimization.
8 743 0.688488590101 Henry Cohn, 2026, needs more optimization.
8 744 0.688503492399 Henry Cohn, 2026, needs more optimization.
8 745 0.688695123939 Henry Cohn, 2026, needs more optimization.
8 746 0.688880112531 Henry Cohn, 2026, needs more optimization.
8 747 0.688930602371 Henry Cohn, 2026, needs more optimization.
8 748 0.689151523100 Henry Cohn, 2026, needs more optimization.
8 749 0.689287042649 Henry Cohn, 2026, needs more optimization.
8 750 0.689288140043 Henry Cohn, 2026, needs more optimization.
8 751 0.689460154813 Henry Cohn, 2026, needs more optimization.
8 752 0.689823941181 Henry Cohn, 2026, needs more optimization.
8 753 0.689960229068 Henry Cohn, 2026, needs more optimization.
8 754 0.690100232196 Henry Cohn, 2026, needs more optimization.
8 755 0.690114410221 Henry Cohn, 2026, needs more optimization.
8 756 0.690114883775 Henry Cohn, 2026, needs more optimization.
8 757 0.690116188828 Henry Cohn, 2026, needs more optimization.
8 758 0.690122987129 Henry Cohn, 2026, needs more optimization.
8 759 0.690123841990 Henry Cohn, 2026, needs more optimization.
8 760 0.690135056164 Henry Cohn, 2026, needs more optimization.
8 761 0.690141727615 Henry Cohn, 2026, needs more optimization.
8 762 0.690160147728 Henry Cohn, 2026, needs more optimization.
8 763 0.690167751101 Henry Cohn, 2026, needs more optimization.
8 764 0.690913804909 Henry Cohn, 2026, needs more optimization.
8 765 0.690992917611 Henry Cohn, 2026, needs more optimization.
8 766 0.691020755491 Henry Cohn, 2026, needs more optimization.
8 767 0.691147895144 Henry Cohn, 2026, needs more optimization.
8 768 0.691267425552 Henry Cohn, 2026, needs more optimization.
8 769 0.691300512552 Henry Cohn, 2026, needs more optimization.
8 770 0.691509780411 Henry Cohn, 2026, needs more optimization.
8 772 0.691654167659 Henry Cohn, 2026, needs more optimization.
8 773 0.691666167477 Henry Cohn, 2026, needs more optimization.
8 774 0.691756106911 Henry Cohn, 2026, needs more optimization.
8 775 0.691782854324 Henry Cohn, 2026, needs more optimization.
8 776 0.692234013674 Henry Cohn, 2026, needs more optimization.
8 777 0.692355899673 Henry Cohn, 2026, needs more optimization.
8 778 0.692449491977 Henry Cohn, 2026, needs more optimization.
8 779 0.692455014879 Henry Cohn, 2026, needs more optimization.
8 780 0.692524977654 Henry Cohn, 2026, needs more optimization.
8 781 0.692550276801 Henry Cohn, 2026, needs more optimization.
8 782 0.692593245786 Henry Cohn, 2026, needs more optimization.
8 783 0.692706223216 Henry Cohn, 2026, needs more optimization.
8 784 0.692778882414 Henry Cohn, 2026, needs more optimization.
8 785 0.693257801262 Henry Cohn, 2026, needs more optimization.
8 786 0.693484797541 Henry Cohn, 2026, needs more optimization.
8 787 0.693718248315 Henry Cohn, 2026, needs more optimization.
8 788 0.693764229432 Henry Cohn, 2026, needs more optimization.
8 789 0.694024847989 Henry Cohn, 2026, needs more optimization.
8 790 0.694166307792 Henry Cohn, 2026, needs more optimization.
8 791 0.694175835659 Henry Cohn, 2026, needs more optimization.
8 792 0.694200945874 Henry Cohn, 2026, needs more optimization.
8 793 0.694574886874 Henry Cohn, 2026, needs more optimization.
8 794 0.694575891557 Henry Cohn, 2026, needs more optimization.
8 795 0.694610743007 Henry Cohn, 2026, needs more optimization.
8 797 0.694616223157 Henry Cohn, 2026, needs more optimization.
8 798 0.694818510805 Henry Cohn, 2026, needs more optimization.
8 799 0.694857444702 Henry Cohn, 2026, needs more optimization.
8 800 0.695061370181 Henry Cohn, 2026, needs more optimization.
8 801 0.695304347472 Henry Cohn, 2026, needs more optimization.
8 802 0.695555433296 Henry Cohn, 2026, needs more optimization.
8 803 0.695615765046 Henry Cohn, 2026, needs more optimization.
8 804 0.695862205632 Henry Cohn, 2026, needs more optimization.
8 805 0.696113574926 Henry Cohn, 2026, needs more optimization.
8 806 0.696185921299 Henry Cohn, 2026, needs more optimization.
8 807 0.696223624518 Henry Cohn, 2026, needs more optimization.
8 808 0.696224980154 Henry Cohn, 2026, needs more optimization.
8 809 0.696281037944 Henry Cohn, 2026, needs more optimization.
8 810 0.696283005890 Henry Cohn, 2026, needs more optimization.
8 811 0.696657617274 Henry Cohn, 2026, needs more optimization.
8 812 0.696674397208 Henry Cohn, 2026, needs more optimization.
8 813 0.696812149779 Henry Cohn, 2026, needs more optimization.
8 814 0.697481447318 Henry Cohn, 2026, needs more optimization.
8 815 0.697483340684 Henry Cohn, 2026, needs more optimization.
8 816 0.697523381131 Henry Cohn, 2026, needs more optimization.
8 817 0.697525638187 Henry Cohn, 2026, needs more optimization.
8 818 0.697548292441 Henry Cohn, 2026, needs more optimization.
8 819 0.697582996521 Henry Cohn, 2026, needs more optimization.
8 820 0.697594792804 Henry Cohn, 2026, needs more optimization.
8 821 0.697663716575 Henry Cohn, 2026, needs more optimization.
8 822 0.697873857389 Henry Cohn, 2026, needs more optimization.
8 823 0.697925211413 Henry Cohn, 2026, needs more optimization.
8 824 0.697960568814 Henry Cohn, 2026, needs more optimization.
8 825 0.697970069881 Henry Cohn, 2026, needs more optimization.
8 826 0.698100435105 Henry Cohn, 2026, needs more optimization.
8 827 0.698590087271 Henry Cohn, 2026, needs more optimization.
8 828 0.698591707280 Henry Cohn, 2026, needs more optimization.
8 829 0.698601819753 Henry Cohn, 2026, needs more optimization.
8 834 0.698864363609 Henry Cohn, 2026, needs more optimization.
8 835 0.698865020716 Henry Cohn, 2026, needs more optimization.
8 836 0.699603335745 Henry Cohn, 2026, needs more optimization.
8 837 0.699603373848 Henry Cohn, 2026, needs more optimization.
8 838 0.699611561691 Henry Cohn, 2026, needs more optimization.
8 839 0.699629697877 Henry Cohn, 2026, needs more optimization.
8 840 0.699985192423 Henry Cohn, 2026, needs more optimization.
8 841 0.700469830127 Henry Cohn, 2026, needs more optimization.
8 842 0.700472203797 Henry Cohn, 2026, needs more optimization.
8 843 0.700499452869 Henry Cohn, 2026, needs more optimization.
8 844 0.700503503046 Henry Cohn, 2026, needs more optimization.
8 845 0.700522927376 Henry Cohn, 2026, needs more optimization.
8 846 0.700522927941 Henry Cohn, 2026, needs more optimization.
8 847 0.700533982466 Henry Cohn, 2026, needs more optimization.
8 848 0.700572017950 Henry Cohn, 2026, needs more optimization.
8 849 0.701122568793 Henry Cohn, 2026, needs more optimization.
8 850 0.701127057686 Henry Cohn, 2026, needs more optimization.
8 851 0.701131193070 Henry Cohn, 2026, needs more optimization.
8 852 0.701213710121 Henry Cohn, 2026, needs more optimization.
8 853 0.701510915944 Henry Cohn, 2026, needs more optimization.
8 854 0.701522424284 Henry Cohn, 2026, needs more optimization.
8 855 0.702080030191 Henry Cohn, 2026, needs more optimization.
8 856 0.702083810030 Henry Cohn, 2026, needs more optimization.
8 858 0.702084532566 Henry Cohn, 2026, needs more optimization.
8 859 0.702245809998 Henry Cohn, 2026, needs more optimization.
8 860 0.702249230538 Henry Cohn, 2026, needs more optimization.
8 861 0.702295952568 Henry Cohn, 2026, needs more optimization.
8 862 0.702296722277 Henry Cohn, 2026, needs more optimization.
8 863 0.702365441300 Henry Cohn, 2026, needs more optimization.
8 864 0.702383736437 Henry Cohn, 2026, needs more optimization.
8 865 0.702385372295 Henry Cohn, 2026, needs more optimization.
8 867 0.702397072192 Henry Cohn, 2026, needs more optimization.
8 868 0.702408568989 Henry Cohn, 2026, needs more optimization.
8 869 0.702429732287 Henry Cohn, 2026, needs more optimization.
8 870 0.702473076227 Henry Cohn, 2026, needs more optimization.
8 871 0.702551470621 Henry Cohn, 2026, needs more optimization.
8 872 0.702552282468 Henry Cohn, 2026, needs more optimization.
8 873 0.702552508389 Henry Cohn, 2026, needs more optimization.
8 874 0.703831065387 Henry Cohn, 2026, needs more optimization.
8 875 0.703833200558 Henry Cohn, 2026, needs more optimization.
8 876 0.703838289709 Henry Cohn, 2026, needs more optimization.
8 877 0.704317420477 Henry Cohn, 2026, needs more optimization.
8 879 0.704337214837 Henry Cohn, 2026, needs more optimization.
8 880 0.704337220924 Henry Cohn, 2026, needs more optimization.
8 881 0.704344481179 Henry Cohn, 2026, needs more optimization.
8 882 0.704360635809 Henry Cohn, 2026, needs more optimization.
8 883 0.704508605558 Henry Cohn, 2026, needs more optimization.
8 884 0.704525277380 Henry Cohn, 2026, needs more optimization.
8 885 0.704530075233 Henry Cohn, 2026, needs more optimization.
8 886 0.704967389494 Henry Cohn, 2026, needs more optimization.
8 887 0.704975045316 Henry Cohn, 2026, needs more optimization.
8 888 0.704975369533 Henry Cohn, 2026, needs more optimization.
8 889 0.705001376746 Henry Cohn, 2026, needs more optimization.
8 890 0.705020031528 Henry Cohn, 2026, needs more optimization.
8 891 0.705379649833 Henry Cohn, 2026, needs more optimization.
8 892 0.705578214796 Henry Cohn, 2026, needs more optimization.
8 893 0.705611415543 Henry Cohn, 2026, needs more optimization.
8 894 0.705629023124 Henry Cohn, 2026, needs more optimization.
8 895 0.705629432320 Henry Cohn, 2026, needs more optimization.
8 896 0.705636079277 Henry Cohn, 2026, needs more optimization.
8 897 0.705645585474 Henry Cohn, 2026, needs more optimization.
8 899 0.705645586835 Henry Cohn, 2026, needs more optimization.
8 901 0.705679510274 Henry Cohn, 2026, needs more optimization.
8 902 0.705679697996 Henry Cohn, 2026, needs more optimization.
8 903 0.705686383091 Henry Cohn, 2026, needs more optimization.
8 905 0.705968178669 Henry Cohn, 2026, needs more optimization.
8 907 0.706399295226 Henry Cohn, 2026, needs more optimization.
8 908 0.706399312606 Henry Cohn, 2026, needs more optimization.
8 909 0.706410351790 Henry Cohn, 2026, needs more optimization.
8 910 0.706410938945 Henry Cohn, 2026, needs more optimization.
8 911 0.706420710584 Henry Cohn, 2026, needs more optimization.
8 912 0.706436806300 Henry Cohn, 2026, needs more optimization.
8 913 0.706456919971 Henry Cohn, 2026, needs more optimization.
8 914 0.706504165263 Henry Cohn, 2026, needs more optimization.
8 915 0.706833105550 Henry Cohn, 2026, needs more optimization.
8 916 0.706855819409 Henry Cohn, 2026, needs more optimization.
8 917 0.706863765181 Henry Cohn, 2026, needs more optimization.
8 918 0.707059124595 Henry Cohn, 2026, needs more optimization.
8 919 0.707061511607 Henry Cohn, 2026, needs more optimization.
8 920 0.707063753500 Henry Cohn, 2026, needs more optimization.
8 922 0.707521798924 Henry Cohn, 2026, needs more optimization.
8 923 0.707522395007 Henry Cohn, 2026, needs more optimization.
8 924 0.707528175294 Henry Cohn, 2026, needs more optimization.
8 925 0.707530737459 Henry Cohn, 2026, needs more optimization.
8 926 0.707629487564 Henry Cohn, 2026, needs more optimization.
8 927 0.707921566319 Henry Cohn, 2026, needs more optimization.
8 928 0.707924185954 Henry Cohn, 2026, needs more optimization.
8 929 0.707937427107 Henry Cohn, 2026, needs more optimization.
8 930 0.707937463592 Henry Cohn, 2026, needs more optimization.
8 931 0.707959339643 Henry Cohn, 2026, needs more optimization.
8 932 0.708007039186 Henry Cohn, 2026, needs more optimization.
8 933 0.708010981503 Henry Cohn, 2026, needs more optimization.
8 934 0.708300738653 Henry Cohn, 2026, needs more optimization.
8 935 0.708304892687 Henry Cohn, 2026, needs more optimization.
8 936 0.708305645813 Henry Cohn, 2026, needs more optimization.
8 937 0.708308291065 Henry Cohn, 2026, needs more optimization.
8 938 0.708312471505 Henry Cohn, 2026, needs more optimization.
8 939 0.708865577378 Henry Cohn, 2026, needs more optimization.
8 940 0.708883933532 Henry Cohn, 2026, needs more optimization.
8 942 0.708890528764 Henry Cohn, 2026, needs more optimization.
8 943 0.708946560679 Henry Cohn, 2026, needs more optimization.
8 944 0.708963899919 Henry Cohn, 2026, needs more optimization.
8 945 0.709111961239 Henry Cohn, 2026, needs more optimization.
8 947 0.709112572916 Henry Cohn, 2026, needs more optimization.
8 949 0.709501088216 Henry Cohn, 2026, needs more optimization.
8 950 0.709503319339 Henry Cohn, 2026, needs more optimization.
8 952 0.709508300380 Henry Cohn, 2026, needs more optimization.
8 953 0.709509145934 Henry Cohn, 2026, needs more optimization.
8 954 0.709513658837 Henry Cohn, 2026, needs more optimization.
8 955 0.709886243434 Henry Cohn, 2026, needs more optimization.
8 956 0.709897828415 Henry Cohn, 2026, needs more optimization.
8 957 0.709964562991 Henry Cohn, 2026, needs more optimization.
8 958 0.709972971954 Henry Cohn, 2026, needs more optimization.
8 960 0.710147303736 Henry Cohn, 2026, needs more optimization.
8 961 0.710158737511 Henry Cohn, 2026, needs more optimization.
8 962 0.710628499637 Henry Cohn, 2026, needs more optimization.
8 963 0.710648011027 Henry Cohn, 2026, needs more optimization.
8 965 0.710726509687 Henry Cohn, 2026, needs more optimization.
8 966 0.710745974509 Henry Cohn, 2026, needs more optimization.
8 968 0.710756399095 Henry Cohn, 2026, needs more optimization.
8 969 0.710775324712 Henry Cohn, 2026, needs more optimization.
8 970 0.710846608769 Henry Cohn, 2026, needs more optimization.
8 971 0.711350464640 Henry Cohn, 2026, needs more optimization.
8 973 0.711410204066 Henry Cohn, 2026, needs more optimization.
8 974 0.711447960845 Henry Cohn, 2026, needs more optimization.
8 977 0.711456061767 Henry Cohn, 2026, needs more optimization.
8 978 0.711467048535 Henry Cohn, 2026, needs more optimization.
8 979 0.711867904686 Henry Cohn, 2026, needs more optimization.
8 980 0.711880854629 Henry Cohn, 2026, needs more optimization.
8 981 0.711912760519 Henry Cohn, 2026, needs more optimization.
8 982 0.711936160110 Henry Cohn, 2026, needs more optimization.
8 983 0.711964888630 Henry Cohn, 2026, needs more optimization.
8 984 0.711973182333 Henry Cohn, 2026, needs more optimization.
8 985 0.712235960038 Henry Cohn, 2026, needs more optimization.
8 986 0.712284544703 Henry Cohn, 2026, needs more optimization.
8 987 0.712301250469 Henry Cohn, 2026, needs more optimization.
8 988 0.712314306274 Henry Cohn, 2026, needs more optimization.
8 989 0.712552964915 Henry Cohn, 2026, needs more optimization.
8 990 0.712933263569 Henry Cohn, 2026, needs more optimization.
8 992 0.712941686235 Henry Cohn, 2026, needs more optimization.
8 993 0.712956020452 Henry Cohn, 2026, needs more optimization.
8 994 0.712957179456 Henry Cohn, 2026, needs more optimization.
8 995 0.712957233174 Henry Cohn, 2026, needs more optimization.
8 996 0.712959603500 Henry Cohn, 2026, needs more optimization.
8 997 0.713013552264 Henry Cohn, 2026, needs more optimization.
8 998 0.713043151819 Henry Cohn, 2026, needs more optimization.
8 999 0.713096076250 Henry Cohn, 2026, needs more optimization.
8 1000 0.713098583408 Henry Cohn, 2026, needs more optimization.
8 1001 0.713158766656 Henry Cohn, 2026, needs more optimization.
8 1002 0.713215587825 Henry Cohn, 2026, needs more optimization.
8 1003 0.713235082189 Henry Cohn, 2026, needs more optimization.
8 1004 0.713270194135 Henry Cohn, 2026, needs more optimization.
8 1005 0.713354016934 Henry Cohn, 2026, needs more optimization.
8 1006 0.713359100983 Henry Cohn, 2026, needs more optimization.
8 1007 0.713455222382 Henry Cohn, 2026, needs more optimization.
8 1008 0.713526411174 Henry Cohn, 2026, needs more optimization.
8 1010 0.713579283128 Henry Cohn, 2026, needs more optimization.
8 1011 0.713623915709 Henry Cohn, 2026, needs more optimization.
8 1012 0.713663547990 Henry Cohn, 2026, needs more optimization.
8 1013 0.713676285237 Henry Cohn, 2026, needs more optimization.
8 1014 0.713690339358 Henry Cohn, 2026, needs more optimization.
8 1015 0.713701562720 Henry Cohn, 2026, needs more optimization.
8 1016 0.713731045343 Henry Cohn, 2026, needs more optimization.
8 1017 0.713765188813 Henry Cohn, 2026, needs more optimization.
8 1018 0.713802269383 Henry Cohn, 2026, needs more optimization.
8 1019 0.713816371591 Henry Cohn, 2026, needs more optimization.
8 1020 0.713821268502 Henry Cohn, 2026, needs more optimization.
8 1021 0.713862208244 Henry Cohn, 2026, needs more optimization.
8 1022 0.713871473459 Henry Cohn, 2026, needs more optimization.
8 1023 0.713876856358 Henry Cohn, 2026, needs more optimization.
8 1024 0.713972714310 Henry Cohn, 2026, needs more optimization.
9 19 0.079067151218 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
441⁢x3−81⁢x2−9⁢x+1
9 20 0.087067958322 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
63⁢x2+6⁢x−1
9 21 0.087067958322 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
63⁢x2+6⁢x−1
9 22 0.109015375240 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
662⁢x4+23⁢x3−67⁢x2−3⁢x+1
9 23 0.114272369686 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
9 24 0.127138702332 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 25 0.135451570712 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 26 0.146662063556 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 27 0.149913487586 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 28 0.150185176423 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9 29 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 30 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 31 0.150221104823 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
31⁢x2+2⁢x−1
9 32 0.150221104823 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x2+2⁢x−1
9 33 0.180525091271 Henry Cohn, 2023.
9 34 0.183408724272 Henry Cohn, 2023.
9 35 0.195176120873 Henry Cohn, 2024.
9 36 0.199856614456 Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
9 37 0.213781170696 Henry Cohn, 2025.
9 38 0.216954638443 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
Minimal polynomial listed in plain text data
9 39 0.222837046412 Henry Cohn, 2023.
9 40 0.225659998291 Henry Cohn, 2025.
9 42 0.226907255686 Henry Cohn, 2025.
190336⁢x6+377632⁢x5−322153⁢x4−82188⁢x3+48762⁢x2−972⁢x−729
9 43 0.231201190091 Henry Cohn, 2023.
9 44 0.233554527157 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
9 47 0.238172399483 Henry Cohn, 2023.
335⁢x2−42⁢x−9
9 48 0.254741665820 Henry Cohn, 2025.
9 50 0.256477368938 Henry Cohn, 2026.
23⁢x2−2⁢x−1
9 51 0.266033138128 Henry Cohn, 2026.
9 52 0.267191024627 Henry Cohn, 2023.
71⁢x2−4⁢x−4
9 53 0.269834758170 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
9 54 0.271671378177 Henry Cohn, 2025.
9 56 0.272133267170 Henry Cohn, 2025.
9 57 0.282916244589 Henry Cohn, 2026.
9 58 0.288070633971 Henry Cohn, 2026.
9 59 0.293943006572 Henry Cohn, 2025.
9 60 0.294882506582 Henry Cohn, 2026.
9 61 0.297699008547 Henry Cohn, 2026.
9 62 0.299403421035 Henry Cohn, 2026, needs more optimization.
9 63 0.302685227391 Henry Cohn, 2025.
9 64 0.306653313780 Henry Cohn, 2023.
9 65 0.310475871050 Henry Cohn, 2026.
9 66 0.313645759189 Henry Cohn, 2026.
9 67 0.317743907015 Henry Cohn, 2026.
9 68 0.322050465427 Henry Cohn, 2025.
9 69 0.324666182383 Henry Cohn, 2025.
9 70 0.327710258396 Henry Cohn, 2026.
9 71 0.328977728606 Henry Cohn, 2026.
9 72 0.329462392786 Henry Cohn, 2026, needs more optimization.
9 74 0.329478113244 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 77 0.329568177750 Henry Cohn, 2026.
9 78 0.330101895521 Henry Cohn, 2025.
9 79 0.330918543665 Henry Cohn, 2024.
9 80 0.332977706545 Henry Cohn, 2025.
9 96 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
9 97 0.371099110252 Henry Cohn, 2024.
9 98 0.372095101498 Henry Cohn, 2025.
9 101 0.375074698542 Henry Cohn, 2025.
3191⁢x4+68⁢x3−350⁢x2−44⁢x−1
9 102 0.378388662601 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 103 0.378849371703 Henry Cohn, 2026, needs more optimization.
9 104 0.379090673532 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 105 0.391186576796 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 106 0.394987130628 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 107 0.397604188310 Henry Cohn, 2026, needs more optimization.
9 108 0.399007954405 Henry Cohn, 2026, needs more optimization.
9 109 0.401769344396 Henry Cohn, 2026, needs more optimization.
9 110 0.404779316037 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 111 0.406315842879 Henry Cohn, 2026, needs more optimization.
9 112 0.408809353891 Henry Cohn, 2026, needs more optimization.
9 113 0.410377411195 Henry Cohn, 2026, needs more optimization.
9 114 0.411211042519 Henry Cohn, 2026, needs more optimization.
9 115 0.412580096190 Henry Cohn, 2026, needs more optimization.
9 116 0.413817760914 Henry Cohn, 2026, needs more optimization.
9 117 0.414582257912 Henry Cohn, 2026, needs more optimization.
9 118 0.415620593621 Henry Cohn, 2026, needs more optimization.
9 119 0.416041502843 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 120 0.416495805218 Henry Cohn, 2026, needs more optimization.
9 121 0.416961478258 Henry Cohn, 2026, needs more optimization.
9 122 0.418282170106 Henry Cohn, 2026.
9 123 0.419103978597 Henry Cohn, 2026, needs more optimization.
9 124 0.419753747332 Henry Cohn, 2026, needs more optimization.
9 126 0.419821271705 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11⁢x2−7⁢x+1
9 127 0.420551973940 Henry Cohn, 2026, needs more optimization.
9 128 0.421868014320 Henry Cohn, 2026, needs more optimization.
9 129 0.422316794068 Henry Cohn, 2026, needs more optimization.
9 130 0.422319484817 Henry Cohn, 2026, needs more optimization.
9 131 0.422480470898 Henry Cohn, 2026, needs more optimization.
9 132 0.425976143955 Henry Cohn, 2026, needs more optimization.
9 133 0.427212759568 Henry Cohn, 2026, needs more optimization.
9 134 0.428489584816 Henry Cohn, 2026, needs more optimization.
9 146 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
9 147 0.441557528570 Henry Cohn, 2026, needs more optimization.
9 148 0.444821513223 Henry Cohn, 2026, needs more optimization.
9 149 0.447202806254 Henry Cohn, 2026, needs more optimization.
9 150 0.449497873762 Henry Cohn, 2026, needs more optimization.
9 151 0.449961748538 Henry Cohn, 2026, needs more optimization.
9 152 0.451307920097 Henry Cohn, 2026, needs more optimization.
9 153 0.453626702170 Henry Cohn, 2026, needs more optimization.
9 165 0.454545454546 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−5
9 168 0.454545454546 Henry Cohn, 2026.
11⁢x−5
9 171 0.454545454546 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11⁢x−5
9 172 0.454948864664 Henry Cohn, 2026, needs more optimization.
9 173 0.455014187143 Henry Cohn, 2026, needs more optimization.
9 174 0.455088915344 Henry Cohn, 2026, needs more optimization.
9 175 0.459538717833 Henry Cohn, 2026, needs more optimization.
9 176 0.461209074451 Henry Cohn, 2026, needs more optimization.
9 177 0.461486205561 Henry Cohn, 2026, needs more optimization.
9 178 0.462055301367 Henry Cohn, 2026, needs more optimization.
9 179 0.462342870942 Henry Cohn, 2026, needs more optimization.
9 180 0.462395900275 Henry Cohn, 2026, needs more optimization.
9 181 0.462508204753 Henry Cohn, 2026, needs more optimization.
9 182 0.462623847130 Henry Cohn, 2026, needs more optimization.
9 183 0.463062143536 Henry Cohn, 2026, needs more optimization.
9 184 0.465002275026 Henry Cohn, 2026, needs more optimization.
9 185 0.467181463168 Henry Cohn, 2026, needs more optimization.
9 186 0.469956128013 Henry Cohn, 2026, needs more optimization.
9 187 0.471258850721 Henry Cohn, 2026, needs more optimization.
9 188 0.471600328943 Henry Cohn, 2026, needs more optimization.
9 189 0.473613163266 Henry Cohn, 2026, needs more optimization.
9 209 0.475156558223 Henry Cohn, 2026.
103⁢x2−30⁢x−9
9 210 0.475233275922 Henry Cohn, 2026, needs more optimization.
9 211 0.478983395991 Henry Cohn, 2026, needs more optimization.
9 212 0.481516213550 Henry Cohn, 2026, needs more optimization.
9 213 0.483364671116 Henry Cohn, 2026, needs more optimization.
9 214 0.484883588902 Henry Cohn, 2026, needs more optimization.
9 215 0.485412606248 Henry Cohn, 2026, needs more optimization.
9 216 0.485998499148 Henry Cohn, 2026, needs more optimization.
9 217 0.486671254685 Henry Cohn, 2026, needs more optimization.
9 218 0.492754741722 Henry Cohn, 2026, needs more optimization.
9 219 0.492903891854 Henry Cohn, 2026, needs more optimization.
9 220 0.495572294206 Henry Cohn, 2026, needs more optimization.
9 221 0.496134694228 Henry Cohn, 2026, needs more optimization.
9 222 0.496435362098 Henry Cohn, 2026, needs more optimization.
9 223 0.496798318202 Henry Cohn, 2026, needs more optimization.
9 224 0.496924052666 Henry Cohn, 2026, needs more optimization.
9 225 0.497076286294 Henry Cohn, 2026, needs more optimization.
9 226 0.497510467903 Henry Cohn, 2026, needs more optimization.
9 227 0.497544352730 Henry Cohn, 2026, needs more optimization.
9 228 0.498094935708 Henry Cohn, 2026, needs more optimization.
9 229 0.498287389798 Henry Cohn, 2026, needs more optimization.
9 230 0.498474484959 Henry Cohn, 2026, needs more optimization.
9 231 0.498559581666 Henry Cohn, 2026, needs more optimization.
9 232 0.498590451834 Henry Cohn, 2026, needs more optimization.
9 233 0.498778733698 Henry Cohn, 2026, needs more optimization.
9 234 0.499007433182 Henry Cohn, 2026, needs more optimization.
9 235 0.499088083167 Henry Cohn, 2026, needs more optimization.
9 236 0.499104815468 Henry Cohn, 2026, needs more optimization.
9 237 0.499185471602 Henry Cohn, 2026, needs more optimization.
9 238 0.499254935500 Henry Cohn, 2026, needs more optimization.
9 239 0.499317251584 Henry Cohn, 2026, needs more optimization.
9 240 0.499480365577 Henry Cohn, 2026, needs more optimization.
9 241 0.499534757219 Henry Cohn, 2026, needs more optimization.
9 242 0.499557186181 Henry Cohn, 2026, needs more optimization.
9 243 0.499577098769 Henry Cohn, 2026, needs more optimization.
9 244 0.499611633443 Henry Cohn, 2026, needs more optimization.
9 245 0.499705075621 Henry Cohn, 2026, needs more optimization.
9 246 0.499835000817 Henry Cohn, 2026, needs more optimization.
9 247 0.499876152028 Henry Cohn, 2026, needs more optimization.
9 248 0.499913067513 Henry Cohn, 2026, needs more optimization.
9 249 0.499962789445 Henry Cohn, 2026, needs more optimization.
9 306 0.5 J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3; H. Cohn and I. Rajagopal, Variations on five-dimensional sphere packings, preprint, 2024, arXiv:2412.00937.
2⁢x−1
9 307 0.517020006376 Henry Cohn, 2026, needs more optimization.
9 308 0.518911020501 Henry Cohn, 2026, needs more optimization.
9 309 0.520835148079 Henry Cohn, 2026, needs more optimization.
9 310 0.521829161479 Henry Cohn, 2026, needs more optimization.
9 311 0.521840732694 Henry Cohn, 2026, needs more optimization.
9 312 0.521845423776 Henry Cohn, 2026, needs more optimization.
9 313 0.522200619152 Henry Cohn, 2026, needs more optimization.
9 330 0.523809523810 Henry Cohn and Ilmari Vahteristo (independently), 2026.
21⁢x−11
9 331 0.528486973796 Henry Cohn, 2026, needs more optimization.
9 332 0.530011486582 Henry Cohn, 2026, needs more optimization.
9 333 0.533317479777 Henry Cohn, 2026, needs more optimization.
9 334 0.534880501029 Henry Cohn, 2026, needs more optimization.
9 335 0.536073163685 Henry Cohn, 2026, needs more optimization.
9 336 0.536191435188 Henry Cohn, 2026, needs more optimization.
9 337 0.536435633791 Henry Cohn, 2026, needs more optimization.
9 338 0.536441576637 Henry Cohn, 2026, needs more optimization.
9 339 0.537017557534 Henry Cohn, 2026, needs more optimization.
9 340 0.538002447067 Henry Cohn, 2026, needs more optimization.
9 341 0.538056434706 Henry Cohn, 2026, needs more optimization.
9 342 0.539405267259 Henry Cohn, 2026, needs more optimization.
9 343 0.540088308685 Henry Cohn, 2026, needs more optimization.
9 344 0.540165093065 Henry Cohn, 2026, needs more optimization.
9 345 0.540668367698 Henry Cohn, 2026, needs more optimization.
9 346 0.541056179355 Henry Cohn, 2026, needs more optimization.
9 347 0.541586860369 Henry Cohn, 2026, needs more optimization.
9 348 0.542525870436 Henry Cohn, 2026, needs more optimization.
9 349 0.543233881535 Henry Cohn, 2026, needs more optimization.
9 350 0.543337505237 Henry Cohn, 2026, needs more optimization.
9 351 0.543634058326 Henry Cohn, 2026, needs more optimization.
9 352 0.543836419842 Henry Cohn, 2026, needs more optimization.
9 353 0.543919733502 Henry Cohn, 2026, needs more optimization.
9 354 0.543988993615 Henry Cohn, 2026, needs more optimization.
9 355 0.544036060116 Henry Cohn, 2026, needs more optimization.
9 356 0.544183215856 Henry Cohn, 2026, needs more optimization.
9 357 0.544707550799 Henry Cohn, 2026, needs more optimization.
9 358 0.544843171827 Henry Cohn, 2026, needs more optimization.
9 359 0.545942513838 Henry Cohn, 2026, needs more optimization.
9 360 0.546522386214 Henry Cohn, 2026, needs more optimization.
9 361 0.546736234637 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
9 482 0.546918160679 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x2−2⁢x−1
9 483 0.555131086100 Henry Cohn, 2026, needs more optimization.
9 484 0.556740696957 Henry Cohn, 2026, needs more optimization.
9 485 0.562156243476 Henry Cohn, 2026, needs more optimization.
9 486 0.565394637504 Henry Cohn, 2026, needs more optimization.
9 487 0.568200798897 Henry Cohn, 2026, needs more optimization.
9 488 0.569244061493 Henry Cohn, 2026, needs more optimization.
9 489 0.570781288936 Henry Cohn, 2026, needs more optimization.
9 490 0.572422283995 Henry Cohn, 2026, needs more optimization.
9 491 0.574075087841 Henry Cohn, 2026, needs more optimization.
9 492 0.574928622693 Henry Cohn, 2026, needs more optimization.
9 493 0.576322163126 Henry Cohn, 2026, needs more optimization.
9 494 0.577910205845 Henry Cohn, 2026, needs more optimization.
9 495 0.578749902869 Henry Cohn, 2026, needs more optimization.
9 496 0.580066368685 Henry Cohn, 2026, needs more optimization.
9 497 0.580561930308 Henry Cohn, 2026, needs more optimization.
9 498 0.581667168990 Henry Cohn, 2026, needs more optimization.
9 499 0.582980383305 Henry Cohn, 2026, needs more optimization.
9 500 0.583854478902 Henry Cohn, 2026, needs more optimization.
9 501 0.584637563736 Henry Cohn, 2026, needs more optimization.
9 502 0.585602287411 Henry Cohn, 2026, needs more optimization.
9 503 0.586187162307 Henry Cohn, 2026, needs more optimization.
9 504 0.586661652201 Henry Cohn, 2026, needs more optimization.
9 505 0.587085107885 Henry Cohn, 2026, needs more optimization.
9 506 0.588068244510 Henry Cohn, 2026, needs more optimization.
9 507 0.588215485331 Henry Cohn, 2026, needs more optimization.
9 508 0.589090891057 Henry Cohn, 2026, needs more optimization.
9 509 0.589558925034 Henry Cohn, 2026, needs more optimization.
9 510 0.589564452964 Henry Cohn, 2026, needs more optimization.
9 511 0.589572824672 Henry Cohn, 2026, needs more optimization.
9 512 0.589586233047 Henry Cohn, 2026, needs more optimization.
9 513 0.589788456224 Henry Cohn, 2026, needs more optimization.
9 514 0.589801365226 Henry Cohn, 2026, needs more optimization.
9 515 0.589810162025 Henry Cohn, 2026, needs more optimization.
9 516 0.589818497100 Henry Cohn, 2026, needs more optimization.
9 517 0.589831570696 Henry Cohn, 2026, needs more optimization.
9 518 0.589848904726 Henry Cohn, 2026, needs more optimization.
9 519 0.589886168140 Henry Cohn, 2026, needs more optimization.
9 520 0.589889828555 Henry Cohn, 2026, needs more optimization.
9 521 0.589894037724 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
9 522 0.589905827862 Henry Cohn, 2026, needs more optimization.
9 523 0.589909801164 Henry Cohn, 2026, needs more optimization.
9 524 0.589915327031 Henry Cohn, 2026, needs more optimization.
9 525 0.590355099436 Henry Cohn, 2026, needs more optimization.
9 526 0.591418930421 Henry Cohn, 2026, needs more optimization.
9 527 0.593589111405 Henry Cohn, 2026, needs more optimization.
9 528 0.594370199339 Henry Cohn, 2026, needs more optimization.
9 529 0.595167862110 Henry Cohn, 2026, needs more optimization.
9 530 0.595851112012 Henry Cohn, 2026, needs more optimization.
9 531 0.596429630514 Henry Cohn, 2026, needs more optimization.
9 532 0.596829158282 Henry Cohn, 2026, needs more optimization.
9 533 0.596958058750 Henry Cohn, 2026, needs more optimization.
9 534 0.597601064105 Henry Cohn, 2026, needs more optimization.
9 535 0.597916522425 Henry Cohn, 2026, needs more optimization.
9 536 0.598621708953 Henry Cohn, 2026, needs more optimization.
9 537 0.598789702993 Henry Cohn, 2026, needs more optimization.
9 538 0.598994748687 Henry Cohn, 2026, needs more optimization.
9 539 0.599422005113 Henry Cohn, 2026, needs more optimization.
9 540 0.599733464770 Henry Cohn, 2026, needs more optimization.
9 541 0.599873219660 Henry Cohn, 2026, needs more optimization.
9 542 0.599968490183 Henry Cohn, 2026, needs more optimization.
9 610 0.6 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−3
9 612 0.6 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
5⁢x−3
9 613 0.605088427460 Henry Cohn, 2026, needs more optimization.
9 614 0.606325587701 Henry Cohn, 2026, needs more optimization.
9 615 0.606815166783 Henry Cohn, 2026, needs more optimization.
9 616 0.607944319544 Henry Cohn, 2026, needs more optimization.
9 617 0.608242601737 Henry Cohn, 2026, needs more optimization.
9 618 0.608318676885 Henry Cohn, 2026, needs more optimization.
9 619 0.608425307198 Henry Cohn, 2026, needs more optimization.
9 620 0.613519935760 Henry Cohn, 2026, needs more optimization.
9 621 0.613559493553 Henry Cohn, 2026, needs more optimization.
9 622 0.613588171699 Henry Cohn, 2026, needs more optimization.
9 623 0.613624922181 Henry Cohn, 2026, needs more optimization.
9 624 0.613705969596 Henry Cohn, 2026, needs more optimization.
9 625 0.613722718844 Henry Cohn, 2026, needs more optimization.
9 626 0.613825285283 Henry Cohn, 2026, needs more optimization.
9 627 0.614356973506 Henry Cohn, 2026, needs more optimization.
9 628 0.614795967734 Henry Cohn, 2026, needs more optimization.
9 629 0.615187181109 Henry Cohn, 2026, needs more optimization.
9 630 0.615581064253 Henry Cohn, 2026, needs more optimization.
9 631 0.615984795497 Henry Cohn, 2026, needs more optimization.
9 632 0.617563315640 Henry Cohn, 2026, needs more optimization.
9 633 0.617725802730 Henry Cohn, 2026, needs more optimization.
9 636 0.618033022014 Henry Cohn, 2026, needs more optimization.
9 637 0.618033194702 Henry Cohn, 2026, needs more optimization.
9 639 0.618033458638 Henry Cohn, 2026, needs more optimization.
9 642 0.618033508794 Henry Cohn, 2026, needs more optimization.
9 643 0.618033524388 Henry Cohn, 2026, needs more optimization.
9 644 0.618033987482 Henry Cohn, 2026, needs more optimization.
9 645 0.618033987526 Henry Cohn, 2026, needs more optimization.
9 722 0.618033988750 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
x2+x−1
9 723 0.624150416976 Henry Cohn, 2026, needs more optimization.
9 724 0.642721550459 Henry Cohn, 2026, needs more optimization.
9 725 0.642927441430 Henry Cohn, 2026, needs more optimization.
9 726 0.643184762181 Henry Cohn, 2026, needs more optimization.
9 727 0.643231869064 Henry Cohn, 2026, needs more optimization.
9 728 0.643354656436 Henry Cohn, 2026, needs more optimization.
9 729 0.643385602690 Henry Cohn, 2026, needs more optimization.
9 730 0.643665745188 Henry Cohn, 2026, needs more optimization.
9 731 0.643689552498 Henry Cohn, 2026, needs more optimization.
9 732 0.643699533537 Henry Cohn, 2026, needs more optimization.
9 733 0.643813751656 Henry Cohn, 2026, needs more optimization.
9 734 0.644253274686 Henry Cohn, 2026, needs more optimization.
9 735 0.644261678977 Henry Cohn, 2026, needs more optimization.
9 736 0.644480253707 Henry Cohn, 2026, needs more optimization.
9 737 0.644548794811 Henry Cohn, 2026, needs more optimization.
9 738 0.644553235061 Henry Cohn, 2026, needs more optimization.
9 739 0.644818860792 Henry Cohn, 2026, needs more optimization.
9 740 0.645076581868 Henry Cohn, 2026, needs more optimization.
9 741 0.645091746802 Henry Cohn, 2026, needs more optimization.
9 742 0.645154937237 Henry Cohn, 2026, needs more optimization.
9 743 0.645211301809 Henry Cohn, 2026, needs more optimization.
9 744 0.645310839370 Henry Cohn, 2026, needs more optimization.
9 745 0.645556374870 Henry Cohn, 2026, needs more optimization.
9 746 0.645572192490 Henry Cohn, 2026, needs more optimization.
9 748 0.645598640733 Henry Cohn, 2026, needs more optimization.
9 750 0.645604199097 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
9 751 0.646101385022 Henry Cohn, 2026, needs more optimization.
9 752 0.646422597531 Henry Cohn, 2026, needs more optimization.
9 753 0.646606512420 Henry Cohn, 2026, needs more optimization.
9 754 0.646623582160 Henry Cohn, 2026, needs more optimization.
9 755 0.646634838428 Henry Cohn, 2026, needs more optimization.
9 756 0.646792062125 Henry Cohn, 2026, needs more optimization.
9 757 0.646987076226 Henry Cohn, 2026, needs more optimization.
9 758 0.647155924233 Henry Cohn, 2026, needs more optimization.
9 759 0.647388729600 Henry Cohn, 2026, needs more optimization.
9 760 0.647388734231 Henry Cohn, 2026, needs more optimization.
9 761 0.647426575799 Henry Cohn, 2026, needs more optimization.
9 762 0.647473630184 Henry Cohn, 2026, needs more optimization.
9 763 0.647857746092 Henry Cohn, 2026, needs more optimization.
9 764 0.647877830663 Henry Cohn, 2026, needs more optimization.
9 765 0.647987343012 Henry Cohn, 2026, needs more optimization.
9 766 0.648003921887 Henry Cohn, 2026, needs more optimization.
9 767 0.648187198212 Henry Cohn, 2026, needs more optimization.
9 768 0.648261029514 Henry Cohn, 2026, needs more optimization.
9 769 0.648382259926 Henry Cohn, 2026, needs more optimization.
9 770 0.648403934987 Henry Cohn, 2026, needs more optimization.
9 771 0.648939063367 Henry Cohn, 2026, needs more optimization.
9 772 0.648955445605 Henry Cohn, 2026, needs more optimization.
9 773 0.648959854991 Henry Cohn, 2026, needs more optimization.
9 774 0.649035260061 Henry Cohn, 2026, needs more optimization.
9 775 0.649278542756 Henry Cohn, 2026, needs more optimization.
9 776 0.649281086109 Henry Cohn, 2026, needs more optimization.
9 777 0.649349526351 Henry Cohn, 2026, needs more optimization.
9 778 0.649374422986 Henry Cohn, 2026, needs more optimization.
9 779 0.649774278938 Henry Cohn, 2026, needs more optimization.
9 780 0.649790501491 Henry Cohn, 2026, needs more optimization.
9 781 0.649812032909 Henry Cohn, 2026, needs more optimization.
9 782 0.649824306662 Henry Cohn, 2026, needs more optimization.
9 783 0.649830143671 Henry Cohn, 2026, needs more optimization.
9 784 0.649832798256 Henry Cohn, 2026, needs more optimization.
9 785 0.649836425384 Henry Cohn, 2026, needs more optimization.
9 786 0.649845564169 Henry Cohn, 2026, needs more optimization.
9 787 0.650694612758 Henry Cohn, 2026, needs more optimization.
9 788 0.650720834278 Henry Cohn, 2026, needs more optimization.
9 789 0.650803478154 Henry Cohn, 2026, needs more optimization.
9 790 0.651025061732 Henry Cohn, 2026, needs more optimization.
9 791 0.651271943139 Henry Cohn, 2026, needs more optimization.
9 792 0.651289302474 Henry Cohn, 2026, needs more optimization.
9 793 0.651366776364 Henry Cohn, 2026, needs more optimization.
9 794 0.651509806082 Henry Cohn, 2026, needs more optimization.
9 795 0.651637308571 Henry Cohn, 2026, needs more optimization.
9 796 0.651645663924 Henry Cohn, 2026, needs more optimization.
9 797 0.651669347520 Henry Cohn, 2026, needs more optimization.
9 798 0.651848609462 Henry Cohn, 2026, needs more optimization.
9 799 0.652135170284 Henry Cohn, 2026, needs more optimization.
9 800 0.652146254708 Henry Cohn, 2026, needs more optimization.
9 801 0.652204274345 Henry Cohn, 2026, needs more optimization.
9 802 0.652260810871 Henry Cohn, 2026, needs more optimization.
9 803 0.652502316213 Henry Cohn, 2026, needs more optimization.
9 804 0.652530431745 Henry Cohn, 2026, needs more optimization.
9 805 0.652542806715 Henry Cohn, 2026, needs more optimization.
9 806 0.652684800167 Henry Cohn, 2026, needs more optimization.
9 807 0.652898820820 Henry Cohn, 2026, needs more optimization.
9 808 0.652936123288 Henry Cohn, 2026, needs more optimization.
9 809 0.653140324908 Henry Cohn, 2026, needs more optimization.
9 810 0.653153306682 Henry Cohn, 2026, needs more optimization.
9 811 0.653206909055 Henry Cohn, 2026, needs more optimization.
9 812 0.653342029628 Henry Cohn, 2026, needs more optimization.
9 813 0.653405722441 Henry Cohn, 2026, needs more optimization.
9 814 0.653661139609 Henry Cohn, 2026, needs more optimization.
9 815 0.653751063201 Henry Cohn, 2026, needs more optimization.
9 816 0.653804441706 Henry Cohn, 2026, needs more optimization.
9 817 0.653831258788 Henry Cohn, 2026, needs more optimization.
9 818 0.653902944622 Henry Cohn, 2026, needs more optimization.
9 819 0.654105743545 Henry Cohn, 2026, needs more optimization.
9 820 0.654112353566 Henry Cohn, 2026, needs more optimization.
9 821 0.654197799002 Henry Cohn, 2026, needs more optimization.
9 822 0.654225453054 Henry Cohn, 2026, needs more optimization.
9 823 0.654353916336 Henry Cohn, 2026, needs more optimization.
9 824 0.654457225209 Henry Cohn, 2026, needs more optimization.
9 825 0.654598832901 Henry Cohn, 2026, needs more optimization.
9 826 0.654786892334 Henry Cohn, 2026, needs more optimization.
9 827 0.654972560413 Henry Cohn, 2026, needs more optimization.
9 828 0.654989475263 Henry Cohn, 2026, needs more optimization.
9 829 0.655125250214 Henry Cohn, 2026, needs more optimization.
9 830 0.655136343664 Henry Cohn, 2026, needs more optimization.
9 831 0.655438451670 Henry Cohn, 2026, needs more optimization.
9 832 0.655440385105 Henry Cohn, 2026, needs more optimization.
9 833 0.655628681968 Henry Cohn, 2026, needs more optimization.
9 834 0.655667589699 Henry Cohn, 2026, needs more optimization.
9 835 0.655710989363 Henry Cohn, 2026, needs more optimization.
9 836 0.655716626101 Henry Cohn, 2026, needs more optimization.
9 837 0.655719657336 Henry Cohn, 2026, needs more optimization.
9 838 0.655721093237 Henry Cohn, 2026, needs more optimization.
9 839 0.656321501567 Henry Cohn, 2026, needs more optimization.
9 840 0.656386662642 Henry Cohn, 2026, needs more optimization.
9 841 0.656784976452 Henry Cohn, 2026, needs more optimization.
9 842 0.656789767792 Henry Cohn, 2026, needs more optimization.
9 843 0.657066189197 Henry Cohn, 2026, needs more optimization.
9 844 0.657082781642 Henry Cohn, 2026, needs more optimization.
9 845 0.657121386185 Henry Cohn, 2026, needs more optimization.
9 846 0.657373055394 Henry Cohn, 2026, needs more optimization.
9 847 0.657402912848 Henry Cohn, 2026, needs more optimization.
9 848 0.657405772792 Henry Cohn, 2026, needs more optimization.
9 849 0.657435023635 Henry Cohn, 2026, needs more optimization.
9 850 0.657500731476 Henry Cohn, 2026, needs more optimization.
9 851 0.657736034323 Henry Cohn, 2026, needs more optimization.
9 852 0.657773430730 Henry Cohn, 2026, needs more optimization.
9 853 0.657782491761 Henry Cohn, 2026, needs more optimization.
9 854 0.657796337547 Henry Cohn, 2026, needs more optimization.
9 855 0.657979574662 Henry Cohn, 2026, needs more optimization.
9 856 0.658300504686 Henry Cohn, 2026, needs more optimization.
9 857 0.658349909104 Henry Cohn, 2026, needs more optimization.
9 858 0.658537634389 Henry Cohn, 2026, needs more optimization.
9 859 0.658589290524 Henry Cohn, 2026, needs more optimization.
9 860 0.658757145787 Henry Cohn, 2026, needs more optimization.
9 861 0.658810454854 Henry Cohn, 2026, needs more optimization.
9 862 0.658978556948 Henry Cohn, 2026, needs more optimization.
9 863 0.658993757116 Henry Cohn, 2026, needs more optimization.
9 864 0.659004522825 Henry Cohn, 2026, needs more optimization.
9 865 0.659013585393 Henry Cohn, 2026, needs more optimization.
9 866 0.659015256630 Henry Cohn, 2026, needs more optimization.
9 867 0.659044027243 Henry Cohn, 2026, needs more optimization.
9 868 0.659053176117 Henry Cohn, 2026, needs more optimization.
9 869 0.659054422792 Henry Cohn, 2026, needs more optimization.
9 870 0.659678076685 Henry Cohn, 2026, needs more optimization.
9 871 0.659689234826 Henry Cohn, 2026, needs more optimization.
9 872 0.659696797840 Henry Cohn, 2026, needs more optimization.
9 873 0.660053938435 Henry Cohn, 2026, needs more optimization.
9 874 0.660062800401 Henry Cohn, 2026, needs more optimization.
9 875 0.660107827693 Henry Cohn, 2026, needs more optimization.
9 876 0.660143249868 Henry Cohn, 2026, needs more optimization.
9 877 0.660145050381 Henry Cohn, 2026, needs more optimization.
9 878 0.660162575446 Henry Cohn, 2026, needs more optimization.
9 879 0.660172552055 Henry Cohn, 2026, needs more optimization.
9 880 0.660177011225 Henry Cohn, 2026, needs more optimization.
9 881 0.660721544654 Henry Cohn, 2026, needs more optimization.
9 882 0.660729553390 Henry Cohn, 2026, needs more optimization.
9 883 0.660742389183 Henry Cohn, 2026, needs more optimization.
9 884 0.660755100845 Henry Cohn, 2026, needs more optimization.
9 885 0.660756320601 Henry Cohn, 2026, needs more optimization.
9 886 0.660758410467 Henry Cohn, 2026, needs more optimization.
9 887 0.661268276229 Henry Cohn, 2026, needs more optimization.
9 888 0.661633277860 Henry Cohn, 2026, needs more optimization.
9 889 0.661680613412 Henry Cohn, 2026, needs more optimization.
9 890 0.661721267704 Henry Cohn, 2026, needs more optimization.
9 891 0.661726950482 Henry Cohn, 2026, needs more optimization.
9 892 0.661919999879 Henry Cohn, 2026, needs more optimization.
9 893 0.661977743210 Henry Cohn, 2026, needs more optimization.
9 894 0.662019738108 Henry Cohn, 2026, needs more optimization.
9 895 0.662235825305 Henry Cohn, 2026, needs more optimization.
9 896 0.662260542367 Henry Cohn, 2026, needs more optimization.
9 897 0.662288539967 Henry Cohn, 2026, needs more optimization.
9 898 0.662503803428 Henry Cohn, 2026, needs more optimization.
9 899 0.662526709311 Henry Cohn, 2026, needs more optimization.
9 900 0.662622893179 Henry Cohn, 2026, needs more optimization.
9 901 0.662630418013 Henry Cohn, 2026, needs more optimization.
9 902 0.662789065134 Henry Cohn, 2026, needs more optimization.
9 903 0.663109913715 Henry Cohn, 2026, needs more optimization.
9 904 0.663115737945 Henry Cohn, 2026, needs more optimization.
9 905 0.663170102283 Henry Cohn, 2026, needs more optimization.
9 906 0.663309828521 Henry Cohn, 2026, needs more optimization.
9 907 0.663359615232 Henry Cohn, 2026, needs more optimization.
9 908 0.663367404082 Henry Cohn, 2026, needs more optimization.
9 909 0.663563683853 Henry Cohn, 2026, needs more optimization.
9 910 0.663608879215 Henry Cohn, 2026, needs more optimization.
9 911 0.663710155730 Henry Cohn, 2026, needs more optimization.
9 912 0.663843208809 Henry Cohn, 2026, needs more optimization.
9 913 0.663863530097 Henry Cohn, 2026, needs more optimization.
9 914 0.663882552648 Henry Cohn, 2026, needs more optimization.
9 915 0.663925987785 Henry Cohn, 2026, needs more optimization.
9 916 0.664189552883 Henry Cohn, 2026, needs more optimization.
9 917 0.664197917476 Henry Cohn, 2026, needs more optimization.
9 918 0.664301007773 Henry Cohn, 2026, needs more optimization.
9 919 0.664661859840 Henry Cohn, 2026, needs more optimization.
9 920 0.664690998439 Henry Cohn, 2026, needs more optimization.
9 921 0.664714683142 Henry Cohn, 2026, needs more optimization.
9 922 0.664739780276 Henry Cohn, 2026, needs more optimization.
9 923 0.665016975622 Henry Cohn, 2026, needs more optimization.
9 924 0.665063570009 Henry Cohn, 2026, needs more optimization.
9 925 0.665317036546 Henry Cohn, 2026, needs more optimization.
9 926 0.665340551485 Henry Cohn, 2026, needs more optimization.
9 927 0.665363967213 Henry Cohn, 2026, needs more optimization.
9 928 0.665634544223 Henry Cohn, 2026, needs more optimization.
9 929 0.665636719726 Henry Cohn, 2026, needs more optimization.
9 930 0.665714354092 Henry Cohn, 2026, needs more optimization.
9 931 0.665761904292 Henry Cohn, 2026, needs more optimization.
9 932 0.665811234885 Henry Cohn, 2026, needs more optimization.
9 933 0.665832526527 Henry Cohn, 2026, needs more optimization.
9 934 0.666169339489 Henry Cohn, 2026, needs more optimization.
9 935 0.666177072927 Henry Cohn, 2026, needs more optimization.
9 936 0.666333729577 Henry Cohn, 2026, needs more optimization.
9 937 0.666434617927 Henry Cohn, 2026, needs more optimization.
9 938 0.666522238951 Henry Cohn, 2026, needs more optimization.
9 939 0.666626705676 Henry Cohn, 2026, needs more optimization.
9 1008 0.666666666667 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−2
9 1024 0.666666666667 Subcode of a code of size 1056 from M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
3⁢x−2
10 21 0.072033139843 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
640⁢x3−100⁢x2−10⁢x+1
10 22 0.083956154719 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 23 0.086853938956 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 24 0.098710133500 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
613376⁢x8−228096⁢x7+40432⁢x6+16416⁢x5−8016⁢x4−216⁢x3+184⁢x2−1
10 25 0.104476374556 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 26 0.104477652124 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 27 0.124212414191 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 28 0.128238684469 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
92⁢x2−4⁢x−1
10 29 0.130634295944 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
10 30 0.138418790027 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
10 31 0.144114939804 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
10 32 0.146959243017 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
279⁢x4−420⁢x3+102⁢x2−1
10 33 0.150071241046 Henry Cohn, 2025.
10 34 0.150182194868 Henry Cohn, 2026.
10 35 0.157397110567 Henry Cohn, 2025.
10 36 0.164041833761 Henry Cohn, 2023.
10 40 0.166666666667 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
6⁢x−1
10 41 0.176776695297 Henry Cohn, 2023.
32⁢x2−1
10 42 0.196163849637 Henry Cohn, 2026.
10 43 0.205622503031 Henry Cohn, 2025.
10 44 0.209906238690 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 45 0.210496566837 Henry Cohn, 2026.
10 46 0.210715021825 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 50 0.210852996458 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
71⁢x2+4⁢x−4
10 51 0.216689708737 Henry Cohn, 2025.
10 52 0.230823073590 Henry Cohn, 2026.
10 57 0.231237647788 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
36⁢x2−4⁢x−1
10 58 0.25 Henry Cohn, 2024.
4⁢x−1
10 59 0.252499828074 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 60 0.252845078510 Henry Cohn, 2026.
10 61 0.255558009804 Henry Cohn, 2026.
10 62 0.257763357141 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 63 0.257944905339 Henry Cohn, 2025.
10 64 0.260558293949 Henry Cohn, 2026.
10 65 0.264885834877 Henry Cohn, 2025.
10 66 0.265168946762 Henry Cohn, 2025.
10 67 0.268064425530 Henry Cohn, 2025.
10 68 0.268886163794 Henry Cohn, 2026, needs more optimization.
10 69 0.269687676246 Henry Cohn, 2026, needs more optimization.
10 70 0.271728059137 Henry Cohn, 2026, needs more optimization.
10 71 0.271905044079 Henry Cohn, 2026.
10 72 0.274447908374 Henry Cohn, 2026.
10 73 0.275987133320 Henry Cohn, 2025.
10 74 0.279604372367 Henry Cohn, 2026, needs more optimization.
10 75 0.283455182208 Henry Cohn, 2026.
10 76 0.284096667917 Henry Cohn, 2025.
10 77 0.284910960402 Henry Cohn, 2025.
10 78 0.289669890099 Henry Cohn, 2026, needs more optimization.
10 79 0.295238353835 Henry Cohn, 2026, needs more optimization.
10 80 0.299105344231 Henry Cohn, 2026, needs more optimization.
10 81 0.301757574480 Henry Cohn, 2026, needs more optimization.
10 82 0.304386276692 Henry Cohn, 2026, needs more optimization.
10 83 0.307850499858 Henry Cohn, 2026, needs more optimization.
10 84 0.310845407658 Henry Cohn, 2026, needs more optimization.
10 85 0.318197566143 Henry Cohn, 2026, needs more optimization.
10 86 0.322133293315 Henry Cohn, 2026.
10 87 0.323321961159 Henry Cohn, 2026.
10 88 0.324088773612 Henry Cohn, 2026, needs more optimization.
10 89 0.324767465421 Henry Cohn, 2026, needs more optimization.
10 90 0.325381371900 Henry Cohn, 2026, needs more optimization.
10 91 0.326253803233 Henry Cohn, 2026, needs more optimization.
10 92 0.327937279523 Henry Cohn, 2026, needs more optimization.
10 93 0.328575896907 Henry Cohn, 2026, needs more optimization.
10 94 0.329287493863 Henry Cohn, 2026, needs more optimization.
10 95 0.329852062553 Henry Cohn, 2026, needs more optimization.
10 96 0.330229858535 Henry Cohn, 2026, needs more optimization.
10 97 0.330407574548 Henry Cohn, 2026, needs more optimization.
10 98 0.330427147753 Henry Cohn, 2026, needs more optimization.
10 99 0.330654923978 Henry Cohn, 2026.
10 100 0.330959501871 Henry Cohn, 2026, needs more optimization.
10 101 0.331169613949 Henry Cohn, 2026, needs more optimization.
10 102 0.331364193607 Henry Cohn, 2026, needs more optimization.
10 103 0.333133191921 Henry Cohn, 2026, needs more optimization.
10 104 0.333225781903 Henry Cohn, 2026, needs more optimization.
10 105 0.333254050100 Henry Cohn, 2026, needs more optimization.
10 106 0.333281841528 Henry Cohn, 2026, needs more optimization.
10 107 0.333303166922 Henry Cohn, 2026, needs more optimization.
10 108 0.333303572055 Henry Cohn, 2026, needs more optimization.
10 109 0.335265623439 Henry Cohn, 2026, needs more optimization.
10 110 0.339290566040 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 111 0.342150831517 Henry Cohn, 2026, needs more optimization.
10 112 0.344823383275 Henry Cohn, 2026, needs more optimization.
10 113 0.347102526263 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
10 114 0.348284889017 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
10 115 0.352515784788 Henry Cohn, 2026, needs more optimization.
10 116 0.353509995249 Henry Cohn, 2026, needs more optimization.
10 117 0.358339646974 Henry Cohn, 2026, needs more optimization.
10 118 0.361650603080 Henry Cohn, 2026, needs more optimization.
10 119 0.363761710067 Henry Cohn, 2026, needs more optimization.
10 120 0.364662416716 Henry Cohn, 2026, needs more optimization.
10 121 0.365191096657 Henry Cohn, 2026.
10 122 0.365459215843 Henry Cohn, 2026, needs more optimization.
10 123 0.365549164220 Henry Cohn, 2026, needs more optimization.
10 124 0.365549399788 Henry Cohn, 2026, needs more optimization.
10 125 0.365549561049 Henry Cohn, 2026, needs more optimization.
10 126 0.365549593044 Henry Cohn, 2026, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367843329086 Henry Cohn, 2026, needs more optimization.
10 129 0.370352757621 Henry Cohn, 2026, needs more optimization.
10 130 0.371246121340 Henry Cohn, 2026, needs more optimization.
10 131 0.371270248439 Henry Cohn, 2026, needs more optimization.
10 132 0.371409893582 Henry Cohn, 2026, needs more optimization.
10 133 0.384836218782 Henry Cohn, 2026, needs more optimization.
10 134 0.389598525532 Henry Cohn, 2026, needs more optimization.
10 135 0.392340579677 Henry Cohn, 2026, needs more optimization.
10 136 0.392922373474 Henry Cohn, 2026, needs more optimization.
10 137 0.396210893031 Henry Cohn, 2026, needs more optimization.
10 138 0.398648215138 Henry Cohn, 2026, needs more optimization.
10 139 0.400187109545 Henry Cohn, 2026, needs more optimization.
10 140 0.401786078881 Henry Cohn, 2026, needs more optimization.
10 141 0.403135634506 Henry Cohn, 2026, needs more optimization.
10 142 0.404394571676 Henry Cohn, 2026, needs more optimization.
10 156 0.405827419558 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x2−2⁢x−1
10 157 0.413095130212 Henry Cohn, 2026, needs more optimization.
10 158 0.414010271837 Henry Cohn, 2026, needs more optimization.
10 159 0.414516421838 Henry Cohn, 2026, needs more optimization.
10 160 0.414818422222 Henry Cohn, 2026, needs more optimization.
10 161 0.415973100701 Henry Cohn, 2026, needs more optimization.
10 162 0.416875406071 Henry Cohn, 2026, needs more optimization.
10 163 0.419201642434 Henry Cohn, 2026, needs more optimization.
10 164 0.420591579742 Henry Cohn, 2026, needs more optimization.
10 165 0.421674879470 Henry Cohn, 2026, needs more optimization.
10 166 0.422482720391 Henry Cohn, 2026, needs more optimization.
10 167 0.423422354737 Henry Cohn, 2026, needs more optimization.
10 168 0.424374959358 Henry Cohn, 2026, needs more optimization.
10 169 0.425515856893 Henry Cohn, 2026, needs more optimization.
10 170 0.425990210032 Henry Cohn, 2026, needs more optimization.
10 171 0.427020432371 Henry Cohn, 2026, needs more optimization.
10 172 0.428113780892 Henry Cohn, 2026, needs more optimization.
10 194 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
10 195 0.438691046336 Henry Cohn, 2026, needs more optimization.
10 196 0.441223753713 Henry Cohn, 2026, needs more optimization.
10 197 0.443187356134 Henry Cohn, 2026, needs more optimization.
10 198 0.445229546342 Henry Cohn, 2026, needs more optimization.
10 199 0.446768072479 Henry Cohn, 2026, needs more optimization.
10 200 0.448180872709 Henry Cohn, 2026, needs more optimization.
10 201 0.449219198671 Henry Cohn, 2026, needs more optimization.
10 202 0.450485067965 Henry Cohn, 2026, needs more optimization.
10 203 0.451662263206 Henry Cohn, 2026, needs more optimization.
10 204 0.452579690892 Henry Cohn, 2026, needs more optimization.
10 205 0.453102833385 Henry Cohn, 2026, needs more optimization.
10 206 0.453167351765 Henry Cohn, 2026, needs more optimization.
10 207 0.453394575095 Henry Cohn, 2026, needs more optimization.
10 209 0.453405059077 Henry Cohn, 2026, needs more optimization.
10 211 0.453408561792 Henry Cohn, 2026, needs more optimization.
10 212 0.453450076021 Henry Cohn, 2026, needs more optimization.
10 213 0.453526301498 Henry Cohn, 2026, needs more optimization.
10 214 0.453677330959 Henry Cohn, 2026, needs more optimization.
10 215 0.453694243319 Henry Cohn, 2026, needs more optimization.
10 216 0.453916688711 Henry Cohn, 2026, needs more optimization.
10 217 0.453919822090 Henry Cohn, 2026, needs more optimization.
10 218 0.454188352433 Henry Cohn, 2026, needs more optimization.
10 219 0.454303615560 Henry Cohn, 2026, needs more optimization.
10 220 0.454350401733 Henry Cohn, 2026, needs more optimization.
10 221 0.454408851287 Henry Cohn, 2026, needs more optimization.
10 222 0.454441650797 Henry Cohn, 2026, needs more optimization.
10 223 0.454447150158 Henry Cohn, 2026, needs more optimization.
10 224 0.454789351030 Henry Cohn, 2026, needs more optimization.
10 225 0.454930571067 Henry Cohn, 2026, needs more optimization.
10 226 0.454965434233 Henry Cohn, 2026, needs more optimization.
10 227 0.455133678347 Henry Cohn, 2026, needs more optimization.
10 228 0.455142649662 Henry Cohn, 2026, needs more optimization.
10 229 0.455148070448 Henry Cohn, 2026, needs more optimization.
10 230 0.455198467023 Henry Cohn, 2026, needs more optimization.
10 231 0.455245204832 Henry Cohn, 2026, needs more optimization.
10 238 0.455341801262 Henry Cohn, 2026.
18⁢x2−6⁢x−1
10 239 0.455395647477 Henry Cohn, 2026, needs more optimization.
10 240 0.455449446822 Henry Cohn, 2026, needs more optimization.
10 241 0.455995382070 Henry Cohn, 2026, needs more optimization.
10 242 0.456233019532 Henry Cohn, 2026, needs more optimization.
10 243 0.456252207057 Henry Cohn, 2026, needs more optimization.
10 244 0.456273291303 Henry Cohn, 2026, needs more optimization.
10 245 0.457668171652 Henry Cohn, 2026, needs more optimization.
10 246 0.458697883911 Henry Cohn, 2026, needs more optimization.
10 247 0.462298051519 Henry Cohn, 2026, needs more optimization.
10 248 0.464406198633 Henry Cohn, 2026, needs more optimization.
10 249 0.464406199341 Henry Cohn, 2026, needs more optimization.
10 250 0.464749674240 Henry Cohn, 2026, needs more optimization.
10 251 0.465012740331 Henry Cohn, 2026, needs more optimization.
10 252 0.465574186354 Henry Cohn, 2026, needs more optimization.
10 253 0.466529762345 Henry Cohn, 2026, needs more optimization.
10 254 0.467457563065 Henry Cohn, 2026, needs more optimization.
10 255 0.469064321491 Henry Cohn, 2026, needs more optimization.
10 256 0.470288548794 Henry Cohn, 2026, needs more optimization.
10 257 0.471256288075 Henry Cohn, 2026, needs more optimization.
10 258 0.471955591729 Henry Cohn, 2026, needs more optimization.
10 259 0.472999048043 Henry Cohn, 2026, needs more optimization.
10 260 0.473990950530 Henry Cohn, 2026, needs more optimization.
10 261 0.474828135575 Henry Cohn, 2026, needs more optimization.
10 262 0.475719020851 Henry Cohn, 2026, needs more optimization.
10 263 0.476507110489 Henry Cohn, 2026, needs more optimization.
10 264 0.477081583018 Henry Cohn, 2026, needs more optimization.
10 266 0.477915755666 Henry Cohn, 2026, needs more optimization.
10 267 0.477986898942 Henry Cohn, 2026, needs more optimization.
10 268 0.478087119170 Henry Cohn, 2026, needs more optimization.
10 269 0.478302273901 Henry Cohn, 2026, needs more optimization.
10 270 0.478467869364 Henry Cohn, 2026, needs more optimization.
10 271 0.478514956142 Henry Cohn, 2026, needs more optimization.
10 272 0.478917145902 Henry Cohn, 2026, needs more optimization.
10 273 0.479226517932 Henry Cohn, 2026, needs more optimization.
10 274 0.479870164082 Henry Cohn, 2026, needs more optimization.
10 275 0.480349804029 Henry Cohn, 2026, needs more optimization.
10 276 0.480910582846 Henry Cohn, 2026, needs more optimization.
10 277 0.481226234682 Henry Cohn, 2026, needs more optimization.
10 278 0.481779153542 Henry Cohn, 2026, needs more optimization.
10 279 0.482395086987 Henry Cohn, 2026, needs more optimization.
10 280 0.482828917620 Henry Cohn, 2026, needs more optimization.
10 281 0.483351829220 Henry Cohn, 2026, needs more optimization.
10 282 0.483444381506 Henry Cohn, 2026, needs more optimization.
10 283 0.483495493072 Henry Cohn, 2026, needs more optimization.
10 284 0.483653278766 Henry Cohn, 2026, needs more optimization.
10 285 0.483682193206 Henry Cohn, 2026, needs more optimization.
10 286 0.484159909361 Henry Cohn, 2026, needs more optimization.
10 287 0.484480563163 Henry Cohn, 2026, needs more optimization.
10 288 0.484717440413 Henry Cohn, 2026, needs more optimization.
10 289 0.484868773673 Henry Cohn, 2026, needs more optimization.
10 290 0.485023022928 Henry Cohn, 2026, needs more optimization.
10 291 0.485274217189 Henry Cohn, 2026, needs more optimization.
10 292 0.485557542568 Henry Cohn, 2026, needs more optimization.
10 293 0.485827317802 Henry Cohn, 2026, needs more optimization.
10 294 0.486079741260 Henry Cohn, 2026, needs more optimization.
10 295 0.486421919894 Henry Cohn, 2026, needs more optimization.
10 296 0.486759151390 Henry Cohn, 2026, needs more optimization.
10 297 0.486978657562 Henry Cohn, 2026, needs more optimization.
10 298 0.487529374675 Henry Cohn, 2026, needs more optimization.
10 299 0.488618803139 Henry Cohn, 2026, needs more optimization.
10 300 0.488932850938 Henry Cohn, 2026, needs more optimization.
10 301 0.489344159188 Henry Cohn, 2026, needs more optimization.
10 302 0.489509798836 Henry Cohn, 2026, needs more optimization.
10 303 0.489654044251 Henry Cohn, 2026, needs more optimization.
10 304 0.490035135291 Henry Cohn, 2026, needs more optimization.
10 305 0.490234940006 Henry Cohn, 2026, needs more optimization.
10 306 0.490338668550 Henry Cohn, 2026, needs more optimization.
10 308 0.490780537236 Henry Cohn, 2026, needs more optimization.
10 309 0.490891845546 Henry Cohn, 2026, needs more optimization.
10 310 0.490991762658 Henry Cohn, 2026, needs more optimization.
10 311 0.491042444886 Henry Cohn, 2026, needs more optimization.
10 312 0.491076777721 Henry Cohn, 2026, needs more optimization.
10 313 0.491231555731 Henry Cohn, 2026, needs more optimization.
10 314 0.491265161773 Henry Cohn, 2026, needs more optimization.
10 315 0.491757762109 Henry Cohn, 2026, needs more optimization.
10 316 0.491770917207 Henry Cohn, 2026, needs more optimization.
10 317 0.491808051676 Henry Cohn, 2026, needs more optimization.
10 318 0.492033043316 Henry Cohn, 2026, needs more optimization.
10 319 0.492123007422 Henry Cohn, 2026, needs more optimization.
10 320 0.492429423383 Henry Cohn, 2026, needs more optimization.
10 321 0.492980299593 Henry Cohn, 2026, needs more optimization.
10 322 0.493346297304 Henry Cohn, 2026, needs more optimization.
10 323 0.493410020006 Henry Cohn, 2026, needs more optimization.
10 324 0.493589614030 Henry Cohn, 2026, needs more optimization.
10 325 0.494146563605 Henry Cohn, 2026, needs more optimization.
10 326 0.494238764561 Henry Cohn, 2026, needs more optimization.
10 327 0.494529351600 Henry Cohn, 2026, needs more optimization.
10 328 0.494880059327 Henry Cohn, 2026, needs more optimization.
10 329 0.495011306803 Henry Cohn, 2026, needs more optimization.
10 330 0.495072609764 Henry Cohn, 2026, needs more optimization.
10 331 0.495280053487 Henry Cohn, 2026, needs more optimization.
10 332 0.495436051848 Henry Cohn, 2026, needs more optimization.
10 333 0.495543093661 Henry Cohn, 2026, needs more optimization.
10 334 0.496248260082 Henry Cohn, 2026, needs more optimization.
10 335 0.496349754282 Henry Cohn, 2026, needs more optimization.
10 336 0.496542311827 Henry Cohn, 2026, needs more optimization.
10 337 0.496745457997 Henry Cohn, 2026, needs more optimization.
10 338 0.496892075028 Henry Cohn, 2026, needs more optimization.
10 339 0.496989076095 Henry Cohn, 2026, needs more optimization.
10 340 0.497144297181 Henry Cohn, 2026, needs more optimization.
10 341 0.497200713345 Henry Cohn, 2026, needs more optimization.
10 342 0.497249987165 Henry Cohn, 2026, needs more optimization.
10 343 0.497344751392 Henry Cohn, 2026, needs more optimization.
10 344 0.497437086376 Henry Cohn, 2026, needs more optimization.
10 345 0.497529391212 Henry Cohn, 2026, needs more optimization.
10 346 0.498117459613 Henry Cohn, 2026, needs more optimization.
10 347 0.498209450353 Henry Cohn, 2026, needs more optimization.
10 348 0.498296929024 Henry Cohn, 2026, needs more optimization.
10 349 0.498367447322 Henry Cohn, 2026, needs more optimization.
10 350 0.498415413091 Henry Cohn, 2026, needs more optimization.
10 351 0.498469565026 Henry Cohn, 2026, needs more optimization.
10 352 0.498482039654 Henry Cohn, 2026, needs more optimization.
10 353 0.498582985165 Henry Cohn, 2026, needs more optimization.
10 354 0.498586283139 Henry Cohn, 2026, needs more optimization.
10 355 0.498745489091 Henry Cohn, 2026, needs more optimization.
10 356 0.498786849568 Henry Cohn, 2026, needs more optimization.
10 358 0.498834255096 Henry Cohn, 2026, needs more optimization.
10 360 0.498892979708 Henry Cohn, 2026, needs more optimization.
10 361 0.498911658551 Henry Cohn, 2026, needs more optimization.
10 363 0.498941593529 Henry Cohn, 2026, needs more optimization.
10 365 0.498997215654 Henry Cohn, 2026, needs more optimization.
10 366 0.499002311530 Henry Cohn, 2026, needs more optimization.
10 368 0.499253169099 Henry Cohn, 2026, needs more optimization.
10 369 0.499262516909 Henry Cohn, 2026, needs more optimization.
10 370 0.499284005095 Henry Cohn, 2026, needs more optimization.
10 371 0.499409622922 Henry Cohn, 2026, needs more optimization.
10 372 0.499528045274 Henry Cohn, 2026, needs more optimization.
10 373 0.499545407898 Henry Cohn, 2026, needs more optimization.
10 374 0.499556123098 Henry Cohn, 2026, needs more optimization.
10 375 0.499632428893 Henry Cohn, 2026, needs more optimization.
10 500 0.5 J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3.
2⁢x−1
10 510 0.5 M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002.
2⁢x−1
10 511 0.526700843530 Henry Cohn, 2026, needs more optimization.
10 512 0.529968269375 Henry Cohn, 2026, needs more optimization.
10 513 0.532736170813 Henry Cohn, 2026, needs more optimization.
10 514 0.533829637767 Henry Cohn, 2026, needs more optimization.
10 515 0.535003141560 Henry Cohn, 2026, needs more optimization.
10 516 0.536921721120 Henry Cohn, 2026, needs more optimization.
10 517 0.538153404654 Henry Cohn, 2026, needs more optimization.
10 518 0.538840381350 Henry Cohn, 2026, needs more optimization.
10 519 0.540276034111 Henry Cohn, 2026, needs more optimization.
10 520 0.541047257346 Henry Cohn, 2026, needs more optimization.
10 521 0.542194287050 Henry Cohn, 2026, needs more optimization.
10 522 0.542988119023 Henry Cohn, 2026, needs more optimization.
10 523 0.543621144840 Henry Cohn, 2026, needs more optimization.
10 524 0.544339656901 Henry Cohn, 2026, needs more optimization.
10 525 0.545204195917 Henry Cohn, 2026, needs more optimization.
10 526 0.545962924895 Henry Cohn, 2026, needs more optimization.
10 527 0.546307325877 Henry Cohn, 2026, needs more optimization.
10 528 0.547355995833 Henry Cohn, 2026, needs more optimization.
10 529 0.548002860353 Henry Cohn, 2026, needs more optimization.
10 530 0.548729340452 Henry Cohn, 2026, needs more optimization.
10 531 0.549323112916 Henry Cohn, 2026, needs more optimization.
10 532 0.549611999393 Henry Cohn, 2026, needs more optimization.
10 533 0.550218266769 Henry Cohn, 2026, needs more optimization.
10 534 0.550797452912 Henry Cohn, 2026, needs more optimization.
10 535 0.551309336286 Henry Cohn, 2026, needs more optimization.
10 536 0.552015030521 Henry Cohn, 2026, needs more optimization.
10 537 0.552488856650 Henry Cohn, 2026, needs more optimization.
10 538 0.553340297291 Henry Cohn, 2026, needs more optimization.
10 539 0.553478729735 Henry Cohn, 2026, needs more optimization.
10 540 0.553993393849 Henry Cohn, 2026, needs more optimization.
10 541 0.554445384435 Henry Cohn, 2026, needs more optimization.
10 542 0.554862258221 Henry Cohn, 2026, needs more optimization.
10 543 0.555232889432 Henry Cohn, 2026, needs more optimization.
10 596 0.555555555556 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
10 608 0.555555555556 Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
10 740 0.564577451054 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
92⁢x2−36⁢x−9
10 771 0.564577451054 Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
92⁢x2−36⁢x−9
10 772 0.567862753450 Henry Cohn, 2026, needs more optimization.
10 773 0.569692442882 Henry Cohn, 2026, needs more optimization.
10 774 0.570752216373 Henry Cohn, 2026, needs more optimization.
10 775 0.571371272653 Henry Cohn, 2026, needs more optimization.
10 776 0.571915092880 Henry Cohn, 2026, needs more optimization.
10 778 0.572424181976 Henry Cohn, 2026, needs more optimization.
10 779 0.572920022008 Henry Cohn, 2026, needs more optimization.
10 781 0.573150882533 Henry Cohn, 2026, needs more optimization.
10 782 0.573320717973 Henry Cohn, 2026, needs more optimization.
10 783 0.573459508621 Henry Cohn, 2026, needs more optimization.
10 784 0.573670334286 Henry Cohn, 2026, needs more optimization.
10 785 0.573704033300 Henry Cohn, 2026, needs more optimization.
10 786 0.576354236937 Henry Cohn, 2026, needs more optimization.
10 787 0.576679947614 Henry Cohn, 2026, needs more optimization.
10 788 0.577086059052 Henry Cohn, 2026, needs more optimization.
10 789 0.577164808110 Henry Cohn, 2026, needs more optimization.
10 790 0.577888360496 Henry Cohn, 2026, needs more optimization.
10 791 0.578162135648 Henry Cohn, 2026, needs more optimization.
10 792 0.578622271094 Henry Cohn, 2026, needs more optimization.
10 793 0.578942385607 Henry Cohn, 2026, needs more optimization.
10 794 0.579618408086 Henry Cohn, 2026, needs more optimization.
10 795 0.579866057750 Henry Cohn, 2026, needs more optimization.
10 796 0.580139667311 Henry Cohn, 2026, needs more optimization.
10 797 0.580537240275 Henry Cohn, 2026, needs more optimization.
10 798 0.580620085106 Henry Cohn, 2026, needs more optimization.
10 799 0.581819272185 Henry Cohn, 2026, needs more optimization.
10 800 0.581951128354 Henry Cohn, 2026, needs more optimization.
10 801 0.582158515551 Henry Cohn, 2026, needs more optimization.
10 802 0.583082012224 Henry Cohn, 2026, needs more optimization.
10 803 0.583367385502 Henry Cohn, 2026, needs more optimization.
10 804 0.583560560726 Henry Cohn, 2026, needs more optimization.
10 805 0.584224992171 Henry Cohn, 2026, needs more optimization.
10 806 0.584338602260 Henry Cohn, 2026, needs more optimization.
10 807 0.584416975288 Henry Cohn, 2026, needs more optimization.
10 808 0.584468723224 Henry Cohn, 2026, needs more optimization.
10 809 0.584763184185 Henry Cohn, 2026, needs more optimization.
10 810 0.585258219893 Henry Cohn, 2026, needs more optimization.
10 811 0.585302876730 Henry Cohn, 2026, needs more optimization.
10 812 0.585398943923 Henry Cohn, 2026, needs more optimization.
10 813 0.585459918517 Henry Cohn, 2026, needs more optimization.
10 814 0.585582515152 Henry Cohn, 2026, needs more optimization.
10 815 0.585648740358 Henry Cohn, 2026, needs more optimization.
10 816 0.585766504641 Henry Cohn, 2026, needs more optimization.
10 817 0.585973684445 Henry Cohn, 2026, needs more optimization.
10 818 0.586207282022 Henry Cohn, 2026, needs more optimization.
10 819 0.586431927284 Henry Cohn, 2026, needs more optimization.
10 820 0.586548309665 Henry Cohn, 2026, needs more optimization.
10 821 0.586785365287 Henry Cohn, 2026, needs more optimization.
10 822 0.587077382092 Henry Cohn, 2026, needs more optimization.
10 823 0.587262181889 Henry Cohn, 2026, needs more optimization.
10 824 0.587273283509 Henry Cohn, 2026, needs more optimization.
10 825 0.587330528431 Henry Cohn, 2026, needs more optimization.
10 826 0.587382499014 Henry Cohn, 2026, needs more optimization.
10 827 0.587577903667 Henry Cohn, 2026, needs more optimization.
10 828 0.588494701308 Henry Cohn, 2026, needs more optimization.
10 829 0.588810393919 Henry Cohn, 2026, needs more optimization.
10 830 0.588990900331 Henry Cohn, 2026, needs more optimization.
10 831 0.589282727810 Henry Cohn, 2026, needs more optimization.
10 833 0.589465656277 Henry Cohn, 2026, needs more optimization.
10 834 0.589687126738 Henry Cohn, 2026, needs more optimization.
10 835 0.589917616135 Henry Cohn, 2026, needs more optimization.
10 836 0.589998487835 Henry Cohn, 2026, needs more optimization.
10 837 0.590066880049 Henry Cohn, 2026, needs more optimization.
10 838 0.590292806899 Henry Cohn, 2026, needs more optimization.
10 839 0.590432481889 Henry Cohn, 2026, needs more optimization.
10 840 0.590665501427 Henry Cohn, 2026, needs more optimization.
10 841 0.590855979153 Henry Cohn, 2026, needs more optimization.
10 842 0.590882355611 Henry Cohn, 2026, needs more optimization.
10 843 0.590898917898 Henry Cohn, 2026, needs more optimization.
10 844 0.590901936788 Henry Cohn, 2026, needs more optimization.
10 845 0.591175960030 Henry Cohn, 2026, needs more optimization.
10 846 0.591512126191 Henry Cohn, 2026, needs more optimization.
10 847 0.591524764667 Henry Cohn, 2026, needs more optimization.
10 848 0.591599858897 Henry Cohn, 2026, needs more optimization.
10 849 0.591629285217 Henry Cohn, 2026, needs more optimization.
10 850 0.591629631021 Henry Cohn, 2026, needs more optimization.
10 851 0.591629634115 Henry Cohn, 2026, needs more optimization.
10 852 0.591777574717 Henry Cohn, 2026, needs more optimization.
10 853 0.591779753534 Henry Cohn, 2026, needs more optimization.
10 854 0.591779754800 Henry Cohn, 2026, needs more optimization.
10 855 0.591881045605 Henry Cohn, 2026, needs more optimization.
10 856 0.591902950548 Henry Cohn, 2026, needs more optimization.
10 857 0.591916201463 Henry Cohn, 2026, needs more optimization.
10 858 0.592017304028 Henry Cohn, 2026, needs more optimization.
10 859 0.592063066033 Henry Cohn, 2026, needs more optimization.
10 860 0.592305990622 Henry Cohn, 2026, needs more optimization.
10 861 0.592409830214 Henry Cohn, 2026, needs more optimization.
10 862 0.592436685178 Henry Cohn, 2026, needs more optimization.
10 863 0.592555993651 Henry Cohn, 2026, needs more optimization.
10 864 0.592569961280 Henry Cohn, 2026, needs more optimization.
10 865 0.592590027083 Henry Cohn, 2026, needs more optimization.
10 866 0.592599455058 Henry Cohn, 2026, needs more optimization.
10 867 0.592603765407 Henry Cohn, 2026, needs more optimization.
10 868 0.592608614432 Henry Cohn, 2026, needs more optimization.
10 869 0.592690014455 Henry Cohn, 2026, needs more optimization.
10 870 0.592694699424 Henry Cohn, 2026, needs more optimization.
10 871 0.592700357020 Henry Cohn, 2026, needs more optimization.
10 872 0.592708238127 Henry Cohn, 2026, needs more optimization.
10 873 0.592710163455 Henry Cohn, 2026, needs more optimization.
10 874 0.592956090523 Henry Cohn, 2026, needs more optimization.
10 876 0.592961727530 Henry Cohn, 2026, needs more optimization.
10 877 0.592965367001 Henry Cohn, 2026, needs more optimization.
10 879 0.592966979810 Henry Cohn, 2026, needs more optimization.
10 880 0.592984015311 Henry Cohn, 2026, needs more optimization.
10 881 0.592984027393 Henry Cohn, 2026, needs more optimization.
10 882 0.593094377679 Henry Cohn, 2026, needs more optimization.
10 883 0.593099494806 Henry Cohn, 2026, needs more optimization.
10 884 0.593126887829 Henry Cohn, 2026, needs more optimization.
10 885 0.593251839956 Henry Cohn, 2026, needs more optimization.
10 886 0.593484742844 Henry Cohn, 2026, needs more optimization.
10 887 0.593560922606 Henry Cohn, 2026, needs more optimization.
10 889 0.593687973997 Henry Cohn, 2026, needs more optimization.
10 890 0.593732805287 Henry Cohn, 2026, needs more optimization.
10 891 0.593809497529 Henry Cohn, 2026, needs more optimization.
10 892 0.593859079687 Henry Cohn, 2026, needs more optimization.
10 893 0.593863648476 Henry Cohn, 2026, needs more optimization.
10 894 0.593888920708 Henry Cohn, 2026, needs more optimization.
10 895 0.593970120364 Henry Cohn, 2026, needs more optimization.
10 896 0.593997073158 Henry Cohn, 2026, needs more optimization.
10 897 0.594068506536 Henry Cohn, 2026, needs more optimization.
10 898 0.594069530907 Henry Cohn, 2026, needs more optimization.
10 903 0.594070221609 Henry Cohn, 2026, needs more optimization.
10 904 0.594071899826 Henry Cohn, 2026, needs more optimization.
10 905 0.594073748128 Henry Cohn, 2026, needs more optimization.
10 907 0.594075130872 Henry Cohn, 2026, needs more optimization.
10 908 0.594076026382 Henry Cohn, 2026, needs more optimization.
10 909 0.594093650334 Henry Cohn, 2026, needs more optimization.
10 910 0.594104432562 Henry Cohn, 2026, needs more optimization.
10 911 0.594165863701 Henry Cohn, 2026, needs more optimization.
10 912 0.594170110558 Henry Cohn, 2026, needs more optimization.
10 913 0.594181942559 Henry Cohn, 2026, needs more optimization.
10 914 0.594195166404 Henry Cohn, 2026, needs more optimization.
10 915 0.594255477421 Henry Cohn, 2026, needs more optimization.
10 916 0.594258341014 Henry Cohn, 2026, needs more optimization.
10 917 0.594272061766 Henry Cohn, 2026, needs more optimization.
10 919 0.594357889128 Henry Cohn, 2026, needs more optimization.
10 920 0.594382201276 Henry Cohn, 2026, needs more optimization.
10 921 0.594390464648 Henry Cohn, 2026, needs more optimization.
10 922 0.594407858597 Henry Cohn, 2026, needs more optimization.
10 923 0.594480281510 Henry Cohn, 2026, needs more optimization.
10 925 0.594542822355 Henry Cohn, 2026, needs more optimization.
10 927 0.594639423957 Henry Cohn, 2026, needs more optimization.
10 928 0.594664103831 Henry Cohn, 2026, needs more optimization.
10 929 0.594787186971 Henry Cohn, 2026, needs more optimization.
10 1024 0.6 Subcode of a code of size 1190 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−3
11 23 0.066201272532 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
891⁢x3−121⁢x2−11⁢x+1
11 24 0.077294525867 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
11 25 0.083618757829 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 26 0.090957106782 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 27 0.096579767338 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 28 0.102062072616 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
96⁢x2−1
11 29 0.108541175054 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
11 30 0.111111111112 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
9⁢x−1
11 31 0.116882716629 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
1880159⁢x4+662980⁢x3+23850⁢x2−9500⁢x−625
11 32 0.127120178791 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
11 33 0.130869404972 Henry Cohn, 2023.
4276703⁢x4+1417464⁢x3−4824⁢x2−23328⁢x−1296
11 35 0.134804262191 Henry Cohn, 2023.
379⁢x2−14⁢x−5
11 36 0.135617659465 Henry Cohn, 2023.
34679⁢x4+11944⁢x3+264⁢x2−224⁢x−16
11 37 0.141119306055 Henry Cohn, 2023.
11 40 0.142857142858 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
7⁢x−1
11 41 0.151608920662 Henry Cohn, 2023.
215⁢x2−26⁢x−1
11 42 0.152689377129 Henry Cohn, 2023.
441⁢x4+84⁢x3−66⁢x2+1
11 43 0.154540745580 Henry Cohn, 2024.
11 44 0.164387348702 Henry Cohn, 2023.
11 45 0.167764862361 Henry Cohn, 2023.
11 46 0.173024920814 Henry Cohn, 2023.
11 47 0.193275935700 Henry Cohn, 2025.
11 48 0.198565163418 Henry Cohn, 2025.
11 49 0.201215495510 Henry Cohn, 2025.
11 50 0.204597123448 Henry Cohn, 2026.
11 51 0.204957387535 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
11 52 0.208005237402 Henry Cohn, 2024.
11 53 0.209746584158 Henry Cohn, 2026.
11 54 0.210461540583 Henry Cohn, 2026, needs more optimization.
11 55 0.211949051009 Henry Cohn, 2026.
11 56 0.214650086321 Henry Cohn, 2026.
11 61 0.214737233855 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x2−2⁢x−1
11 68 0.231819094924 Ilmari Vahteristo, 2026.
79⁢x2−14⁢x−1
11 69 0.241565014044 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
11 70 0.244726315701 Henry Cohn, 2026.
263⁢x8−408⁢x7+27724⁢x6−10136⁢x5−11182⁢x4+5880⁢x3−932⁢x2+56⁢x−1
11 71 0.251063071270 Henry Cohn, 2026.
11 72 0.253208781592 Henry Cohn, 2026, needs more optimization.
11 73 0.253336079743 Henry Cohn, 2026, needs more optimization.
11 74 0.253820985074 Henry Cohn, 2026, needs more optimization.
11 75 0.255729129431 Henry Cohn, 2026, needs more optimization.
11 76 0.255742147054 Henry Cohn, 2026, needs more optimization.
11 77 0.259831037896 Henry Cohn, 2026, needs more optimization.
11 78 0.260087123998 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 79 0.260685334645 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 80 0.261163095118 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 81 0.261593527993 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 82 0.263058219772 Henry Cohn, 2026, needs more optimization.
11 83 0.263833259782 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 84 0.265027768210 Henry Cohn, 2026, needs more optimization.
11 85 0.266212317417 Henry Cohn, 2026, needs more optimization.
11 90 0.267191024627 Henry Cohn, 2026.
71⁢x2−4⁢x−4
11 91 0.273036354862 Henry Cohn, 2026, needs more optimization.
11 92 0.280337729368 Henry Cohn, 2026, needs more optimization.
11 93 0.281375279748 Henry Cohn, 2026, needs more optimization.
11 94 0.282354248588 Henry Cohn, 2026, needs more optimization.
11 95 0.283407724046 Henry Cohn, 2026, needs more optimization.
11 96 0.284687649120 Henry Cohn, 2026, needs more optimization.
11 97 0.285749102311 Henry Cohn, 2026, needs more optimization.
11 98 0.287338503170 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 99 0.288695059572 Henry Cohn, 2026, needs more optimization.
11 100 0.299860274395 Henry Cohn, 2026, needs more optimization.
11 101 0.302856211133 Henry Cohn, 2026, needs more optimization.
11 102 0.304440333187 Henry Cohn, 2026, needs more optimization.
11 103 0.305190088554 Henry Cohn, 2026, needs more optimization.
11 104 0.305208716329 Henry Cohn, 2026, needs more optimization.
11 105 0.305250484673 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 106 0.306417420784 Henry Cohn, 2026, needs more optimization.
11 107 0.309833952988 Henry Cohn, 2026, needs more optimization.
11 108 0.313206839612 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 109 0.319003371306 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 110 0.321697566241 Henry Cohn, 2026, needs more optimization.
11 111 0.322266842253 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 112 0.322353350453 Henry Cohn, 2026, needs more optimization.
11 113 0.322494933339 Henry Cohn, 2026, needs more optimization.
11 114 0.322741523989 Henry Cohn, 2026, needs more optimization.
11 115 0.322930921448 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 116 0.323595455196 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 117 0.324275804961 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 118 0.324838464869 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 119 0.324907761719 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 120 0.325028609540 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 121 0.325463885933 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11 122 0.325937891107 Henry Cohn, 2026, needs more optimization.
11 123 0.328143225937 Henry Cohn, 2026, needs more optimization.
11 124 0.328653380506 Henry Cohn, 2026, needs more optimization.
11 125 0.330504741260 Henry Cohn, 2026, needs more optimization.
11 126 0.331457049045 Henry Cohn, 2026, needs more optimization.
11 127 0.332257208889 Henry Cohn, 2026, needs more optimization.
11 128 0.332276380864 Henry Cohn, 2026, needs more optimization.
11 129 0.332381304622 Henry Cohn, 2026, needs more optimization.
11 130 0.332405292666 Henry Cohn, 2026, needs more optimization.
11 131 0.332603143771 Henry Cohn, 2026, needs more optimization.
11 132 0.333235664603 Henry Cohn, 2026, needs more optimization.
11 136 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
11 156 0.333333333334 M. Ganzhinov, Highly symmetric lines, Linear Algebra Appl. 722 (2025), 12–37, doi:10.1016/j.laa.2025.05.002.
3⁢x−1
11 157 0.360394875114 Henry Cohn, 2026, needs more optimization.
11 158 0.363568772396 Henry Cohn, 2026, needs more optimization.
11 159 0.366526726832 Henry Cohn, 2026, needs more optimization.
11 160 0.369838729921 Henry Cohn, 2026, needs more optimization.
11 161 0.372327081061 Henry Cohn, 2026, needs more optimization.
11 162 0.374570692088 Henry Cohn, 2026, needs more optimization.
11 166 0.375 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
8⁢x−3
11 167 0.384617317894 Henry Cohn, 2026, needs more optimization.
11 168 0.384978573058 Henry Cohn, 2026, needs more optimization.
11 169 0.386585972528 Henry Cohn, 2026, needs more optimization.
11 170 0.387126249386 Henry Cohn, 2026, needs more optimization.
11 171 0.388085468660 Henry Cohn, 2026, needs more optimization.
11 172 0.388522362921 Henry Cohn, 2026, needs more optimization.
11 173 0.388974001808 Henry Cohn, 2026, needs more optimization.
11 174 0.390572450192 Henry Cohn, 2026, needs more optimization.
11 175 0.391423234157 Henry Cohn, 2026, needs more optimization.
11 176 0.392314640999 Henry Cohn, 2026, needs more optimization.
11 177 0.393242405877 Henry Cohn, 2026, needs more optimization.
11 178 0.394048052088 Henry Cohn, 2026, needs more optimization.
11 179 0.394871092765 Henry Cohn, 2026, needs more optimization.
11 180 0.395420310188 Henry Cohn, 2026, needs more optimization.
11 181 0.395832552943 Henry Cohn, 2026, needs more optimization.
11 183 0.396111564846 Henry Cohn, 2026, needs more optimization.
11 184 0.396243457509 Henry Cohn, 2026, needs more optimization.
11 185 0.396546291008 Henry Cohn, 2026, needs more optimization.
11 186 0.396924508716 Henry Cohn, 2026, needs more optimization.
11 187 0.397172315245 Henry Cohn, 2026, needs more optimization.
11 188 0.397806985735 Henry Cohn, 2026, needs more optimization.
11 189 0.399606360361 Henry Cohn, 2026, needs more optimization.
11 190 0.399815458114 Henry Cohn, 2026, needs more optimization.
11 191 0.399933712991 Henry Cohn, 2026, needs more optimization.
11 192 0.400513468823 Henry Cohn, 2026, needs more optimization.
11 193 0.401325297911 Henry Cohn, 2026, needs more optimization.
11 194 0.401674030770 Henry Cohn, 2026, needs more optimization.
11 195 0.402757785875 Henry Cohn, 2026, needs more optimization.
11 196 0.403460700549 Henry Cohn, 2026, needs more optimization.
11 197 0.404917908913 Henry Cohn, 2026, needs more optimization.
11 198 0.405334678624 Henry Cohn, 2026, needs more optimization.
11 199 0.405515898102 Henry Cohn, 2026, needs more optimization.
11 200 0.405547956294 Henry Cohn, 2026, needs more optimization.
11 201 0.406124759072 Henry Cohn, 2026, needs more optimization.
11 202 0.406234428012 Henry Cohn, 2026, needs more optimization.
11 203 0.406441532344 Henry Cohn, 2026, needs more optimization.
11 204 0.406912349976 Henry Cohn, 2026, needs more optimization.
11 205 0.406914296478 Henry Cohn, 2026, needs more optimization.
11 206 0.408442857125 Henry Cohn, 2026, needs more optimization.
11 207 0.408993986114 Henry Cohn, 2026, needs more optimization.
11 208 0.409993900999 Henry Cohn, 2026, needs more optimization.
11 209 0.410533770993 Henry Cohn, 2026, needs more optimization.
11 210 0.413851943495 Henry Cohn, 2026, needs more optimization.
11 211 0.415129733546 Henry Cohn, 2026, needs more optimization.
11 212 0.415799382788 Henry Cohn, 2026, needs more optimization.
11 213 0.416361764761 Henry Cohn, 2026, needs more optimization.
11 214 0.416778483474 Henry Cohn, 2026, needs more optimization.
11 215 0.417154920896 Henry Cohn, 2026, needs more optimization.
11 216 0.417697818868 Henry Cohn, 2026, needs more optimization.
11 217 0.418150169773 Henry Cohn, 2026, needs more optimization.
11 218 0.418728016536 Henry Cohn, 2026, needs more optimization.
11 219 0.419251333482 Henry Cohn, 2026, needs more optimization.
11 220 0.419604860004 Henry Cohn, 2026, needs more optimization.
11 221 0.420244077974 Henry Cohn, 2026, needs more optimization.
11 222 0.420732339661 Henry Cohn, 2026, needs more optimization.
11 223 0.421275889026 Henry Cohn, 2026, needs more optimization.
11 224 0.421837123076 Henry Cohn, 2026, needs more optimization.
11 225 0.422384739197 Henry Cohn, 2026, needs more optimization.
11 226 0.423118320012 Henry Cohn, 2026, needs more optimization.
11 227 0.423755507524 Henry Cohn, 2026, needs more optimization.
11 228 0.424182257026 Henry Cohn, 2026, needs more optimization.
11 229 0.424444814260 Henry Cohn, 2026, needs more optimization.
11 230 0.425093292777 Henry Cohn, 2026, needs more optimization.
11 231 0.425397886400 Henry Cohn, 2026, needs more optimization.
11 232 0.425729356188 Henry Cohn, 2026, needs more optimization.
11 233 0.425933761830 Henry Cohn, 2026, needs more optimization.
11 234 0.426257702989 Henry Cohn, 2026, needs more optimization.
11 235 0.426723097429 Henry Cohn, 2026, needs more optimization.
11 236 0.426950029038 Henry Cohn, 2026, needs more optimization.
11 237 0.427230542446 Henry Cohn, 2026, needs more optimization.
11 238 0.427618172813 Henry Cohn, 2026, needs more optimization.
11 239 0.427787183317 Henry Cohn, 2026, needs more optimization.
11 240 0.427985898371 Henry Cohn, 2026, needs more optimization.
11 241 0.428354657251 Henry Cohn, 2026, needs more optimization.
11 242 0.428508464469 Henry Cohn, 2026, needs more optimization.
11 243 0.429023370577 Henry Cohn, 2026, needs more optimization.
11 244 0.429658115918 Henry Cohn, 2026, needs more optimization.
11 245 0.430429644699 Henry Cohn, 2026, needs more optimization.
11 246 0.430675186638 Henry Cohn, 2026, needs more optimization.
11 247 0.430832323294 Henry Cohn, 2026, needs more optimization.
11 248 0.431478153074 Henry Cohn, 2026, needs more optimization.
11 249 0.432389959062 Henry Cohn, 2026, needs more optimization.
11 250 0.433204833363 Henry Cohn, 2026, needs more optimization.
11 251 0.433533268527 Henry Cohn, 2026, needs more optimization.
11 252 0.433970212583 Henry Cohn, 2026, needs more optimization.
11 253 0.435457660988 Henry Cohn, 2026, needs more optimization.
11 254 0.435930198568 Henry Cohn, 2026, needs more optimization.
11 255 0.436494254014 Henry Cohn, 2026, needs more optimization.
11 256 0.437615884370 Henry Cohn, 2026, needs more optimization.
11 257 0.437643990551 Henry Cohn, 2026, needs more optimization.
11 258 0.437666342520 Henry Cohn, 2026, needs more optimization.
11 259 0.437675985452 Henry Cohn, 2026, needs more optimization.
11 260 0.437710770681 Henry Cohn, 2026, needs more optimization.
11 261 0.437726886061 Henry Cohn, 2026, needs more optimization.
11 262 0.437926355668 Henry Cohn, 2026, needs more optimization.
11 263 0.438213429849 Henry Cohn, 2026, needs more optimization.
11 264 0.438245632254 Henry Cohn, 2026, needs more optimization.
11 265 0.438303497288 Henry Cohn, 2026, needs more optimization.
11 266 0.438328102689 Henry Cohn, 2026, needs more optimization.
11 267 0.438390793382 Henry Cohn, 2026, needs more optimization.
11 268 0.438457432292 Henry Cohn, 2026, needs more optimization.
11 269 0.438511413571 Henry Cohn, 2026, needs more optimization.
11 270 0.438922597833 Henry Cohn, 2026, needs more optimization.
11 271 0.439348089884 Henry Cohn, 2026, needs more optimization.
11 272 0.439852921871 Henry Cohn, 2026, needs more optimization.
11 273 0.440062842998 Henry Cohn, 2026, needs more optimization.
11 274 0.440154454081 Henry Cohn, 2026, needs more optimization.
11 275 0.440514829953 Henry Cohn, 2026, needs more optimization.
11 276 0.440743684956 Henry Cohn, 2026, needs more optimization.
11 277 0.441102538143 Henry Cohn, 2026, needs more optimization.
11 278 0.441352282052 Henry Cohn, 2026, needs more optimization.
11 279 0.441566676336 Henry Cohn, 2026, needs more optimization.
11 280 0.441918075500 Henry Cohn, 2026, needs more optimization.
11 281 0.442403955308 Henry Cohn, 2026, needs more optimization.
11 282 0.442668484852 Henry Cohn, 2026, needs more optimization.
11 283 0.442750421802 Henry Cohn, 2026, needs more optimization.
11 284 0.443022311582 Henry Cohn, 2026, needs more optimization.
11 285 0.443552753842 Henry Cohn, 2026, needs more optimization.
11 286 0.444107667372 Henry Cohn, 2026, needs more optimization.
11 287 0.444177209674 Henry Cohn, 2026, needs more optimization.
11 288 0.444755470281 Henry Cohn, 2026, needs more optimization.
11 289 0.444819334341 Henry Cohn, 2026, needs more optimization.
11 290 0.445397832902 Henry Cohn, 2026, needs more optimization.
11 291 0.445589616791 Henry Cohn, 2026, needs more optimization.
11 292 0.445935466373 Henry Cohn, 2026, needs more optimization.
11 293 0.446800346421 Henry Cohn, 2026, needs more optimization.
11 294 0.447616472155 Henry Cohn, 2026, needs more optimization.
11 295 0.449273722304 Henry Cohn, 2026, needs more optimization.
11 296 0.449988061122 Henry Cohn, 2026, needs more optimization.
11 297 0.450921675658 Henry Cohn, 2026, needs more optimization.
11 298 0.453173236480 Henry Cohn, 2026, needs more optimization.
11 299 0.454249702836 Henry Cohn, 2026, needs more optimization.
11 300 0.455140157003 Henry Cohn, 2026, needs more optimization.
11 301 0.455677387701 Henry Cohn, 2026, needs more optimization.
11 302 0.456169784216 Henry Cohn, 2026, needs more optimization.
11 303 0.457617522036 Henry Cohn, 2026, needs more optimization.
11 304 0.458902650656 Henry Cohn, 2026, needs more optimization.
11 305 0.459742670442 Henry Cohn, 2026, needs more optimization.
11 306 0.460525123129 Henry Cohn, 2026, needs more optimization.
11 307 0.461214061773 Henry Cohn, 2026, needs more optimization.
11 308 0.462078242397 Henry Cohn, 2026, needs more optimization.
11 309 0.462661679627 Henry Cohn, 2026, needs more optimization.
11 310 0.463354826215 Henry Cohn, 2026, needs more optimization.
11 311 0.463571722709 Henry Cohn, 2026, needs more optimization.
11 312 0.464070090154 Henry Cohn, 2026, needs more optimization.
11 313 0.464235486257 Henry Cohn, 2026, needs more optimization.
11 314 0.464721021375 Henry Cohn, 2026, needs more optimization.
11 315 0.464908846245 Henry Cohn, 2026, needs more optimization.
11 316 0.465130645598 Henry Cohn, 2026, needs more optimization.
11 317 0.465593832556 Henry Cohn, 2026, needs more optimization.
11 318 0.465932854299 Henry Cohn, 2026, needs more optimization.
11 319 0.466187906799 Henry Cohn, 2026, needs more optimization.
11 320 0.466344800145 Henry Cohn, 2026, needs more optimization.
11 321 0.466865203979 Henry Cohn, 2026, needs more optimization.
11 322 0.466979933669 Henry Cohn, 2026, needs more optimization.
11 323 0.467734163640 Henry Cohn, 2026, needs more optimization.
11 324 0.468123615315 Henry Cohn, 2026, needs more optimization.
11 325 0.468668772711 Henry Cohn, 2026, needs more optimization.
11 326 0.468899947245 Henry Cohn, 2026, needs more optimization.
11 327 0.469196735150 Henry Cohn, 2026, needs more optimization.
11 328 0.469735476208 Henry Cohn, 2026, needs more optimization.
11 329 0.470020051052 Henry Cohn, 2026, needs more optimization.
11 342 0.470588235295 Henry Cohn, 2026.
17⁢x−8
11 343 0.472339723600 Henry Cohn, 2026, needs more optimization.
11 344 0.473621574774 Henry Cohn, 2026, needs more optimization.
11 345 0.474461114066 Henry Cohn, 2026, needs more optimization.
11 346 0.474889752173 Henry Cohn, 2026, needs more optimization.
11 347 0.475248140219 Henry Cohn, 2026, needs more optimization.
11 348 0.475927666990 Henry Cohn, 2026, needs more optimization.
11 349 0.476438839637 Henry Cohn, 2026, needs more optimization.
11 350 0.476739838502 Henry Cohn, 2026, needs more optimization.
11 351 0.477069630196 Henry Cohn, 2026, needs more optimization.
11 352 0.477382706441 Henry Cohn, 2026, needs more optimization.
11 353 0.477681459767 Henry Cohn, 2026, needs more optimization.
11 354 0.478289674205 Henry Cohn, 2026, needs more optimization.
11 355 0.478646417992 Henry Cohn, 2026, needs more optimization.
11 356 0.478966074576 Henry Cohn, 2026, needs more optimization.
11 357 0.479084561022 Henry Cohn, 2026, needs more optimization.
11 358 0.479214096907 Henry Cohn, 2026, needs more optimization.
11 359 0.479314906378 Henry Cohn, 2026, needs more optimization.
11 360 0.479396593369 Henry Cohn, 2026, needs more optimization.
11 361 0.479466700368 Henry Cohn, 2026, needs more optimization.
11 362 0.479502947340 Henry Cohn, 2026, needs more optimization.
11 363 0.479728916103 Henry Cohn, 2026, needs more optimization.
11 364 0.479760009599 Henry Cohn, 2026, needs more optimization.
11 365 0.479889451064 Henry Cohn, 2026, needs more optimization.
11 366 0.480002506612 Henry Cohn, 2026, needs more optimization.
11 367 0.480017665109 Henry Cohn, 2026, needs more optimization.
11 368 0.480104575510 Henry Cohn, 2026, needs more optimization.
11 369 0.480173010036 Henry Cohn, 2026, needs more optimization.
11 370 0.480212528064 Henry Cohn, 2026, needs more optimization.
11 371 0.480344407320 Henry Cohn, 2026, needs more optimization.
11 372 0.480453605949 Henry Cohn, 2026, needs more optimization.
11 373 0.480471299131 Henry Cohn, 2026, needs more optimization.
11 374 0.480682039278 Henry Cohn, 2026, needs more optimization.
11 375 0.480991178967 Henry Cohn, 2026, needs more optimization.
11 376 0.481602953724 Henry Cohn, 2026, needs more optimization.
11 377 0.481675556161 Henry Cohn, 2026, needs more optimization.
11 378 0.481773140374 Henry Cohn, 2026, needs more optimization.
11 379 0.482256141410 Henry Cohn, 2026, needs more optimization.
11 380 0.482734751497 Henry Cohn, 2026, needs more optimization.
11 381 0.482924317335 Henry Cohn, 2026, needs more optimization.
11 382 0.483170871234 Henry Cohn, 2026, needs more optimization.
11 383 0.483499274500 Henry Cohn, 2026, needs more optimization.
11 384 0.483874382861 Henry Cohn, 2026, needs more optimization.
11 385 0.483968031222 Henry Cohn, 2026, needs more optimization.
11 386 0.484125868862 Henry Cohn, 2026, needs more optimization.
11 387 0.484234004684 Henry Cohn, 2026, needs more optimization.
11 388 0.484853522480 Henry Cohn, 2026, needs more optimization.
11 389 0.485093946068 Henry Cohn, 2026, needs more optimization.
11 390 0.485113696378 Henry Cohn, 2026, needs more optimization.
11 391 0.485150542505 Henry Cohn, 2026, needs more optimization.
11 392 0.485155365019 Henry Cohn, 2026, needs more optimization.
11 393 0.485164156630 Henry Cohn, 2026, needs more optimization.
11 394 0.485193976927 Henry Cohn, 2026, needs more optimization.
11 395 0.485220831282 Henry Cohn, 2026, needs more optimization.
11 396 0.485241754556 Henry Cohn, 2026, needs more optimization.
11 397 0.485679429339 Henry Cohn, 2026, needs more optimization.
11 398 0.485685027673 Henry Cohn, 2026, needs more optimization.
11 399 0.485731040517 Henry Cohn, 2026, needs more optimization.
11 400 0.486000062121 Henry Cohn, 2026, needs more optimization.
11 402 0.486163146789 Henry Cohn, 2026, needs more optimization.
11 403 0.486168804296 Henry Cohn, 2026, needs more optimization.
11 404 0.486171492421 Henry Cohn, 2026, needs more optimization.
11 406 0.486242683878 Henry Cohn, 2026, needs more optimization.
11 407 0.486252630685 Henry Cohn, 2026, needs more optimization.
11 408 0.486443788132 Henry Cohn, 2026, needs more optimization.
11 409 0.486577300085 Henry Cohn, 2026, needs more optimization.
11 410 0.486713124819 Henry Cohn, 2026, needs more optimization.
11 411 0.487340513034 Henry Cohn, 2026, needs more optimization.
11 412 0.488064045584 Henry Cohn, 2026, needs more optimization.
11 413 0.488446898300 Henry Cohn, 2026, needs more optimization.
11 414 0.488884429023 Henry Cohn, 2026, needs more optimization.
11 415 0.488928658754 Henry Cohn, 2026, needs more optimization.
11 416 0.489055020963 Henry Cohn, 2026, needs more optimization.
11 417 0.489129797021 Henry Cohn, 2026, needs more optimization.
11 418 0.489294759994 Henry Cohn, 2026, needs more optimization.
11 419 0.489364102298 Henry Cohn, 2026, needs more optimization.
11 420 0.489550356237 Henry Cohn, 2026, needs more optimization.
11 421 0.489622839175 Henry Cohn, 2026, needs more optimization.
11 422 0.489823273852 Henry Cohn, 2026, needs more optimization.
11 423 0.489852565710 Henry Cohn, 2026, needs more optimization.
11 424 0.489999775387 Henry Cohn, 2026, needs more optimization.
11 425 0.490472223232 Henry Cohn, 2026, needs more optimization.
11 426 0.490680318201 Henry Cohn, 2026, needs more optimization.
11 427 0.490903274851 Henry Cohn, 2026, needs more optimization.
11 428 0.491079817838 Henry Cohn, 2026, needs more optimization.
11 429 0.491310248440 Henry Cohn, 2026, needs more optimization.
11 430 0.491584748822 Henry Cohn, 2026, needs more optimization.
11 431 0.491815871554 Henry Cohn, 2026, needs more optimization.
11 432 0.491935419166 Henry Cohn, 2026, needs more optimization.
11 433 0.492098014031 Henry Cohn, 2026, needs more optimization.
11 434 0.492275289861 Henry Cohn, 2026, needs more optimization.
11 435 0.492573519111 Henry Cohn, 2026, needs more optimization.
11 436 0.492638245443 Henry Cohn, 2026, needs more optimization.
11 437 0.492776045213 Henry Cohn, 2026, needs more optimization.
11 438 0.492801745659 Henry Cohn, 2026, needs more optimization.
11 439 0.492843547870 Henry Cohn, 2026, needs more optimization.
11 440 0.493000314328 Henry Cohn, 2026, needs more optimization.
11 441 0.493006785931 Henry Cohn, 2026, needs more optimization.
11 442 0.493039780268 Henry Cohn, 2026, needs more optimization.
11 443 0.493050395666 Henry Cohn, 2026, needs more optimization.
11 444 0.493229032726 Henry Cohn, 2026, needs more optimization.
11 445 0.493280755347 Henry Cohn, 2026, needs more optimization.
11 446 0.493337197691 Henry Cohn, 2026, needs more optimization.
11 447 0.493349761158 Henry Cohn, 2026, needs more optimization.
11 448 0.493368224186 Henry Cohn, 2026, needs more optimization.
11 449 0.495052645906 Henry Cohn, 2026, needs more optimization.
11 450 0.495212966880 Henry Cohn, 2026, needs more optimization.
11 451 0.495413781957 Henry Cohn, 2026, needs more optimization.
11 452 0.495517893355 Henry Cohn, 2026, needs more optimization.
11 453 0.495604901355 Henry Cohn, 2026, needs more optimization.
11 454 0.495826135841 Henry Cohn, 2026, needs more optimization.
11 456 0.495912981914 Henry Cohn, 2026, needs more optimization.
11 457 0.495993139966 Henry Cohn, 2026, needs more optimization.
11 458 0.496132806367 Henry Cohn, 2026, needs more optimization.
11 459 0.496346674062 Henry Cohn, 2026, needs more optimization.
11 460 0.496626444852 Henry Cohn, 2026, needs more optimization.
11 461 0.496826082453 Henry Cohn, 2026, needs more optimization.
11 462 0.496875499593 Henry Cohn, 2026, needs more optimization.
11 463 0.496955535300 Henry Cohn, 2026, needs more optimization.
11 464 0.497222843028 Henry Cohn, 2026, needs more optimization.
11 465 0.497335134446 Henry Cohn, 2026, needs more optimization.
11 466 0.497349849444 Henry Cohn, 2026, needs more optimization.
11 467 0.497484967579 Henry Cohn, 2026, needs more optimization.
11 468 0.497559924389 Henry Cohn, 2026, needs more optimization.
11 469 0.497715309414 Henry Cohn, 2026, needs more optimization.
11 470 0.497776461049 Henry Cohn, 2026, needs more optimization.
11 471 0.497902677954 Henry Cohn, 2026, needs more optimization.
11 472 0.497975919362 Henry Cohn, 2026, needs more optimization.
11 473 0.498391093376 Henry Cohn, 2026, needs more optimization.
11 474 0.498438058237 Henry Cohn, 2026, needs more optimization.
11 475 0.498722492688 Henry Cohn, 2026, needs more optimization.
11 476 0.498801765162 Henry Cohn, 2026, needs more optimization.
11 477 0.498893893612 Henry Cohn, 2026, needs more optimization.
11 482 0.499630490823 Henry Cohn, 2026, needs more optimization.
11 483 0.499630962562 Henry Cohn, 2026, needs more optimization.
11 484 0.499630962714 Henry Cohn, 2026, needs more optimization.
11 486 0.499632895147 Henry Cohn, 2026, needs more optimization.
11 487 0.499633597765 Henry Cohn, 2026, needs more optimization.
11 488 0.499634897908 Henry Cohn, 2026, needs more optimization.
11 489 0.499634897923 Henry Cohn, 2026, needs more optimization.
11 490 0.499635396139 Henry Cohn, 2026, needs more optimization.
11 492 0.499635857743 Henry Cohn, 2026, needs more optimization.
11 493 0.499635857786 Henry Cohn, 2026, needs more optimization.
11 494 0.499635979656 Henry Cohn, 2026, needs more optimization.
11 495 0.499637906554 Henry Cohn, 2026, needs more optimization.
11 496 0.499638052830 Henry Cohn, 2026, needs more optimization.
11 497 0.499638409199 Henry Cohn, 2026, needs more optimization.
11 498 0.499640759784 Henry Cohn, 2026, needs more optimization.
11 499 0.499642635892 Henry Cohn, 2026, needs more optimization.
11 500 0.499642635895 Henry Cohn, 2026, needs more optimization.
11 501 0.499642635897 Henry Cohn, 2026, needs more optimization.
11 502 0.499642635988 Henry Cohn, 2026, needs more optimization.
11 503 0.499642635993 Henry Cohn, 2026, needs more optimization.
11 505 0.499644577951 Henry Cohn, 2026, needs more optimization.
11 507 0.499645238658 Henry Cohn, 2026, needs more optimization.
11 512 0.499645873559 Henry Cohn, 2026, needs more optimization.
11 513 0.499646973359 Henry Cohn, 2026, needs more optimization.
11 514 0.499646973675 Henry Cohn, 2026, needs more optimization.
11 516 0.499648375785 Henry Cohn, 2026, needs more optimization.
11 517 0.499649549252 Henry Cohn, 2026, needs more optimization.
11 518 0.499649581044 Henry Cohn, 2026, needs more optimization.
11 521 0.499650778622 Henry Cohn, 2026, needs more optimization.
11 522 0.499650778624 Henry Cohn, 2026, needs more optimization.
11 523 0.499651522160 Henry Cohn, 2026, needs more optimization.
11 524 0.499651978873 Henry Cohn, 2026, needs more optimization.
11 525 0.499651979739 Henry Cohn, 2026, needs more optimization.
11 526 0.499652347581 Henry Cohn, 2026, needs more optimization.
11 527 0.499652633231 Henry Cohn, 2026, needs more optimization.
11 529 0.499652907864 Henry Cohn, 2026, needs more optimization.
11 530 0.499653655985 Henry Cohn, 2026, needs more optimization.
11 532 0.499654106241 Henry Cohn, 2026, needs more optimization.
11 535 0.499655103199 Henry Cohn, 2026, needs more optimization.
11 536 0.499655206527 Henry Cohn, 2026, needs more optimization.
11 537 0.499657430706 Henry Cohn, 2026, needs more optimization.
11 539 0.499658154259 Henry Cohn, 2026, needs more optimization.
11 540 0.499658652314 Henry Cohn, 2026, needs more optimization.
11 541 0.499658695596 Henry Cohn, 2026, needs more optimization.
11 542 0.499659025235 Henry Cohn, 2026, needs more optimization.
11 543 0.499659025238 Henry Cohn, 2026, needs more optimization.
11 545 0.499660031290 Henry Cohn, 2026, needs more optimization.
11 549 0.499660740131 Henry Cohn, 2026, needs more optimization.
11 550 0.499660876129 Henry Cohn, 2026, needs more optimization.
11 554 0.499660995711 Henry Cohn, 2026, needs more optimization.
11 555 0.499661194303 Henry Cohn, 2026, needs more optimization.
11 556 0.499661267405 Henry Cohn, 2026, needs more optimization.
11 558 0.499661607406 Henry Cohn, 2026, needs more optimization.
11 559 0.499661686664 Henry Cohn, 2026, needs more optimization.
11 564 0.499662184841 Henry Cohn, 2026, needs more optimization.
11 569 0.499662536249 Henry Cohn, 2026, needs more optimization.
11 571 0.499662568274 Henry Cohn, 2026, needs more optimization.
11 573 0.499662636177 Henry Cohn, 2026, needs more optimization.
11 574 0.499662700402 Henry Cohn, 2026, needs more optimization.
11 576 0.499662827575 Henry Cohn, 2026, needs more optimization.
11 578 0.499662888363 Henry Cohn, 2026, needs more optimization.
11 581 0.499663590024 Henry Cohn, 2026, needs more optimization.
11 582 0.499663808280 Henry Cohn, 2026, needs more optimization.
11 584 0.499663825564 Henry Cohn, 2026, needs more optimization.
11 585 0.499664042002 Henry Cohn, 2026, needs more optimization.
11 586 0.499665774267 Henry Cohn, 2026, needs more optimization.
11 588 0.499666200407 Henry Cohn, 2026, needs more optimization.
11 590 0.499666322813 Henry Cohn, 2026, needs more optimization.
11 591 0.499666324119 Henry Cohn, 2026, needs more optimization.
11 592 0.499669023519 Henry Cohn, 2026, needs more optimization.
11 593 0.499999985865 Henry Cohn, 2026, needs more optimization.
11 604 0.5 F. Bianchi, Y. Kwon, A. Pappu, and J. Zou, Harnessing the collective intelligence of AI agents in the wild for new discoveries, preprint, 2026, arXiv:2606.10402.
2⁢x−1
11 605 0.507413332419 Henry Cohn, 2026, needs more optimization.
11 606 0.511334746644 Henry Cohn, 2026, needs more optimization.
11 607 0.511427483391 Henry Cohn, 2026, needs more optimization.
11 608 0.511756770445 Henry Cohn, 2026, needs more optimization.
11 609 0.512058511307 Henry Cohn, 2026, needs more optimization.
11 610 0.512091999400 Henry Cohn, 2026, needs more optimization.
11 611 0.512191227418 Henry Cohn, 2026, needs more optimization.
11 612 0.512248140282 Henry Cohn, 2026, needs more optimization.
11 614 0.512273853966 Henry Cohn, 2026, needs more optimization.
11 615 0.512584222677 Henry Cohn, 2026, needs more optimization.
11 616 0.512831351181 Henry Cohn, 2026, needs more optimization.
11 617 0.513085855497 Henry Cohn, 2026, needs more optimization.
11 618 0.513409142984 Henry Cohn, 2026, needs more optimization.
11 619 0.513919037146 Henry Cohn, 2026, needs more optimization.
11 620 0.514034337065 Henry Cohn, 2026, needs more optimization.
11 621 0.514680206062 Henry Cohn, 2026, needs more optimization.
11 622 0.515098607599 Henry Cohn, 2026, needs more optimization.
11 623 0.515450457804 Henry Cohn, 2026, needs more optimization.
11 624 0.515632661368 Henry Cohn, 2026, needs more optimization.
11 625 0.516067289326 Henry Cohn, 2026, needs more optimization.
11 626 0.516368206781 Henry Cohn, 2026, needs more optimization.
11 627 0.516458341121 Henry Cohn, 2026, needs more optimization.
11 628 0.516912908428 Henry Cohn, 2026, needs more optimization.
11 629 0.517526764655 Henry Cohn, 2026, needs more optimization.
11 630 0.518189100259 Henry Cohn, 2026, needs more optimization.
11 631 0.518835977925 Henry Cohn, 2026, needs more optimization.
11 632 0.519498418693 Henry Cohn, 2026, needs more optimization.
11 633 0.520251271084 Henry Cohn, 2026, needs more optimization.
11 634 0.520673052001 Henry Cohn, 2026, needs more optimization.
11 636 0.521921332641 Henry Cohn, 2026, needs more optimization.
11 637 0.523121573768 Henry Cohn, 2026, needs more optimization.
11 638 0.525024754724 Henry Cohn, 2026, needs more optimization.
11 639 0.525602218748 Henry Cohn, 2026, needs more optimization.
11 640 0.527322345354 Henry Cohn, 2026, needs more optimization.
11 641 0.528403377015 Henry Cohn, 2026, needs more optimization.
11 642 0.528403377017 Henry Cohn, 2026, needs more optimization.
11 643 0.528436159168 Henry Cohn, 2026, needs more optimization.
11 644 0.528441720432 Henry Cohn, 2026, needs more optimization.
11 645 0.528462868895 Henry Cohn, 2026, needs more optimization.
11 646 0.528485414134 Henry Cohn, 2026, needs more optimization.
11 647 0.528487362722 Henry Cohn, 2026, needs more optimization.
11 648 0.528504631827 Henry Cohn, 2026, needs more optimization.
11 649 0.528507780149 Henry Cohn, 2026, needs more optimization.
11 650 0.528520163029 Henry Cohn, 2026, needs more optimization.
11 651 0.528528859902 Henry Cohn, 2026, needs more optimization.
11 652 0.528587219450 Henry Cohn, 2026, needs more optimization.
11 653 0.528600187620 Henry Cohn, 2026, needs more optimization.
11 654 0.528953642020 Henry Cohn, 2026, needs more optimization.
11 655 0.529242290751 Henry Cohn, 2026, needs more optimization.
11 656 0.529764697247 Henry Cohn, 2026, needs more optimization.
11 657 0.530449221076 Henry Cohn, 2026, needs more optimization.
11 658 0.531022194476 Henry Cohn, 2026, needs more optimization.
11 659 0.531484096547 Henry Cohn, 2026, needs more optimization.
11 660 0.531983308820 Henry Cohn, 2026, needs more optimization.
11 661 0.533046653638 Henry Cohn, 2026, needs more optimization.
11 662 0.533551260185 Henry Cohn, 2026, needs more optimization.
11 663 0.533924478679 Henry Cohn, 2026, needs more optimization.
11 664 0.534256124698 Henry Cohn, 2026, needs more optimization.
11 665 0.534795157400 Henry Cohn, 2026, needs more optimization.
11 666 0.535077719659 Henry Cohn, 2026, needs more optimization.
11 667 0.535548553842 Henry Cohn, 2026, needs more optimization.
11 668 0.535862258538 Henry Cohn, 2026, needs more optimization.
11 669 0.536128810992 Henry Cohn, 2026, needs more optimization.
11 670 0.536273359852 Henry Cohn, 2026, needs more optimization.
11 671 0.536536507370 Henry Cohn, 2026, needs more optimization.
11 672 0.536578346444 Henry Cohn, 2026, needs more optimization.
11 673 0.536598175623 Henry Cohn, 2026, needs more optimization.
11 674 0.536631242013 Henry Cohn, 2026, needs more optimization.
11 675 0.536802020392 Henry Cohn, 2026, needs more optimization.
11 676 0.537173287935 Henry Cohn, 2026, needs more optimization.
11 677 0.537532374050 Henry Cohn, 2026, needs more optimization.
11 678 0.537625014467 Henry Cohn, 2026, needs more optimization.
11 679 0.538273972955 Henry Cohn, 2026, needs more optimization.
11 680 0.538611405667 Henry Cohn, 2026, needs more optimization.
11 681 0.538845523450 Henry Cohn, 2026, needs more optimization.
11 682 0.539212580374 Henry Cohn, 2026, needs more optimization.
11 683 0.539543090339 Henry Cohn, 2026, needs more optimization.
11 684 0.539701665576 Henry Cohn, 2026, needs more optimization.
11 685 0.540117186552 Henry Cohn, 2026, needs more optimization.
11 686 0.540468788231 Henry Cohn, 2026, needs more optimization.
11 687 0.540802923471 Henry Cohn, 2026, needs more optimization.
11 688 0.541251257537 Henry Cohn, 2026, needs more optimization.
11 689 0.541715386864 Henry Cohn, 2026, needs more optimization.
11 690 0.541756885018 Henry Cohn, 2026, needs more optimization.
11 691 0.541790727676 Henry Cohn, 2026, needs more optimization.
11 692 0.541801617504 Henry Cohn, 2026, needs more optimization.
11 693 0.543043354638 Henry Cohn, 2026, needs more optimization.
11 694 0.543157432216 Henry Cohn, 2026, needs more optimization.
11 695 0.543555728977 Henry Cohn, 2026, needs more optimization.
11 696 0.543954502401 Henry Cohn, 2026, needs more optimization.
11 697 0.544270824967 Henry Cohn, 2026, needs more optimization.
11 698 0.544565588946 Henry Cohn, 2026, needs more optimization.
11 699 0.544776026559 Henry Cohn, 2026, needs more optimization.
11 700 0.545121269019 Henry Cohn, 2026, needs more optimization.
11 701 0.545369195352 Henry Cohn, 2026, needs more optimization.
11 702 0.545656541094 Henry Cohn, 2026, needs more optimization.
11 703 0.545930145563 Henry Cohn, 2026, needs more optimization.
11 704 0.546179814777 Henry Cohn, 2026, needs more optimization.
11 705 0.546481495647 Henry Cohn, 2026, needs more optimization.
11 706 0.546635222001 Henry Cohn, 2026, needs more optimization.
11 707 0.546883098968 Henry Cohn, 2026, needs more optimization.
11 708 0.547091124829 Henry Cohn, 2026, needs more optimization.
11 709 0.547354576374 Henry Cohn, 2026, needs more optimization.
11 710 0.547628840060 Henry Cohn, 2026, needs more optimization.
11 711 0.547919116469 Henry Cohn, 2026, needs more optimization.
11 712 0.548092532543 Henry Cohn, 2026, needs more optimization.
11 713 0.548313693350 Henry Cohn, 2026, needs more optimization.
11 714 0.548353641039 Henry Cohn, 2026, needs more optimization.
11 715 0.548575659344 Henry Cohn, 2026, needs more optimization.
11 716 0.549027631606 Henry Cohn, 2026, needs more optimization.
11 717 0.549069777161 Henry Cohn, 2026, needs more optimization.
11 718 0.549403849239 Henry Cohn, 2026, needs more optimization.
11 719 0.549951686582 Henry Cohn, 2026, needs more optimization.
11 720 0.549976778980 Henry Cohn, 2026, needs more optimization.
11 721 0.550349070569 Henry Cohn, 2026, needs more optimization.
11 722 0.550409943565 Henry Cohn, 2026, needs more optimization.
11 723 0.550581538009 Henry Cohn, 2026, needs more optimization.
11 724 0.550745557498 Henry Cohn, 2026, needs more optimization.
11 725 0.550804806942 Henry Cohn, 2026, needs more optimization.
11 726 0.551350396507 Henry Cohn, 2026, needs more optimization.
11 729 0.551396457801 Henry Cohn, 2026, needs more optimization.
11 730 0.551430520565 Henry Cohn, 2026, needs more optimization.
11 731 0.551595208688 Henry Cohn, 2026, needs more optimization.
11 732 0.551632210562 Henry Cohn, 2026, needs more optimization.
11 733 0.551653992846 Henry Cohn, 2026, needs more optimization.
11 734 0.551716484910 Henry Cohn, 2026, needs more optimization.
11 735 0.551829484133 Henry Cohn, 2026, needs more optimization.
11 736 0.551875610035 Henry Cohn, 2026, needs more optimization.
11 737 0.551926845967 Henry Cohn, 2026, needs more optimization.
11 738 0.551956411241 Henry Cohn, 2026, needs more optimization.
11 739 0.551980405370 Henry Cohn, 2026, needs more optimization.
11 740 0.552000928694 Henry Cohn, 2026, needs more optimization.
11 741 0.554261249534 Henry Cohn, 2026, needs more optimization.
11 742 0.554461992437 Henry Cohn, 2026, needs more optimization.
11 743 0.555079239741 Henry Cohn, 2026, needs more optimization.
11 745 0.555164367093 Henry Cohn, 2026, needs more optimization.
11 746 0.555377568571 Henry Cohn, 2026, needs more optimization.
11 982 0.555555555556 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
11 983 0.560837712291 Henry Cohn, 2026, needs more optimization.
11 984 0.562683436497 Henry Cohn, 2026, needs more optimization.
11 985 0.563555041159 Henry Cohn, 2026, needs more optimization.
11 986 0.564050281072 Henry Cohn, 2026, needs more optimization.
11 987 0.564337407640 Henry Cohn, 2026, needs more optimization.
11 988 0.564553406404 Henry Cohn, 2026, needs more optimization.
11 989 0.564687624931 Henry Cohn, 2026, needs more optimization.
11 990 0.564792369027 Henry Cohn, 2026, needs more optimization.
11 991 0.564854598281 Henry Cohn, 2026, needs more optimization.
11 992 0.564876279179 Henry Cohn, 2026, needs more optimization.
11 993 0.566242252707 Henry Cohn, 2026, needs more optimization.
11 994 0.566797825097 Henry Cohn, 2026, needs more optimization.
11 995 0.567169769314 Henry Cohn, 2026, needs more optimization.
11 996 0.567445669574 Henry Cohn, 2026, needs more optimization.
11 997 0.568088054736 Henry Cohn, 2026, needs more optimization.
11 998 0.568464514582 Henry Cohn, 2026, needs more optimization.
11 999 0.568867616635 Henry Cohn, 2026, needs more optimization.
11 1000 0.569144539244 Henry Cohn, 2026, needs more optimization.
11 1001 0.569383205151 Henry Cohn, 2026, needs more optimization.
11 1002 0.569639187125 Henry Cohn, 2026, needs more optimization.
11 1003 0.569901705762 Henry Cohn, 2026, needs more optimization.
11 1004 0.570106258479 Henry Cohn, 2026, needs more optimization.
11 1005 0.570296080258 Henry Cohn, 2026, needs more optimization.
11 1006 0.570500058264 Henry Cohn, 2026, needs more optimization.
11 1007 0.570631082127 Henry Cohn, 2026, needs more optimization.
11 1008 0.570782302936 Henry Cohn, 2026, needs more optimization.
11 1009 0.570923533789 Henry Cohn, 2026, needs more optimization.
11 1010 0.571063138926 Henry Cohn, 2026, needs more optimization.
11 1011 0.571312666118 Henry Cohn, 2026, needs more optimization.
11 1012 0.571445118983 Henry Cohn, 2026, needs more optimization.
11 1013 0.571626936085 Henry Cohn, 2026, needs more optimization.
11 1014 0.571814910707 Henry Cohn, 2026, needs more optimization.
11 1015 0.571936514515 Henry Cohn, 2026, needs more optimization.
11 1016 0.572062845248 Henry Cohn, 2026, needs more optimization.
11 1017 0.572191616321 Henry Cohn, 2026, needs more optimization.
11 1018 0.572359041645 Henry Cohn, 2026, needs more optimization.
11 1019 0.572477142229 Henry Cohn, 2026, needs more optimization.
11 1020 0.572598770046 Henry Cohn, 2026, needs more optimization.
11 1021 0.572657388467 Henry Cohn, 2026, needs more optimization.
11 1022 0.572792000072 Henry Cohn, 2026, needs more optimization.
11 1023 0.572912542306 Henry Cohn, 2026, needs more optimization.
11 1024 0.573028867713 Henry Cohn, 2026, needs more optimization.
12 25 0.061281914575 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
1200⁢x3−144⁢x2−12⁢x+1
12 26 0.071428571429 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
14⁢x−1
12 27 0.074764926182 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12 28 0.082592206268 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
12 29 0.084348009310 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
496⁢x4+92⁢x3−57⁢x2−8⁢x+1
12 30 0.089146601434 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
3856⁢x4+1456⁢x3+100⁢x2−12⁢x−1
12 31 0.098704091241 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
863⁢x2+6⁢x−9
12 32 0.098704091241 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
863⁢x2+6⁢x−9
12 34 0.112004618870 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2+4⁢x−1
12 35 0.119914058434 Henry Cohn, 2025.
12 36 0.121730661114 Henry Cohn, 2026.
12 37 0.121971459128 Henry Cohn, 2023.
359⁢x2+30⁢x−9
12 38 0.130785955647 Henry Cohn, 2026.
12 39 0.132497435001 Henry Cohn, 2023.
12 40 0.133638243588 Henry Cohn, 2023.
12 41 0.135922539556 Henry Cohn, 2023.
12 42 0.136597789057 Henry Cohn, 2023.
5296⁢x4+1248⁢x3−40⁢x2−24⁢x−1
12 43 0.139595542735 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
12 44 0.141964936980 Henry Cohn, 2023.
736256⁢x8−133120⁢x7−146176⁢x6−13824⁢x5+8368⁢x4+1568⁢x3−72⁢x2−24⁢x−1
12 45 0.149653254074 Henry Cohn, 2024.
12 46 0.150221879934 Henry Cohn, 2025.
12 50 0.150442862439 Henry Cohn, 2023.
956⁢x2−84⁢x−9
12 51 0.159810400056 Henry Cohn, 2023.
3600⁢x5−1080⁢x4−252⁢x3+36⁢x2+9⁢x−1
12 52 0.180095470186 Henry Cohn, 2025.
12 53 0.187397967438 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 54 0.189746662791 Henry Cohn, 2024.
12 55 0.193319611131 Henry Cohn, 2025.
12 60 0.193457871625 Henry Cohn, 2026.
3088⁢x4−1184⁢x3−120⁢x2+40⁢x+1
12 61 0.196565668411 Henry Cohn, 2026.
12 62 0.197162933815 Henry Cohn, 2026.
24⁢x3+92⁢x2−14⁢x−1
12 63 0.207401048725 Henry Cohn, 2026.
12 64 0.210566554872 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 65 0.214409160183 Henry Cohn, 2026.
12 66 0.215014726391 Henry Cohn, 2026, needs more optimization.
12 67 0.215314925312 Henry Cohn, 2026.
12 68 0.219996342799 Henry Cohn, 2026, needs more optimization.
12 69 0.225125869660 Henry Cohn, 2026, needs more optimization.
12 70 0.228644479119 Henry Cohn, 2026, needs more optimization.
12 71 0.230376507650 Henry Cohn, 2026, needs more optimization.
12 72 0.231122123377 Henry Cohn, 2026, needs more optimization.
12 73 0.232372131619 Henry Cohn, 2026, needs more optimization.
12 74 0.233297480125 Henry Cohn, 2026, needs more optimization.
12 75 0.235708679441 Henry Cohn, 2026, needs more optimization.
12 76 0.236478077666 Henry Cohn, 2026, needs more optimization.
12 77 0.237968057446 Henry Cohn, 2025.
12 78 0.239700240785 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 79 0.241071143297 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 80 0.243291248047 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 81 0.243910094468 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 90 0.244488618750 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
29⁢x2−3⁢x−1
12 91 0.250930942836 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 92 0.260985425422 Henry Cohn, 2026.
12 93 0.263892498486 Henry Cohn, 2026, needs more optimization.
12 94 0.264622689337 Henry Cohn, 2026, needs more optimization.
12 95 0.265090859018 Henry Cohn, 2026, needs more optimization.
12 96 0.265464666410 Henry Cohn, 2026.
12 97 0.266011538356 Henry Cohn, 2026, needs more optimization.
12 98 0.266355304603 Henry Cohn, 2026, needs more optimization.
12 99 0.266726367381 Henry Cohn, 2026, needs more optimization.
12 100 0.266944125804 Henry Cohn, 2026, needs more optimization.
12 101 0.267152384930 Henry Cohn, 2026, needs more optimization.
12 102 0.267190937318 Henry Cohn, 2026, needs more optimization.
12 103 0.268906072958 Henry Cohn, 2026, needs more optimization.
12 104 0.271239751983 Henry Cohn, 2026, needs more optimization.
12 106 0.271795861692 A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 107 0.273390144482 Henry Cohn, 2026, needs more optimization.
12 108 0.276780660842 Henry Cohn, 2026, needs more optimization.
12 109 0.277477856254 Henry Cohn, 2026, needs more optimization.
12 110 0.277860216925 Henry Cohn, 2026, needs more optimization.
12 111 0.278763622738 Henry Cohn, 2026, needs more optimization.
12 112 0.279437764553 Henry Cohn, 2026, needs more optimization.
12 113 0.281952057612 Henry Cohn, 2026, needs more optimization.
12 114 0.290427137529 Henry Cohn, 2026, needs more optimization.
12 115 0.291590399976 Henry Cohn, 2026, needs more optimization.
12 116 0.292122911916 Henry Cohn, 2026, needs more optimization.
12 117 0.292984686786 Henry Cohn, 2026, needs more optimization.
12 118 0.293554161812 Henry Cohn, 2026, needs more optimization.
12 119 0.294495187689 Henry Cohn, 2026, needs more optimization.
12 121 0.294708984704 Henry Cohn, 2026, needs more optimization.
12 122 0.303297509342 Henry Cohn, 2026, needs more optimization.
12 123 0.304340402292 Henry Cohn, 2026, needs more optimization.
12 124 0.304347104984 Henry Cohn, 2026, needs more optimization.
12 125 0.304349310948 Henry Cohn, 2026, needs more optimization.
12 126 0.304786531258 Henry Cohn, 2026, needs more optimization.
12 127 0.306791570832 Henry Cohn, 2026, needs more optimization.
12 128 0.307553168206 Henry Cohn, 2026, needs more optimization.
12 129 0.307763277497 Henry Cohn, 2026, needs more optimization.
12 130 0.308010886392 Henry Cohn, 2026, needs more optimization.
12 131 0.308541209229 Henry Cohn, 2026, needs more optimization.
12 132 0.309434696384 Henry Cohn, 2026, needs more optimization.
12 133 0.310040610178 Henry Cohn, 2026, needs more optimization.
12 134 0.311212709651 Henry Cohn, 2026, needs more optimization.
12 135 0.312205898262 Henry Cohn, 2026, needs more optimization.
12 136 0.313692305444 Henry Cohn, 2026, needs more optimization.
12 137 0.315154708721 Henry Cohn, 2026, needs more optimization.
12 138 0.317519068918 Henry Cohn, 2026, needs more optimization.
12 139 0.319376149051 Henry Cohn, 2026, needs more optimization.
12 140 0.320852276568 Henry Cohn, 2026, needs more optimization.
12 141 0.321037723381 Henry Cohn, 2026, needs more optimization.
12 142 0.321446219409 Henry Cohn, 2026, needs more optimization.
12 143 0.321956604160 Henry Cohn, 2026, needs more optimization.
12 144 0.322208812921 Henry Cohn, 2026, needs more optimization.
12 145 0.322827125634 Henry Cohn, 2026, needs more optimization.
12 146 0.323227165595 Henry Cohn, 2026, needs more optimization.
12 147 0.323627557525 Henry Cohn, 2026, needs more optimization.
12 148 0.323943562914 Henry Cohn, 2026, needs more optimization.
12 149 0.324585401488 Henry Cohn, 2026, needs more optimization.
12 150 0.325167015463 Henry Cohn, 2026, needs more optimization.
12 151 0.325731851337 Henry Cohn, 2026, needs more optimization.
12 152 0.326250303496 Henry Cohn, 2026, needs more optimization.
12 153 0.326723289966 Henry Cohn, 2026, needs more optimization.
12 154 0.327870301541 Henry Cohn, 2026, needs more optimization.
12 155 0.328447575635 Henry Cohn, 2026, needs more optimization.
12 156 0.328919278165 Henry Cohn, 2026, needs more optimization.
12 157 0.329271048552 Henry Cohn, 2026, needs more optimization.
12 158 0.329534265828 Henry Cohn, 2026, needs more optimization.
12 159 0.329703151838 Henry Cohn, 2026, needs more optimization.
12 160 0.329843942518 Henry Cohn, 2026, needs more optimization.
12 161 0.329968850670 Henry Cohn, 2026, needs more optimization.
12 162 0.330007403970 Henry Cohn, 2026, needs more optimization.
12 163 0.330725614742 Henry Cohn, 2026, needs more optimization.
12 164 0.331357233806 Henry Cohn, 2026, needs more optimization.
12 165 0.331785597824 Henry Cohn, 2026, needs more optimization.
12 166 0.331969026976 Henry Cohn, 2026, needs more optimization.
12 167 0.332237271565 Henry Cohn, 2026, needs more optimization.
12 168 0.332638449418 Henry Cohn, 2026, needs more optimization.
12 169 0.332921527867 Henry Cohn, 2026, needs more optimization.
12 170 0.332977503054 Henry Cohn, 2026, needs more optimization.
12 171 0.333031413184 Henry Cohn, 2026, needs more optimization.
12 172 0.333034015350 Henry Cohn, 2026, needs more optimization.
12 173 0.333098827234 Henry Cohn, 2026, needs more optimization.
12 174 0.333131471166 Henry Cohn, 2026, needs more optimization.
12 175 0.333161138611 Henry Cohn, 2026, needs more optimization.
12 176 0.333177539283 Henry Cohn, 2026, needs more optimization.
12 177 0.333201846938 Henry Cohn, 2026, needs more optimization.
12 178 0.333235347883 Henry Cohn, 2026, needs more optimization.
12 179 0.333346677265 Henry Cohn, 2026, needs more optimization.
12 180 0.335312850489 Henry Cohn, 2026, needs more optimization.
12 181 0.344148686919 Henry Cohn, 2026, needs more optimization.
12 182 0.345636247720 Henry Cohn, 2026, needs more optimization.
12 183 0.346644013461 Henry Cohn, 2026, needs more optimization.
12 184 0.348694352840 Henry Cohn, 2026, needs more optimization.
12 185 0.349454238959 Henry Cohn, 2026, needs more optimization.
12 186 0.351906012475 Henry Cohn, 2026, needs more optimization.
12 187 0.352415521913 Henry Cohn, 2026, needs more optimization.
12 188 0.353581000452 Henry Cohn, 2026, needs more optimization.
12 189 0.355128146640 Henry Cohn, 2026, needs more optimization.
12 190 0.356345856687 Henry Cohn, 2026, needs more optimization.
12 191 0.356862088810 Henry Cohn, 2026, needs more optimization.
12 192 0.357660444273 Henry Cohn, 2026, needs more optimization.
12 193 0.359150447966 Henry Cohn, 2026, needs more optimization.
12 194 0.360548921080 Henry Cohn, 2026, needs more optimization.
12 195 0.361980775927 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 196 0.362338640235 Henry Cohn, 2026, needs more optimization.
12 197 0.363758321144 Henry Cohn, 2026, needs more optimization.
12 198 0.364883882012 Henry Cohn, 2026, needs more optimization.
12 199 0.365934343589 Henry Cohn, 2026, needs more optimization.
12 200 0.366249368541 Henry Cohn, 2026, needs more optimization.
12 201 0.367604391611 Henry Cohn, 2026, needs more optimization.
12 202 0.368628396151 Henry Cohn, 2026, needs more optimization.
12 203 0.369532811879 Henry Cohn, 2026, needs more optimization.
12 204 0.370826755296 Henry Cohn, 2026, needs more optimization.
12 205 0.371699954838 Henry Cohn, 2026, needs more optimization.
12 206 0.372659947186 Henry Cohn, 2026, needs more optimization.
12 207 0.374065651005 Henry Cohn, 2026, needs more optimization.
12 208 0.374452500076 Henry Cohn, 2026, needs more optimization.
12 210 0.375 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Appendix D.12.12. The appendix lists the code size as 209, but the construction works just as well for 210.
8⁢x−3
12 211 0.377471081829 Henry Cohn, 2026, needs more optimization.
12 212 0.377570073734 Henry Cohn, 2026, needs more optimization.
12 213 0.377985375892 Henry Cohn, 2026, needs more optimization.
12 214 0.378515368883 Henry Cohn, 2026, needs more optimization.
12 215 0.378709392251 Henry Cohn, 2026, needs more optimization.
12 216 0.379082360440 Henry Cohn, 2026, needs more optimization.
12 217 0.381194389339 Henry Cohn, 2026, needs more optimization.
12 218 0.382022608328 Henry Cohn, 2026, needs more optimization.
12 219 0.382423865981 Henry Cohn, 2026, needs more optimization.
12 220 0.383208207401 Henry Cohn, 2026, needs more optimization.
12 221 0.383672103947 Henry Cohn, 2026, needs more optimization.
12 222 0.383972812306 Henry Cohn, 2026, needs more optimization.
12 223 0.384266326597 Henry Cohn, 2026, needs more optimization.
12 224 0.384461339446 Henry Cohn, 2026, needs more optimization.
12 225 0.384639793523 Henry Cohn, 2026, needs more optimization.
12 226 0.384815175768 Henry Cohn, 2026, needs more optimization.
12 227 0.385766508009 Henry Cohn, 2026, needs more optimization.
12 228 0.386255165655 Henry Cohn, 2026, needs more optimization.
12 229 0.386651444836 Henry Cohn, 2026, needs more optimization.
12 230 0.387173471865 Henry Cohn, 2026, needs more optimization.
12 231 0.387705779018 Henry Cohn, 2026, needs more optimization.
12 232 0.390350773378 Henry Cohn, 2026, needs more optimization.
12 233 0.390812596946 Henry Cohn, 2026, needs more optimization.
12 234 0.391009962308 Henry Cohn, 2026, needs more optimization.
12 235 0.391144615774 Henry Cohn, 2026, needs more optimization.
12 236 0.391294602608 Henry Cohn, 2026, needs more optimization.
12 237 0.391471686319 Henry Cohn, 2026, needs more optimization.
12 238 0.392101367616 Henry Cohn, 2026, needs more optimization.
12 239 0.392516205806 Henry Cohn, 2026, needs more optimization.
12 240 0.392766424465 Henry Cohn, 2026, needs more optimization.
12 241 0.392893844986 Henry Cohn, 2026, needs more optimization.
12 242 0.395034950842 Henry Cohn, 2026, needs more optimization.
12 243 0.396583198276 Henry Cohn, 2026, needs more optimization.
12 244 0.398235408485 Henry Cohn, 2026, needs more optimization.
12 245 0.398953742937 Henry Cohn, 2026, needs more optimization.
12 246 0.399394502677 Henry Cohn, 2026, needs more optimization.
12 247 0.399914723665 Henry Cohn, 2026, needs more optimization.
12 248 0.399973075441 Henry Cohn, 2026, needs more optimization.
12 288 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
12 290 0.4 Henry Cohn, 2026.
5⁢x−2
12 291 0.401561520802 Henry Cohn, 2026, needs more optimization.
12 292 0.405515920492 Henry Cohn, 2026, needs more optimization.
12 293 0.408660678679 Henry Cohn, 2026, needs more optimization.
12 294 0.410762637706 Henry Cohn, 2026, needs more optimization.
12 295 0.412718266420 Henry Cohn, 2026, needs more optimization.
12 296 0.413780346363 Henry Cohn, 2026, needs more optimization.
12 297 0.414730280943 Henry Cohn, 2026, needs more optimization.
12 298 0.416899741629 Henry Cohn, 2026, needs more optimization.
12 299 0.418364081444 Henry Cohn, 2026, needs more optimization.
12 300 0.419713173378 Henry Cohn, 2026, needs more optimization.
12 301 0.420799040424 Henry Cohn, 2026, needs more optimization.
12 302 0.422032349066 Henry Cohn, 2026, needs more optimization.
12 303 0.423112224865 Henry Cohn, 2026, needs more optimization.
12 304 0.424101038022 Henry Cohn, 2026, needs more optimization.
12 305 0.425035079679 Henry Cohn, 2026, needs more optimization.
12 306 0.426437192483 Henry Cohn, 2026, needs more optimization.
12 307 0.427413446826 Henry Cohn, 2026, needs more optimization.
12 308 0.427677217668 Henry Cohn, 2026, needs more optimization.
12 309 0.428197862131 Henry Cohn, 2026, needs more optimization.
12 310 0.429227554548 Henry Cohn, 2026, needs more optimization.
12 311 0.430175105984 Henry Cohn, 2026, needs more optimization.
12 312 0.430420981483 Henry Cohn, 2026, needs more optimization.
12 314 0.430422635344 Henry Cohn, 2026, needs more optimization.
12 315 0.430427268086 Henry Cohn, 2026, needs more optimization.
12 316 0.430432079052 Henry Cohn, 2026, needs more optimization.
12 317 0.430444601898 Henry Cohn, 2026, needs more optimization.
12 318 0.430456421477 Henry Cohn, 2026, needs more optimization.
12 319 0.430459987798 Henry Cohn, 2026, needs more optimization.
12 320 0.430466327247 Henry Cohn, 2026, needs more optimization.
12 321 0.430467717903 Henry Cohn, 2026, needs more optimization.
12 323 0.430468691104 Henry Cohn, 2026, needs more optimization.
12 324 0.430472628413 Henry Cohn, 2026, needs more optimization.
12 325 0.430474693737 Henry Cohn, 2026, needs more optimization.
12 326 0.430502196752 Henry Cohn, 2026, needs more optimization.
12 327 0.430505653574 Henry Cohn, 2026, needs more optimization.
12 328 0.430518947973 Henry Cohn, 2026, needs more optimization.
12 329 0.430520276211 Henry Cohn, 2026, needs more optimization.
12 330 0.430535688261 Henry Cohn, 2026, needs more optimization.
12 331 0.430552864321 Henry Cohn, 2026, needs more optimization.
12 332 0.430560272040 Henry Cohn, 2026, needs more optimization.
12 333 0.430560931480 Henry Cohn, 2026, needs more optimization.
12 334 0.430575850148 Henry Cohn, 2026, needs more optimization.
12 335 0.430587339527 Henry Cohn, 2026, needs more optimization.
12 336 0.430600927134 Henry Cohn, 2026, needs more optimization.
12 337 0.430618437783 Henry Cohn, 2026, needs more optimization.
12 338 0.430620779543 Henry Cohn, 2026, needs more optimization.
12 339 0.430622940540 Henry Cohn, 2026, needs more optimization.
12 341 0.430630101563 Henry Cohn, 2026, needs more optimization.
12 342 0.430630451187 Henry Cohn, 2026, needs more optimization.
12 343 0.430635589169 Henry Cohn, 2026, needs more optimization.
12 344 0.430642531845 Henry Cohn, 2026, needs more optimization.
12 345 0.430651706191 Henry Cohn, 2026, needs more optimization.
12 346 0.430662699062 Henry Cohn, 2026, needs more optimization.
12 347 0.430679114502 Henry Cohn, 2026, needs more optimization.
12 348 0.430698091721 Henry Cohn, 2026, needs more optimization.
12 349 0.430712282884 Henry Cohn, 2026, needs more optimization.
12 350 0.430719503201 Henry Cohn, 2026, needs more optimization.
12 351 0.430730204092 Henry Cohn, 2026, needs more optimization.
12 352 0.430893783911 Henry Cohn, 2026, needs more optimization.
12 353 0.431000601602 Henry Cohn, 2026, needs more optimization.
12 354 0.431034104427 Henry Cohn, 2026, needs more optimization.
12 355 0.434295350745 Henry Cohn, 2026, needs more optimization.
12 356 0.436638326064 Henry Cohn, 2026, needs more optimization.
12 357 0.438056208318 Henry Cohn, 2026, needs more optimization.
12 358 0.438979534791 Henry Cohn, 2026, needs more optimization.
12 359 0.439621720814 Henry Cohn, 2026, needs more optimization.
12 360 0.439769950837 Henry Cohn, 2026, needs more optimization.
12 361 0.440114640129 Henry Cohn, 2026, needs more optimization.
12 362 0.440420208430 Henry Cohn, 2026, needs more optimization.
12 363 0.441097810836 Henry Cohn, 2026, needs more optimization.
12 364 0.441313957892 Henry Cohn, 2026, needs more optimization.
12 366 0.441432473732 Henry Cohn, 2026, needs more optimization.
12 367 0.441668846857 Henry Cohn, 2026, needs more optimization.
12 368 0.441713586254 Henry Cohn, 2026, needs more optimization.
12 369 0.441865731528 Henry Cohn, 2026, needs more optimization.
12 370 0.442064764112 Henry Cohn, 2026, needs more optimization.
12 371 0.442367578851 Henry Cohn, 2026, needs more optimization.
12 372 0.442436643853 Henry Cohn, 2026, needs more optimization.
12 373 0.442749031779 Henry Cohn, 2026, needs more optimization.
12 374 0.443286559848 Henry Cohn, 2026, needs more optimization.
12 408 0.444444444445 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
9⁢x−4
12 409 0.447146015856 Henry Cohn, 2026, needs more optimization.
12 410 0.447927222103 Henry Cohn, 2026, needs more optimization.
12 411 0.448614438877 Henry Cohn, 2026, needs more optimization.
12 412 0.449177210531 Henry Cohn, 2026, needs more optimization.
12 414 0.450178469819 Henry Cohn, 2026, needs more optimization.
12 415 0.450346673674 Henry Cohn, 2026, needs more optimization.
12 416 0.450350613072 Henry Cohn, 2026, needs more optimization.
12 417 0.450647728368 Henry Cohn, 2026, needs more optimization.
12 418 0.450927601529 Henry Cohn, 2026, needs more optimization.
12 419 0.451165602385 Henry Cohn, 2026, needs more optimization.
12 420 0.451467882545 Henry Cohn, 2026, needs more optimization.
12 421 0.451743725235 Henry Cohn, 2026, needs more optimization.
12 422 0.452044046012 Henry Cohn, 2026, needs more optimization.
12 423 0.452511732690 Henry Cohn, 2026, needs more optimization.
12 424 0.456866164527 Henry Cohn, 2026, needs more optimization.
12 425 0.457275783082 Henry Cohn, 2026, needs more optimization.
12 426 0.458828564947 Henry Cohn, 2026, needs more optimization.
12 427 0.461035002412 Henry Cohn, 2026, needs more optimization.
12 428 0.461062317640 Henry Cohn, 2026, needs more optimization.
12 429 0.462329224326 Henry Cohn, 2026, needs more optimization.
12 430 0.462789541978 Henry Cohn, 2026, needs more optimization.
12 431 0.462825433409 Henry Cohn, 2026, needs more optimization.
12 432 0.463001909311 Henry Cohn, 2026, needs more optimization.
12 433 0.463787725405 Henry Cohn, 2026, needs more optimization.
12 434 0.463942210788 Henry Cohn, 2026, needs more optimization.
12 435 0.464551251880 Henry Cohn, 2026, needs more optimization.
12 436 0.464656078267 Henry Cohn, 2026, needs more optimization.
12 437 0.465590568417 Henry Cohn, 2026, needs more optimization.
12 438 0.466348829841 Henry Cohn, 2026, needs more optimization.
12 439 0.466413761120 Henry Cohn, 2026, needs more optimization.
12 440 0.466422343903 Henry Cohn, 2026, needs more optimization.
12 441 0.466520804646 Henry Cohn, 2026, needs more optimization.
12 442 0.466669284819 Henry Cohn, 2026, needs more optimization.
12 443 0.466767769785 Henry Cohn, 2026, needs more optimization.
12 444 0.466840408052 Henry Cohn, 2026, needs more optimization.
12 445 0.467482199307 Henry Cohn, 2026, needs more optimization.
12 446 0.467547527909 Henry Cohn, 2026, needs more optimization.
12 447 0.467790501639 Henry Cohn, 2026, needs more optimization.
12 448 0.467959022347 Henry Cohn, 2026, needs more optimization.
12 449 0.468542577450 Henry Cohn, 2026, needs more optimization.
12 450 0.468599885507 Henry Cohn, 2026, needs more optimization.
12 451 0.468746776649 Henry Cohn, 2026, needs more optimization.
12 452 0.468778032019 Henry Cohn, 2026, needs more optimization.
12 453 0.468843637978 Henry Cohn, 2026, needs more optimization.
12 454 0.469163609346 Henry Cohn, 2026, needs more optimization.
12 455 0.469244289869 Henry Cohn, 2026, needs more optimization.
12 456 0.469275545075 Henry Cohn, 2026, needs more optimization.
12 457 0.469575179308 Henry Cohn, 2026, needs more optimization.
12 458 0.469994935894 Henry Cohn, 2026, needs more optimization.
12 459 0.470103387061 Henry Cohn, 2026, needs more optimization.
12 460 0.470285068863 Henry Cohn, 2026, needs more optimization.
12 461 0.470404029779 Henry Cohn, 2026, needs more optimization.
12 462 0.470450032134 Henry Cohn, 2026, needs more optimization.
12 463 0.470760058428 Henry Cohn, 2026, needs more optimization.
12 464 0.471169009244 Henry Cohn, 2026, needs more optimization.
12 465 0.471248170429 Henry Cohn, 2026, needs more optimization.
12 466 0.471615016317 Henry Cohn, 2026, needs more optimization.
12 467 0.472118095725 Henry Cohn, 2026, needs more optimization.
12 468 0.472310288236 Henry Cohn, 2026, needs more optimization.
12 469 0.472485559232 Henry Cohn, 2026, needs more optimization.
12 470 0.472535601841 Henry Cohn, 2026, needs more optimization.
12 471 0.472610840036 Henry Cohn, 2026, needs more optimization.
12 473 0.472812956110 Henry Cohn, 2026, needs more optimization.
12 474 0.472899373849 Henry Cohn, 2026, needs more optimization.
12 475 0.472994783077 Henry Cohn, 2026, needs more optimization.
12 476 0.473070502878 Henry Cohn, 2026, needs more optimization.
12 477 0.473214934053 Henry Cohn, 2026, needs more optimization.
12 478 0.473499787361 Henry Cohn, 2026, needs more optimization.
12 479 0.473617192178 Henry Cohn, 2026, needs more optimization.
12 480 0.473949020935 Henry Cohn, 2026, needs more optimization.
12 481 0.473957161247 Henry Cohn, 2026, needs more optimization.
12 482 0.474322374727 Henry Cohn, 2026, needs more optimization.
12 483 0.474341801161 Henry Cohn, 2026, needs more optimization.
12 484 0.474663969502 Henry Cohn, 2026, needs more optimization.
12 485 0.474719662627 Henry Cohn, 2026, needs more optimization.
12 486 0.474837263661 Henry Cohn, 2026, needs more optimization.
12 487 0.474983246800 Henry Cohn, 2026, needs more optimization.
12 488 0.475229217482 Henry Cohn, 2026, needs more optimization.
12 489 0.475978091995 Henry Cohn, 2026, needs more optimization.
12 490 0.476005407128 Henry Cohn, 2026, needs more optimization.
12 491 0.476106237520 Henry Cohn, 2026, needs more optimization.
12 492 0.476233665352 Henry Cohn, 2026, needs more optimization.
12 493 0.476383110035 Henry Cohn, 2026, needs more optimization.
12 494 0.476541652328 Henry Cohn, 2026, needs more optimization.
12 495 0.476698430706 Henry Cohn, 2026, needs more optimization.
12 496 0.476740534811 Henry Cohn, 2026, needs more optimization.
12 497 0.476923449525 Henry Cohn, 2026, needs more optimization.
12 498 0.476932518177 Henry Cohn, 2026, needs more optimization.
12 499 0.477020276420 Henry Cohn, 2026, needs more optimization.
12 500 0.477509639188 Henry Cohn, 2026, needs more optimization.
12 501 0.477557105777 Henry Cohn, 2026, needs more optimization.
12 502 0.477685320777 Henry Cohn, 2026, needs more optimization.
12 503 0.477805256950 Henry Cohn, 2026, needs more optimization.
12 504 0.478167714735 Henry Cohn, 2026, needs more optimization.
12 505 0.478466028275 Henry Cohn, 2026, needs more optimization.
12 506 0.478482196543 Henry Cohn, 2026, needs more optimization.
12 507 0.478770452519 Henry Cohn, 2026, needs more optimization.
12 508 0.478880564566 Henry Cohn, 2026, needs more optimization.
12 509 0.479081090783 Henry Cohn, 2026, needs more optimization.
12 510 0.479099561354 Henry Cohn, 2026, needs more optimization.
12 511 0.479137513004 Henry Cohn, 2026, needs more optimization.
12 512 0.479521386731 Henry Cohn, 2026, needs more optimization.
12 513 0.479702417844 Henry Cohn, 2026, needs more optimization.
12 514 0.479777297898 Henry Cohn, 2026, needs more optimization.
12 515 0.479890315335 Henry Cohn, 2026, needs more optimization.
12 516 0.479928901751 Henry Cohn, 2026, needs more optimization.
12 517 0.480063348307 Henry Cohn, 2026, needs more optimization.
12 518 0.480159241864 Henry Cohn, 2026, needs more optimization.
12 519 0.480426021685 Henry Cohn, 2026, needs more optimization.
12 520 0.480534298299 Henry Cohn, 2026, needs more optimization.
12 521 0.481138392458 Henry Cohn, 2026, needs more optimization.
12 522 0.481212034105 Henry Cohn, 2026, needs more optimization.
12 523 0.481353578991 Henry Cohn, 2026, needs more optimization.
12 524 0.481404907784 Henry Cohn, 2026, needs more optimization.
12 525 0.481599164014 Henry Cohn, 2026, needs more optimization.
12 526 0.481771147512 Henry Cohn, 2026, needs more optimization.
12 527 0.481858139849 Henry Cohn, 2026, needs more optimization.
12 528 0.481996420952 Henry Cohn, 2026, needs more optimization.
12 529 0.482178025482 Henry Cohn, 2026, needs more optimization.
12 530 0.482356609298 Henry Cohn, 2026, needs more optimization.
12 531 0.482422201792 Henry Cohn, 2026, needs more optimization.
12 532 0.482566213654 Henry Cohn, 2026, needs more optimization.
12 533 0.482694142697 Henry Cohn, 2026, needs more optimization.
12 534 0.482747561086 Henry Cohn, 2026, needs more optimization.
12 535 0.482901517752 Henry Cohn, 2026, needs more optimization.
12 536 0.483032034576 Henry Cohn, 2026, needs more optimization.
12 537 0.483093972435 Henry Cohn, 2026, needs more optimization.
12 538 0.483222007313 Henry Cohn, 2026, needs more optimization.
12 539 0.483378786936 Henry Cohn, 2026, needs more optimization.
12 540 0.483444980384 Henry Cohn, 2026, needs more optimization.
12 541 0.483497320991 Henry Cohn, 2026, needs more optimization.
12 542 0.483651699496 Henry Cohn, 2026, needs more optimization.
12 543 0.483800168058 Henry Cohn, 2026, needs more optimization.
12 544 0.483882695517 Henry Cohn, 2026, needs more optimization.
12 545 0.483952027812 Henry Cohn, 2026, needs more optimization.
12 546 0.484045588295 Henry Cohn, 2026, needs more optimization.
12 547 0.484339956729 Henry Cohn, 2026, needs more optimization.
12 548 0.484586301765 Henry Cohn, 2026, needs more optimization.
12 549 0.484841100896 Henry Cohn, 2026, needs more optimization.
12 550 0.484981298171 Henry Cohn, 2026, needs more optimization.
12 551 0.485174668895 Henry Cohn, 2026, needs more optimization.
12 552 0.485306355339 Henry Cohn, 2026, needs more optimization.
12 553 0.485358004863 Henry Cohn, 2026, needs more optimization.
12 554 0.485574768390 Henry Cohn, 2026, needs more optimization.
12 555 0.485663708947 Henry Cohn, 2026, needs more optimization.
12 556 0.485706852458 Henry Cohn, 2026, needs more optimization.
12 557 0.485818699274 Henry Cohn, 2026, needs more optimization.
12 558 0.485925977534 Henry Cohn, 2026, needs more optimization.
12 559 0.486090145437 Henry Cohn, 2026, needs more optimization.
12 560 0.486178495191 Henry Cohn, 2026, needs more optimization.
12 561 0.486273486061 Henry Cohn, 2026, needs more optimization.
12 562 0.486315195484 Henry Cohn, 2026, needs more optimization.
12 563 0.486510884877 Henry Cohn, 2026, needs more optimization.
12 564 0.486580466039 Henry Cohn, 2026, needs more optimization.
12 565 0.486657444885 Henry Cohn, 2026, needs more optimization.
12 566 0.486739370927 Henry Cohn, 2026, needs more optimization.
12 567 0.486788948459 Henry Cohn, 2026, needs more optimization.
12 568 0.486972438721 Henry Cohn, 2026, needs more optimization.
12 569 0.487087978064 Henry Cohn, 2026, needs more optimization.
12 570 0.487246673637 Henry Cohn, 2026, needs more optimization.
12 571 0.487377309575 Henry Cohn, 2026, needs more optimization.
12 572 0.487472208467 Henry Cohn, 2026, needs more optimization.
12 573 0.487552873867 Henry Cohn, 2026, needs more optimization.
12 574 0.487641381282 Henry Cohn, 2026, needs more optimization.
12 575 0.487707513704 Henry Cohn, 2026, needs more optimization.
12 576 0.487733531022 Henry Cohn, 2026, needs more optimization.
12 577 0.487967916772 Henry Cohn, 2026, needs more optimization.
12 578 0.488175586175 Henry Cohn, 2026, needs more optimization.
12 579 0.488253933250 Henry Cohn, 2026, needs more optimization.
12 580 0.488293008535 Henry Cohn, 2026, needs more optimization.
12 581 0.488319653405 Henry Cohn, 2026, needs more optimization.
12 582 0.488343237488 Henry Cohn, 2026, needs more optimization.
12 583 0.488408207489 Henry Cohn, 2026, needs more optimization.
12 584 0.488463716431 Henry Cohn, 2026, needs more optimization.
12 585 0.488589264354 Henry Cohn, 2026, needs more optimization.
12 586 0.488670499655 Henry Cohn, 2026, needs more optimization.
12 587 0.488735680627 Henry Cohn, 2026, needs more optimization.
12 588 0.488884800461 Henry Cohn, 2026, needs more optimization.
12 589 0.488952163067 Henry Cohn, 2026, needs more optimization.
12 590 0.489086425008 Henry Cohn, 2026, needs more optimization.
12 591 0.489143484142 Henry Cohn, 2026, needs more optimization.
12 592 0.489205861053 Henry Cohn, 2026, needs more optimization.
12 593 0.489322973899 Henry Cohn, 2026, needs more optimization.
12 594 0.489369056816 Henry Cohn, 2026, needs more optimization.
12 595 0.489506239005 Henry Cohn, 2026, needs more optimization.
12 596 0.489544972415 Henry Cohn, 2026, needs more optimization.
12 597 0.489560448819 Henry Cohn, 2026, needs more optimization.
12 600 0.489609781277 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
12 601 0.489887820141 Henry Cohn, 2026, needs more optimization.
12 602 0.489957703199 Henry Cohn, 2026, needs more optimization.
12 603 0.490096682082 Henry Cohn, 2026, needs more optimization.
12 604 0.490191163616 Henry Cohn, 2026, needs more optimization.
12 605 0.490270460010 Henry Cohn, 2026, needs more optimization.
12 606 0.490337756181 Henry Cohn, 2026, needs more optimization.
12 608 0.490482286803 Henry Cohn, 2026, needs more optimization.
12 609 0.490533456113 Henry Cohn, 2026, needs more optimization.
12 610 0.490598020794 Henry Cohn, 2026, needs more optimization.
12 611 0.490685800298 Henry Cohn, 2026, needs more optimization.
12 612 0.490702554661 Henry Cohn, 2026, needs more optimization.
12 613 0.490899994536 Henry Cohn, 2026, needs more optimization.
12 614 0.490939128439 Henry Cohn, 2026, needs more optimization.
12 615 0.491015844280 Henry Cohn, 2026, needs more optimization.
12 616 0.491192316570 Henry Cohn, 2026, needs more optimization.
12 617 0.491317477147 Henry Cohn, 2026, needs more optimization.
12 618 0.491404556726 Henry Cohn, 2026, needs more optimization.
12 619 0.491421033992 Henry Cohn, 2026, needs more optimization.
12 620 0.491572956921 Henry Cohn, 2026, needs more optimization.
12 621 0.491651143242 Henry Cohn, 2026, needs more optimization.
12 622 0.491714917653 Henry Cohn, 2026, needs more optimization.
12 623 0.491746455396 Henry Cohn, 2026, needs more optimization.
12 624 0.491800789148 Henry Cohn, 2026, needs more optimization.
12 625 0.491851605183 Henry Cohn, 2026, needs more optimization.
12 626 0.491913734247 Henry Cohn, 2026, needs more optimization.
12 627 0.491951420745 Henry Cohn, 2026, needs more optimization.
12 628 0.492034179870 Henry Cohn, 2026, needs more optimization.
12 629 0.492053839775 Henry Cohn, 2026, needs more optimization.
12 630 0.492088698678 Henry Cohn, 2026, needs more optimization.
12 631 0.492161985659 Henry Cohn, 2026, needs more optimization.
12 632 0.492161985672 Henry Cohn, 2026, needs more optimization.
12 633 0.492161985771 Henry Cohn, 2026, needs more optimization.
12 634 0.492213695524 Henry Cohn, 2026, needs more optimization.
12 635 0.492308594931 Henry Cohn, 2026, needs more optimization.
12 636 0.492350381115 Henry Cohn, 2026, needs more optimization.
12 637 0.492373853348 Henry Cohn, 2026, needs more optimization.
12 638 0.492377665372 Henry Cohn, 2026, needs more optimization.
12 639 0.492429234599 Henry Cohn, 2026, needs more optimization.
12 640 0.492492989722 Henry Cohn, 2026, needs more optimization.
12 642 0.492523636541 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
12 643 0.492547636068 Henry Cohn, 2026, needs more optimization.
12 644 0.492657612477 Henry Cohn, 2026, needs more optimization.
12 645 0.492708266693 Henry Cohn, 2026, needs more optimization.
12 646 0.492759103091 Henry Cohn, 2026, needs more optimization.
12 647 0.492853669088 Henry Cohn, 2026, needs more optimization.
12 648 0.493227056734 Henry Cohn, 2026, needs more optimization.
12 649 0.493306621546 Henry Cohn, 2026, needs more optimization.
12 650 0.493332610751 Henry Cohn, 2026, needs more optimization.
12 651 0.493392379152 Henry Cohn, 2026, needs more optimization.
12 652 0.493416020952 Henry Cohn, 2026, needs more optimization.
12 653 0.493456898456 Henry Cohn, 2026, needs more optimization.
12 654 0.493464460978 Henry Cohn, 2026, needs more optimization.
12 655 0.493581543319 Henry Cohn, 2026, needs more optimization.
12 656 0.493609502553 Henry Cohn, 2026, needs more optimization.
12 657 0.493627829302 Henry Cohn, 2026, needs more optimization.
12 658 0.493747682805 Henry Cohn, 2026, needs more optimization.
12 659 0.493791353794 Henry Cohn, 2026, needs more optimization.
12 660 0.493821640264 Henry Cohn, 2026, needs more optimization.
12 661 0.493873424218 Henry Cohn, 2026, needs more optimization.
12 662 0.493926928959 Henry Cohn, 2026, needs more optimization.
12 663 0.493968698294 Henry Cohn, 2026, needs more optimization.
12 664 0.494074595627 Henry Cohn, 2026, needs more optimization.
12 665 0.494217888821 Henry Cohn, 2026, needs more optimization.
12 666 0.494267121833 Henry Cohn, 2026, needs more optimization.
12 667 0.494298241642 Henry Cohn, 2026, needs more optimization.
12 668 0.494334022869 Henry Cohn, 2026, needs more optimization.
12 669 0.494382801932 Henry Cohn, 2026, needs more optimization.
12 670 0.494520996870 Henry Cohn, 2026, needs more optimization.
12 671 0.494558391033 Henry Cohn, 2026, needs more optimization.
12 672 0.494615919301 Henry Cohn, 2026, needs more optimization.
12 673 0.494658462789 Henry Cohn, 2026, needs more optimization.
12 674 0.494665888569 Henry Cohn, 2026, needs more optimization.
12 675 0.494681531894 Henry Cohn, 2026, needs more optimization.
12 676 0.494681931415 Henry Cohn, 2026, needs more optimization.
12 677 0.494705933149 Henry Cohn, 2026, needs more optimization.
12 678 0.494725518894 Henry Cohn, 2026, needs more optimization.
12 679 0.494814407232 Henry Cohn, 2026, needs more optimization.
12 680 0.494849783525 Henry Cohn, 2026, needs more optimization.
12 681 0.494893044408 Henry Cohn, 2026, needs more optimization.
12 682 0.494993789230 Henry Cohn, 2026, needs more optimization.
12 683 0.495069705326 Henry Cohn, 2026, needs more optimization.
12 684 0.495093178447 Henry Cohn, 2026, needs more optimization.
12 685 0.495105440290 Henry Cohn, 2026, needs more optimization.
12 686 0.495127979813 Henry Cohn, 2026, needs more optimization.
12 687 0.495149332070 Henry Cohn, 2026, needs more optimization.
12 688 0.495231942905 Henry Cohn, 2026, needs more optimization.
12 689 0.495307247895 Henry Cohn, 2026, needs more optimization.
12 690 0.495365091700 Henry Cohn, 2026, needs more optimization.
12 691 0.495423547493 Henry Cohn, 2026, needs more optimization.
12 692 0.495456251636 Henry Cohn, 2026, needs more optimization.
12 693 0.495522315605 Henry Cohn, 2026, needs more optimization.
12 694 0.495537054463 Henry Cohn, 2026, needs more optimization.
12 695 0.495565322365 Henry Cohn, 2026, needs more optimization.
12 696 0.495586526229 Henry Cohn, 2026, needs more optimization.
12 697 0.495633690964 Henry Cohn, 2026, needs more optimization.
12 698 0.495661940988 Henry Cohn, 2026, needs more optimization.
12 699 0.495744203103 Henry Cohn, 2026, needs more optimization.
12 700 0.495759898284 Henry Cohn, 2026, needs more optimization.
12 701 0.495787977182 Henry Cohn, 2026, needs more optimization.
12 702 0.495867425908 Henry Cohn, 2026, needs more optimization.
12 703 0.495876149484 Henry Cohn, 2026, needs more optimization.
12 704 0.495918117941 Henry Cohn, 2026, needs more optimization.
12 705 0.495950620536 Henry Cohn, 2026, needs more optimization.
12 706 0.496023541608 Henry Cohn, 2026, needs more optimization.
12 707 0.496045470137 Henry Cohn, 2026, needs more optimization.
12 708 0.496105995942 Henry Cohn, 2026, needs more optimization.
12 709 0.496148756017 Henry Cohn, 2026, needs more optimization.
12 710 0.496160059262 Henry Cohn, 2026, needs more optimization.
12 711 0.496192783299 Henry Cohn, 2026, needs more optimization.
12 712 0.496206978344 Henry Cohn, 2026, needs more optimization.
12 713 0.496298835914 Henry Cohn, 2026, needs more optimization.
12 714 0.496310217994 Henry Cohn, 2026, needs more optimization.
12 715 0.496312677292 Henry Cohn, 2026, needs more optimization.
12 716 0.496332031333 Henry Cohn, 2026, needs more optimization.
12 717 0.496345547187 Henry Cohn, 2026, needs more optimization.
12 718 0.496378845270 Henry Cohn, 2026, needs more optimization.
12 719 0.496392961677 Henry Cohn, 2026, needs more optimization.
12 721 0.496415698881 Henry Cohn, 2026, needs more optimization.
12 722 0.496425377526 Henry Cohn, 2026, needs more optimization.
12 723 0.496438945854 Henry Cohn, 2026, needs more optimization.
12 724 0.496460807359 Henry Cohn, 2026, needs more optimization.
12 725 0.496467156030 Henry Cohn, 2026, needs more optimization.
12 726 0.496499695381 Henry Cohn, 2026, needs more optimization.
12 727 0.496502941230 Henry Cohn, 2026, needs more optimization.
12 728 0.496520347494 Henry Cohn, 2026, needs more optimization.
12 729 0.496537573656 Henry Cohn, 2026, needs more optimization.
12 730 0.496544341520 Henry Cohn, 2026, needs more optimization.
12 731 0.496553384019 Henry Cohn, 2026, needs more optimization.
12 732 0.496554314494 Henry Cohn, 2026, needs more optimization.
12 733 0.496557727650 Henry Cohn, 2026, needs more optimization.
12 734 0.496562605962 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
12 735 0.496805826607 Henry Cohn, 2026, needs more optimization.
12 736 0.496814587849 Henry Cohn, 2026, needs more optimization.
12 737 0.496821363308 Henry Cohn, 2026, needs more optimization.
12 738 0.496822821518 Henry Cohn, 2026, needs more optimization.
12 739 0.496836308240 Henry Cohn, 2026, needs more optimization.
12 740 0.496848315034 Henry Cohn, 2026, needs more optimization.
12 741 0.496848317838 Henry Cohn, 2026, needs more optimization.
12 742 0.496848317845 Henry Cohn, 2026, needs more optimization.
12 743 0.496857590046 Henry Cohn, 2026, needs more optimization.
12 744 0.496868381489 Henry Cohn, 2026, needs more optimization.
12 745 0.496904373102 Henry Cohn, 2026, needs more optimization.
12 746 0.496933049888 Henry Cohn, 2026, needs more optimization.
12 747 0.496982913400 Henry Cohn, 2026, needs more optimization.
12 748 0.496982932794 Henry Cohn, 2026, needs more optimization.
12 749 0.496995989444 Henry Cohn, 2026, needs more optimization.
12 750 0.496999953215 Henry Cohn, 2026, needs more optimization.
12 751 0.497004001329 Henry Cohn, 2026, needs more optimization.
12 752 0.497013845982 Henry Cohn, 2026, needs more optimization.
12 753 0.497025337336 Henry Cohn, 2026, needs more optimization.
12 754 0.497032657887 Henry Cohn, 2026, needs more optimization.
12 755 0.497036321009 Henry Cohn, 2026, needs more optimization.
12 756 0.497124126338 Henry Cohn, 2026, needs more optimization.
12 757 0.498329547922 Henry Cohn, 2026, needs more optimization.
12 758 0.499172295718 Henry Cohn, 2026, needs more optimization.
12 760 0.499172725033 Henry Cohn, 2026, needs more optimization.
12 763 0.499554975272 Henry Cohn, 2026, needs more optimization.
12 766 0.499893563856 Henry Cohn, 2026, needs more optimization.
12 773 0.499926585465 Henry Cohn, 2026, needs more optimization.
12 797 0.499957006943 Henry Cohn, 2026, needs more optimization.
12 803 0.499957230634 Henry Cohn, 2026, needs more optimization.
12 806 0.499957880759 Henry Cohn, 2026, needs more optimization.
12 809 0.499958320391 Henry Cohn, 2026, needs more optimization.
12 820 0.499966857813 Henry Cohn, 2026, needs more optimization.
12 822 0.499967239240 Henry Cohn, 2026, needs more optimization.
12 829 0.499999010977 Henry Cohn, 2026, needs more optimization.
12 841 0.499999937615 R. Takhanov, Z. Assylbekov, and S. Yun, Structure of kissing arrangements in ℝ12 and a place for the 841st sphere, preprint, 2026, arXiv:2606.18984, after some further optimization.
12 842 0.500899993878 R. Takhanov, Z. Assylbekov, and S. Yun, Structure of kissing arrangements in ℝ12 and a place for the 841st sphere, preprint, 2026, arXiv:2606.18984, after some further optimization.
12 843 0.504400740396 Henry Cohn, 2026, needs more optimization.
12 844 0.504401014939 R. Takhanov, Z. Assylbekov, and S. Yun, Structure of kissing arrangements in ℝ12 and a place for the 841st sphere, preprint, 2026, arXiv:2606.18984, after some further optimization.
12 845 0.506045425340 Henry Cohn, 2026, needs more optimization.
12 846 0.507106256247 Henry Cohn, 2026, needs more optimization.
12 847 0.508067390206 Henry Cohn, 2026, needs more optimization.
12 848 0.517686184341 Henry Cohn, 2026, needs more optimization.
12 849 0.518017150297 Henry Cohn, 2026, needs more optimization.
12 850 0.518717239921 Henry Cohn, 2026, needs more optimization.
12 851 0.518970283783 Henry Cohn, 2026, needs more optimization.
12 852 0.519377989954 Henry Cohn, 2026, needs more optimization.
12 853 0.519696640376 Henry Cohn, 2026, needs more optimization.
12 854 0.520097466812 Henry Cohn, 2026, needs more optimization.
12 855 0.520364150513 Henry Cohn, 2026, needs more optimization.
12 856 0.520792896350 Henry Cohn, 2026, needs more optimization.
12 857 0.521077991009 Henry Cohn, 2026, needs more optimization.
12 858 0.521414623072 Henry Cohn, 2026, needs more optimization.
12 859 0.521986420735 Henry Cohn, 2026, needs more optimization.
12 860 0.522315220966 Henry Cohn, 2026, needs more optimization.
12 861 0.522616969149 Henry Cohn, 2026, needs more optimization.
12 862 0.522858940827 Henry Cohn, 2026, needs more optimization.
12 863 0.523058375771 Henry Cohn, 2026, needs more optimization.
12 864 0.523300613571 Henry Cohn, 2026, needs more optimization.
12 865 0.523710475073 Henry Cohn, 2026, needs more optimization.
12 866 0.524007363767 Henry Cohn, 2026, needs more optimization.
12 867 0.524196125019 Henry Cohn, 2026, needs more optimization.
12 868 0.524344821285 Henry Cohn, 2026, needs more optimization.
12 869 0.524650305971 Henry Cohn, 2026, needs more optimization.
12 870 0.524845341597 Henry Cohn, 2026, needs more optimization.
12 871 0.525046212182 Henry Cohn, 2026, needs more optimization.
12 872 0.525522245976 Henry Cohn, 2026, needs more optimization.
12 873 0.525784410651 Henry Cohn, 2026, needs more optimization.
12 874 0.526138865345 Henry Cohn, 2026, needs more optimization.
12 875 0.526343467278 Henry Cohn, 2026, needs more optimization.
12 876 0.526600605895 Henry Cohn, 2026, needs more optimization.
12 877 0.526852176484 Henry Cohn, 2026, needs more optimization.
12 878 0.527157332639 Henry Cohn, 2026, needs more optimization.
12 879 0.527385126322 Henry Cohn, 2026, needs more optimization.
12 880 0.527622512134 Henry Cohn, 2026, needs more optimization.
12 881 0.527861360126 Henry Cohn, 2026, needs more optimization.
12 882 0.528190450719 Henry Cohn, 2026, needs more optimization.
12 883 0.528427821760 Henry Cohn, 2026, needs more optimization.
12 884 0.528781555152 Henry Cohn, 2026, needs more optimization.
12 885 0.528980835915 Henry Cohn, 2026, needs more optimization.
12 886 0.529157138827 Henry Cohn, 2026, needs more optimization.
12 887 0.529452243147 Henry Cohn, 2026, needs more optimization.
12 888 0.529685496805 Henry Cohn, 2026, needs more optimization.
12 889 0.530263758876 Henry Cohn, 2026, needs more optimization.
12 890 0.530460922857 Henry Cohn, 2026, needs more optimization.
12 891 0.530609571053 Henry Cohn, 2026, needs more optimization.
12 892 0.530883046337 Henry Cohn, 2026, needs more optimization.
12 893 0.531077153079 Henry Cohn, 2026, needs more optimization.
12 894 0.531313661280 Henry Cohn, 2026, needs more optimization.
12 895 0.531646775346 Henry Cohn, 2026, needs more optimization.
12 896 0.531865762034 Henry Cohn, 2026, needs more optimization.
12 897 0.532169550814 Henry Cohn, 2026, needs more optimization.
12 898 0.532311248588 Henry Cohn, 2026, needs more optimization.
12 899 0.532500066803 Henry Cohn, 2026, needs more optimization.
12 900 0.532652169265 Henry Cohn, 2026, needs more optimization.
12 901 0.532807526621 Henry Cohn, 2026, needs more optimization.
12 902 0.533033613020 Henry Cohn, 2026, needs more optimization.
12 903 0.533209191248 Henry Cohn, 2026, needs more optimization.
12 904 0.533473804053 Henry Cohn, 2026, needs more optimization.
12 905 0.533685857088 Henry Cohn, 2026, needs more optimization.
12 906 0.533919853859 Henry Cohn, 2026, needs more optimization.
12 907 0.534081315421 Henry Cohn, 2026, needs more optimization.
12 908 0.534327667395 Henry Cohn, 2026, needs more optimization.
12 909 0.534456789223 Henry Cohn, 2026, needs more optimization.
12 910 0.534629755901 Henry Cohn, 2026, needs more optimization.
12 911 0.534842797321 Henry Cohn, 2026, needs more optimization.
12 912 0.535045848033 Henry Cohn, 2026, needs more optimization.
12 913 0.535246951189 Henry Cohn, 2026, needs more optimization.
12 914 0.535524843434 Henry Cohn, 2026, needs more optimization.
12 915 0.535846418115 Henry Cohn, 2026, needs more optimization.
12 916 0.536052481198 Henry Cohn, 2026, needs more optimization.
12 917 0.536204743307 Henry Cohn, 2026, needs more optimization.
12 918 0.536563227526 Henry Cohn, 2026, needs more optimization.
12 919 0.536795852037 Henry Cohn, 2026, needs more optimization.
12 920 0.537016420471 Henry Cohn, 2026, needs more optimization.
12 921 0.537165340236 Henry Cohn, 2026, needs more optimization.
12 922 0.537350914699 Henry Cohn, 2026, needs more optimization.
12 923 0.537540522020 Henry Cohn, 2026, needs more optimization.
12 924 0.537750809722 Henry Cohn, 2026, needs more optimization.
12 925 0.537830775879 Henry Cohn, 2026, needs more optimization.
12 926 0.538085952025 Henry Cohn, 2026, needs more optimization.
12 927 0.538206426974 Henry Cohn, 2026, needs more optimization.
12 928 0.538368754194 Henry Cohn, 2026, needs more optimization.
12 929 0.538551546033 Henry Cohn, 2026, needs more optimization.
12 930 0.538707431129 Henry Cohn, 2026, needs more optimization.
12 931 0.538968617019 Henry Cohn, 2026, needs more optimization.
12 932 0.539136573559 Henry Cohn, 2026, needs more optimization.
12 933 0.539324390652 Henry Cohn, 2026, needs more optimization.
12 934 0.539473095216 Henry Cohn, 2026, needs more optimization.
12 935 0.539689533385 Henry Cohn, 2026, needs more optimization.
12 936 0.539859172724 Henry Cohn, 2026, needs more optimization.
12 937 0.540070215688 Henry Cohn, 2026, needs more optimization.
12 938 0.540266321336 Henry Cohn, 2026, needs more optimization.
12 939 0.540482281632 Henry Cohn, 2026, needs more optimization.
12 940 0.540661281878 Henry Cohn, 2026, needs more optimization.
12 941 0.540895485589 Henry Cohn, 2026, needs more optimization.
12 942 0.540999617645 Henry Cohn, 2026, needs more optimization.
12 943 0.541120754755 Henry Cohn, 2026, needs more optimization.
12 944 0.541292469118 Henry Cohn, 2026, needs more optimization.
12 945 0.541511780471 Henry Cohn, 2026, needs more optimization.
12 946 0.541663245936 Henry Cohn, 2026, needs more optimization.
12 947 0.541978111219 Henry Cohn, 2026, needs more optimization.
12 948 0.542096137815 Henry Cohn, 2026, needs more optimization.
12 949 0.542233502887 Henry Cohn, 2026, needs more optimization.
12 950 0.542378675131 Henry Cohn, 2026, needs more optimization.
12 951 0.542524033807 Henry Cohn, 2026, needs more optimization.
12 952 0.542744163452 Henry Cohn, 2026, needs more optimization.
12 953 0.543027432752 Henry Cohn, 2026, needs more optimization.
12 954 0.543178403699 Henry Cohn, 2026, needs more optimization.
12 955 0.543395511806 Henry Cohn, 2026, needs more optimization.
12 956 0.543465676739 Henry Cohn, 2026, needs more optimization.
12 957 0.543654500089 Henry Cohn, 2026, needs more optimization.
12 958 0.543787132289 Henry Cohn, 2026, needs more optimization.
12 959 0.543952988026 Henry Cohn, 2026, needs more optimization.
12 960 0.544099818497 Henry Cohn, 2026, needs more optimization.
12 961 0.544223344267 Henry Cohn, 2026, needs more optimization.
12 962 0.544426897329 Henry Cohn, 2026, needs more optimization.
12 963 0.544526881503 Henry Cohn, 2026, needs more optimization.
12 964 0.544703159819 Henry Cohn, 2026, needs more optimization.
12 965 0.544829625286 Henry Cohn, 2026, needs more optimization.
12 966 0.544918164152 Henry Cohn, 2026, needs more optimization.
12 967 0.545087678736 Henry Cohn, 2026, needs more optimization.
12 968 0.545246320206 Henry Cohn, 2026, needs more optimization.
12 969 0.545451919686 Henry Cohn, 2026, needs more optimization.
12 970 0.545506331144 Henry Cohn, 2026, needs more optimization.
12 971 0.545619092607 Henry Cohn, 2026, needs more optimization.
12 972 0.545732127244 Henry Cohn, 2026, needs more optimization.
12 973 0.545924266909 Henry Cohn, 2026, needs more optimization.
12 974 0.546122213032 Henry Cohn, 2026, needs more optimization.
12 975 0.546255943937 Henry Cohn, 2026, needs more optimization.
12 976 0.546389425161 Henry Cohn, 2026, needs more optimization.
12 977 0.546545620525 Henry Cohn, 2026, needs more optimization.
12 978 0.546665990647 Henry Cohn, 2026, needs more optimization.
12 979 0.546788199315 Henry Cohn, 2026, needs more optimization.
12 980 0.546873620223 Henry Cohn, 2026, needs more optimization.
12 981 0.547035295019 Henry Cohn, 2026, needs more optimization.
12 982 0.547118713835 Henry Cohn, 2026, needs more optimization.
12 983 0.547260031115 Henry Cohn, 2026, needs more optimization.
12 984 0.547412972815 Henry Cohn, 2026, needs more optimization.
12 985 0.547576624066 Henry Cohn, 2026, needs more optimization.
12 986 0.547709646964 Henry Cohn, 2026, needs more optimization.
12 987 0.547790484298 Henry Cohn, 2026, needs more optimization.
12 988 0.547911000171 Henry Cohn, 2026, needs more optimization.
12 989 0.548045215094 Henry Cohn, 2026, needs more optimization.
12 990 0.548081776463 Henry Cohn, 2026, needs more optimization.
12 991 0.548240568462 Henry Cohn, 2026, needs more optimization.
12 992 0.548347068406 Henry Cohn, 2026, needs more optimization.
12 993 0.548478446017 Henry Cohn, 2026, needs more optimization.
12 994 0.548658309408 Henry Cohn, 2026, needs more optimization.
12 995 0.548760540913 Henry Cohn, 2026, needs more optimization.
12 996 0.548971732961 Henry Cohn, 2026, needs more optimization.
12 997 0.549075935513 Henry Cohn, 2026, needs more optimization.
12 998 0.549237785545 Henry Cohn, 2026, needs more optimization.
12 999 0.549401582486 Henry Cohn, 2026, needs more optimization.
12 1000 0.549615493408 Henry Cohn, 2026, needs more optimization.
12 1001 0.549717487268 Henry Cohn, 2026, needs more optimization.
12 1002 0.549943785795 Henry Cohn, 2026, needs more optimization.
12 1003 0.550026997008 Henry Cohn, 2026, needs more optimization.
12 1004 0.550197666972 Henry Cohn, 2026, needs more optimization.
12 1005 0.550279760211 Henry Cohn, 2026, needs more optimization.
12 1006 0.550380200380 Henry Cohn, 2026, needs more optimization.
12 1007 0.550479044028 Henry Cohn, 2026, needs more optimization.
12 1008 0.550633895416 Henry Cohn, 2026, needs more optimization.
12 1009 0.550758849875 Henry Cohn, 2026, needs more optimization.
12 1010 0.550949862900 Henry Cohn, 2026, needs more optimization.
12 1011 0.551068178249 Henry Cohn, 2026, needs more optimization.
12 1012 0.551129855040 Henry Cohn, 2026, needs more optimization.
12 1013 0.551303186800 Henry Cohn, 2026, needs more optimization.
12 1014 0.551385287291 Henry Cohn, 2026, needs more optimization.
12 1015 0.551476148140 Henry Cohn, 2026, needs more optimization.
12 1016 0.551681079084 Henry Cohn, 2026, needs more optimization.
12 1017 0.551770165452 Henry Cohn, 2026, needs more optimization.
12 1018 0.551870194532 Henry Cohn, 2026, needs more optimization.
12 1019 0.552078760480 Henry Cohn, 2026, needs more optimization.
12 1020 0.552196406888 Henry Cohn, 2026, needs more optimization.
12 1021 0.552334382079 Henry Cohn, 2026, needs more optimization.
12 1022 0.552430454215 Henry Cohn, 2026, needs more optimization.
12 1023 0.552557326345 Henry Cohn, 2026, needs more optimization.
12 1024 0.552757840131 Henry Cohn, 2026, needs more optimization.
13 27 0.057072523783 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
1573⁢x3−169⁢x2−13⁢x+1
13 28 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
15⁢x−1
13 29 0.068098609479 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
2576⁢x4−640⁢x3−184⁢x2+1
13 30 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 31 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 32 0.071714034728 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
55⁢x2+10⁢x−1
13 33 0.089833578043 Henry Cohn, 2026.
13 34 0.090095382331 Henry Cohn, 2023.
13 36 0.092610094433 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
95⁢x2+2⁢x−1
13 37 0.111409136725 Henry Cohn, 2023.
13 38 0.112004618870 Henry Cohn, 2023.
44⁢x2+4⁢x−1
13 39 0.116893063508 Henry Cohn, 2024.
13 40 0.121353571480 Henry Cohn, 2026.
13 42 0.125 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
8⁢x−1
13 44 0.126079252818 Henry Cohn, 2025.
6095⁢x2−126⁢x−81
13 48 0.126131983623 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2+2⁢x−1
13 49 0.141095436175 Henry Cohn, 2025.
13 50 0.142459427551 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 51 0.145120831484 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 52 0.147159522238 Henry Cohn, 2023.
613567⁢x7+96585⁢x6−98333⁢x5−8219⁢x4+381⁢x3+539⁢x2+33⁢x−9
13 53 0.147908231498 Henry Cohn, 2026.
13 54 0.148576022240 Henry Cohn, 2025.
13 55 0.148805252884 Henry Cohn, 2024.
13 56 0.148975682089 Henry Cohn, 2023.
13 57 0.166162190421 Henry Cohn, 2024.
13 58 0.173474302723 Henry Cohn, 2023.
13 66 0.180076545649 Ilmari Vahteristo, 2026.
197541⁢x6−1327980⁢x5+842815⁢x4+93800⁢x3−58725⁢x2+500⁢x+625
13 67 0.204059765290 Henry Cohn, 2026.
13 68 0.206352808699 Henry Cohn, 2026, needs more optimization.
13 69 0.207586830294 Henry Cohn, 2026, needs more optimization.
13 70 0.208514068764 Henry Cohn, 2026, needs more optimization.
13 71 0.209182927728 Henry Cohn, 2026, needs more optimization.
13 72 0.210111567528 Henry Cohn, 2026, needs more optimization.
13 73 0.211125887543 Henry Cohn, 2026, needs more optimization.
13 74 0.212024291504 Henry Cohn, 2026, needs more optimization.
13 75 0.213015639549 Henry Cohn, 2026, needs more optimization.
13 84 0.214312873432 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 85 0.228127035426 Henry Cohn, 2026, needs more optimization.
13 86 0.232137795509 Henry Cohn, 2026, needs more optimization.
13 87 0.234506754689 Henry Cohn, 2026, needs more optimization.
13 88 0.234777351570 Henry Cohn, 2026, needs more optimization.
13 89 0.238133133066 Henry Cohn, 2026, needs more optimization.
13 90 0.241064086572 Henry Cohn, 2026, needs more optimization.
13 91 0.242549626752 Henry Cohn, 2026, needs more optimization.
13 92 0.243154829020 Henry Cohn, 2026, needs more optimization.
13 93 0.244059192336 Henry Cohn, 2026, needs more optimization.
13 94 0.244139892955 Henry Cohn, 2026, needs more optimization.
13 95 0.244205973294 Henry Cohn, 2026, needs more optimization.
13 96 0.244319671577 Henry Cohn, 2026, needs more optimization.
13 97 0.244402829414 Henry Cohn, 2026, needs more optimization.
13 98 0.244474377631 Henry Cohn, 2026, needs more optimization.
13 99 0.245223251497 Henry Cohn, 2026, needs more optimization.
13 100 0.246831261561 Henry Cohn, 2026, needs more optimization.
13 101 0.249341456787 Henry Cohn, 2026, needs more optimization.
13 104 0.25 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4⁢x−1
13 106 0.251575083557 Henry Cohn, 2026.
1031⁢x2−160⁢x−25
13 107 0.257875984734 Henry Cohn, 2026, needs more optimization.
13 108 0.258192353671 Henry Cohn, 2026, needs more optimization.
13 109 0.258968662985 Henry Cohn, 2026, needs more optimization.
13 110 0.259435840974 Henry Cohn, 2026, needs more optimization.
13 111 0.259779807465 Henry Cohn, 2026, needs more optimization.
13 112 0.260588811666 Henry Cohn, 2026, needs more optimization.
13 113 0.261321679347 Henry Cohn, 2026, needs more optimization.
13 114 0.263142706341 Henry Cohn, 2026, needs more optimization.
13 115 0.264240006648 Henry Cohn, 2026, needs more optimization.
13 116 0.266454669306 Henry Cohn, 2026, needs more optimization.
13 117 0.267682521531 Henry Cohn, 2026, needs more optimization.
13 118 0.269176208942 Henry Cohn, 2026, needs more optimization.
13 119 0.270164057548 Henry Cohn, 2026, needs more optimization.
13 120 0.271257292113 Henry Cohn, 2026, needs more optimization.
13 121 0.271353350623 Henry Cohn, 2026, needs more optimization.
13 122 0.272081042155 Henry Cohn, 2026, needs more optimization.
13 123 0.272106103873 Henry Cohn, 2026, needs more optimization.
13 124 0.275835352799 Henry Cohn, 2026, needs more optimization.
13 125 0.276037827247 Henry Cohn, 2026, needs more optimization.
13 126 0.276196851259 Henry Cohn, 2026, needs more optimization.
13 127 0.278070861529 Henry Cohn, 2026, needs more optimization.
13 128 0.280210578252 Henry Cohn, 2026, needs more optimization.
13 129 0.282329057010 Henry Cohn, 2026, needs more optimization.
13 130 0.284583847124 Henry Cohn, 2026, needs more optimization.
13 131 0.285558611951 Henry Cohn, 2026, needs more optimization.
13 132 0.286036831201 Henry Cohn, 2026, needs more optimization.
13 133 0.286604641933 Henry Cohn, 2026, needs more optimization.
13 134 0.287973974370 Henry Cohn, 2026, needs more optimization.
13 135 0.289066225897 Henry Cohn, 2026, needs more optimization.
13 136 0.289953880493 Henry Cohn, 2026, needs more optimization.
13 137 0.291821333651 Henry Cohn, 2026, needs more optimization.
13 138 0.293173059622 Henry Cohn, 2026, needs more optimization.
13 139 0.294579898578 Henry Cohn, 2026, needs more optimization.
13 140 0.294922160446 Henry Cohn, 2026, needs more optimization.
13 141 0.296429535016 Henry Cohn, 2026, needs more optimization.
13 142 0.296603170414 Henry Cohn, 2026, needs more optimization.
13 143 0.296817906649 Henry Cohn, 2026, needs more optimization.
13 144 0.298604577534 Henry Cohn, 2026, needs more optimization.
13 145 0.300070363140 Henry Cohn, 2026, needs more optimization.
13 146 0.300144857952 Henry Cohn, 2026, needs more optimization.
13 147 0.300272432751 Henry Cohn, 2026, needs more optimization.
13 148 0.300834705383 Henry Cohn, 2026, needs more optimization.
13 149 0.300892993985 Henry Cohn, 2026, needs more optimization.
13 150 0.300977858049 Henry Cohn, 2026, needs more optimization.
13 151 0.301154345105 Henry Cohn, 2026, needs more optimization.
13 152 0.301825004338 Henry Cohn, 2026, needs more optimization.
13 153 0.302640407629 Henry Cohn, 2026, needs more optimization.
13 154 0.303985650564 Henry Cohn, 2026, needs more optimization.
13 155 0.305870647068 Henry Cohn, 2026, needs more optimization.
13 156 0.307224073716 Henry Cohn, 2026, needs more optimization.
13 157 0.308345101531 Henry Cohn, 2026, needs more optimization.
13 158 0.309197626955 Henry Cohn, 2026, needs more optimization.
13 159 0.310123923102 Henry Cohn, 2026, needs more optimization.
13 160 0.311669630393 Henry Cohn, 2026, needs more optimization.
13 161 0.312205177299 Henry Cohn, 2026, needs more optimization.
13 162 0.312465614328 Henry Cohn, 2026, needs more optimization.
13 163 0.313057469622 Henry Cohn, 2026, needs more optimization.
13 164 0.313972910021 Henry Cohn, 2026, needs more optimization.
13 165 0.315032500346 Henry Cohn, 2026, needs more optimization.
13 166 0.316127243280 Henry Cohn, 2026, needs more optimization.
13 167 0.316332632628 Henry Cohn, 2026, needs more optimization.
13 168 0.316376439119 Henry Cohn, 2026, needs more optimization.
13 169 0.316706801264 Henry Cohn, 2026, needs more optimization.
13 170 0.316898056314 Henry Cohn, 2026, needs more optimization.
13 171 0.317064388528 Henry Cohn, 2026, needs more optimization.
13 172 0.317884064804 Henry Cohn, 2026, needs more optimization.
13 173 0.318715389085 Henry Cohn, 2026, needs more optimization.
13 174 0.319067699564 Henry Cohn, 2026, needs more optimization.
13 175 0.319477949675 Henry Cohn, 2026, needs more optimization.
13 176 0.320346939120 Henry Cohn, 2026, needs more optimization.
13 177 0.321006237992 Henry Cohn, 2026, needs more optimization.
13 178 0.321232195655 Henry Cohn, 2026, needs more optimization.
13 179 0.322006058650 Henry Cohn, 2026, needs more optimization.
13 180 0.322566593319 Henry Cohn, 2026, needs more optimization.
13 181 0.323155553694 Henry Cohn, 2026, needs more optimization.
13 182 0.323700009013 Henry Cohn, 2026, needs more optimization.
13 183 0.324278449693 Henry Cohn, 2026, needs more optimization.
13 184 0.324830154353 Henry Cohn, 2026, needs more optimization.
13 185 0.325196509666 Henry Cohn, 2026, needs more optimization.
13 186 0.325465833710 Henry Cohn, 2026, needs more optimization.
13 187 0.325972815186 Henry Cohn, 2026, needs more optimization.
13 188 0.326259146235 Henry Cohn, 2026, needs more optimization.
13 189 0.326624960460 Henry Cohn, 2026, needs more optimization.
13 190 0.326795990132 Henry Cohn, 2026, needs more optimization.
13 191 0.327160204824 Henry Cohn, 2026, needs more optimization.
13 192 0.327351317399 Henry Cohn, 2026, needs more optimization.
13 193 0.327450762894 Henry Cohn, 2026, needs more optimization.
13 194 0.327681553994 Henry Cohn, 2026, needs more optimization.
13 195 0.327773526488 Henry Cohn, 2026, needs more optimization.
13 196 0.328728695571 Henry Cohn, 2026, needs more optimization.
13 197 0.328861067857 Henry Cohn, 2026, needs more optimization.
13 198 0.328986484093 Henry Cohn, 2026, needs more optimization.
13 199 0.329136599356 Henry Cohn, 2026, needs more optimization.
13 200 0.329342398496 Henry Cohn, 2026, needs more optimization.
13 201 0.329522676574 Henry Cohn, 2026, needs more optimization.
13 202 0.329689115378 Henry Cohn, 2026, needs more optimization.
13 203 0.332312465069 Henry Cohn, 2026, needs more optimization.
13 208 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
13 209 0.349907019200 Henry Cohn, 2026, needs more optimization.
13 210 0.350627746669 Henry Cohn, 2026, needs more optimization.
13 211 0.351184748629 Henry Cohn, 2026, needs more optimization.
13 212 0.352089484899 Henry Cohn, 2026, needs more optimization.
13 213 0.353022154893 Henry Cohn, 2026, needs more optimization.
13 214 0.353887252099 Henry Cohn, 2026, needs more optimization.
13 215 0.354712797584 Henry Cohn, 2026, needs more optimization.
13 216 0.355426821286 Henry Cohn, 2026, needs more optimization.
13 217 0.356056637463 Henry Cohn, 2026, needs more optimization.
13 218 0.357592618572 Henry Cohn, 2026, needs more optimization.
13 219 0.358094866062 Henry Cohn, 2026, needs more optimization.
13 220 0.358706735494 Henry Cohn, 2026, needs more optimization.
13 221 0.359500767450 Henry Cohn, 2026, needs more optimization.
13 222 0.360485874453 Henry Cohn, 2026, needs more optimization.
13 223 0.361328997576 Henry Cohn, 2026, needs more optimization.
13 224 0.362377333699 Henry Cohn, 2026, needs more optimization.
13 225 0.363135324150 Henry Cohn, 2026, needs more optimization.
13 226 0.363888859734 Henry Cohn, 2026, needs more optimization.
13 227 0.364771642640 Henry Cohn, 2026, needs more optimization.
13 228 0.365433262447 Henry Cohn, 2026, needs more optimization.
13 229 0.366022331715 Henry Cohn, 2026, needs more optimization.
13 230 0.366886065019 Henry Cohn, 2026, needs more optimization.
13 231 0.367679712011 Henry Cohn, 2026, needs more optimization.
13 240 0.368421052632 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
19⁢x−7
13 246 0.368421052632 Henry Cohn, 2026.
19⁢x−7
13 247 0.371938174469 Henry Cohn, 2026, needs more optimization.
13 248 0.372967207624 Henry Cohn, 2026, needs more optimization.
13 249 0.373012134312 Henry Cohn, 2026, needs more optimization.
13 250 0.374396896200 Henry Cohn, 2026, needs more optimization.
13 251 0.375269252644 Henry Cohn, 2026, needs more optimization.
13 291 0.376384967370 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
23⁢x2−6⁢x−1
13 292 0.380271337242 Henry Cohn, 2026, needs more optimization.
13 293 0.380277837845 Henry Cohn, 2026, needs more optimization.
13 294 0.382494726372 Henry Cohn, 2026, needs more optimization.
13 295 0.383317096989 Henry Cohn, 2026, needs more optimization.
13 296 0.383910031961 Henry Cohn, 2026, needs more optimization.
13 306 0.384615384616 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−5
13 313 0.384615384616 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
13⁢x−5
13 314 0.389008395420 Henry Cohn, 2026, needs more optimization.
13 315 0.391819490904 Henry Cohn, 2026, needs more optimization.
13 316 0.393356320290 Henry Cohn, 2026, needs more optimization.
13 317 0.393953119873 Henry Cohn, 2026, needs more optimization.
13 318 0.395165669041 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 319 0.396151413323 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 320 0.396819602114 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 321 0.397924129332 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 322 0.398266726877 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
13 336 0.4 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
5⁢x−2
13 337 0.4 Henry Cohn, 2026.
5⁢x−2
13 339 0.4 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
5⁢x−2
13 340 0.405636400249 Henry Cohn, 2026, needs more optimization.
13 341 0.407417917914 Henry Cohn, 2026, needs more optimization.
13 342 0.407610253146 Henry Cohn, 2026, needs more optimization.
13 343 0.407664506590 Henry Cohn, 2026, needs more optimization.
13 344 0.408190728765 Henry Cohn, 2026, needs more optimization.
13 345 0.408396629481 Henry Cohn, 2026, needs more optimization.
13 346 0.408737460629 Henry Cohn, 2026, needs more optimization.
13 347 0.409548877064 Henry Cohn, 2026, needs more optimization.
13 348 0.410344005137 Henry Cohn, 2026, needs more optimization.
13 349 0.410707299942 Henry Cohn, 2026, needs more optimization.
13 350 0.410933626845 Henry Cohn, 2026, needs more optimization.
13 351 0.411013167434 Henry Cohn, 2026, needs more optimization.
13 352 0.411768412640 Henry Cohn, 2026, needs more optimization.
13 353 0.412552092950 Henry Cohn, 2026, needs more optimization.
13 354 0.413356465293 Henry Cohn, 2026, needs more optimization.
13 355 0.413992205093 Henry Cohn, 2026, needs more optimization.
13 356 0.414611053466 Henry Cohn, 2026, needs more optimization.
13 357 0.415090646981 Henry Cohn, 2026, needs more optimization.
13 358 0.415644665671 Henry Cohn, 2026, needs more optimization.
13 359 0.416137975944 Henry Cohn, 2026, needs more optimization.
13 360 0.416431424286 Henry Cohn, 2026, needs more optimization.
13 383 0.416666666667 Henry Cohn, 2026.
12⁢x−5
13 384 0.419641221594 Henry Cohn, 2026, needs more optimization.
13 385 0.420757215535 Henry Cohn, 2026, needs more optimization.
13 386 0.421199764176 Henry Cohn, 2026, needs more optimization.
13 387 0.421589411372 Henry Cohn, 2026, needs more optimization.
13 388 0.422314069764 Henry Cohn, 2026, needs more optimization.
13 389 0.423829072352 Henry Cohn, 2026, needs more optimization.
13 390 0.424217243490 Henry Cohn, 2026, needs more optimization.
13 391 0.424690202491 Henry Cohn, 2026, needs more optimization.
13 392 0.425194639844 Henry Cohn, 2026, needs more optimization.
13 393 0.425963316763 Henry Cohn, 2026, needs more optimization.
13 394 0.426551336375 Henry Cohn, 2026, needs more optimization.
13 395 0.427199871974 Henry Cohn, 2026, needs more optimization.
13 396 0.427815954099 Henry Cohn, 2026, needs more optimization.
13 397 0.427873150934 Henry Cohn, 2026, needs more optimization.
13 416 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
13 492 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
13 498 0.428571428572 Henry Cohn, 2026.
7⁢x−3
13 499 0.428679829897 Henry Cohn, 2026, needs more optimization.
13 500 0.429496475416 Henry Cohn, 2026, needs more optimization.
13 501 0.429602642763 Henry Cohn, 2026, needs more optimization.
13 502 0.429673395583 Henry Cohn, 2026, needs more optimization.
13 503 0.429681978125 Henry Cohn, 2026, needs more optimization.
13 504 0.429684856413 Henry Cohn, 2026, needs more optimization.
13 505 0.436906969175 Henry Cohn, 2026, needs more optimization.
13 506 0.439525222627 Henry Cohn, 2026, needs more optimization.
13 507 0.441378005941 Henry Cohn, 2026, needs more optimization.
13 508 0.441559000333 Henry Cohn, 2026, needs more optimization.
13 509 0.441576139648 Henry Cohn, 2026, needs more optimization.
13 510 0.441603924413 Henry Cohn, 2026, needs more optimization.
13 511 0.441612098424 Henry Cohn, 2026, needs more optimization.
13 512 0.441637783969 Henry Cohn, 2026, needs more optimization.
13 513 0.441637784180 Henry Cohn, 2026, needs more optimization.
13 514 0.441652296184 Henry Cohn, 2026, needs more optimization.
13 515 0.441652296212 Henry Cohn, 2026, needs more optimization.
13 516 0.441652296269 Henry Cohn, 2026, needs more optimization.
13 517 0.441805350741 Henry Cohn, 2026, needs more optimization.
13 518 0.441854584351 Henry Cohn, 2026, needs more optimization.
13 519 0.442260233799 Henry Cohn, 2026, needs more optimization.
13 520 0.442276183066 Henry Cohn, 2026, needs more optimization.
13 521 0.446597322382 Henry Cohn, 2026, needs more optimization.
13 522 0.446667925349 Henry Cohn, 2026, needs more optimization.
13 523 0.446692434193 Henry Cohn, 2026, needs more optimization.
13 524 0.446701846535 Henry Cohn, 2026, needs more optimization.
13 525 0.446703323257 Henry Cohn, 2026, needs more optimization.
13 526 0.446718520990 Henry Cohn, 2026, needs more optimization.
13 527 0.446718520995 Henry Cohn, 2026, needs more optimization.
13 528 0.446718520999 Henry Cohn, 2026, needs more optimization.
13 529 0.446730450570 Henry Cohn, 2026, needs more optimization.
13 530 0.446730450668 Henry Cohn, 2026, needs more optimization.
13 531 0.447369863579 Henry Cohn, 2026, needs more optimization.
13 532 0.447369863588 Henry Cohn, 2026, needs more optimization.
13 533 0.447369863594 Henry Cohn, 2026, needs more optimization.
13 534 0.447369863601 Henry Cohn, 2026, needs more optimization.
13 535 0.447369863603 Henry Cohn, 2026, needs more optimization.
13 536 0.447369863605 Henry Cohn, 2026, needs more optimization.
13 537 0.447381653024 Henry Cohn, 2026, needs more optimization.
13 538 0.447384286122 Henry Cohn, 2026, needs more optimization.
13 539 0.447727721135 Henry Cohn, 2026, needs more optimization.
13 540 0.447745030968 Henry Cohn, 2026, needs more optimization.
13 541 0.448179158232 Henry Cohn, 2026, needs more optimization.
13 542 0.448633886208 Henry Cohn, 2026, needs more optimization.
13 543 0.448653803481 Henry Cohn, 2026, needs more optimization.
13 544 0.448686046322 Henry Cohn, 2026, needs more optimization.
13 546 0.448699082684 Henry Cohn, 2026, needs more optimization.
13 547 0.448724655673 Henry Cohn, 2026, needs more optimization.
13 548 0.449043472378 Henry Cohn, 2026, needs more optimization.
13 549 0.449055306383 Henry Cohn, 2026, needs more optimization.
13 550 0.449063863835 Henry Cohn, 2026, needs more optimization.
13 551 0.449394736841 Henry Cohn, 2026, needs more optimization.
13 552 0.449399829320 Henry Cohn, 2026, needs more optimization.
13 553 0.449407705448 Henry Cohn, 2026, needs more optimization.
13 554 0.449412376669 Henry Cohn, 2026, needs more optimization.
13 555 0.449414344959 Henry Cohn, 2026, needs more optimization.
13 556 0.449420607127 Henry Cohn, 2026, needs more optimization.
13 557 0.449439344520 Henry Cohn, 2026, needs more optimization.
13 558 0.450060096654 Henry Cohn, 2026, needs more optimization.
13 559 0.450060096741 Henry Cohn, 2026, needs more optimization.
13 560 0.450060096768 Henry Cohn, 2026, needs more optimization.
13 561 0.450060096775 Henry Cohn, 2026, needs more optimization.
13 562 0.450065645845 Henry Cohn, 2026, needs more optimization.
13 563 0.450653858561 Henry Cohn, 2026, needs more optimization.
13 578 0.454545454546 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
11⁢x−5
13 579 0.458822457704 Henry Cohn, 2026, needs more optimization.
13 580 0.458837254470 Henry Cohn, 2026, needs more optimization.
13 581 0.458840696457 Henry Cohn, 2026, needs more optimization.
13 582 0.458841201980 Henry Cohn, 2026, needs more optimization.
13 583 0.458853108485 Henry Cohn, 2026, needs more optimization.
13 584 0.458859397207 Henry Cohn, 2026, needs more optimization.
13 585 0.458888201718 Henry Cohn, 2026, needs more optimization.
13 586 0.458912910236 Henry Cohn, 2026, needs more optimization.
13 587 0.459811649571 Henry Cohn, 2026, needs more optimization.
13 588 0.459825463586 Henry Cohn, 2026, needs more optimization.
13 589 0.459827993859 Henry Cohn, 2026, needs more optimization.
13 590 0.459847758267 Henry Cohn, 2026, needs more optimization.
13 591 0.459849708614 Henry Cohn, 2026, needs more optimization.
13 592 0.459903539927 Henry Cohn, 2026, needs more optimization.
13 593 0.461563407017 Henry Cohn, 2026, needs more optimization.
13 594 0.461590678404 Henry Cohn, 2026, needs more optimization.
13 595 0.462287712483 Henry Cohn, 2026, needs more optimization.
13 596 0.462992166747 Henry Cohn, 2026, needs more optimization.
13 597 0.463686117444 Henry Cohn, 2026, needs more optimization.
13 598 0.464200566775 Henry Cohn, 2026, needs more optimization.
13 599 0.464692196513 Henry Cohn, 2026, needs more optimization.
13 600 0.465425079641 Henry Cohn, 2026, needs more optimization.
13 601 0.465918438616 Henry Cohn, 2026, needs more optimization.
13 602 0.466218401878 Henry Cohn, 2026, needs more optimization.
13 603 0.466256999770 Henry Cohn, 2026, needs more optimization.
13 604 0.466277367754 Henry Cohn, 2026, needs more optimization.
13 605 0.466367888178 Henry Cohn, 2026, needs more optimization.
13 606 0.466433117259 Henry Cohn, 2026, needs more optimization.
13 607 0.466444271841 Henry Cohn, 2026, needs more optimization.
13 608 0.466515257075 Henry Cohn, 2026, needs more optimization.
13 609 0.466527856816 Henry Cohn, 2026, needs more optimization.
13 610 0.466539256208 Henry Cohn, 2026, needs more optimization.
13 611 0.466546874490 Henry Cohn, 2026, needs more optimization.
13 612 0.466558342333 Henry Cohn, 2026, needs more optimization.
13 613 0.466628212892 Henry Cohn, 2026, needs more optimization.
13 614 0.466635229463 Henry Cohn, 2026, needs more optimization.
13 615 0.466838150517 Henry Cohn, 2026, needs more optimization.
13 616 0.466906378811 Henry Cohn, 2026, needs more optimization.
13 617 0.466909780888 Henry Cohn, 2026, needs more optimization.
13 618 0.467032546948 Henry Cohn, 2026, needs more optimization.
13 619 0.467055940936 Henry Cohn, 2026, needs more optimization.
13 620 0.467126991951 Henry Cohn, 2026, needs more optimization.
13 621 0.467164183950 Henry Cohn, 2026, needs more optimization.
13 622 0.467195640085 Henry Cohn, 2026, needs more optimization.
13 623 0.467259204585 Henry Cohn, 2026, needs more optimization.
13 624 0.467295007000 Henry Cohn, 2026, needs more optimization.
13 625 0.467321962889 Henry Cohn, 2026, needs more optimization.
13 626 0.467363045446 Henry Cohn, 2026, needs more optimization.
13 627 0.467452854873 Henry Cohn, 2026, needs more optimization.
13 628 0.467539321477 Henry Cohn, 2026, needs more optimization.
13 629 0.467675777668 Henry Cohn, 2026, needs more optimization.
13 630 0.467690223590 Henry Cohn, 2026, needs more optimization.
13 631 0.469220588768 Henry Cohn, 2026, needs more optimization.
13 632 0.469478435337 Henry Cohn, 2026, needs more optimization.
13 633 0.470306420796 Henry Cohn, 2026, needs more optimization.
13 634 0.470981134008 Henry Cohn, 2026, needs more optimization.
13 635 0.471590792822 Henry Cohn, 2026, needs more optimization.
13 636 0.472064426288 Henry Cohn, 2026, needs more optimization.
13 637 0.472520732421 Henry Cohn, 2026, needs more optimization.
13 638 0.473147617712 Henry Cohn, 2026, needs more optimization.
13 639 0.473598388271 Henry Cohn, 2026, needs more optimization.
13 640 0.474108800947 Henry Cohn, 2026, needs more optimization.
13 641 0.474359091901 Henry Cohn, 2026, needs more optimization.
13 642 0.474903457010 Henry Cohn, 2026, needs more optimization.
13 644 0.475 Henry Cohn, 2026.
40⁢x−19
13 645 0.476047770169 Henry Cohn, 2026, needs more optimization.
13 646 0.476501061919 Henry Cohn, 2026, needs more optimization.
13 647 0.476809824497 Henry Cohn, 2026, needs more optimization.
13 648 0.477170201871 Henry Cohn, 2026, needs more optimization.
13 649 0.477412847807 Henry Cohn, 2026, needs more optimization.
13 650 0.477678409059 Henry Cohn, 2026, needs more optimization.
13 651 0.477831226570 Henry Cohn, 2026, needs more optimization.
13 652 0.477951373563 Henry Cohn, 2026, needs more optimization.
13 653 0.478129266405 Henry Cohn, 2026, needs more optimization.
13 654 0.478244001042 Henry Cohn, 2026, needs more optimization.
13 655 0.478402444181 Henry Cohn, 2026, needs more optimization.
13 656 0.478530057937 Henry Cohn, 2026, needs more optimization.
13 657 0.478693941382 Henry Cohn, 2026, needs more optimization.
13 658 0.478809728451 Henry Cohn, 2026, needs more optimization.
13 659 0.478974454126 Henry Cohn, 2026, needs more optimization.
13 660 0.479187554323 Henry Cohn, 2026, needs more optimization.
13 661 0.479296344414 Henry Cohn, 2026, needs more optimization.
13 662 0.479438529011 Henry Cohn, 2026, needs more optimization.
13 663 0.479588387537 Henry Cohn, 2026, needs more optimization.
13 664 0.479697098454 Henry Cohn, 2026, needs more optimization.
13 665 0.479829399188 Henry Cohn, 2026, needs more optimization.
13 666 0.479905157128 Henry Cohn, 2026, needs more optimization.
13 667 0.480038366060 Henry Cohn, 2026, needs more optimization.
13 668 0.480163154938 Henry Cohn, 2026, needs more optimization.
13 669 0.480330815409 Henry Cohn, 2026, needs more optimization.
13 670 0.480510204175 Henry Cohn, 2026, needs more optimization.
13 671 0.480658509282 Henry Cohn, 2026, needs more optimization.
13 672 0.480729331643 Henry Cohn, 2026, needs more optimization.
13 673 0.480863552365 Henry Cohn, 2026, needs more optimization.
13 674 0.480967410374 Henry Cohn, 2026, needs more optimization.
13 675 0.481089887809 Henry Cohn, 2026, needs more optimization.
13 676 0.481203676997 Henry Cohn, 2026, needs more optimization.
13 677 0.481317640400 Henry Cohn, 2026, needs more optimization.
13 678 0.481378215741 Henry Cohn, 2026, needs more optimization.
13 679 0.482028700210 Henry Cohn, 2026, needs more optimization.
13 680 0.482124105252 Henry Cohn, 2026, needs more optimization.
13 681 0.482148952807 Henry Cohn, 2026, needs more optimization.
13 682 0.482306260450 Henry Cohn, 2026, needs more optimization.
13 683 0.482451004777 Henry Cohn, 2026, needs more optimization.
13 684 0.482452523658 Henry Cohn, 2026, needs more optimization.
13 686 0.482460756550 Henry Cohn, 2026, needs more optimization.
13 687 0.482467838096 Henry Cohn, 2026, needs more optimization.
13 688 0.482472639387 Henry Cohn, 2026, needs more optimization.
13 689 0.482495942121 Henry Cohn, 2026, needs more optimization.
13 690 0.482510680633 Henry Cohn, 2026, needs more optimization.
13 691 0.482512080804 Henry Cohn, 2026, needs more optimization.
13 692 0.482923761515 Henry Cohn, 2026, needs more optimization.
13 693 0.483008266700 Henry Cohn, 2026, needs more optimization.
13 694 0.483119911517 Henry Cohn, 2026, needs more optimization.
13 695 0.483290804160 Henry Cohn, 2026, needs more optimization.
13 696 0.483407567843 Henry Cohn, 2026, needs more optimization.
13 697 0.483513289454 Henry Cohn, 2026, needs more optimization.
13 698 0.483784545533 Henry Cohn, 2026, needs more optimization.
13 699 0.483907257037 Henry Cohn, 2026, needs more optimization.
13 700 0.483971258348 Henry Cohn, 2026, needs more optimization.
13 701 0.484204757751 Henry Cohn, 2026, needs more optimization.
13 702 0.484240030561 Henry Cohn, 2026, needs more optimization.
13 703 0.484273727055 Henry Cohn, 2026, needs more optimization.
13 704 0.484291429134 Henry Cohn, 2026, needs more optimization.
13 705 0.484305117152 Henry Cohn, 2026, needs more optimization.
13 706 0.484356272899 Henry Cohn, 2026, needs more optimization.
13 707 0.484463330598 Henry Cohn, 2026, needs more optimization.
13 708 0.484559347911 Henry Cohn, 2026, needs more optimization.
13 709 0.484663663383 Henry Cohn, 2026, needs more optimization.
13 710 0.484673270997 Henry Cohn, 2026, needs more optimization.
13 711 0.484673270999 Henry Cohn, 2026, needs more optimization.
13 712 0.484715404700 Henry Cohn, 2026, needs more optimization.
13 713 0.484721764240 Henry Cohn, 2026, needs more optimization.
13 714 0.484745378680 Henry Cohn, 2026, needs more optimization.
13 715 0.484759501907 Henry Cohn, 2026, needs more optimization.
13 716 0.484822754561 Henry Cohn, 2026, needs more optimization.
13 717 0.484843313642 Henry Cohn, 2026, needs more optimization.
13 718 0.484856473066 Henry Cohn, 2026, needs more optimization.
13 719 0.484882019677 Henry Cohn, 2026, needs more optimization.
13 720 0.484892591325 Henry Cohn, 2026, needs more optimization.
13 721 0.484896205408 Henry Cohn, 2026, needs more optimization.
13 722 0.484915730169 Henry Cohn, 2026, needs more optimization.
13 723 0.484933432958 Henry Cohn, 2026, needs more optimization.
13 724 0.484943888342 Henry Cohn, 2026, needs more optimization.
13 725 0.484956519260 Henry Cohn, 2026, needs more optimization.
13 726 0.485548383362 Henry Cohn, 2026, needs more optimization.
13 727 0.485565760480 Henry Cohn, 2026, needs more optimization.
13 728 0.485635286523 Henry Cohn, 2026, needs more optimization.
13 729 0.485722868886 Henry Cohn, 2026, needs more optimization.
13 730 0.485788020426 Henry Cohn, 2026, needs more optimization.
13 731 0.485804780361 Henry Cohn, 2026, needs more optimization.
13 732 0.485865893207 Henry Cohn, 2026, needs more optimization.
13 733 0.485945265396 Henry Cohn, 2026, needs more optimization.
13 734 0.486002424531 Henry Cohn, 2026, needs more optimization.
13 735 0.486120834099 Henry Cohn, 2026, needs more optimization.
13 736 0.486156952171 Henry Cohn, 2026, needs more optimization.
13 737 0.486218124311 Henry Cohn, 2026, needs more optimization.
13 738 0.486267498139 Henry Cohn, 2026, needs more optimization.
13 739 0.486311153377 Henry Cohn, 2026, needs more optimization.
13 740 0.486360709490 Henry Cohn, 2026, needs more optimization.
13 741 0.486426782607 Henry Cohn, 2026, needs more optimization.
13 742 0.486456585312 Henry Cohn, 2026, needs more optimization.
13 743 0.486502421681 Henry Cohn, 2026, needs more optimization.
13 744 0.486604957345 Henry Cohn, 2026, needs more optimization.
13 745 0.486664134387 Henry Cohn, 2026, needs more optimization.
13 746 0.486708575963 Henry Cohn, 2026, needs more optimization.
13 747 0.486727041989 Henry Cohn, 2026, needs more optimization.
13 748 0.486741823141 Henry Cohn, 2026, needs more optimization.
13 749 0.486780182004 Henry Cohn, 2026, needs more optimization.
13 750 0.486848556106 Henry Cohn, 2026, needs more optimization.
13 751 0.486928618864 Henry Cohn, 2026, needs more optimization.
13 752 0.487021120145 Henry Cohn, 2026, needs more optimization.
13 753 0.487134872422 Henry Cohn, 2026, needs more optimization.
13 754 0.487139425151 Henry Cohn, 2026, needs more optimization.
13 755 0.487165921157 Henry Cohn, 2026, needs more optimization.
13 756 0.487214469152 Henry Cohn, 2026, needs more optimization.
13 757 0.487282397082 Henry Cohn, 2026, needs more optimization.
13 758 0.487395930180 Henry Cohn, 2026, needs more optimization.
13 759 0.487406301930 Henry Cohn, 2026, needs more optimization.
13 760 0.487476067618 Henry Cohn, 2026, needs more optimization.
13 761 0.487588597557 Henry Cohn, 2026, needs more optimization.
13 762 0.487609855747 Henry Cohn, 2026, needs more optimization.
13 763 0.487671594343 Henry Cohn, 2026, needs more optimization.
13 764 0.487708783969 Henry Cohn, 2026, needs more optimization.
13 765 0.487740856757 Henry Cohn, 2026, needs more optimization.
13 766 0.487795735617 Henry Cohn, 2026, needs more optimization.
13 767 0.487881337449 Henry Cohn, 2026, needs more optimization.
13 768 0.487918572167 Henry Cohn, 2026, needs more optimization.
13 769 0.487936613260 Henry Cohn, 2026, needs more optimization.
13 770 0.487957665117 Henry Cohn, 2026, needs more optimization.
13 771 0.487974242829 Henry Cohn, 2026, needs more optimization.
13 772 0.488012948379 Henry Cohn, 2026, needs more optimization.
13 773 0.488071835557 Henry Cohn, 2026, needs more optimization.
13 774 0.488111138824 Henry Cohn, 2026, needs more optimization.
13 775 0.488190322885 Henry Cohn, 2026, needs more optimization.
13 776 0.488200886192 Henry Cohn, 2026, needs more optimization.
13 777 0.488258545133 Henry Cohn, 2026, needs more optimization.
13 778 0.488335450942 Henry Cohn, 2026, needs more optimization.
13 779 0.488363885536 Henry Cohn, 2026, needs more optimization.
13 780 0.488463381689 Henry Cohn, 2026, needs more optimization.
13 782 0.488516802769 Henry Cohn, 2026, needs more optimization.
13 783 0.488561296153 Henry Cohn, 2026, needs more optimization.
13 784 0.488643820423 Henry Cohn, 2026, needs more optimization.
13 785 0.488672702780 Henry Cohn, 2026, needs more optimization.
13 786 0.488726382451 Henry Cohn, 2026, needs more optimization.
13 787 0.488754749901 Henry Cohn, 2026, needs more optimization.
13 788 0.488833902831 Henry Cohn, 2026, needs more optimization.
13 789 0.488905157076 Henry Cohn, 2026, needs more optimization.
13 790 0.488920343241 Henry Cohn, 2026, needs more optimization.
13 791 0.488922129034 Henry Cohn, 2026, needs more optimization.
13 793 0.488922293355 Henry Cohn, 2026, needs more optimization.
13 794 0.488964487543 Henry Cohn, 2026, needs more optimization.
13 795 0.489003003599 Henry Cohn, 2026, needs more optimization.
13 797 0.489058732635 Henry Cohn, 2026, needs more optimization.
13 798 0.489094790879 Henry Cohn, 2026, needs more optimization.
13 799 0.489099611883 Henry Cohn, 2026, needs more optimization.
13 800 0.489135987170 Henry Cohn, 2026, needs more optimization.
13 801 0.489153910808 Henry Cohn, 2026, needs more optimization.
13 802 0.489157333543 Henry Cohn, 2026, needs more optimization.
13 805 0.489217003188 Henry Cohn, 2026, needs more optimization.
13 806 0.489233665896 Henry Cohn, 2026, needs more optimization.
13 807 0.489256220580 Henry Cohn, 2026, needs more optimization.
13 808 0.489271241225 Henry Cohn, 2026, needs more optimization.
13 809 0.489282368529 Henry Cohn, 2026, needs more optimization.
13 810 0.489293963188 Henry Cohn, 2026, needs more optimization.
13 811 0.489299478405 Henry Cohn, 2026, needs more optimization.
13 812 0.489304030593 Henry Cohn, 2026, needs more optimization.
13 813 0.489315276319 Henry Cohn, 2026, needs more optimization.
13 814 0.489317866802 Henry Cohn, 2026, needs more optimization.
13 815 0.489333087857 Henry Cohn, 2026, needs more optimization.
13 816 0.489344423260 Henry Cohn, 2026, needs more optimization.
13 817 0.489353411457 Henry Cohn, 2026, needs more optimization.
13 818 0.489357868118 Henry Cohn, 2026, needs more optimization.
13 819 0.490539319699 Henry Cohn, 2026, needs more optimization.
13 820 0.490707698168 Henry Cohn, 2026, needs more optimization.
13 821 0.490745798815 Henry Cohn, 2026, needs more optimization.
13 822 0.490792583670 Henry Cohn, 2026, needs more optimization.
13 823 0.490819542083 Henry Cohn, 2026, needs more optimization.
13 824 0.490850204374 Henry Cohn, 2026, needs more optimization.
13 825 0.490889747775 Henry Cohn, 2026, needs more optimization.
13 826 0.490922878974 Henry Cohn, 2026, needs more optimization.
13 827 0.490926952773 Henry Cohn, 2026, needs more optimization.
13 828 0.491023595145 Henry Cohn, 2026, needs more optimization.
13 829 0.491165720778 Henry Cohn, 2026, needs more optimization.
13 830 0.491213296411 Henry Cohn, 2026, needs more optimization.
13 831 0.491255534935 Henry Cohn, 2026, needs more optimization.
13 832 0.491326609666 Henry Cohn, 2026, needs more optimization.
13 834 0.491407228786 Henry Cohn, 2026, needs more optimization.
13 835 0.491436480299 Henry Cohn, 2026, needs more optimization.
13 836 0.491482409560 Henry Cohn, 2026, needs more optimization.
13 837 0.491508882484 Henry Cohn, 2026, needs more optimization.
13 838 0.491590001114 Henry Cohn, 2026, needs more optimization.
13 839 0.491653882147 Henry Cohn, 2026, needs more optimization.
13 840 0.491669109228 Henry Cohn, 2026, needs more optimization.
13 841 0.491720364039 Henry Cohn, 2026, needs more optimization.
13 842 0.491737101756 Henry Cohn, 2026, needs more optimization.
13 843 0.491924696810 Henry Cohn, 2026, needs more optimization.
13 844 0.492018804568 Henry Cohn, 2026, needs more optimization.
13 845 0.492061955436 Henry Cohn, 2026, needs more optimization.
13 846 0.492085928102 Henry Cohn, 2026, needs more optimization.
13 847 0.492163801896 Henry Cohn, 2026, needs more optimization.
13 848 0.492268137592 Henry Cohn, 2026, needs more optimization.
13 849 0.492416430466 Henry Cohn, 2026, needs more optimization.
13 851 0.492582302940 Henry Cohn, 2026, needs more optimization.
13 852 0.492584133542 Henry Cohn, 2026, needs more optimization.
13 856 0.492787826256 Henry Cohn, 2026, needs more optimization.
13 857 0.493162519315 Henry Cohn, 2026, needs more optimization.
13 858 0.493214674862 Henry Cohn, 2026, needs more optimization.
13 859 0.493229452746 Henry Cohn, 2026, needs more optimization.
13 860 0.493297079023 Henry Cohn, 2026, needs more optimization.
13 861 0.493352746172 Henry Cohn, 2026, needs more optimization.
13 862 0.493681987152 Henry Cohn, 2026, needs more optimization.
13 863 0.493756986226 Henry Cohn, 2026, needs more optimization.
13 864 0.493784696845 Henry Cohn, 2026, needs more optimization.
13 865 0.494154640330 Henry Cohn, 2026, needs more optimization.
13 866 0.494194610795 Henry Cohn, 2026, needs more optimization.
13 867 0.494207384409 Henry Cohn, 2026, needs more optimization.
13 868 0.494278319044 Henry Cohn, 2026, needs more optimization.
13 869 0.494647464652 Henry Cohn, 2026, needs more optimization.
13 870 0.494757903047 Henry Cohn, 2026, needs more optimization.
13 871 0.494855482228 Henry Cohn, 2026, needs more optimization.
13 872 0.495128045117 Henry Cohn, 2026, needs more optimization.
13 874 0.495214711441 Henry Cohn, 2026, needs more optimization.
13 875 0.495431837309 Henry Cohn, 2026, needs more optimization.
13 876 0.495439091762 Henry Cohn, 2026, needs more optimization.
13 877 0.495545857349 Henry Cohn, 2026, needs more optimization.
13 878 0.495550498533 Henry Cohn, 2026, needs more optimization.
13 879 0.495568229300 Henry Cohn, 2026, needs more optimization.
13 880 0.495589169070 Henry Cohn, 2026, needs more optimization.
13 881 0.495628526181 Henry Cohn, 2026, needs more optimization.
13 882 0.495634955742 Henry Cohn, 2026, needs more optimization.
13 883 0.497158360755 Henry Cohn, 2026, needs more optimization.
13 884 0.497239302064 Henry Cohn, 2026, needs more optimization.
13 885 0.497290000604 Henry Cohn, 2026, needs more optimization.
13 886 0.497406797918 Henry Cohn, 2026, needs more optimization.
13 887 0.497863215824 Henry Cohn, 2026, needs more optimization.
13 888 0.497910956049 Henry Cohn, 2026, needs more optimization.
13 889 0.497958556778 Henry Cohn, 2026, needs more optimization.
13 890 0.498442557682 Henry Cohn, 2026, needs more optimization.
13 891 0.498618094482 Henry Cohn, 2026, needs more optimization.
13 892 0.498797488738 Henry Cohn, 2026, needs more optimization.
13 893 0.499160098630 Henry Cohn, 2026, needs more optimization.
13 894 0.499395389629 Henry Cohn, 2026, needs more optimization.
13 895 0.499575203795 Henry Cohn, 2026, needs more optimization.
13 896 0.499702812528 Henry Cohn, 2026, needs more optimization.
13 897 0.499811837600 Henry Cohn, 2026, needs more optimization.
13 1024 0.5 Subcode of a kissing configuration from J. Leech and N. J. A. Sloane, Sphere packings and error-correcting codes, Canadian J. Math. 23 (1971), 718–745, doi:10.4153/CJM-1971-081-3.
2⁢x−1
14 29 0.053426987342 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
2016⁢x3−196⁢x2−14⁢x+1
14 30 0.0625 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
16⁢x−1
14 31 0.067582771839 H. Cohn, Small spherical and projective codes, data set, updated 2025, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14 32 0.071430901841 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
14 33 0.071678780313 Henry Cohn, 2025.
14 34 0.071706747799 Henry Cohn, 2025.
14 36 0.080003299193 Henry Cohn, 2023.
2156⁢x2+140⁢x−25
14 37 0.087892856445 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
14 38 0.092604004700 Henry Cohn, 2025.
14 39 0.094407135777 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
14 42 0.1 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
10⁢x−1
14 43 0.112894921393 Henry Cohn, 2025.
14 45 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
14 46 0.114212424977 Henry Cohn, 2024.
14 47 0.114744370065 Henry Cohn, 2026.
14 48 0.114785923011 Henry Cohn, 2023.
1988352⁢x8+1963008⁢x7−108672⁢x6−513152⁢x5−92592⁢x4+19616⁢x3+5240⁢x2+72⁢x−81
14 49 0.125031168050 Henry Cohn, 2025.
14 50 0.126129943174 Henry Cohn, 2025.
14 52 0.126131983623 Henry Cohn, 2023.
47⁢x2+2⁢x−1
14 53 0.127206627186 Henry Cohn, 2025.
14 54 0.135105967369 Henry Cohn, 2024.
14 55 0.136745922263 Henry Cohn, 2023.
14 56 0.139995758129 Henry Cohn, 2024.
14 57 0.142106619426 Henry Cohn, 2025.
14 64 0.142857142858 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−1
14 65 0.165287555076 Henry Cohn, 2024.
25600⁢x4−5616⁢x3−2736⁢x2+81
14 70 0.166666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
6⁢x−1
14 71 0.177427267176 Henry Cohn, 2024.
196⁢x4−56⁢x3−28⁢x2+1
14 72 0.180979034910 Henry Cohn, 2026.
14 73 0.184667025692 Henry Cohn, 2026, needs more optimization.
14 75 0.185110498562 Henry Cohn, 2026.
14 76 0.189883320237 Henry Cohn, 2026, needs more optimization.
14 77 0.190266040190 Henry Cohn, 2026, needs more optimization.
14 78 0.191436403337 Henry Cohn, 2026, needs more optimization.
14 79 0.193295826526 Henry Cohn, 2026, needs more optimization.
14 80 0.195567546353 Henry Cohn, 2026, needs more optimization.
14 81 0.198103716529 Henry Cohn, 2026, needs more optimization.
14 82 0.198235129127 Henry Cohn, 2026, needs more optimization.
14 83 0.198270163042 Henry Cohn, 2026, needs more optimization.
14 84 0.198299573201 Henry Cohn, 2026, needs more optimization.
14 85 0.198385443665 Henry Cohn, 2026, needs more optimization.
14 86 0.198448405525 Henry Cohn, 2026, needs more optimization.
14 87 0.198500455261 Henry Cohn, 2026, needs more optimization.
14 88 0.198573144765 Henry Cohn, 2026, needs more optimization.
14 89 0.198677096722 Henry Cohn, 2026, needs more optimization.
14 90 0.198771632430 Henry Cohn, 2026, needs more optimization.
14 91 0.198843416030 Henry Cohn, 2026, needs more optimization.
14 92 0.208456809641 Henry Cohn, 2026, needs more optimization.
14 93 0.211749206649 Henry Cohn, 2026, needs more optimization.
14 94 0.211903258988 Henry Cohn, 2026, needs more optimization.
14 95 0.212179543064 Henry Cohn, 2026, needs more optimization.
14 96 0.212295215604 Henry Cohn, 2026, needs more optimization.
14 98 0.212297015491 Henry Cohn, 2026, needs more optimization.
14 99 0.219093745535 Henry Cohn, 2026, needs more optimization.
14 100 0.223666699046 Henry Cohn, 2026, needs more optimization.
14 101 0.225613148985 Henry Cohn, 2026, needs more optimization.
14 102 0.227325287320 Henry Cohn, 2026, needs more optimization.
14 103 0.228469233047 Henry Cohn, 2026, needs more optimization.
14 112 0.229910395528 Henry Cohn, 2026.
14 113 0.234902627893 Henry Cohn, 2026, needs more optimization.
14 114 0.237359837687 Henry Cohn, 2026, needs more optimization.
14 115 0.239305162774 Henry Cohn, 2026, needs more optimization.
14 116 0.240624684314 Henry Cohn, 2026, needs more optimization.
14 117 0.242104427872 Henry Cohn, 2026, needs more optimization.
14 118 0.243566011410 Henry Cohn, 2026, needs more optimization.
14 119 0.244891424825 Henry Cohn, 2026, needs more optimization.
14 120 0.245340349030 Henry Cohn, 2026, needs more optimization.
14 121 0.245811136405 Henry Cohn, 2026, needs more optimization.
14 122 0.247977863199 Henry Cohn, 2026, needs more optimization.
14 123 0.249943295711 Henry Cohn, 2026, needs more optimization.
14 124 0.251242938878 Henry Cohn, 2026, needs more optimization.
14 125 0.252284736063 Henry Cohn, 2026, needs more optimization.
14 126 0.253277127544 Henry Cohn, 2026, needs more optimization.
14 127 0.254058650995 Henry Cohn, 2026, needs more optimization.
14 128 0.254656731729 Henry Cohn, 2026, needs more optimization.
14 129 0.255353344722 Henry Cohn, 2026, needs more optimization.
14 130 0.255997659114 Henry Cohn, 2026, needs more optimization.
14 131 0.258087107391 Henry Cohn, 2026, needs more optimization.
14 132 0.259496241033 Henry Cohn, 2026, needs more optimization.
14 133 0.261787152048 Henry Cohn, 2026, needs more optimization.
14 134 0.263496073967 Henry Cohn, 2026, needs more optimization.
14 135 0.265026647516 Henry Cohn, 2026, needs more optimization.
14 136 0.266892083265 Henry Cohn, 2026, needs more optimization.
14 137 0.268271970629 Henry Cohn, 2026, needs more optimization.
14 138 0.269360512777 Henry Cohn, 2026, needs more optimization.
14 139 0.269360512850 Henry Cohn, 2026, needs more optimization.
14 140 0.269363487446 Henry Cohn, 2026, needs more optimization.
14 141 0.269364430800 Henry Cohn, 2026, needs more optimization.
14 142 0.269374096266 Henry Cohn, 2026, needs more optimization.
14 143 0.269376035718 Henry Cohn, 2026, needs more optimization.
14 144 0.269378581522 Henry Cohn, 2026, needs more optimization.
14 145 0.269385016398 Henry Cohn, 2026, needs more optimization.
14 146 0.269391352219 Henry Cohn, 2026, needs more optimization.
14 147 0.269406350518 Henry Cohn, 2026, needs more optimization.
14 148 0.269435946677 Henry Cohn, 2026, needs more optimization.
14 149 0.269470068873 Henry Cohn, 2026, needs more optimization.
14 150 0.269507460863 Henry Cohn, 2026, needs more optimization.
14 151 0.269752143485 Henry Cohn, 2026, needs more optimization.
14 152 0.269752143670 Henry Cohn, 2026, needs more optimization.
14 153 0.273185531222 Henry Cohn, 2026, needs more optimization.
14 154 0.273722355435 Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
14 156 0.276322194174 Henry Cohn, 2026, needs more optimization.
14 157 0.276370176302 Henry Cohn, 2026, needs more optimization.
14 158 0.276416052417 Henry Cohn, 2026, needs more optimization.
14 159 0.276642401665 Henry Cohn, 2026, needs more optimization.
14 160 0.276958558542 Henry Cohn, 2026, needs more optimization.
14 161 0.277317972001 Henry Cohn, 2026, needs more optimization.
14 162 0.277834331200 Henry Cohn, 2026, needs more optimization.
14 163 0.278238574775 Henry Cohn, 2026, needs more optimization.
14 164 0.278743459698 Henry Cohn, 2026, needs more optimization.
14 165 0.279341015854 Henry Cohn, 2026, needs more optimization.
14 166 0.280058776393 Henry Cohn, 2026, needs more optimization.
14 167 0.281202891940 Henry Cohn, 2026, needs more optimization.
14 168 0.285612020413 Henry Cohn, 2026, needs more optimization.
14 169 0.287344419414 Henry Cohn, 2026, needs more optimization.
14 170 0.288129945819 Henry Cohn, 2026, needs more optimization.
14 171 0.289699475551 Henry Cohn, 2026, needs more optimization.
14 172 0.290661068570 Henry Cohn, 2026, needs more optimization.
14 173 0.290943142102 Henry Cohn, 2026, needs more optimization.
14 174 0.291997251418 Henry Cohn, 2026, needs more optimization.
14 175 0.293044074117 Henry Cohn, 2026, needs more optimization.
14 176 0.293619972837 Henry Cohn, 2026, needs more optimization.
14 177 0.294400736495 Henry Cohn, 2026, needs more optimization.
14 178 0.295360088420 Henry Cohn, 2026, needs more optimization.
14 179 0.295912433792 Henry Cohn, 2026, needs more optimization.
14 180 0.296632637267 Henry Cohn, 2026, needs more optimization.
14 181 0.297692423050 Henry Cohn, 2026, needs more optimization.
14 182 0.297707209243 Henry Cohn, 2026, needs more optimization.
14 183 0.297827646424 Henry Cohn, 2026, needs more optimization.
14 184 0.298055553329 Henry Cohn, 2026, needs more optimization.
14 185 0.298562024794 Henry Cohn, 2026, needs more optimization.
14 186 0.299217895272 Henry Cohn, 2026, needs more optimization.
14 187 0.299608316265 Henry Cohn, 2026, needs more optimization.
14 188 0.300673452952 Henry Cohn, 2026, needs more optimization.
14 189 0.301652341546 Henry Cohn, 2026, needs more optimization.
14 190 0.301796959534 Henry Cohn, 2026, needs more optimization.
14 191 0.302341332725 Henry Cohn, 2026, needs more optimization.
14 192 0.303606913413 Henry Cohn, 2026, needs more optimization.
14 193 0.304407454247 Henry Cohn, 2026, needs more optimization.
14 194 0.305382980344 Henry Cohn, 2026, needs more optimization.
14 195 0.306358075385 Henry Cohn, 2026, needs more optimization.
14 196 0.307724207969 Henry Cohn, 2026, needs more optimization.
14 197 0.308786259392 Henry Cohn, 2026, needs more optimization.
14 198 0.309612845635 Henry Cohn, 2026, needs more optimization.
14 199 0.310675176432 Henry Cohn, 2026, needs more optimization.
14 200 0.311235878990 Henry Cohn, 2026, needs more optimization.
14 201 0.312451764048 Henry Cohn, 2026, needs more optimization.
14 202 0.313107695002 Henry Cohn, 2026, needs more optimization.
14 203 0.313773164450 Henry Cohn, 2026, needs more optimization.
14 204 0.313834945291 Henry Cohn, 2026, needs more optimization.
14 205 0.314016868165 Henry Cohn, 2026, needs more optimization.
14 206 0.314247254047 Henry Cohn, 2026, needs more optimization.
14 207 0.314602210095 Henry Cohn, 2026, needs more optimization.
14 208 0.315008632390 Henry Cohn, 2026, needs more optimization.
14 209 0.315336329197 Henry Cohn, 2026, needs more optimization.
14 210 0.315601511295 Henry Cohn, 2026, needs more optimization.
14 211 0.315962561524 Henry Cohn, 2026, needs more optimization.
14 212 0.316357183557 Henry Cohn, 2026, needs more optimization.
14 213 0.317114762863 Henry Cohn, 2026, needs more optimization.
14 214 0.317568377424 Henry Cohn, 2026, needs more optimization.
14 215 0.318075813082 Henry Cohn, 2026, needs more optimization.
14 216 0.318599501830 Henry Cohn, 2026, needs more optimization.
14 217 0.319043082612 Henry Cohn, 2026, needs more optimization.
14 218 0.319620393724 Henry Cohn, 2026, needs more optimization.
14 219 0.320684355301 Henry Cohn, 2026, needs more optimization.
14 220 0.321037853801 Henry Cohn, 2026, needs more optimization.
14 221 0.321532131197 Henry Cohn, 2026, needs more optimization.
14 222 0.321921125427 Henry Cohn, 2026, needs more optimization.
14 223 0.322282342892 Henry Cohn, 2026, needs more optimization.
14 224 0.322794899144 Henry Cohn, 2026, needs more optimization.
14 225 0.323217541574 Henry Cohn, 2026, needs more optimization.
14 226 0.324023119483 Henry Cohn, 2026, needs more optimization.
14 227 0.324621195681 Henry Cohn, 2026, needs more optimization.
14 228 0.325269661259 Henry Cohn, 2026, needs more optimization.
14 229 0.325836108338 Henry Cohn, 2026, needs more optimization.
14 230 0.326362962735 Henry Cohn, 2026, needs more optimization.
14 231 0.326882166972 Henry Cohn, 2026, needs more optimization.
14 232 0.327532348496 Henry Cohn, 2026, needs more optimization.
14 233 0.328692917189 Henry Cohn, 2026, needs more optimization.
14 234 0.329427065277 Henry Cohn, 2026, needs more optimization.
14 235 0.330538260614 Henry Cohn, 2026, needs more optimization.
14 236 0.331740098004 Henry Cohn, 2026, needs more optimization.
14 237 0.333113714509 Henry Cohn, 2026, needs more optimization.
14 240 0.333333333334 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
3⁢x−1
14 252 0.333333333334 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
14 257 0.333850719248 Henry Cohn, 2026, needs more optimization.
14 258 0.333960038658 Henry Cohn, 2026, needs more optimization.
14 259 0.334305077304 Henry Cohn, 2026, needs more optimization.
14 260 0.335158927097 Henry Cohn, 2026, needs more optimization.
14 261 0.335218676985 Henry Cohn, 2026, needs more optimization.
14 262 0.335651706996 Henry Cohn, 2026, needs more optimization.
14 263 0.335681369465 Henry Cohn, 2026, needs more optimization.
14 264 0.335964934807 Henry Cohn, 2026, needs more optimization.
14 265 0.336035645253 Henry Cohn, 2026, needs more optimization.
14 266 0.337042497131 Henry Cohn, 2026, needs more optimization.
14 281 0.339465385360 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 282 0.339465386509 Henry Cohn, 2026, needs more optimization.
14 283 0.339670814489 Henry Cohn, 2026, needs more optimization.
14 284 0.340031495117 Henry Cohn, 2026, needs more optimization.
14 285 0.340438892686 Henry Cohn, 2026, needs more optimization.
14 286 0.341157407414 Henry Cohn, 2026, needs more optimization.
14 287 0.342450460514 Henry Cohn, 2026, needs more optimization.
14 288 0.343995590690 Henry Cohn, 2026, needs more optimization.
14 289 0.345251722390 Henry Cohn, 2026, needs more optimization.
14 290 0.345936189573 Henry Cohn, 2026, needs more optimization.
14 294 0.347198310291 Henry Cohn, 2026, needs more optimization.
14 295 0.347770940574 Henry Cohn, 2026, needs more optimization.
14 296 0.347770940856 Henry Cohn, 2026, needs more optimization.
14 297 0.347770941371 Henry Cohn, 2026, needs more optimization.
14 298 0.348275214172 Henry Cohn, 2026, needs more optimization.
14 299 0.348275216506 Henry Cohn, 2026, needs more optimization.
14 300 0.348336783144 Henry Cohn, 2026, needs more optimization.
14 301 0.348673532059 Henry Cohn, 2026, needs more optimization.
14 302 0.349590187951 Henry Cohn, 2026, needs more optimization.
14 303 0.352667012589 Henry Cohn, 2026, needs more optimization.
14 304 0.353975404146 Henry Cohn, 2026, needs more optimization.
14 305 0.355015572306 Henry Cohn, 2026, needs more optimization.
14 306 0.355015572314 Henry Cohn, 2026, needs more optimization.
14 307 0.355015572324 Henry Cohn, 2026, needs more optimization.
14 308 0.355015572334 Henry Cohn, 2026, needs more optimization.
14 309 0.355015572346 Henry Cohn, 2026, needs more optimization.
14 310 0.355015572361 Henry Cohn, 2026, needs more optimization.
14 311 0.355015572376 Henry Cohn, 2026, needs more optimization.
14 312 0.355015572394 Henry Cohn, 2026, needs more optimization.
14 313 0.355015572404 Henry Cohn, 2026, needs more optimization.
14 314 0.355015572409 Henry Cohn, 2026, needs more optimization.
14 315 0.355015572411 Henry Cohn, 2026, needs more optimization.
14 316 0.355015572414 Henry Cohn, 2026, needs more optimization.
14 330 0.355015572415 Henry Cohn, 2026, needs more optimization.
14 335 0.355045564946 Henry Cohn, 2026, needs more optimization.
14 336 0.355078330108 Henry Cohn, 2026, needs more optimization.
14 338 0.355125671090 Henry Cohn, 2026, needs more optimization.
14 339 0.355578825476 Henry Cohn, 2026, needs more optimization.
14 340 0.357142669567 Henry Cohn, 2026, needs more optimization.
14 341 0.358054740256 Henry Cohn, 2026, needs more optimization.
14 342 0.358519266808 Henry Cohn, 2026, needs more optimization.
14 343 0.358546741458 Henry Cohn, 2026, needs more optimization.
14 344 0.359877349878 Henry Cohn, 2026, needs more optimization.
14 345 0.360769864293 Henry Cohn, 2026, needs more optimization.
14 346 0.362854178838 Henry Cohn, 2026, needs more optimization.
14 347 0.364120180273 Henry Cohn, 2026, needs more optimization.
14 348 0.365652407337 Henry Cohn, 2026, needs more optimization.
14 349 0.366605326823 Henry Cohn, 2026, needs more optimization.
14 351 0.366857294830 Henry Cohn, 2026, needs more optimization.
14 352 0.367344197828 Henry Cohn, 2026, needs more optimization.
14 353 0.368112627388 Henry Cohn, 2026, needs more optimization.
14 354 0.369258883088 Henry Cohn, 2026, needs more optimization.
14 355 0.370391928645 Henry Cohn, 2026, needs more optimization.
14 356 0.371138045717 Henry Cohn, 2026, needs more optimization.
14 357 0.371999609029 Henry Cohn, 2026, needs more optimization.
14 358 0.373029409189 Henry Cohn, 2026, needs more optimization.
14 359 0.374138339300 Henry Cohn, 2026, needs more optimization.
14 360 0.374986459037 Henry Cohn, 2026, needs more optimization.
14 361 0.375773879507 Henry Cohn, 2026, needs more optimization.
14 362 0.376466786088 Henry Cohn, 2026, needs more optimization.
14 363 0.377442542739 Henry Cohn, 2026, needs more optimization.
14 364 0.377442542836 Henry Cohn, 2026, needs more optimization.
14 365 0.377442542890 Henry Cohn, 2026, needs more optimization.
14 380 0.377442542892 Henry Cohn, 2026, needs more optimization.
14 381 0.377456239542 Henry Cohn, 2026, needs more optimization.
14 382 0.377632934057 Henry Cohn, 2026, needs more optimization.
14 383 0.377759801302 Henry Cohn, 2026, needs more optimization.
14 384 0.377830162024 Henry Cohn, 2026, needs more optimization.
14 385 0.377913400306 Henry Cohn, 2026, needs more optimization.
14 386 0.378444520871 Henry Cohn, 2026, needs more optimization.
14 387 0.380850202037 Henry Cohn, 2026, needs more optimization.
14 388 0.381594736575 Henry Cohn, 2026, needs more optimization.
14 389 0.381960106701 Henry Cohn, 2026, needs more optimization.
14 390 0.383154197192 Henry Cohn, 2026, needs more optimization.
14 391 0.383158267295 Henry Cohn, 2026, needs more optimization.
14 392 0.384922069754 Henry Cohn, 2026, needs more optimization.
14 393 0.385302984360 Henry Cohn, 2026, needs more optimization.
14 394 0.385377650657 Henry Cohn, 2026, needs more optimization.
14 395 0.385393603470 Henry Cohn, 2026, needs more optimization.
14 396 0.385415381998 Henry Cohn, 2026, needs more optimization.
14 397 0.385484319024 Henry Cohn, 2026, needs more optimization.
14 398 0.385497607343 Henry Cohn, 2026, needs more optimization.
14 399 0.386603323756 Henry Cohn, 2026, needs more optimization.
14 400 0.386745704494 Henry Cohn, 2026, needs more optimization.
14 404 0.386745717940 Henry Cohn, 2026, needs more optimization.
14 405 0.386786126168 Henry Cohn, 2026, needs more optimization.
14 406 0.387142581468 Henry Cohn, 2026, needs more optimization.
14 407 0.387221791339 Henry Cohn, 2026, needs more optimization.
14 410 0.387221791341 Henry Cohn, 2026, needs more optimization.
14 411 0.387356624320 Henry Cohn, 2026, needs more optimization.
14 412 0.387378589463 Henry Cohn, 2026, needs more optimization.
14 413 0.387381626176 Henry Cohn, 2026, needs more optimization.
14 417 0.387398876783 Henry Cohn, 2026, needs more optimization.
14 418 0.387501343891 Henry Cohn, 2026, needs more optimization.
14 419 0.387554367345 Henry Cohn, 2026, needs more optimization.
14 420 0.388282822630 Henry Cohn, 2026, needs more optimization.
14 421 0.390111917456 Henry Cohn, 2026, needs more optimization.
14 422 0.391129706485 Henry Cohn, 2026, needs more optimization.
14 423 0.391547846054 Henry Cohn, 2026, needs more optimization.
14 435 0.391891891892 Henry Cohn, 2026.
74⁢x−29
14 436 0.394834515682 Henry Cohn, 2026, needs more optimization.
14 437 0.395905398651 Henry Cohn, 2026, needs more optimization.
14 438 0.396519314534 Henry Cohn, 2026, needs more optimization.
14 439 0.396988101982 Henry Cohn, 2026, needs more optimization.
14 440 0.397345835808 Henry Cohn, 2026, needs more optimization.
14 441 0.397630040289 Henry Cohn, 2026, needs more optimization.
14 442 0.398091174693 Henry Cohn, 2026, needs more optimization.
14 443 0.398789626161 Henry Cohn, 2026, needs more optimization.
14 444 0.399265345571 Henry Cohn, 2026, needs more optimization.
14 445 0.399600978200 Henry Cohn, 2026, needs more optimization.
14 466 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
14 496 0.4 Henry Cohn, 2026.
5⁢x−2
14 497 0.402761649589 Henry Cohn, 2026, needs more optimization.
14 498 0.402852311822 Henry Cohn, 2026, needs more optimization.
14 500 0.403337141701 Henry Cohn, 2026, needs more optimization.
14 501 0.406001190218 Henry Cohn, 2026, needs more optimization.
14 502 0.407333850812 Henry Cohn, 2026, needs more optimization.
14 503 0.407824490830 Henry Cohn, 2026, needs more optimization.
14 504 0.409461291585 Henry Cohn, 2026, needs more optimization.
14 505 0.410156338966 Henry Cohn, 2026, needs more optimization.
14 506 0.411338597247 Henry Cohn, 2026, needs more optimization.
14 507 0.411596563973 Henry Cohn, 2026, needs more optimization.
14 508 0.411618555955 Henry Cohn, 2026, needs more optimization.
14 509 0.411762370807 Henry Cohn, 2026, needs more optimization.
14 510 0.411762370815 Henry Cohn, 2026, needs more optimization.
14 511 0.411764640030 Henry Cohn, 2026, needs more optimization.
14 512 0.411778208374 Henry Cohn, 2026, needs more optimization.
14 513 0.411923951535 Henry Cohn, 2026, needs more optimization.
14 514 0.411930583095 Henry Cohn, 2026, needs more optimization.
14 516 0.412182132197 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
14 517 0.416173793462 Henry Cohn, 2026, needs more optimization.
14 555 0.423076923077 Henry Cohn, 2026.
26⁢x−11
14 557 0.423119543564 Henry Cohn, 2026, needs more optimization.
14 558 0.423210157909 Henry Cohn, 2026, needs more optimization.
14 559 0.427438420763 Henry Cohn, 2026, needs more optimization.
14 560 0.427989895905 Henry Cohn, 2026, needs more optimization.
14 600 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
14 601 0.429745296210 Henry Cohn, 2026, needs more optimization.
14 602 0.430053755657 Henry Cohn, 2026, needs more optimization.
14 603 0.430222247126 Henry Cohn, 2026, needs more optimization.
14 604 0.430588037803 Henry Cohn, 2026, needs more optimization.
14 605 0.430985253197 Henry Cohn, 2026, needs more optimization.
14 606 0.431126007685 Henry Cohn, 2026, needs more optimization.
14 607 0.431171763469 Henry Cohn, 2026, needs more optimization.
14 608 0.431346627107 Henry Cohn, 2026, needs more optimization.
14 609 0.431487430824 Henry Cohn, 2026, needs more optimization.
14 610 0.431596528937 Henry Cohn, 2026, needs more optimization.
14 611 0.431618164267 Henry Cohn, 2026, needs more optimization.
14 612 0.432117953753 Henry Cohn, 2026, needs more optimization.
14 613 0.432207255349 Henry Cohn, 2026, needs more optimization.
14 614 0.432252067042 Henry Cohn, 2026, needs more optimization.
14 615 0.432780377353 Henry Cohn, 2026, needs more optimization.
14 616 0.432816753034 Henry Cohn, 2026, needs more optimization.
14 617 0.432835926516 Henry Cohn, 2026, needs more optimization.
14 618 0.432858114320 Henry Cohn, 2026, needs more optimization.
14 619 0.432902559735 Henry Cohn, 2026, needs more optimization.
14 620 0.432930978770 Henry Cohn, 2026, needs more optimization.
14 621 0.432954486433 Henry Cohn, 2026, needs more optimization.
14 622 0.432987678956 Henry Cohn, 2026, needs more optimization.
14 623 0.433026637553 Henry Cohn, 2026, needs more optimization.
14 624 0.433072299984 Henry Cohn, 2026, needs more optimization.
14 625 0.433115349238 Henry Cohn, 2026, needs more optimization.
14 626 0.433166865030 Henry Cohn, 2026, needs more optimization.
14 627 0.433208879232 Henry Cohn, 2026, needs more optimization.
14 628 0.433473045427 Henry Cohn, 2026, needs more optimization.
14 629 0.433493931321 Henry Cohn, 2026, needs more optimization.
14 630 0.433537385144 Henry Cohn, 2026, needs more optimization.
14 631 0.433593060159 Henry Cohn, 2026, needs more optimization.
14 632 0.433638979000 Henry Cohn, 2026, needs more optimization.
14 633 0.433680736169 Henry Cohn, 2026, needs more optimization.
14 634 0.433704563406 Henry Cohn, 2026, needs more optimization.
14 635 0.433771210325 Henry Cohn, 2026, needs more optimization.
14 636 0.433799652228 Henry Cohn, 2026, needs more optimization.
14 637 0.433851930348 Henry Cohn, 2026, needs more optimization.
14 638 0.433905114901 Henry Cohn, 2026, needs more optimization.
14 639 0.433911696986 Henry Cohn, 2026, needs more optimization.
14 640 0.434133429899 Henry Cohn, 2026, needs more optimization.
14 641 0.434170041665 Henry Cohn, 2026, needs more optimization.
14 642 0.434171528392 Henry Cohn, 2026, needs more optimization.
14 643 0.434174602953 Henry Cohn, 2026, needs more optimization.
14 644 0.434211377790 Henry Cohn, 2026, needs more optimization.
14 645 0.434400093766 Henry Cohn, 2026, needs more optimization.
14 646 0.434956965237 Henry Cohn, 2026, needs more optimization.
14 647 0.435567861350 Henry Cohn, 2026, needs more optimization.
14 648 0.436671417638 Henry Cohn, 2026, needs more optimization.
14 649 0.437226701844 Henry Cohn, 2026, needs more optimization.
14 650 0.437719535500 Henry Cohn, 2026, needs more optimization.
14 651 0.437994517226 Henry Cohn, 2026, needs more optimization.
14 652 0.438069875655 Henry Cohn, 2026, needs more optimization.
14 653 0.438800355276 Henry Cohn, 2026, needs more optimization.
14 654 0.439315975672 Henry Cohn, 2026, needs more optimization.
14 655 0.439485969791 Henry Cohn, 2026, needs more optimization.
14 656 0.440441298649 Henry Cohn, 2026, needs more optimization.
14 657 0.440811515906 Henry Cohn, 2026, needs more optimization.
14 658 0.440996094740 Henry Cohn, 2026, needs more optimization.
14 659 0.441381701019 Henry Cohn, 2026, needs more optimization.
14 660 0.442014618778 Henry Cohn, 2026, needs more optimization.
14 661 0.442055299190 Henry Cohn, 2026, needs more optimization.
14 662 0.442182376864 Henry Cohn, 2026, needs more optimization.
14 663 0.442317725230 Henry Cohn, 2026, needs more optimization.
14 664 0.442782410266 Henry Cohn, 2026, needs more optimization.
14 665 0.443554077890 Henry Cohn, 2026, needs more optimization.
14 666 0.444032080231 Henry Cohn, 2026, needs more optimization.
14 667 0.444478760836 Henry Cohn, 2026, needs more optimization.
14 668 0.444532997399 Henry Cohn, 2026, needs more optimization.
14 669 0.444866864617 Henry Cohn, 2026, needs more optimization.
14 670 0.445466308299 Henry Cohn, 2026, needs more optimization.
14 671 0.445792517561 Henry Cohn, 2026, needs more optimization.
14 672 0.446304390108 Henry Cohn, 2026, needs more optimization.
14 673 0.446396304384 Henry Cohn, 2026, needs more optimization.
14 674 0.446492655472 Henry Cohn, 2026, needs more optimization.
14 675 0.446774594539 Henry Cohn, 2026, needs more optimization.
14 676 0.446906446587 Henry Cohn, 2026, needs more optimization.
14 677 0.447030001070 Henry Cohn, 2026, needs more optimization.
14 678 0.447152620116 Henry Cohn, 2026, needs more optimization.
14 679 0.447431242209 Henry Cohn, 2026, needs more optimization.
14 680 0.447698746938 Henry Cohn, 2026, needs more optimization.
14 681 0.447768938383 Henry Cohn, 2026, needs more optimization.
14 682 0.448145003333 Henry Cohn, 2026, needs more optimization.
14 683 0.448486061192 Henry Cohn, 2026, needs more optimization.
14 684 0.448742984312 Henry Cohn, 2026, needs more optimization.
14 685 0.448763454280 Henry Cohn, 2026, needs more optimization.
14 686 0.448878145355 Henry Cohn, 2026, needs more optimization.
14 687 0.448981217031 Henry Cohn, 2026, needs more optimization.
14 688 0.449138893039 Henry Cohn, 2026, needs more optimization.
14 689 0.449411125024 Henry Cohn, 2026, needs more optimization.
14 690 0.449617603806 Henry Cohn, 2026, needs more optimization.
14 691 0.449751617549 Henry Cohn, 2026, needs more optimization.
14 692 0.449840976988 Henry Cohn, 2026, needs more optimization.
14 693 0.450073533714 Henry Cohn, 2026, needs more optimization.
14 694 0.450300775313 Henry Cohn, 2026, needs more optimization.
14 695 0.450519771924 Henry Cohn, 2026, needs more optimization.
14 696 0.450624236322 Henry Cohn, 2026, needs more optimization.
14 697 0.450767192547 Henry Cohn, 2026, needs more optimization.
14 698 0.450913515560 Henry Cohn, 2026, needs more optimization.
14 699 0.453775173076 Henry Cohn, 2026, needs more optimization.
14 700 0.453780459755 Henry Cohn, 2026, needs more optimization.
14 703 0.453807414296 Henry Cohn, 2026, needs more optimization.
14 704 0.453820990171 Henry Cohn, 2026, needs more optimization.
14 705 0.453867297030 Henry Cohn, 2026, needs more optimization.
14 706 0.453930301063 Henry Cohn, 2026, needs more optimization.
14 707 0.453944028662 Henry Cohn, 2026, needs more optimization.
14 708 0.453956508663 Henry Cohn, 2026, needs more optimization.
14 719 0.454132370353 Henry Cohn, 2026, needs more optimization.
14 896 0.454545454546 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−5
14 897 0.454719198234 Henry Cohn, 2026, needs more optimization.
14 898 0.454817707458 Henry Cohn, 2026, needs more optimization.
14 899 0.454840724962 Henry Cohn, 2026, needs more optimization.
14 900 0.454885871897 Henry Cohn, 2026, needs more optimization.
14 901 0.454907173238 Henry Cohn, 2026, needs more optimization.
14 902 0.454950116357 Henry Cohn, 2026, needs more optimization.
14 903 0.454976116300 Henry Cohn, 2026, needs more optimization.
14 904 0.455052940943 Henry Cohn, 2026, needs more optimization.
14 905 0.455088331951 Henry Cohn, 2026, needs more optimization.
14 906 0.455095632717 Henry Cohn, 2026, needs more optimization.
14 907 0.455107633265 Henry Cohn, 2026, needs more optimization.
14 908 0.455119003802 Henry Cohn, 2026, needs more optimization.
14 909 0.455139329462 Henry Cohn, 2026, needs more optimization.
14 910 0.455157160639 Henry Cohn, 2026, needs more optimization.
14 911 0.455173517118 Henry Cohn, 2026, needs more optimization.
14 912 0.455184614470 Henry Cohn, 2026, needs more optimization.
14 913 0.455195886360 Henry Cohn, 2026, needs more optimization.
14 914 0.455207946351 Henry Cohn, 2026, needs more optimization.
14 915 0.455222091838 Henry Cohn, 2026, needs more optimization.
14 916 0.455247174489 Henry Cohn, 2026, needs more optimization.
14 917 0.455257903552 Henry Cohn, 2026, needs more optimization.
14 918 0.455283172844 Henry Cohn, 2026, needs more optimization.
14 919 0.455313504579 Henry Cohn, 2026, needs more optimization.
14 920 0.455324157524 Henry Cohn, 2026, needs more optimization.
14 921 0.455337173630 Henry Cohn, 2026, needs more optimization.
14 922 0.455343293378 Henry Cohn, 2026, needs more optimization.
14 924 0.455348877733 Henry Cohn, 2026, needs more optimization.
14 925 0.455351188659 Henry Cohn, 2026, needs more optimization.
14 926 0.455358542333 Henry Cohn, 2026, needs more optimization.
14 927 0.455366110182 Henry Cohn, 2026, needs more optimization.
14 928 0.455369049035 Henry Cohn, 2026, needs more optimization.
14 929 0.455374081578 Henry Cohn, 2026, needs more optimization.
14 930 0.455378549770 Henry Cohn, 2026, needs more optimization.
14 931 0.455380551192 Henry Cohn, 2026, needs more optimization.
14 932 0.455388143438 Henry Cohn, 2026, needs more optimization.
14 933 0.455393478193 Henry Cohn, 2026, needs more optimization.
14 934 0.455394905989 Henry Cohn, 2026, needs more optimization.
14 935 0.455397012670 Henry Cohn, 2026, needs more optimization.
14 936 0.455402841336 Henry Cohn, 2026, needs more optimization.
14 937 0.455408313066 Henry Cohn, 2026, needs more optimization.
14 938 0.455412876904 Henry Cohn, 2026, needs more optimization.
14 939 0.455418947029 Henry Cohn, 2026, needs more optimization.
14 940 0.455424788022 Henry Cohn, 2026, needs more optimization.
14 941 0.455428863437 Henry Cohn, 2026, needs more optimization.
14 942 0.455435016622 Henry Cohn, 2026, needs more optimization.
14 943 0.455440169151 Henry Cohn, 2026, needs more optimization.
14 944 0.455446818148 Henry Cohn, 2026, needs more optimization.
14 945 0.455450475846 Henry Cohn, 2026, needs more optimization.
14 946 0.455456609224 Henry Cohn, 2026, needs more optimization.
14 947 0.455459482695 Henry Cohn, 2026, needs more optimization.
14 948 0.455469386987 Henry Cohn, 2026, needs more optimization.
14 949 0.455472889372 Henry Cohn, 2026, needs more optimization.
14 950 0.455477222340 Henry Cohn, 2026, needs more optimization.
14 951 0.455486008927 Henry Cohn, 2026, needs more optimization.
14 952 0.455492832900 Henry Cohn, 2026, needs more optimization.
14 953 0.455498351276 Henry Cohn, 2026, needs more optimization.
14 954 0.455509117681 Henry Cohn, 2026, needs more optimization.
14 955 0.455512258888 Henry Cohn, 2026, needs more optimization.
14 956 0.455534335290 Henry Cohn, 2026, needs more optimization.
14 957 0.455539836384 Henry Cohn, 2026, needs more optimization.
14 958 0.455546195090 Henry Cohn, 2026, needs more optimization.
14 959 0.455553482331 Henry Cohn, 2026, needs more optimization.
14 960 0.455556776941 Henry Cohn, 2026, needs more optimization.
14 961 0.455562802960 Henry Cohn, 2026, needs more optimization.
14 962 0.455567603271 Henry Cohn, 2026, needs more optimization.
14 963 0.455576955555 Henry Cohn, 2026, needs more optimization.
14 964 0.455585384124 Henry Cohn, 2026, needs more optimization.
14 965 0.455592439169 Henry Cohn, 2026, needs more optimization.
14 966 0.455598534709 Henry Cohn, 2026, needs more optimization.
14 967 0.455603819071 Henry Cohn, 2026, needs more optimization.
14 968 0.455609700138 Henry Cohn, 2026, needs more optimization.
14 969 0.455612698212 Henry Cohn, 2026, needs more optimization.
14 970 0.455615956573 Henry Cohn, 2026, needs more optimization.
14 971 0.455625945878 Henry Cohn, 2026, needs more optimization.
14 972 0.455631642185 Henry Cohn, 2026, needs more optimization.
14 973 0.455635600541 Henry Cohn, 2026, needs more optimization.
14 974 0.455639915566 Henry Cohn, 2026, needs more optimization.
14 975 0.455647040535 Henry Cohn, 2026, needs more optimization.
14 976 0.455654175916 Henry Cohn, 2026, needs more optimization.
14 978 0.456270213286 Henry Cohn, 2026, needs more optimization.
14 979 0.456270553639 Henry Cohn, 2026, needs more optimization.
14 980 0.456270920194 Henry Cohn, 2026, needs more optimization.
14 982 0.456273066617 Henry Cohn, 2026, needs more optimization.
14 983 0.456274487963 Henry Cohn, 2026, needs more optimization.
14 984 0.456277074440 Henry Cohn, 2026, needs more optimization.
14 985 0.456278004750 Henry Cohn, 2026, needs more optimization.
14 987 0.456280183280 Henry Cohn, 2026, needs more optimization.
14 988 0.456282218928 Henry Cohn, 2026, needs more optimization.
14 989 0.456282964705 Henry Cohn, 2026, needs more optimization.
14 990 0.456284653756 Henry Cohn, 2026, needs more optimization.
14 992 0.456286910871 Henry Cohn, 2026, needs more optimization.
14 993 0.456287390494 Henry Cohn, 2026, needs more optimization.
14 994 0.456288190816 Henry Cohn, 2026, needs more optimization.
14 995 0.456291824501 Henry Cohn, 2026, needs more optimization.
14 996 0.456293284700 Henry Cohn, 2026, needs more optimization.
14 997 0.456295230436 Henry Cohn, 2026, needs more optimization.
14 999 0.456296662870 Henry Cohn, 2026, needs more optimization.
14 1002 0.456301200345 Henry Cohn, 2026, needs more optimization.
14 1003 0.456301994551 Henry Cohn, 2026, needs more optimization.
14 1006 0.456303361436 Henry Cohn, 2026, needs more optimization.
14 1007 0.456303659429 Henry Cohn, 2026, needs more optimization.
14 1008 0.456304776155 Henry Cohn, 2026, needs more optimization.
14 1009 0.456305521962 Henry Cohn, 2026, needs more optimization.
14 1010 0.456308633287 Henry Cohn, 2026, needs more optimization.
14 1012 0.456313699489 Henry Cohn, 2026, needs more optimization.
14 1014 0.456314669115 Henry Cohn, 2026, needs more optimization.
14 1015 0.456314875046 Henry Cohn, 2026, needs more optimization.
14 1016 0.457548169871 Henry Cohn, 2026, needs more optimization.
14 1017 0.457550741966 Henry Cohn, 2026, needs more optimization.
14 1018 0.457552821662 Henry Cohn, 2026, needs more optimization.
14 1019 0.457558058881 Henry Cohn, 2026, needs more optimization.
14 1020 0.457564663014 Henry Cohn, 2026, needs more optimization.
14 1021 0.457573589435 Henry Cohn, 2026, needs more optimization.
14 1022 0.457580621303 Henry Cohn, 2026, needs more optimization.
14 1023 0.457585138859 Henry Cohn, 2026, needs more optimization.
14 1024 0.457589681649 Henry Cohn, 2026, needs more optimization.
15 31 0.050237120373 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
2535⁢x3−225⁢x2−15⁢x+1
15 32 0.058900808489 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
15 33 0.062706770083 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
15 34 0.066570393658 Henry Cohn, 2025.
15 35 0.070509992992 Henry Cohn, 2023.
15 36 0.070779968044 Henry Cohn, 2023.
5937⁢x4+412⁢x3−202⁢x2−4⁢x+1
15 37 0.078785666352 Henry Cohn, 2025.
15 38 0.079970260232 Henry Cohn, 2026.
15 39 0.082681671944 Henry Cohn, 2023.
347087⁢x8+1080416⁢x7+305012⁢x6+3648⁢x5−20054⁢x4−160⁢x3+276⁢x2−1
15 40 0.086159367074 Henry Cohn, 2023.
15 41 0.093058708471 Henry Cohn, 2026.
15 42 0.096809796022 Henry Cohn, 2023.
15 43 0.099863843733 Henry Cohn, 2025.
15 44 0.099976426707 Henry Cohn, 2025.
15 45 0.102626460761 Henry Cohn, 2026.
15 46 0.110795000982 Henry Cohn, 2025.
15 47 0.111165028345 Henry Cohn, 2026.
15 48 0.112519700675 Henry Cohn, 2026.
15 52 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
15 57 0.115470053838 Henry Cohn, 2024.
75⁢x2−1
15 58 0.119568772343 Henry Cohn, 2025.
15 61 0.128458591981 Henry Cohn, 2025.
263⁢x2−26⁢x−1
15 62 0.129608604388 Henry Cohn, 2026.
15 63 0.129675303921 Henry Cohn, 2026, needs more optimization.
15 64 0.129676245976 Henry Cohn, 2025, needs more optimization.
15 65 0.129676247045 Henry Cohn, 2026, needs more optimization.
15 66 0.142849849465 Henry Cohn, 2025.
15 67 0.144353409494 Henry Cohn, 2023.
15 68 0.146740451793 Henry Cohn, 2026.
15 69 0.160033734974 Henry Cohn, 2024.
15 70 0.160964563056 Henry Cohn, 2024.
15 73 0.161462093425 Henry Cohn, 2026.
15 76 0.168269539561 Henry Cohn, 2026, needs more optimization.
15 77 0.168276608035 Henry Cohn, 2026, needs more optimization.
15 78 0.168276608054 Henry Cohn, 2026, needs more optimization.
15 92 0.168685175113 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2−2⁢x−1
15 93 0.169916676995 Henry Cohn, 2025.
169⁢x4−56⁢x3−30⁢x2+1
15 94 0.186858652290 Henry Cohn, 2026.
15 95 0.187077042680 Henry Cohn, 2026, needs more optimization.
15 96 0.187887288776 Henry Cohn, 2026, needs more optimization.
15 99 0.188666328568 Henry Cohn, 2026, needs more optimization.
15 100 0.189726990664 Henry Cohn, 2026, needs more optimization.
15 101 0.197671409630 Henry Cohn, 2026, needs more optimization.
15 102 0.197755973849 Henry Cohn, 2026, needs more optimization.
15 108 0.199301661815 Henry Cohn, 2026.
347⁢x2−24⁢x−9
15 128 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
15 129 0.209693852047 Henry Cohn, 2026.
15 130 0.216435024466 Henry Cohn, 2026, needs more optimization.
15 131 0.219738366868 Henry Cohn, 2026, needs more optimization.
15 132 0.221692066410 Henry Cohn, 2026, needs more optimization.
15 135 0.223068626266 Henry Cohn, 2026, needs more optimization.
15 136 0.225990151252 Henry Cohn, 2026.
15 137 0.226886066966 Henry Cohn, 2026, needs more optimization.
15 142 0.227160244714 Henry Cohn, 2026.
15 143 0.232245360831 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
15 144 0.235179709766 Henry Cohn, 2026, needs more optimization.
15 145 0.237559192043 Henry Cohn, 2026, needs more optimization.
15 146 0.238420967062 Henry Cohn, 2026, needs more optimization.
15 147 0.238761559964 Henry Cohn, 2026, needs more optimization.
15 148 0.239285306886 Henry Cohn, 2026, needs more optimization.
15 149 0.239286614792 Henry Cohn, 2026, needs more optimization.
15 150 0.239558257200 Henry Cohn, 2026, needs more optimization.
15 151 0.239558257213 Henry Cohn, 2026, needs more optimization.
15 152 0.244616813220 Henry Cohn, 2026, needs more optimization.
15 153 0.245232909425 Henry Cohn, 2026, needs more optimization.
15 156 0.248124762896 Henry Cohn, 2026, needs more optimization.
15 157 0.249069470433 Henry Cohn, 2026.
15 158 0.253983477493 Henry Cohn, 2026, needs more optimization.
15 159 0.254468237300 Henry Cohn, 2026, needs more optimization.
15 160 0.254872967843 Henry Cohn, 2026, needs more optimization.
15 161 0.255430928344 Henry Cohn, 2026, needs more optimization.
15 162 0.255981615796 Henry Cohn, 2026, needs more optimization.
15 163 0.257075007382 Henry Cohn, 2026, needs more optimization.
15 164 0.257358933891 Henry Cohn, 2026, needs more optimization.
15 165 0.257391616061 Henry Cohn, 2026, needs more optimization.
15 166 0.257475869843 Henry Cohn, 2026, needs more optimization.
15 167 0.257675997624 Henry Cohn, 2026, needs more optimization.
15 168 0.257852945319 Henry Cohn, 2026, needs more optimization.
15 169 0.258053738583 Henry Cohn, 2026, needs more optimization.
15 170 0.258178686101 Henry Cohn, 2026, needs more optimization.
15 171 0.258365884796 Henry Cohn, 2026, needs more optimization.
15 172 0.258496407094 Henry Cohn, 2026, needs more optimization.
15 173 0.258642110145 Henry Cohn, 2026, needs more optimization.
15 174 0.258727923801 Henry Cohn, 2026, needs more optimization.
15 175 0.258887566011 Henry Cohn, 2026, needs more optimization.
15 176 0.259187685500 Henry Cohn, 2026, needs more optimization.
15 177 0.259562221585 Henry Cohn, 2026, needs more optimization.
15 178 0.259842954216 Henry Cohn, 2026, needs more optimization.
15 179 0.259991881328 Henry Cohn, 2026, needs more optimization.
15 180 0.259992093897 Henry Cohn, 2026, needs more optimization.
15 181 0.260002727632 Henry Cohn, 2026, needs more optimization.
15 182 0.260020123456 Henry Cohn, 2026, needs more optimization.
15 183 0.260128334592 Henry Cohn, 2026, needs more optimization.
15 184 0.260236479265 Henry Cohn, 2026, needs more optimization.
15 185 0.260319702777 Henry Cohn, 2026, needs more optimization.
15 186 0.260377899433 Henry Cohn, 2026, needs more optimization.
15 187 0.260799388302 Henry Cohn, 2026, needs more optimization.
15 188 0.261261054494 Henry Cohn, 2026, needs more optimization.
15 189 0.261738780508 Henry Cohn, 2026, needs more optimization.
15 190 0.262062298383 Henry Cohn, 2026, needs more optimization.
15 191 0.262528162934 Henry Cohn, 2026, needs more optimization.
15 192 0.262840127254 Henry Cohn, 2026, needs more optimization.
15 193 0.263166332004 Henry Cohn, 2026, needs more optimization.
15 194 0.263449663501 Henry Cohn, 2026, needs more optimization.
15 195 0.263683053780 Henry Cohn, 2026, needs more optimization.
15 196 0.263857026320 Henry Cohn, 2026, needs more optimization.
15 197 0.264006783474 Henry Cohn, 2026, needs more optimization.
15 198 0.264187682206 Henry Cohn, 2026, needs more optimization.
15 199 0.264359466322 Henry Cohn, 2026, needs more optimization.
15 200 0.264511777160 Henry Cohn, 2026, needs more optimization.
15 201 0.264666624852 Henry Cohn, 2026, needs more optimization.
15 202 0.264800152461 Henry Cohn, 2026, needs more optimization.
15 203 0.264941288374 Henry Cohn, 2026, needs more optimization.
15 204 0.265062531047 Henry Cohn, 2026, needs more optimization.
15 205 0.265168350415 Henry Cohn, 2026, needs more optimization.
15 206 0.265268446500 Henry Cohn, 2026, needs more optimization.
15 207 0.265415153885 Henry Cohn, 2026, needs more optimization.
15 208 0.265531313478 Henry Cohn, 2026, needs more optimization.
15 209 0.265668671339 Henry Cohn, 2026, needs more optimization.
15 210 0.265783974255 Henry Cohn, 2026, needs more optimization.
15 211 0.265951552753 Henry Cohn, 2026, needs more optimization.
15 212 0.265981663211 Henry Cohn, 2026, needs more optimization.
15 213 0.266095931907 Henry Cohn, 2026, needs more optimization.
15 214 0.266230466933 Henry Cohn, 2026, needs more optimization.
15 215 0.266322309599 Henry Cohn, 2026, needs more optimization.
15 218 0.266362814739 Henry Cohn, 2026, needs more optimization.
15 219 0.266440308323 Henry Cohn, 2026, needs more optimization.
15 220 0.266583431141 Henry Cohn, 2026, needs more optimization.
15 221 0.273150769639 Henry Cohn, 2026, needs more optimization.
15 222 0.284143682340 Henry Cohn, 2026, needs more optimization.
15 223 0.284248870339 Henry Cohn, 2026, needs more optimization.
15 224 0.284358483604 Henry Cohn, 2026, needs more optimization.
15 225 0.285295962957 Henry Cohn, 2026, needs more optimization.
15 226 0.285513042178 Henry Cohn, 2026, needs more optimization.
15 227 0.285513066644 Henry Cohn, 2026, needs more optimization.
15 229 0.285513240806 Henry Cohn, 2026, needs more optimization.
15 230 0.285514836485 Henry Cohn, 2026, needs more optimization.
15 231 0.285518561993 Henry Cohn, 2026, needs more optimization.
15 232 0.285523107515 Henry Cohn, 2026, needs more optimization.
15 233 0.285536057804 Henry Cohn, 2026, needs more optimization.
15 234 0.285542657506 Henry Cohn, 2026, needs more optimization.
15 235 0.285554981345 Henry Cohn, 2026, needs more optimization.
15 236 0.285562819070 Henry Cohn, 2026, needs more optimization.
15 237 0.285572812305 Henry Cohn, 2026, needs more optimization.
15 238 0.285588158592 Henry Cohn, 2026, needs more optimization.
15 239 0.285607662545 Henry Cohn, 2026, needs more optimization.
15 240 0.285631201311 Henry Cohn, 2026, needs more optimization.
15 241 0.285655301473 Henry Cohn, 2026, needs more optimization.
15 242 0.285672695618 Henry Cohn, 2026, needs more optimization.
15 243 0.286368647226 Henry Cohn, 2026, needs more optimization.
15 244 0.286856225757 Henry Cohn, 2026, needs more optimization.
15 245 0.287242437340 Henry Cohn, 2026, needs more optimization.
15 246 0.287606375359 Henry Cohn, 2026, needs more optimization.
15 247 0.288090813571 Henry Cohn, 2026, needs more optimization.
15 248 0.288361312607 Henry Cohn, 2026, needs more optimization.
15 249 0.291752354751 Henry Cohn, 2026, needs more optimization.
15 250 0.294425452579 Henry Cohn, 2026, needs more optimization.
15 251 0.296522246141 Henry Cohn, 2026, needs more optimization.
15 252 0.297708757564 Henry Cohn, 2026, needs more optimization.
15 253 0.297826535305 Henry Cohn, 2026, needs more optimization.
15 254 0.297925421026 Henry Cohn, 2026, needs more optimization.
15 256 0.297926304913 Henry Cohn, 2026.
15 257 0.302589971289 Henry Cohn, 2026, needs more optimization.
15 258 0.304376252703 Henry Cohn, 2026, needs more optimization.
15 259 0.305956223911 Henry Cohn, 2026, needs more optimization.
15 260 0.307183763306 Henry Cohn, 2026, needs more optimization.
15 261 0.308188882124 Henry Cohn, 2026, needs more optimization.
15 262 0.309418185500 Henry Cohn, 2026, needs more optimization.
15 263 0.309487826951 Henry Cohn, 2026, needs more optimization.
15 264 0.309629622269 Henry Cohn, 2026, needs more optimization.
15 265 0.312019009206 Henry Cohn, 2026, needs more optimization.
15 266 0.313588007088 Henry Cohn, 2026, needs more optimization.
15 267 0.314827659634 Henry Cohn, 2026, needs more optimization.
15 268 0.315491881485 Henry Cohn, 2026, needs more optimization.
15 269 0.316298128504 Henry Cohn, 2026, needs more optimization.
15 270 0.316564747477 Henry Cohn, 2026, needs more optimization.
15 271 0.318994600900 Henry Cohn, 2026, needs more optimization.
15 272 0.321140957954 Henry Cohn, 2026, needs more optimization.
15 273 0.323221962930 Henry Cohn, 2026, needs more optimization.
15 274 0.324905714146 Henry Cohn, 2026, needs more optimization.
15 275 0.326533357513 Henry Cohn, 2026, needs more optimization.
15 276 0.328150083286 Henry Cohn, 2026, needs more optimization.
15 277 0.329935100778 Henry Cohn, 2026, needs more optimization.
15 278 0.331043559236 Henry Cohn, 2026, needs more optimization.
15 279 0.332709973686 Henry Cohn, 2026, needs more optimization.
15 320 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
15 321 0.339294291647 Henry Cohn, 2026, needs more optimization.
15 322 0.340372593682 Henry Cohn, 2026, needs more optimization.
15 323 0.341167529363 Henry Cohn, 2026, needs more optimization.
15 324 0.341829497223 Henry Cohn, 2026, needs more optimization.
15 325 0.342381374003 Henry Cohn, 2026, needs more optimization.
15 326 0.342761028495 Henry Cohn, 2026, needs more optimization.
15 327 0.343116641126 Henry Cohn, 2026, needs more optimization.
15 328 0.343550710210 Henry Cohn, 2026, needs more optimization.
15 329 0.343818999479 Henry Cohn, 2026, needs more optimization.
15 330 0.344477595746 Henry Cohn, 2026, needs more optimization.
15 331 0.345410642400 Henry Cohn, 2026, needs more optimization.
15 332 0.345738285773 Henry Cohn, 2026, needs more optimization.
15 333 0.346488969209 Henry Cohn, 2026, needs more optimization.
15 334 0.347005482769 Henry Cohn, 2026, needs more optimization.
15 335 0.347208952821 Henry Cohn, 2026, needs more optimization.
15 336 0.347471523838 Henry Cohn, 2026, needs more optimization.
15 337 0.347843277456 Henry Cohn, 2026, needs more optimization.
15 338 0.347997449467 Henry Cohn, 2026, needs more optimization.
15 339 0.348165976160 Henry Cohn, 2026, needs more optimization.
15 340 0.348371420269 Henry Cohn, 2026, needs more optimization.
15 341 0.348550143761 Henry Cohn, 2026, needs more optimization.
15 342 0.348831040924 Henry Cohn, 2026, needs more optimization.
15 343 0.349068817683 Henry Cohn, 2026, needs more optimization.
15 344 0.349235140520 Henry Cohn, 2026, needs more optimization.
15 345 0.349398986403 Henry Cohn, 2026, needs more optimization.
15 346 0.349616451122 Henry Cohn, 2026, needs more optimization.
15 347 0.350144714574 Henry Cohn, 2026, needs more optimization.
15 348 0.350468623509 Henry Cohn, 2026, needs more optimization.
15 349 0.350824928373 Henry Cohn, 2026, needs more optimization.
15 350 0.351097195930 Henry Cohn, 2026, needs more optimization.
15 351 0.351295761303 Henry Cohn, 2026, needs more optimization.
15 352 0.351647176973 Henry Cohn, 2026, needs more optimization.
15 353 0.352022838447 Henry Cohn, 2026, needs more optimization.
15 354 0.352269568195 Henry Cohn, 2026, needs more optimization.
15 355 0.352542875815 Henry Cohn, 2026, needs more optimization.
15 356 0.352743610903 Henry Cohn, 2026, needs more optimization.
15 357 0.352948147731 Henry Cohn, 2026, needs more optimization.
15 358 0.353274967188 Henry Cohn, 2026, needs more optimization.
15 359 0.353524426473 Henry Cohn, 2026, needs more optimization.
15 360 0.353747557081 Henry Cohn, 2026, needs more optimization.
15 362 0.355511428880 Henry Cohn, 2026, needs more optimization.
15 363 0.355524296626 Henry Cohn, 2026, needs more optimization.
15 364 0.355533728276 Henry Cohn, 2026, needs more optimization.
15 365 0.355572293386 Henry Cohn, 2026, needs more optimization.
15 366 0.355576839993 Henry Cohn, 2026, needs more optimization.
15 367 0.355613220331 Henry Cohn, 2026, needs more optimization.
15 368 0.355626877757 Henry Cohn, 2026, needs more optimization.
15 369 0.355652248375 Henry Cohn, 2026, needs more optimization.
15 370 0.355682689943 Henry Cohn, 2026, needs more optimization.
15 371 0.355741629825 Henry Cohn, 2026, needs more optimization.
15 372 0.355760698116 Henry Cohn, 2026, needs more optimization.
15 373 0.356497085974 Henry Cohn, 2026, needs more optimization.
15 374 0.356836770389 Henry Cohn, 2026, needs more optimization.
15 375 0.356847132881 Henry Cohn, 2026, needs more optimization.
15 376 0.358253660425 Henry Cohn, 2026, needs more optimization.
15 377 0.358275553798 Henry Cohn, 2026, needs more optimization.
15 378 0.358282791964 Henry Cohn, 2026, needs more optimization.
15 379 0.358283349013 Henry Cohn, 2026, needs more optimization.
15 380 0.358286657805 Henry Cohn, 2026, needs more optimization.
15 381 0.360085867462 Henry Cohn, 2026, needs more optimization.
15 382 0.360735575469 Henry Cohn, 2026, needs more optimization.
15 383 0.361398999321 Henry Cohn, 2026, needs more optimization.
15 384 0.362686502900 Henry Cohn, 2026, needs more optimization.
15 385 0.363039002574 Henry Cohn, 2026, needs more optimization.
15 386 0.363873811230 Henry Cohn, 2026, needs more optimization.
15 387 0.364543981306 Henry Cohn, 2026, needs more optimization.
15 388 0.365651331254 Henry Cohn, 2026, needs more optimization.
15 389 0.366149129447 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 390 0.366783064617 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 391 0.367234215010 Henry Cohn, 2026, needs more optimization.
15 392 0.367945346703 Henry Cohn, 2026, needs more optimization.
15 393 0.368560034725 Henry Cohn, 2026, needs more optimization.
15 394 0.368923180772 Henry Cohn, 2026, needs more optimization.
15 395 0.369455747927 Henry Cohn, 2026, needs more optimization.
15 396 0.370024820660 Henry Cohn, 2026, needs more optimization.
15 397 0.370266340422 Henry Cohn, 2026, needs more optimization.
15 424 0.370431040067 Henry Cohn, 2026.
287⁢x2−190⁢x+31
15 425 0.370431040067 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
287⁢x2−190⁢x+31
15 426 0.372209293489 Henry Cohn, 2026, needs more optimization.
15 427 0.373360008117 Henry Cohn, 2026, needs more optimization.
15 428 0.374921306726 Henry Cohn, 2026, needs more optimization.
15 430 0.374922602359 Henry Cohn, 2026, needs more optimization.
15 431 0.374922944117 Henry Cohn, 2026, needs more optimization.
15 432 0.374922997977 Henry Cohn, 2026, needs more optimization.
15 433 0.374963897659 Henry Cohn, 2026, needs more optimization.
15 434 0.374964026594 Henry Cohn, 2026, needs more optimization.
15 435 0.375011818645 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
15 461 0.376462890262 Henry Cohn, 2026, needs more optimization.
15 462 0.376564758957 Henry Cohn, 2026, needs more optimization.
15 466 0.376621612570 Henry Cohn, 2026, needs more optimization.
15 467 0.381192425811 Henry Cohn, 2026, needs more optimization.
15 468 0.382726692018 Henry Cohn, 2026, needs more optimization.
15 469 0.383963705951 Henry Cohn, 2026, needs more optimization.
15 470 0.385340985961 Henry Cohn, 2026, needs more optimization.
15 471 0.386197400456 Henry Cohn, 2026, needs more optimization.
15 472 0.386905286449 Henry Cohn, 2026, needs more optimization.
15 480 0.387503296749 Henry Cohn, 2026, needs more optimization.
15 481 0.390135295151 Henry Cohn, 2026, needs more optimization.
15 482 0.392363245767 Henry Cohn, 2026, needs more optimization.
15 483 0.392370003925 Henry Cohn, 2026, needs more optimization.
15 485 0.392370004218 Henry Cohn, 2026, needs more optimization.
15 486 0.392420077155 Henry Cohn, 2026, needs more optimization.
15 487 0.392427801597 Henry Cohn, 2026, needs more optimization.
15 489 0.392497530212 Henry Cohn, 2026, needs more optimization.
15 490 0.392498693543 Henry Cohn, 2026, needs more optimization.
15 491 0.392521307576 Henry Cohn, 2026, needs more optimization.
15 492 0.392523115553 Henry Cohn, 2026, needs more optimization.
15 494 0.392680159723 Henry Cohn, 2026, needs more optimization.
15 495 0.392695924429 Henry Cohn, 2026, needs more optimization.
15 496 0.392787420722 Henry Cohn, 2026, needs more optimization.
15 498 0.392831410484 Henry Cohn, 2026, needs more optimization.
15 499 0.392897440243 Henry Cohn, 2026, needs more optimization.
15 500 0.392908790451 Henry Cohn, 2026, needs more optimization.
15 501 0.392917782687 Henry Cohn, 2026, needs more optimization.
15 502 0.392988724966 Henry Cohn, 2026, needs more optimization.
15 504 0.393001971678 Henry Cohn, 2026, needs more optimization.
15 505 0.393078814625 Henry Cohn, 2026, needs more optimization.
15 506 0.393129805521 Henry Cohn, 2026, needs more optimization.
15 507 0.393141534758 Henry Cohn, 2026, needs more optimization.
15 508 0.393142500437 Henry Cohn, 2026, needs more optimization.
15 509 0.393311789983 Henry Cohn, 2026, needs more optimization.
15 510 0.393830776886 Henry Cohn, 2026, needs more optimization.
15 511 0.393876051420 Henry Cohn, 2026, needs more optimization.
15 513 0.393897596375 Henry Cohn, 2026, needs more optimization.
15 514 0.394023011920 Henry Cohn, 2026, needs more optimization.
15 515 0.394054735730 Henry Cohn, 2026, needs more optimization.
15 516 0.394256286682 Henry Cohn, 2026, needs more optimization.
15 517 0.394319672447 Henry Cohn, 2026, needs more optimization.
15 518 0.394665710177 Henry Cohn, 2026, needs more optimization.
15 519 0.394880818814 Henry Cohn, 2026, needs more optimization.
15 520 0.395130785636 Henry Cohn, 2026, needs more optimization.
15 521 0.395280035337 Henry Cohn, 2026, needs more optimization.
15 522 0.395565882482 Henry Cohn, 2026, needs more optimization.
15 523 0.395958736763 Henry Cohn, 2026, needs more optimization.
15 524 0.396031386804 Henry Cohn, 2026, needs more optimization.
15 525 0.396074200253 Henry Cohn, 2026, needs more optimization.
15 526 0.396111945964 Henry Cohn, 2026, needs more optimization.
15 527 0.396559557370 Henry Cohn, 2026, needs more optimization.
15 528 0.396569801880 Henry Cohn, 2026, needs more optimization.
15 529 0.396812529039 Henry Cohn, 2026, needs more optimization.
15 530 0.396961977256 Henry Cohn, 2026, needs more optimization.
15 531 0.397062301645 Henry Cohn, 2026, needs more optimization.
15 532 0.397153416304 Henry Cohn, 2026, needs more optimization.
15 533 0.397555373410 Henry Cohn, 2026, needs more optimization.
15 534 0.397569692805 Henry Cohn, 2026, needs more optimization.
15 535 0.397747358785 Henry Cohn, 2026, needs more optimization.
15 536 0.397786399450 Henry Cohn, 2026, needs more optimization.
15 537 0.398147020325 Henry Cohn, 2026, needs more optimization.
15 538 0.398189358755 Henry Cohn, 2026, needs more optimization.
15 539 0.398414580623 Henry Cohn, 2026, needs more optimization.
15 540 0.398518645544 Henry Cohn, 2026, needs more optimization.
15 541 0.398593343048 Henry Cohn, 2026, needs more optimization.
15 542 0.398707050023 Henry Cohn, 2026, needs more optimization.
15 543 0.398776092783 Henry Cohn, 2026, needs more optimization.
15 545 0.399113952468 Henry Cohn, 2026, needs more optimization.
15 546 0.399334960367 Henry Cohn, 2026, needs more optimization.
15 547 0.399632654880 Henry Cohn, 2026, needs more optimization.
15 672 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
15 688 0.4 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
15 689 0.404117037740 Henry Cohn, 2026.
15 690 0.407439006131 Henry Cohn, 2026, needs more optimization.
15 691 0.410953442127 Henry Cohn, 2026, needs more optimization.
15 692 0.413563803824 Henry Cohn, 2026, needs more optimization.
15 693 0.414188074043 Henry Cohn, 2026, needs more optimization.
15 694 0.414195190365 Henry Cohn, 2026, needs more optimization.
15 695 0.415967427216 Henry Cohn, 2026, needs more optimization.
15 696 0.416264002161 Henry Cohn, 2026, needs more optimization.
15 697 0.417431299204 Henry Cohn, 2026, needs more optimization.
15 698 0.417432222510 Henry Cohn, 2026, needs more optimization.
15 699 0.417743391434 Henry Cohn, 2026, needs more optimization.
15 700 0.417752262870 Henry Cohn, 2026, needs more optimization.
15 701 0.418064007338 Henry Cohn, 2026, needs more optimization.
15 702 0.418401271081 Henry Cohn, 2026, needs more optimization.
15 703 0.418583334400 Henry Cohn, 2026, needs more optimization.
15 704 0.419086303313 Henry Cohn, 2026, needs more optimization.
15 705 0.419255253759 Henry Cohn, 2026, needs more optimization.
15 706 0.419667569912 Henry Cohn, 2026, needs more optimization.
15 707 0.420428789054 Henry Cohn, 2026, needs more optimization.
15 709 0.420934514593 Henry Cohn, 2026, needs more optimization.
15 710 0.420978775921 Henry Cohn, 2026, needs more optimization.
15 711 0.421051900412 Henry Cohn, 2026, needs more optimization.
15 712 0.421219003827 Henry Cohn, 2026, needs more optimization.
15 713 0.421326308911 Henry Cohn, 2026, needs more optimization.
15 714 0.421440736020 Henry Cohn, 2026, needs more optimization.
15 715 0.421602559228 Henry Cohn, 2026, needs more optimization.
15 716 0.421817584702 Henry Cohn, 2026, needs more optimization.
15 717 0.422130765270 Henry Cohn, 2026, needs more optimization.
15 718 0.422327754240 Henry Cohn, 2026, needs more optimization.
15 719 0.422630897613 Henry Cohn, 2026, needs more optimization.
15 720 0.422830779963 Henry Cohn, 2026, needs more optimization.
15 721 0.423000732623 Henry Cohn, 2026, needs more optimization.
15 722 0.423247446390 Henry Cohn, 2026, needs more optimization.
15 723 0.423564814775 Henry Cohn, 2026, needs more optimization.
15 724 0.423840231754 Henry Cohn, 2026, needs more optimization.
15 725 0.424178017649 Henry Cohn, 2026, needs more optimization.
15 726 0.424346141948 Henry Cohn, 2026, needs more optimization.
15 727 0.424521052384 Henry Cohn, 2026, needs more optimization.
15 728 0.424714699956 Henry Cohn, 2026, needs more optimization.
15 729 0.425034597580 Henry Cohn, 2026, needs more optimization.
15 730 0.425114756965 Henry Cohn, 2026, needs more optimization.
15 731 0.425312394982 Henry Cohn, 2026, needs more optimization.
15 732 0.425480531804 Henry Cohn, 2026, needs more optimization.
15 733 0.425629431745 Henry Cohn, 2026, needs more optimization.
15 734 0.425816154088 Henry Cohn, 2026, needs more optimization.
15 735 0.426015174939 Henry Cohn, 2026, needs more optimization.
15 736 0.426104537605 Henry Cohn, 2026, needs more optimization.
15 737 0.426443765160 Henry Cohn, 2026, needs more optimization.
15 738 0.426650021407 Henry Cohn, 2026, needs more optimization.
15 739 0.426758056118 Henry Cohn, 2026, needs more optimization.
15 740 0.427037436018 Henry Cohn, 2026, needs more optimization.
15 741 0.427282269264 Henry Cohn, 2026, needs more optimization.
15 742 0.427392405474 Henry Cohn, 2026, needs more optimization.
15 743 0.427621101559 Henry Cohn, 2026, needs more optimization.
15 744 0.427677705968 Henry Cohn, 2026, needs more optimization.
15 745 0.427857894067 Henry Cohn, 2026, needs more optimization.
15 746 0.427953687978 Henry Cohn, 2026, needs more optimization.
15 747 0.428130329477 Henry Cohn, 2026, needs more optimization.
15 748 0.428318682340 Henry Cohn, 2026, needs more optimization.
15 749 0.428527494801 Henry Cohn, 2026, needs more optimization.
15 990 0.428571428572 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
15 991 0.439533619978 Henry Cohn, 2026, needs more optimization.
15 1024 0.454545454546 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
11⁢x−5
16 33 0.047421028894 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3136⁢x3−256⁢x2−16⁢x+1
16 34 0.055555555556 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
18⁢x−1
16 36 0.056002309435 Henry Cohn, 2023.
176⁢x2+8⁢x−1
16 38 0.065186804094 Henry Cohn, 2023.
7312⁢x4+864⁢x3−200⁢x2−8⁢x+1
16 39 0.074285234713 Henry Cohn, 2025.
16 40 0.077433436468 Henry Cohn, 2024.
16 41 0.078328485376 Henry Cohn, 2023.
16 42 0.085112299907 Henry Cohn, 2025.
16 44 0.085376587737 Henry Cohn, 2023.
512⁢x2−32⁢x−1
16 45 0.090651346396 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
16 46 0.093714773474 Ilmari Vahteristo, 2026.
793984⁢x8+2769888⁢x7−316860⁢x6−393992⁢x5−62620⁢x4−1308⁢x3+460⁢x2+40⁢x+1
16 47 0.097443031003 Henry Cohn, 2025.
16 48 0.098771717854 Henry Cohn, 2023.
143⁢x2−4⁢x−1
16 49 0.105254154031 Henry Cohn, 2025.
16 50 0.108974791166 Henry Cohn, 2026.
16 51 0.111198306019 Henry Cohn, 2025.
16 52 0.111567586034 Henry Cohn, 2026.
16 54 0.112897448890 Henry Cohn, 2026.
16 55 0.113130733100 Henry Cohn, 2026, needs more optimization.
16 58 0.113835450316 Henry Cohn, 2026.
288⁢x2−24⁢x−1
16 59 0.115468708787 Henry Cohn, 2026, needs more optimization.
16 60 0.115470049065 Henry Cohn, 2026, needs more optimization.
16 61 0.119371454413 Henry Cohn, 2025.
16 62 0.125768177302 Henry Cohn, 2025.
16 63 0.127283408651 Henry Cohn, 2026, needs more optimization.
16 74 0.127284656799 Henry Cohn, 2023.
156⁢x2−12⁢x−1
16 75 0.142328493208 Henry Cohn, 2026, needs more optimization.
16 76 0.155906734582 Henry Cohn, 2026, needs more optimization.
16 77 0.156180532207 Henry Cohn, 2026, needs more optimization.
16 78 0.156308507756 Henry Cohn, 2026, needs more optimization.
16 79 0.156684906967 Henry Cohn, 2026, needs more optimization.
16 80 0.156933594040 Henry Cohn, 2026, needs more optimization.
16 81 0.157231026163 Henry Cohn, 2026, needs more optimization.
16 82 0.158312309770 Henry Cohn, 2026, needs more optimization.
16 83 0.158831583909 Henry Cohn, 2026, needs more optimization.
16 84 0.159473252851 Ilmari Vahteristo, 2026.
17856⁢x3+2064⁢x2−476⁢x−49
16 85 0.161142075511 Henry Cohn, 2026, needs more optimization.
16 88 0.168668499420 Henry Cohn, 2025, needs more optimization.
16 89 0.168682927803 Henry Cohn, 2026, needs more optimization.
16 90 0.168683666808 Henry Cohn, 2026, needs more optimization.
16 92 0.168684604646 Henry Cohn, 2025, needs more optimization.
16 94 0.168684943107 Henry Cohn, 2025, needs more optimization.
16 95 0.168685553807 Henry Cohn, 2026, needs more optimization.
16 96 0.168685570157 Henry Cohn, 2026, needs more optimization.
16 97 0.169880683941 Henry Cohn, 2026, needs more optimization.
16 102 0.170753175474 Henry Cohn, 2026.
128⁢x2−16⁢x−1
16 103 0.174178397911 Henry Cohn, 2026.
16 104 0.179202077195 Henry Cohn, 2026, needs more optimization.
16 105 0.183402640902 Henry Cohn, 2026, needs more optimization.
16 106 0.185708758318 Henry Cohn, 2026, needs more optimization.
16 107 0.188005548159 Henry Cohn, 2026, needs more optimization.
16 108 0.190685070898 Henry Cohn, 2026, needs more optimization.
16 109 0.191584444724 Henry Cohn, 2026, needs more optimization.
16 110 0.192049208641 Henry Cohn, 2026, needs more optimization.
16 111 0.192381712285 Henry Cohn, 2026, needs more optimization.
16 112 0.192392772262 Henry Cohn, 2026, needs more optimization.
16 117 0.192450089730 Henry Cohn, 2026.
27⁢x2−1
16 118 0.192450164499 Henry Cohn, 2026, needs more optimization.
16 119 0.198881757541 Henry Cohn, 2026, needs more optimization.
16 120 0.199966090978 Henry Cohn, 2026, needs more optimization.
16 121 0.199966090985 Henry Cohn, 2026, needs more optimization.
16 122 0.199966090996 Henry Cohn, 2026, needs more optimization.
16 123 0.199988607051 Henry Cohn, 2026, needs more optimization.
16 124 0.199989165732 Henry Cohn, 2026, needs more optimization.
16 126 0.199993997090 Henry Cohn, 2026, needs more optimization.
16 127 0.199995845425 Henry Cohn, 2025, needs more optimization.
16 130 0.199999918321 Henry Cohn, 2025, needs more optimization.
16 131 0.200001027914 Henry Cohn, 2026, needs more optimization.
16 132 0.200001470228 Henry Cohn, 2026, needs more optimization.
16 133 0.202538913614 Henry Cohn, 2026, needs more optimization.
16 159 0.202913709779 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2−4⁢x−1
16 160 0.204974865153 Henry Cohn, 2026, needs more optimization.
16 161 0.221693162701 Henry Cohn, 2026, needs more optimization.
16 162 0.229546342871 Henry Cohn, 2026, needs more optimization.
16 165 0.230995927542 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 166 0.234433486339 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
16 169 0.236031010307 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 170 0.237449050011 Henry Cohn, 2026, needs more optimization.
16 171 0.240174280990 Henry Cohn, 2026, needs more optimization.
16 172 0.240961076092 Henry Cohn, 2026, needs more optimization.
16 173 0.241850342448 Henry Cohn, 2026, needs more optimization.
16 175 0.242225294068 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
16 176 0.244617594140 Henry Cohn, 2026, needs more optimization.
16 177 0.245302043558 Henry Cohn, 2026, needs more optimization.
16 178 0.245846854130 Henry Cohn, 2026, needs more optimization.
16 179 0.246244513461 Henry Cohn, 2026, needs more optimization.
16 180 0.246520320615 Henry Cohn, 2026, needs more optimization.
16 181 0.246838695030 Henry Cohn, 2026, needs more optimization.
16 182 0.247089284947 Henry Cohn, 2026, needs more optimization.
16 183 0.247330494250 Henry Cohn, 2026, needs more optimization.
16 184 0.247502757077 Henry Cohn, 2026, needs more optimization.
16 185 0.247619572543 Henry Cohn, 2026, needs more optimization.
16 186 0.247722494584 Henry Cohn, 2026, needs more optimization.
16 187 0.247805814315 Henry Cohn, 2026, needs more optimization.
16 188 0.247973748457 Henry Cohn, 2026, needs more optimization.
16 189 0.248088828374 Henry Cohn, 2026, needs more optimization.
16 190 0.248390607208 Henry Cohn, 2026, needs more optimization.
16 191 0.248617792160 Henry Cohn, 2026, needs more optimization.
16 192 0.248905690264 Henry Cohn, 2026, needs more optimization.
16 193 0.248965784957 Henry Cohn, 2026, needs more optimization.
16 194 0.249838014888 Henry Cohn, 2026, needs more optimization.
16 195 0.249848275540 Henry Cohn, 2026, needs more optimization.
16 196 0.249858765703 Henry Cohn, 2026, needs more optimization.
16 197 0.249881316052 Henry Cohn, 2026, needs more optimization.
16 198 0.249902173991 Henry Cohn, 2026, needs more optimization.
16 199 0.249977572178 Henry Cohn, 2026, needs more optimization.
16 288* 0.25 V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
4⁢x−1
16 289 0.285672450592 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 290 0.288751040893 Henry Cohn, 2026, needs more optimization.
16 291 0.294622761817 Henry Cohn, 2026, needs more optimization.
16 294 0.296166885763 Henry Cohn, 2026, needs more optimization.
16 295 0.296915522708 Henry Cohn, 2026, needs more optimization.
16 296 0.298636138368 Henry Cohn, 2026, needs more optimization.
16 300 0.302467449516 Henry Cohn, 2026, needs more optimization.
16 301 0.302628562261 Henry Cohn, 2026, needs more optimization.
16 302 0.302628578498 Henry Cohn, 2026, needs more optimization.
16 303 0.308229010927 Henry Cohn, 2026, needs more optimization.
16 311 0.308244056578 Henry Cohn, 2026, needs more optimization.
16 312 0.308244064042 Henry Cohn, 2026, needs more optimization.
16 313 0.308884372590 Henry Cohn, 2026, needs more optimization.
16 314 0.310247967952 Henry Cohn, 2026, needs more optimization.
16 315 0.311923313132 Henry Cohn, 2026, needs more optimization.
16 316 0.313287094637 Henry Cohn, 2026, needs more optimization.
16 317 0.317288938011 Henry Cohn, 2026, needs more optimization.
16 318 0.319994972294 Henry Cohn, 2026, needs more optimization.
16 319 0.321893724667 Henry Cohn, 2026, needs more optimization.
16 320 0.324159552780 Henry Cohn, 2026, needs more optimization.
16 321 0.326120810377 Henry Cohn, 2026, needs more optimization.
16 322 0.326887405901 Henry Cohn, 2026, needs more optimization.
16 323 0.327980212062 Henry Cohn, 2026, needs more optimization.
16 324 0.328120233229 Henry Cohn, 2026, needs more optimization.
16 325 0.328353332564 Henry Cohn, 2026, needs more optimization.
16 326 0.328381689752 Henry Cohn, 2026, needs more optimization.
16 327 0.328596664656 Henry Cohn, 2026, needs more optimization.
16 328 0.328632195465 Henry Cohn, 2026, needs more optimization.
16 329 0.328727632621 Henry Cohn, 2026, needs more optimization.
16 330 0.328800543486 Henry Cohn, 2026, needs more optimization.
16 340 0.328947368422 Henry Cohn, 2026.
76⁢x−25
16 341 0.329842105372 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
16 342 0.329865971255 Henry Cohn, 2026, needs more optimization.
16 343 0.329977231353 Henry Cohn, 2026, needs more optimization.
16 344 0.330268455069 Henry Cohn, 2026, needs more optimization.
16 345 0.330437877403 Henry Cohn, 2026, needs more optimization.
16 346 0.330552441048 Henry Cohn, 2026, needs more optimization.
16 347 0.330595865520 Henry Cohn, 2026, needs more optimization.
16 348 0.330664617105 Henry Cohn, 2026, needs more optimization.
16 349 0.330749507871 Henry Cohn, 2026, needs more optimization.
16 350 0.330893098516 Henry Cohn, 2026, needs more optimization.
16 351 0.331027458725 Henry Cohn, 2026, needs more optimization.
16 352 0.331312288854 Henry Cohn, 2026, needs more optimization.
16 353 0.331426392088 Henry Cohn, 2026, needs more optimization.
16 354 0.331532838006 Henry Cohn, 2026, needs more optimization.
16 355 0.331679576492 Henry Cohn, 2026, needs more optimization.
16 356 0.331805619447 Henry Cohn, 2026, needs more optimization.
16 357 0.331824785305 Henry Cohn, 2026, needs more optimization.
16 358 0.332028665977 Henry Cohn, 2026, needs more optimization.
16 359 0.332084211809 Henry Cohn, 2026, needs more optimization.
16 360 0.332247983559 Henry Cohn, 2026, needs more optimization.
16 361 0.332492640029 Henry Cohn, 2026, needs more optimization.
16 362 0.332564629325 Henry Cohn, 2026, needs more optimization.
16 363 0.332720445806 Henry Cohn, 2026, needs more optimization.
16 364 0.332751038454 Henry Cohn, 2026, needs more optimization.
16 365 0.332909062161 Henry Cohn, 2026, needs more optimization.
16 366 0.333013492608 Henry Cohn, 2026, needs more optimization.
16 367 0.333036569583 Henry Cohn, 2026, needs more optimization.
16 368 0.333067959916 Henry Cohn, 2026, needs more optimization.
16 369 0.333177470788 Henry Cohn, 2026, needs more optimization.
16 370 0.333194954637 Henry Cohn, 2026, needs more optimization.
16 512 0.333333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
3⁢x−1
16 513 0.350752485725 Henry Cohn, 2026, needs more optimization.
16 514 0.351225079852 Henry Cohn, 2026, needs more optimization.
16 515 0.352910706436 Henry Cohn, 2026, needs more optimization.
16 516 0.356556141084 Henry Cohn, 2026, needs more optimization.
16 517 0.357826410163 Henry Cohn, 2026, needs more optimization.
16 518 0.358500153052 Henry Cohn, 2026, needs more optimization.
16 519 0.358882991394 Henry Cohn, 2026, needs more optimization.
16 520 0.359930449609 Henry Cohn, 2026, needs more optimization.
16 521 0.360637233963 Henry Cohn, 2026, needs more optimization.
16 522 0.360830307826 Henry Cohn, 2026, needs more optimization.
16 523 0.361224336943 Henry Cohn, 2026, needs more optimization.
16 524 0.362555292160 Henry Cohn, 2026, needs more optimization.
16 525 0.362991539912 Henry Cohn, 2026, needs more optimization.
16 526 0.363465271215 Henry Cohn, 2026, needs more optimization.
16 527 0.363996766447 Henry Cohn, 2026, needs more optimization.
16 528 0.364542752317 Henry Cohn, 2026, needs more optimization.
16 529 0.365192629510 Henry Cohn, 2026, needs more optimization.
16 530 0.365498715594 Henry Cohn, 2026, needs more optimization.
16 531 0.365822066303 Henry Cohn, 2026, needs more optimization.
16 532 0.366425368135 Henry Cohn, 2026, needs more optimization.
16 533 0.366970107261 Henry Cohn, 2026, needs more optimization.
16 534 0.367326144566 A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233, after some further optimization.
16 535 0.367806261339 Henry Cohn, 2026, needs more optimization.
16 536 0.368166411232 Henry Cohn, 2026, needs more optimization.
16 537 0.368383676862 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
16 538 0.369122459547 Henry Cohn, 2026, needs more optimization.
16 567 0.369248411466 Henry Cohn, 2026.
29⁢x2−8⁢x−1
16 575 0.375 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
8⁢x−3
16 583 0.375 Henry Cohn, 2026.
8⁢x−3
16 588 0.378265790137 Henry Cohn, 2026, needs more optimization.
16 589 0.378265790147 Henry Cohn, 2026, needs more optimization.
16 593 0.378265791204 Henry Cohn, 2026, needs more optimization.
16 594 0.378266158007 Henry Cohn, 2026, needs more optimization.
16 595 0.378266223586 Henry Cohn, 2026, needs more optimization.
16 596 0.378397115436 Henry Cohn, 2026, needs more optimization.
16 597 0.378397537728 Henry Cohn, 2026, needs more optimization.
16 598 0.379362265835 Henry Cohn, 2026, needs more optimization.
16 599 0.379362266884 Henry Cohn, 2026, needs more optimization.
16 601 0.380089227351 Henry Cohn, 2026, needs more optimization.
16 602 0.380181985023 Henry Cohn, 2026, needs more optimization.
16 603 0.380197971946 Henry Cohn, 2026, needs more optimization.
16 604 0.380633363837 Henry Cohn, 2026, needs more optimization.
16 605 0.380633532278 Henry Cohn, 2026, needs more optimization.
16 606 0.380714282748 Henry Cohn, 2026, needs more optimization.
16 607 0.381179141548 Henry Cohn, 2026, needs more optimization.
16 608 0.381179435416 Henry Cohn, 2026, needs more optimization.
16 609 0.381749843705 Henry Cohn, 2026, needs more optimization.
16 610 0.381990574904 Henry Cohn, 2026, needs more optimization.
16 611 0.382290420240 Henry Cohn, 2026, needs more optimization.
16 612 0.382737294051 Henry Cohn, 2026, needs more optimization.
16 613 0.383148875889 Henry Cohn, 2026, needs more optimization.
16 614 0.383459752997 Henry Cohn, 2026, needs more optimization.
16 615 0.383633333675 Henry Cohn, 2026, needs more optimization.
16 616 0.384232676764 Henry Cohn, 2026, needs more optimization.
16 617 0.384324042440 Henry Cohn, 2026, needs more optimization.
16 642 0.384615384616 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
13⁢x−5
16 643 0.386118036398 Henry Cohn, 2026, needs more optimization.
16 680 0.392857142858 Henry Cohn, 2026.
28⁢x−11
16 681 0.394879531732 Henry Cohn, 2026, needs more optimization.
16 682 0.395905977863 Henry Cohn, 2026, needs more optimization.
16 683 0.396406823965 Henry Cohn, 2026, needs more optimization.
16 684 0.396849267277 Henry Cohn, 2026, needs more optimization.
16 685 0.397220533342 Henry Cohn, 2026, needs more optimization.
16 715 0.397260273973 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
73⁢x−29
16 716 0.398933971983 Henry Cohn, 2026, needs more optimization.
16 768 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
16 769 0.4 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
16 771 0.4 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
5⁢x−2
16 772 0.400742606619 Henry Cohn, 2026, needs more optimization.
16 773 0.405991027137 Henry Cohn, 2026, needs more optimization.
16 775 0.405998727797 Henry Cohn, 2026, needs more optimization.
16 776 0.406145276070 Henry Cohn, 2026, needs more optimization.
16 780 0.406202653823 Henry Cohn, 2026, needs more optimization.
16 781 0.406407204108 Henry Cohn, 2026, needs more optimization.
16 782 0.407310559409 Henry Cohn, 2026, needs more optimization.
16 784 0.407550316932 Henry Cohn, 2026, needs more optimization.
16 785 0.407559401778 Henry Cohn, 2026, needs more optimization.
16 787 0.407693853476 Henry Cohn, 2026, needs more optimization.
16 788 0.408127819684 Henry Cohn, 2026, needs more optimization.
16 793 0.408464287892 Henry Cohn, 2026, needs more optimization.
16 794 0.408545936310 Henry Cohn, 2026, needs more optimization.
16 795 0.408556051158 Henry Cohn, 2026, needs more optimization.
16 796 0.408779890111 Henry Cohn, 2026, needs more optimization.
16 797 0.408942651020 Henry Cohn, 2026, needs more optimization.
16 798 0.409038256076 Henry Cohn, 2026, needs more optimization.
16 799 0.409104689215 Henry Cohn, 2026, needs more optimization.
16 800 0.409156398377 Henry Cohn, 2026, needs more optimization.
16 801 0.409175522137 Henry Cohn, 2026, needs more optimization.
16 802 0.409205307961 Henry Cohn, 2026, needs more optimization.
16 803 0.409231073525 Henry Cohn, 2026, needs more optimization.
16 804 0.409293943474 Henry Cohn, 2026, needs more optimization.
16 805 0.409353382684 Henry Cohn, 2026, needs more optimization.
16 806 0.409365174080 Henry Cohn, 2026, needs more optimization.
16 807 0.409374312669 Henry Cohn, 2026, needs more optimization.
16 808 0.409374388517 Henry Cohn, 2026, needs more optimization.
16 810 0.409374389059 Henry Cohn, 2026, needs more optimization.
16 811 0.411793489076 Henry Cohn, 2026, needs more optimization.
16 812 0.411876734681 Henry Cohn, 2026, needs more optimization.
16 813 0.411878442841 Henry Cohn, 2026, needs more optimization.
16 815 0.414310254871 Henry Cohn, 2026, needs more optimization.
16 816 0.414313295317 Henry Cohn, 2026, needs more optimization.
16 817 0.414319259282 Henry Cohn, 2026, needs more optimization.
16 818 0.414322836170 Henry Cohn, 2026, needs more optimization.
16 820 0.414346153608 Henry Cohn, 2026, needs more optimization.
16 823 0.414349793504 Henry Cohn, 2026, needs more optimization.
16 826 0.414684415460 Henry Cohn, 2026, needs more optimization.
16 827 0.414684822708 Henry Cohn, 2026, needs more optimization.
16 828 0.414688299212 Henry Cohn, 2026, needs more optimization.
16 829 0.414741579627 Henry Cohn, 2026, needs more optimization.
16 830 0.414747564696 Henry Cohn, 2026, needs more optimization.
16 831 0.414791310655 Henry Cohn, 2026, needs more optimization.
16 832 0.414858375611 Henry Cohn, 2026, needs more optimization.
16 833 0.414979478319 Henry Cohn, 2026, needs more optimization.
16 915 0.423076923077 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
26⁢x−11
16 916 0.425366936003 Henry Cohn, 2026, needs more optimization.
16 1024 0.428571428572 Subcode of a code of size 1056 from T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−3
17 35 0.044915529038 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3825⁢x3−289⁢x2−17⁢x+1
17 36 0.052701899358 Henry Cohn, 2025.
17 37 0.055949316790 Henry Cohn, 2026.
17 38 0.055983875620 Henry Cohn, 2025.
17 39 0.062879614874 Henry Cohn, 2024.
17 40 0.064964413617 Henry Cohn, 2025.
17 41 0.070153821556 Henry Cohn, 2025.
17 42 0.073269797523 Henry Cohn, 2025.
17 45 0.073591871415 Henry Cohn, 2023.
239⁢x2−4⁢x−1
17 46 0.080184930575 Henry Cohn, 2026.
17 52 0.084342587557 Henry Cohn, 2023.
188⁢x2−4⁢x−1
17 53 0.098937215086 Henry Cohn, 2024.
2304⁢x4−96⁢x3−95⁢x2−2⁢x+1
17 55 0.099686435548 Henry Cohn, 2026.
153⁢x4+480⁢x3−150⁢x2+1
17 56 0.102993455487 Henry Cohn, 2026.
17 64 0.111111111112 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
17 65 0.120819518077 Henry Cohn, 2026.
17 66 0.124823699080 Henry Cohn, 2026.
17 67 0.127087890038 Henry Cohn, 2026.
17 68 0.127206280067 Henry Cohn, 2026, needs more optimization.
17 69 0.127241105668 Henry Cohn, 2026.
17 71 0.127270310008 Henry Cohn, 2025.
17 74 0.127284404862 Henry Cohn, 2025.
17 76 0.127284594471 Henry Cohn, 2025.
17 77 0.127301957060 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
17 78 0.135230868852 Henry Cohn, 2026, needs more optimization.
17 79 0.142557324566 Henry Cohn, 2026, needs more optimization.
17 80 0.147987559048 Henry Cohn, 2026, needs more optimization.
17 81 0.149882873176 Henry Cohn, 2026, needs more optimization.
17 82 0.149951006483 Henry Cohn, 2026, needs more optimization.
17 86 0.149999887893 Henry Cohn, 2026, needs more optimization.
17 87 0.151340636611 Henry Cohn, 2026, needs more optimization.
17 88 0.156527132256 Henry Cohn, 2026, needs more optimization.
17 89 0.158629294707 Henry Cohn, 2026, needs more optimization.
17 90 0.163948884050 Henry Cohn, 2026, needs more optimization.
17 91 0.167225196650 Henry Cohn, 2026, needs more optimization.
17 92 0.167349745004 Henry Cohn, 2026, needs more optimization.
17 93 0.167542852217 Henry Cohn, 2026, needs more optimization.
17 94 0.167882241424 Henry Cohn, 2026, needs more optimization.
17 95 0.168038484208 Henry Cohn, 2026, needs more optimization.
17 96 0.168351687272 Henry Cohn, 2026, needs more optimization.
17 97 0.168526080939 Henry Cohn, 2026, needs more optimization.
17 98 0.168598785968 Henry Cohn, 2026, needs more optimization.
17 99 0.168667155022 Henry Cohn, 2026, needs more optimization.
17 100 0.168671171604 Henry Cohn, 2026, needs more optimization.
17 101 0.168688903748 Henry Cohn, 2026, needs more optimization.
17 102 0.169861595736 Henry Cohn, 2026, needs more optimization.
17 104 0.170751369934 Henry Cohn, 2026, needs more optimization.
17 105 0.170751990216 Henry Cohn, 2026, needs more optimization.
17 106 0.170751990218 Henry Cohn, 2026, needs more optimization.
17 107 0.170759868811 Henry Cohn, 2026, needs more optimization.
17 108 0.175086042960 Henry Cohn, 2026, needs more optimization.
17 109 0.179282321815 Henry Cohn, 2026, needs more optimization.
17 110 0.180269680392 Henry Cohn, 2026, needs more optimization.
17 111 0.182397366102 Henry Cohn, 2026, needs more optimization.
17 115 0.184252183279 Henry Cohn, 2026.
17 116 0.184847526037 Henry Cohn, 2026, needs more optimization.
17 117 0.186660513707 Henry Cohn, 2026, needs more optimization.
17 118 0.187738674484 Henry Cohn, 2026, needs more optimization.
17 119 0.189940926437 Henry Cohn, 2026, needs more optimization.
17 120 0.190640777156 Henry Cohn, 2026, needs more optimization.
17 121 0.192288823399 Henry Cohn, 2026, needs more optimization.
17 122 0.192374688767 Henry Cohn, 2026, needs more optimization.
17 123 0.192449019139 Henry Cohn, 2026, needs more optimization.
17 124 0.192956780977 Henry Cohn, 2026, needs more optimization.
17 125 0.192981578828 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 126 0.192986064278 Henry Cohn, 2026, needs more optimization.
17 127 0.193832467127 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 128 0.196253513246 Henry Cohn, 2026, needs more optimization.
17 129 0.196782248787 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
17 130 0.197511599382 Henry Cohn, 2026, needs more optimization.
17 131 0.198977669576 Henry Cohn, 2026, needs more optimization.
17 132 0.199042801573 Henry Cohn, 2026, needs more optimization.
17 133 0.199556912163 Henry Cohn, 2026, needs more optimization.
17 134 0.199787163866 Henry Cohn, 2026, needs more optimization.
17 135 0.199854744383 Henry Cohn, 2026, needs more optimization.
17 136 0.199968458583 Henry Cohn, 2026, needs more optimization.
17 137 0.199987855897 Henry Cohn, 2026, needs more optimization.
17 138 0.200011208550 Henry Cohn, 2026, needs more optimization.
17 139 0.200152198943 Henry Cohn, 2026, needs more optimization.
17 140 0.200232133402 Henry Cohn, 2026, needs more optimization.
17 141 0.202594126282 Henry Cohn, 2026, needs more optimization.
17 142 0.202849583915 Henry Cohn, 2026, needs more optimization.
17 143 0.202861011779 Henry Cohn, 2026, needs more optimization.
17 144 0.202881188804 Henry Cohn, 2026, needs more optimization.
17 146 0.202890799240 Henry Cohn, 2026, needs more optimization.
17 148 0.202893418199 Henry Cohn, 2026, needs more optimization.
17 150 0.202894858760 Henry Cohn, 2026, needs more optimization.
17 151 0.202899026653 Henry Cohn, 2026, needs more optimization.
17 153 0.202909339588 Henry Cohn, 2026, needs more optimization.
17 154 0.202910810791 Henry Cohn, 2026, needs more optimization.
17 155 0.202910811935 Henry Cohn, 2026, needs more optimization.
17 156 0.202911272393 Henry Cohn, 2026, needs more optimization.
17 162 0.202913709779 Henry Cohn, 2026.
44⁢x2−4⁢x−1
17 163 0.202914134197 Henry Cohn, 2026, needs more optimization.
17 164 0.202916942575 Henry Cohn, 2026, needs more optimization.
17 165 0.203269398832 Henry Cohn, 2026, needs more optimization.
17 166 0.209283250769 Henry Cohn, 2026, needs more optimization.
17 167 0.209413222423 Henry Cohn, 2026, needs more optimization.
17 168 0.209696026939 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
17 177 0.214580576913 Henry Cohn, 2026.
59⁢x2−8⁢x−1
17 178 0.215890678299 Henry Cohn, 2026, needs more optimization.
17 179 0.223732515175 Henry Cohn, 2026, needs more optimization.
17 180 0.224759879600 Henry Cohn, 2026, needs more optimization.
17 181 0.227585848114 Henry Cohn, 2026, needs more optimization.
17 190 0.228481712325 Henry Cohn, 2026.
17 192 0.228757976713 Henry Cohn, 2026, needs more optimization.
17 193 0.233272136703 Henry Cohn, 2026, needs more optimization.
17 194 0.234602056768 Henry Cohn, 2026, needs more optimization.
17 195 0.235727130538 Henry Cohn, 2026, needs more optimization.
17 196 0.237300483965 Henry Cohn, 2026, needs more optimization.
17 197 0.238196700986 Henry Cohn, 2026, needs more optimization.
17 198 0.238369443363 Henry Cohn, 2026, needs more optimization.
17 199 0.238930481613 Henry Cohn, 2026, needs more optimization.
17 200 0.239014609954 Henry Cohn, 2026, needs more optimization.
17 201 0.239060954511 Henry Cohn, 2026, needs more optimization.
17 202 0.241470646979 Henry Cohn, 2026, needs more optimization.
17 203 0.242177530318 Henry Cohn, 2026, needs more optimization.
17 204 0.242732974420 Henry Cohn, 2026, needs more optimization.
17 205 0.243353345923 Henry Cohn, 2026, needs more optimization.
17 206 0.243655880899 Henry Cohn, 2026, needs more optimization.
17 207 0.244111432229 Henry Cohn, 2026, needs more optimization.
17 208 0.244388560569 Henry Cohn, 2026, needs more optimization.
17 209 0.244633440533 Henry Cohn, 2026, needs more optimization.
17 210 0.244930985388 Henry Cohn, 2026, needs more optimization.
17 211 0.245265660579 Henry Cohn, 2026, needs more optimization.
17 212 0.245550716330 Henry Cohn, 2026, needs more optimization.
17 213 0.245841976894 Henry Cohn, 2026, needs more optimization.
17 214 0.246006656395 Henry Cohn, 2026, needs more optimization.
17 215 0.246204941872 Henry Cohn, 2026, needs more optimization.
17 216 0.246521443732 Henry Cohn, 2026, needs more optimization.
17 217 0.246827994054 Henry Cohn, 2026, needs more optimization.
17 218 0.247258273707 Henry Cohn, 2026, needs more optimization.
17 219 0.247594087513 Henry Cohn, 2026, needs more optimization.
17 220 0.247773216871 Henry Cohn, 2026, needs more optimization.
17 221 0.247906130260 Henry Cohn, 2026, needs more optimization.
17 222 0.248038203280 Henry Cohn, 2026, needs more optimization.
17 223 0.248241434329 Henry Cohn, 2026, needs more optimization.
17 224 0.248474831094 Henry Cohn, 2026, needs more optimization.
17 225 0.248624025888 Henry Cohn, 2026, needs more optimization.
17 226 0.248718093043 Henry Cohn, 2026, needs more optimization.
17 227 0.248818511662 Henry Cohn, 2026, needs more optimization.
17 228 0.248923945467 Henry Cohn, 2026, needs more optimization.
17 229 0.249062262842 Henry Cohn, 2026, needs more optimization.
17 230 0.249136193147 Henry Cohn, 2026, needs more optimization.
17 231 0.249178401699 Henry Cohn, 2026, needs more optimization.
17 232 0.249215034542 Henry Cohn, 2026, needs more optimization.
17 233 0.249265920016 Henry Cohn, 2026, needs more optimization.
17 234 0.249304511735 Henry Cohn, 2026, needs more optimization.
17 235 0.249353971596 Henry Cohn, 2026, needs more optimization.
17 236 0.249391044809 Henry Cohn, 2026, needs more optimization.
17 237 0.249493546260 Henry Cohn, 2026, needs more optimization.
17 238 0.249518929284 Henry Cohn, 2026, needs more optimization.
17 239 0.249633073466 Henry Cohn, 2026, needs more optimization.
17 240 0.249681714047 Henry Cohn, 2026, needs more optimization.
17 241 0.249785205582 Henry Cohn, 2026, needs more optimization.
17 242 0.249805618448 Henry Cohn, 2026, needs more optimization.
17 243 0.249837474501 Henry Cohn, 2026, needs more optimization.
17 244 0.249848692223 Henry Cohn, 2026, needs more optimization.
17 245 0.249861344609 Henry Cohn, 2026, needs more optimization.
17 246 0.249880357304 Henry Cohn, 2026, needs more optimization.
17 247 0.249901365939 Henry Cohn, 2026, needs more optimization.
17 248 0.249911998484 Henry Cohn, 2026, needs more optimization.
17 249 0.249924171542 Henry Cohn, 2026, needs more optimization.
17 250 0.249928131167 Henry Cohn, 2026, needs more optimization.
17 251 0.249975159625 Henry Cohn, 2026, needs more optimization.
17 253 0.249997107913 Henry Cohn, 2026, needs more optimization.
17 254 0.249997107920 Henry Cohn, 2026, needs more optimization.
17 255 0.249998856322 Henry Cohn, 2026, needs more optimization.
17 256 0.249998856332 Henry Cohn, 2026, needs more optimization.
17 257 0.249999029843 Henry Cohn, 2026, needs more optimization.
17 258 0.249999292042 Henry Cohn, 2026, needs more optimization.
17 259 0.249999292043 Henry Cohn, 2026, needs more optimization.
17 260 0.249999494968 Henry Cohn, 2026, needs more optimization.
17 261 0.249999495165 Henry Cohn, 2026, needs more optimization.
17 262 0.249999496458 Henry Cohn, 2026, needs more optimization.
17 263 0.249999497844 Henry Cohn, 2026, needs more optimization.
17 264 0.249999497846 Henry Cohn, 2026, needs more optimization.
17 284 0.249999885378 Henry Cohn, 2026, needs more optimization.
17 285 0.249999889767 Henry Cohn, 2026, needs more optimization.
17 292 0.25 Henry Cohn, 2026.
4⁢x−1
17 293 0.250000009127 Henry Cohn, 2026, needs more optimization.
17 294 0.250000045907 Henry Cohn, 2026, needs more optimization.
17 295 0.250769445804 Henry Cohn, 2026, needs more optimization.
17 296 0.253949329853 Henry Cohn, 2026, needs more optimization.
17 297 0.255601472253 Henry Cohn, 2026, needs more optimization.
17 298 0.259856876489 Henry Cohn, 2026, needs more optimization.
17 299 0.261085287635 Henry Cohn, 2026, needs more optimization.
17 300 0.261085336767 Henry Cohn, 2026, needs more optimization.
17 301 0.261087158996 Henry Cohn, 2026, needs more optimization.
17 302 0.261087765066 Henry Cohn, 2026, needs more optimization.
17 303 0.261088441255 Henry Cohn, 2026, needs more optimization.
17 304 0.261089733804 Henry Cohn, 2026, needs more optimization.
17 305 0.261090762758 Henry Cohn, 2026, needs more optimization.
17 306 0.261091588230 Henry Cohn, 2026, needs more optimization.
17 307 0.261092231325 Henry Cohn, 2026, needs more optimization.
17 308 0.261094001700 Henry Cohn, 2026, needs more optimization.
17 309 0.261094114302 Henry Cohn, 2026, needs more optimization.
17 310 0.261094118382 Henry Cohn, 2026, needs more optimization.
17 311 0.261094123147 Henry Cohn, 2026, needs more optimization.
17 312 0.261094127870 Henry Cohn, 2026, needs more optimization.
17 313 0.261094127951 Henry Cohn, 2026, needs more optimization.
17 314 0.261094129727 Henry Cohn, 2026, needs more optimization.
17 315 0.261094129997 Henry Cohn, 2026, needs more optimization.
17 316 0.261094133378 Henry Cohn, 2026, needs more optimization.
17 317 0.261094135790 Henry Cohn, 2026, needs more optimization.
17 318 0.261094137455 Henry Cohn, 2026, needs more optimization.
17 319 0.261094140536 Henry Cohn, 2026, needs more optimization.
17 320 0.261094143848 Henry Cohn, 2026, needs more optimization.
17 321 0.281913036169 Henry Cohn, 2026, needs more optimization.
17 322 0.286550122965 Henry Cohn, 2026, needs more optimization.
17 323 0.289492000465 Henry Cohn, 2026, needs more optimization.
17 324 0.291642147986 Henry Cohn, 2026, needs more optimization.
17 325 0.293577577268 Henry Cohn, 2026, needs more optimization.
17 352 0.294117647059 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
17⁢x−5
17 353 0.296535165409 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
8⁢x2+x−1
17 354 0.303054210944 Henry Cohn, 2026, needs more optimization.
17 355 0.304366843817 Henry Cohn, 2026, needs more optimization.
17 356 0.305238436676 Henry Cohn, 2026, needs more optimization.
17 357 0.306093176694 Henry Cohn, 2026, needs more optimization.
17 358 0.306688821556 Henry Cohn, 2026, needs more optimization.
17 359 0.307431989275 Henry Cohn, 2026, needs more optimization.
17 360 0.308031916973 Henry Cohn, 2026, needs more optimization.
17 361 0.308321977495 Henry Cohn, 2026, needs more optimization.
17 362 0.308713746196 Henry Cohn, 2026, needs more optimization.
17 363 0.309147467592 Henry Cohn, 2026, needs more optimization.
17 364 0.309522584536 Henry Cohn, 2026, needs more optimization.
17 365 0.309893244928 Henry Cohn, 2026, needs more optimization.
17 366 0.310326698847 Henry Cohn, 2026, needs more optimization.
17 367 0.310570751029 Henry Cohn, 2026, needs more optimization.
17 368 0.310892865539 Henry Cohn, 2026, needs more optimization.
17 369 0.311196812673 Henry Cohn, 2026, needs more optimization.
17 370 0.311456278517 Henry Cohn, 2026, needs more optimization.
17 371 0.311796494659 Henry Cohn, 2026, needs more optimization.
17 372 0.312062592910 Henry Cohn, 2026, needs more optimization.
17 373 0.312278861220 Henry Cohn, 2026, needs more optimization.
17 374 0.312606521202 Henry Cohn, 2026, needs more optimization.
17 375 0.312911979586 Henry Cohn, 2026, needs more optimization.
17 376 0.313083595443 Henry Cohn, 2026, needs more optimization.
17 377 0.313357447443 Henry Cohn, 2026, needs more optimization.
17 378 0.313536738639 Henry Cohn, 2026, needs more optimization.
17 379 0.313732464800 Henry Cohn, 2026, needs more optimization.
17 380 0.313949573533 Henry Cohn, 2026, needs more optimization.
17 381 0.314179492414 Henry Cohn, 2026, needs more optimization.
17 382 0.314316910013 Henry Cohn, 2026, needs more optimization.
17 383 0.314496104585 Henry Cohn, 2026, needs more optimization.
17 384 0.314683590490 Henry Cohn, 2026, needs more optimization.
17 385 0.314908168456 Henry Cohn, 2026, needs more optimization.
17 386 0.315165460008 Henry Cohn, 2026, needs more optimization.
17 387 0.315312005663 Henry Cohn, 2026, needs more optimization.
17 388 0.315541064492 Henry Cohn, 2026, needs more optimization.
17 389 0.315791026034 Henry Cohn, 2026, needs more optimization.
17 390 0.316045379523 Henry Cohn, 2026, needs more optimization.
17 391 0.316325399990 Henry Cohn, 2026, needs more optimization.
17 392 0.316533322294 Henry Cohn, 2026, needs more optimization.
17 393 0.316765604715 Henry Cohn, 2026, needs more optimization.
17 394 0.317037733584 Henry Cohn, 2026, needs more optimization.
17 395 0.317455634187 Henry Cohn, 2026, needs more optimization.
17 396 0.317582782487 Henry Cohn, 2026, needs more optimization.
17 397 0.317677025938 Henry Cohn, 2026, needs more optimization.
17 398 0.317836887691 Henry Cohn, 2026, needs more optimization.
17 399 0.317871472497 Henry Cohn, 2026, needs more optimization.
17 400 0.318018885073 Henry Cohn, 2026, needs more optimization.
17 401 0.318071248408 Henry Cohn, 2026, needs more optimization.
17 402 0.318209695085 Henry Cohn, 2026, needs more optimization.
17 403 0.318264771224 Henry Cohn, 2026, needs more optimization.
17 404 0.318329129031 Henry Cohn, 2026, needs more optimization.
17 405 0.318359481109 Henry Cohn, 2026, needs more optimization.
17 406 0.318520583521 Henry Cohn, 2026, needs more optimization.
17 407 0.318577095696 Henry Cohn, 2026, needs more optimization.
17 408 0.318676544378 Henry Cohn, 2026, needs more optimization.
17 409 0.318766263332 Henry Cohn, 2026, needs more optimization.
17 410 0.318870411921 Henry Cohn, 2026, needs more optimization.
17 411 0.318942520152 Henry Cohn, 2026, needs more optimization.
17 412 0.318993706254 Henry Cohn, 2026, needs more optimization.
17 434 0.319025504452 Henry Cohn, 2026, needs more optimization.
17 435 0.320843412971 Henry Cohn, 2026, needs more optimization.
17 436 0.322285603017 Henry Cohn, 2026, needs more optimization.
17 437 0.322623839615 Henry Cohn, 2026, needs more optimization.
17 438 0.323530361415 Henry Cohn, 2026, needs more optimization.
17 439 0.323875331574 Henry Cohn, 2026, needs more optimization.
17 440 0.324304801178 Henry Cohn, 2026, needs more optimization.
17 441 0.324671092754 Henry Cohn, 2026, needs more optimization.
17 442 0.325040748627 Henry Cohn, 2026, needs more optimization.
17 443 0.325685307496 Henry Cohn, 2026, needs more optimization.
17 444 0.326566425656 Henry Cohn, 2026, needs more optimization.
17 445 0.326830579423 Henry Cohn, 2026, needs more optimization.
17 446 0.327291045476 Henry Cohn, 2026, needs more optimization.
17 447 0.327506470220 Henry Cohn, 2026, needs more optimization.
17 448 0.327648888589 Henry Cohn, 2026, needs more optimization.
17 449 0.327798878247 Henry Cohn, 2026, needs more optimization.
17 450 0.329748484248 Henry Cohn, 2026, needs more optimization.
17 451 0.330606260298 Henry Cohn, 2026, needs more optimization.
17 452 0.331444024543 Henry Cohn, 2026, needs more optimization.
17 453 0.332563467409 Henry Cohn, 2026, needs more optimization.
17 546 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
17 578 0.333333333334 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
17 579 0.345190388449 Henry Cohn, 2026, needs more optimization.
17 580 0.345191408397 Henry Cohn, 2026, needs more optimization.
17 581 0.345192255108 Henry Cohn, 2026, needs more optimization.
17 582 0.345292988462 Henry Cohn, 2026, needs more optimization.
17 583 0.345295375957 Henry Cohn, 2026, needs more optimization.
17 586 0.345313998004 Henry Cohn, 2026, needs more optimization.
17 589 0.345318862835 Henry Cohn, 2026, needs more optimization.
17 591 0.345319819552 Henry Cohn, 2026, needs more optimization.
17 592 0.349709097758 Henry Cohn, 2026, needs more optimization.
17 593 0.349760452774 Henry Cohn, 2026, needs more optimization.
17 594 0.349760452800 Henry Cohn, 2026, needs more optimization.
17 596 0.349766929116 Henry Cohn, 2026, needs more optimization.
17 597 0.349767253113 Henry Cohn, 2026, needs more optimization.
17 599 0.349791312612 Henry Cohn, 2026, needs more optimization.
17 600 0.350124818207 Henry Cohn, 2026, needs more optimization.
17 601 0.351971326767 Henry Cohn, 2026, needs more optimization.
17 603 0.352118258238 Henry Cohn, 2026, needs more optimization.
17 604 0.352142286536 Henry Cohn, 2026, needs more optimization.
17 605 0.352142298229 Henry Cohn, 2026, needs more optimization.
17 606 0.352352878524 Henry Cohn, 2026, needs more optimization.
17 607 0.352366519606 Henry Cohn, 2026, needs more optimization.
17 608 0.352427782371 Henry Cohn, 2026, needs more optimization.
17 609 0.352558435204 Henry Cohn, 2026, needs more optimization.
17 610 0.352561589292 Henry Cohn, 2026, needs more optimization.
17 611 0.352566157113 Henry Cohn, 2026, needs more optimization.
17 612 0.352572089785 Henry Cohn, 2026, needs more optimization.
17 613 0.353050925872 Henry Cohn, 2026, needs more optimization.
17 614 0.353066801049 Henry Cohn, 2026, needs more optimization.
17 615 0.353184395538 Henry Cohn, 2026, needs more optimization.
17 616 0.353188688613 Henry Cohn, 2026, needs more optimization.
17 617 0.353195983374 Henry Cohn, 2026, needs more optimization.
17 618 0.353198498691 Henry Cohn, 2026, needs more optimization.
17 619 0.353213425112 Henry Cohn, 2026, needs more optimization.
17 620 0.353472050936 Henry Cohn, 2026, needs more optimization.
17 622 0.353511076336 Henry Cohn, 2026, needs more optimization.
17 623 0.353970621418 Henry Cohn, 2026, needs more optimization.
17 624 0.354864628934 Henry Cohn, 2026, needs more optimization.
17 625 0.354872894419 Henry Cohn, 2026, needs more optimization.
17 626 0.354875305609 Henry Cohn, 2026, needs more optimization.
17 628 0.354933901543 Henry Cohn, 2026, needs more optimization.
17 629 0.354937723129 Henry Cohn, 2026, needs more optimization.
17 630 0.354950058946 Henry Cohn, 2026, needs more optimization.
17 631 0.354964739249 Henry Cohn, 2026, needs more optimization.
17 632 0.354964744502 Henry Cohn, 2026, needs more optimization.
17 633 0.354988753241 Henry Cohn, 2026, needs more optimization.
17 634 0.355036416033 Henry Cohn, 2026, needs more optimization.
17 635 0.355036502045 Henry Cohn, 2026, needs more optimization.
17 636 0.362516962038 Henry Cohn, 2026, needs more optimization.
17 637 0.362531067348 Henry Cohn, 2026, needs more optimization.
17 638 0.362545003951 Henry Cohn, 2026, needs more optimization.
17 639 0.362555295111 Henry Cohn, 2026, needs more optimization.
17 640 0.362555295113 Henry Cohn, 2026, needs more optimization.
17 641 0.362557322802 Henry Cohn, 2026, needs more optimization.
17 642 0.362561996077 Henry Cohn, 2026, needs more optimization.
17 643 0.362561996182 Henry Cohn, 2026, needs more optimization.
17 644 0.362565783391 Henry Cohn, 2026, needs more optimization.
17 645 0.362574858714 Henry Cohn, 2026, needs more optimization.
17 646 0.362587518332 Henry Cohn, 2026, needs more optimization.
17 647 0.362602699521 Henry Cohn, 2026, needs more optimization.
17 648 0.362661419170 Henry Cohn, 2026, needs more optimization.
17 649 0.362670060966 Henry Cohn, 2026, needs more optimization.
17 650 0.362736934484 Henry Cohn, 2026, needs more optimization.
17 654 0.362789266505 Henry Cohn, 2026, needs more optimization.
17 656 0.362795290741 Henry Cohn, 2026, needs more optimization.
17 657 0.362795290847 Henry Cohn, 2026, needs more optimization.
17 658 0.362827416643 Henry Cohn, 2026, needs more optimization.
17 659 0.362829207504 Henry Cohn, 2026, needs more optimization.
17 660 0.362832028779 Henry Cohn, 2026, needs more optimization.
17 662 0.362839195677 Henry Cohn, 2026, needs more optimization.
17 663 0.362839195689 Henry Cohn, 2026, needs more optimization.
17 664 0.362841182590 Henry Cohn, 2026, needs more optimization.
17 667 0.362860806585 Henry Cohn, 2026, needs more optimization.
17 668 0.362864986661 Henry Cohn, 2026, needs more optimization.
17 669 0.362867874828 Henry Cohn, 2026, needs more optimization.
17 670 0.362875807426 Henry Cohn, 2026, needs more optimization.
17 671 0.362875807460 Henry Cohn, 2026, needs more optimization.
17 672 0.362879059235 Henry Cohn, 2026, needs more optimization.
17 673 0.362903471279 Henry Cohn, 2026, needs more optimization.
17 674 0.362919472574 Henry Cohn, 2026, needs more optimization.
17 676 0.362934229033 Henry Cohn, 2026, needs more optimization.
17 678 0.362998124919 Henry Cohn, 2026, needs more optimization.
17 682 0.363026714873 Henry Cohn, 2026, needs more optimization.
17 683 0.363062384155 Henry Cohn, 2026, needs more optimization.
17 686 0.363069128037 Henry Cohn, 2026, needs more optimization.
17 687 0.363069145870 Henry Cohn, 2026, needs more optimization.
17 688 0.363196603953 Henry Cohn, 2026, needs more optimization.
17 691 0.363201935541 Henry Cohn, 2026, needs more optimization.
17 696 0.363215424619 Henry Cohn, 2026, needs more optimization.
17 701 0.363217389424 Henry Cohn, 2026, needs more optimization.
17 702 0.363226244850 Henry Cohn, 2026, needs more optimization.
17 703 0.363226244914 Henry Cohn, 2026, needs more optimization.
17 708 0.363226246036 Henry Cohn, 2026, needs more optimization.
17 709 0.363232864281 Henry Cohn, 2026, needs more optimization.
17 710 0.363235260125 Henry Cohn, 2026, needs more optimization.
17 711 0.363253701228 Henry Cohn, 2026, needs more optimization.
17 712 0.363265950929 Henry Cohn, 2026, needs more optimization.
17 714 0.363282758459 Henry Cohn, 2026, needs more optimization.
17 716 0.363290074720 Henry Cohn, 2026, needs more optimization.
17 717 0.363290303534 Henry Cohn, 2026, needs more optimization.
17 720 0.363290310842 Henry Cohn, 2026, needs more optimization.
17 724 0.363299357394 Henry Cohn, 2026, needs more optimization.
17 726 0.363305955175 Henry Cohn, 2026, needs more optimization.
17 727 0.363312680705 Henry Cohn, 2026, needs more optimization.
17 728 0.363317267771 Henry Cohn, 2026, needs more optimization.
17 729 0.363317299068 Henry Cohn, 2026, needs more optimization.
17 730 0.363318957561 Henry Cohn, 2026, needs more optimization.
17 731 0.363318960015 Henry Cohn, 2026, needs more optimization.
17 732 0.363318965953 Henry Cohn, 2026, needs more optimization.
17 733 0.363318968175 Henry Cohn, 2026, needs more optimization.
17 734 0.363320660663 Henry Cohn, 2026, needs more optimization.
17 735 0.363321718888 Henry Cohn, 2026, needs more optimization.
17 736 0.363321724467 Henry Cohn, 2026, needs more optimization.
17 737 0.363325617236 Henry Cohn, 2026, needs more optimization.
17 739 0.363326802100 Henry Cohn, 2026, needs more optimization.
17 742 0.363327043396 Henry Cohn, 2026, needs more optimization.
17 744 0.363332275949 Henry Cohn, 2026, needs more optimization.
17 747 0.363338751387 Henry Cohn, 2026, needs more optimization.
17 749 0.363338789439 Henry Cohn, 2026, needs more optimization.
17 751 0.363338802847 Henry Cohn, 2026, needs more optimization.
17 752 0.363338824276 Henry Cohn, 2026, needs more optimization.
17 753 0.363354405169 Henry Cohn, 2026, needs more optimization.
17 754 0.363354405238 Henry Cohn, 2026, needs more optimization.
17 755 0.371240308917 Henry Cohn, 2026, needs more optimization.
17 757 0.371399719351 Henry Cohn, 2026, needs more optimization.
17 758 0.371470313618 Henry Cohn, 2026, needs more optimization.
17 759 0.371474811118 Henry Cohn, 2026, needs more optimization.
17 760 0.371612893067 Henry Cohn, 2026, needs more optimization.
17 761 0.371612901145 Henry Cohn, 2026, needs more optimization.
17 765 0.371632178650 Henry Cohn, 2026, needs more optimization.
17 766 0.371636099652 Henry Cohn, 2026, needs more optimization.
17 768 0.378516119721 Henry Cohn, 2026, needs more optimization.
17 1024 0.384615384616 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
13⁢x−5
18 37 0.042671058118 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
4608⁢x3−324⁢x2−18⁢x+1
18 38 0.050097352046 Henry Cohn, 2025.
18 39 0.055224148787 Henry Cohn, 2025.
18 40 0.055678193348 Henry Cohn, 2025.
1856⁢x4+736⁢x3+204⁢x2+4⁢x−1
18 41 0.060967744952 Henry Cohn, 2023.
18 42 0.063513513654 Henry Cohn, 2023.
18 43 0.066629754705 Henry Cohn, 2025.
18 44 0.066804066179 Henry Cohn, 2023.
18 45 0.071480323505 Henry Cohn, 2026.
18 46 0.073552043366 Henry Cohn, 2025.
18 47 0.073575768177 Henry Cohn, 2025.
Minimal polynomial listed in plain text data
18 48 0.074706792917 Henry Cohn, 2024.
49250304⁢x8−30019584⁢x7−3769088⁢x6−1665536⁢x5+436432⁢x4+8256⁢x3−3792⁢x2+9
18 50 0.078219048073 Henry Cohn, 2025.
368⁢x2−16⁢x−1
18 51 0.084307082149 Henry Cohn, 2026, needs more optimization.
18 54 0.084331756971 Henry Cohn, 2026, needs more optimization.
18 55 0.087707155784 Henry Cohn, 2025.
18 57 0.092724727985 Henry Cohn, 2025.
332⁢x2−20⁢x−1
18 59 0.096317631192 Henry Cohn, 2025.
18 60 0.096621974569 Henry Cohn, 2025.
1392⁢x5+5600⁢x4−2304⁢x3+152⁢x2+12⁢x−1
18 69 0.101456854890 Henry Cohn, 2024.
176⁢x2−8⁢x−1
18 71 0.107360417201 Henry Cohn, 2026.
18 72 0.109540130282 Henry Cohn, 2026.
18 73 0.117134464846 Henry Cohn, 2026, needs more optimization.
18 74 0.120049808519 Henry Cohn, 2026, needs more optimization.
18 75 0.120367585573 Henry Cohn, 2026, needs more optimization.
18 80 0.121417162017 Ilmari Vahteristo, 2026.
31⁢x2−12⁢x+1
18 81 0.126904281672 Henry Cohn, 2026, needs more optimization.
18 82 0.127626483898 Henry Cohn, 2026, needs more optimization.
18 83 0.129098755666 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 84 0.130579477836 Henry Cohn, 2026, needs more optimization.
18 85 0.132293288623 Henry Cohn, 2026, needs more optimization.
18 86 0.132700025640 Henry Cohn, 2026, needs more optimization.
18 87 0.133639152637 Henry Cohn, 2026, needs more optimization.
18 88 0.134264346430 Henry Cohn, 2025.
18 96 0.142857142858 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
18 97 0.152402949200 Henry Cohn, 2026.
16⁢x2−9⁢x+1
18 98 0.155249851767 Henry Cohn, 2026.
18 100 0.157894736843 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
19⁢x−3
18 101 0.161087011866 Henry Cohn, 2026.
52⁢x2−27⁢x+3
18 104 0.162407002682 Henry Cohn, 2026.
18 105 0.164921962691 Henry Cohn, 2026, needs more optimization.
18 106 0.166070837083 Henry Cohn, 2026, needs more optimization.
18 108 0.166586736179 Henry Cohn, 2026, needs more optimization.
18 109 0.167620540781 Henry Cohn, 2026, needs more optimization.
18 110 0.168468671425 Henry Cohn, 2026, needs more optimization.
18 111 0.169252744043 Henry Cohn, 2026, needs more optimization.
18 112 0.169845856324 Henry Cohn, 2026, needs more optimization.
18 113 0.170643155962 Henry Cohn, 2026, needs more optimization.
18 114 0.172123407013 Henry Cohn, 2026, needs more optimization.
18 115 0.172920395517 Henry Cohn, 2026, needs more optimization.
18 116 0.174475313522 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 117 0.177748575135 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
18 118 0.183010965768 Henry Cohn, 2026, needs more optimization.
18 119 0.184589004858 Henry Cohn, 2026, needs more optimization.
18 120 0.185137714594 Henry Cohn, 2026, needs more optimization.
18 121 0.185552099379 Henry Cohn, 2026, needs more optimization.
18 122 0.186958434117 Henry Cohn, 2026, needs more optimization.
18 123 0.188113485779 Henry Cohn, 2026, needs more optimization.
18 128 0.188405797102 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
69⁢x−13
18 129 0.188801925845 Henry Cohn, 2026, needs more optimization.
18 130 0.188961019797 Henry Cohn, 2026, needs more optimization.
18 131 0.190523556591 Henry Cohn, 2026, needs more optimization.
18 132 0.191489361703 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x−9
18 133 0.193070622507 Henry Cohn, 2026, needs more optimization.
18 134 0.193719906753 Henry Cohn, 2026, needs more optimization.
18 135 0.194298207706 Henry Cohn, 2026, needs more optimization.
18 136 0.194621813477 Henry Cohn, 2026, needs more optimization.
18 137 0.194954296396 Henry Cohn, 2026, needs more optimization.
18 138 0.195229084001 Henry Cohn, 2026, needs more optimization.
18 140 0.195281232517 Henry Cohn, 2026, needs more optimization.
18 141 0.196394547566 Henry Cohn, 2026, needs more optimization.
18 142 0.196568683980 Henry Cohn, 2026, needs more optimization.
18 143 0.196782414195 Henry Cohn, 2026, needs more optimization.
18 144 0.197035851642 Henry Cohn, 2026, needs more optimization.
18 145 0.197324459260 Henry Cohn, 2026, needs more optimization.
18 146 0.197533592804 Henry Cohn, 2026, needs more optimization.
18 147 0.197851582967 Henry Cohn, 2026, needs more optimization.
18 148 0.198476046456 Henry Cohn, 2026, needs more optimization.
18 149 0.198690421545 Henry Cohn, 2026, needs more optimization.
18 150 0.199162218543 Henry Cohn, 2026, needs more optimization.
18 151 0.199542820809 Henry Cohn, 2026, needs more optimization.
18 152 0.200047282793 Henry Cohn, 2026, needs more optimization.
18 153 0.200206380696 Henry Cohn, 2026, needs more optimization.
18 154 0.200206946436 Henry Cohn, 2026, needs more optimization.
18 155 0.200715299240 Henry Cohn, 2026, needs more optimization.
18 156 0.201466840595 Henry Cohn, 2026, needs more optimization.
18 157 0.201537049669 Henry Cohn, 2026, needs more optimization.
18 158 0.201574760148 Henry Cohn, 2026, needs more optimization.
18 159 0.201591813556 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
18 160 0.201667601115 Henry Cohn, 2026, needs more optimization.
18 161 0.202046880323 Henry Cohn, 2026, needs more optimization.
18 162 0.202215061649 Henry Cohn, 2026, needs more optimization.
18 163 0.202373950268 Henry Cohn, 2026, needs more optimization.
18 164 0.202373953251 Henry Cohn, 2026, needs more optimization.
18 165 0.202511859410 Henry Cohn, 2026, needs more optimization.
18 166 0.202838475895 Henry Cohn, 2026, needs more optimization.
18 167 0.202883134607 Henry Cohn, 2026, needs more optimization.
18 168 0.202914717097 Henry Cohn, 2026, needs more optimization.
18 169 0.202915400882 Henry Cohn, 2026, needs more optimization.
18 170 0.202915857308 Henry Cohn, 2026, needs more optimization.
18 171 0.203068308082 Henry Cohn, 2026, needs more optimization.
18 172 0.204247596597 Henry Cohn, 2026, needs more optimization.
18 173 0.205761435149 Henry Cohn, 2026, needs more optimization.
18 174 0.208697490137 Henry Cohn, 2026, needs more optimization.
18 175 0.211741833034 Henry Cohn, 2026, needs more optimization.
18 176 0.212878279100 Henry Cohn, 2026, needs more optimization.
18 177 0.214221051510 Henry Cohn, 2026, needs more optimization.
18 179 0.214580042766 Henry Cohn, 2026, needs more optimization.
18 180 0.214580042773 Henry Cohn, 2026, needs more optimization.
18 181 0.214580603161 Henry Cohn, 2026, needs more optimization.
18 184 0.214580882717 Henry Cohn, 2026, needs more optimization.
18 186 0.214580882720 Henry Cohn, 2026, needs more optimization.
18 187 0.214582420281 Henry Cohn, 2026, needs more optimization.
18 188 0.214699919856 Henry Cohn, 2026, needs more optimization.
18 189 0.217221147574 Henry Cohn, 2026, needs more optimization.
18 194 0.218769485284 Henry Cohn, 2026, needs more optimization.
18 210 0.224009237740 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
11⁢x2+2⁢x−1
18 211 0.225934388930 Henry Cohn, 2026, needs more optimization.
18 212 0.228827044519 Henry Cohn, 2026, needs more optimization.
18 213 0.230059638045 Henry Cohn, 2026, needs more optimization.
18 214 0.231925611869 Henry Cohn, 2026, needs more optimization.
18 215 0.231925621384 Henry Cohn, 2026, needs more optimization.
18 216 0.231981377181 Henry Cohn, 2026, needs more optimization.
18 217 0.231984292198 Henry Cohn, 2026, needs more optimization.
18 218 0.231985488574 Henry Cohn, 2026, needs more optimization.
18 221 0.231986761271 Henry Cohn, 2026, needs more optimization.
18 222 0.231993329060 Henry Cohn, 2026, needs more optimization.
18 223 0.231999388456 Henry Cohn, 2026, needs more optimization.
18 224 0.232006807751 Henry Cohn, 2026, needs more optimization.
18 225 0.232174158851 Henry Cohn, 2026, needs more optimization.
18 226 0.232652301187 Henry Cohn, 2026, needs more optimization.
18 227 0.236145325554 Henry Cohn, 2026, needs more optimization.
18 228 0.237245100629 Henry Cohn, 2026, needs more optimization.
18 229 0.237870510050 Henry Cohn, 2026, needs more optimization.
18 230 0.238348799208 Henry Cohn, 2026, needs more optimization.
18 231 0.238843898235 Henry Cohn, 2026, needs more optimization.
18 232 0.239426340392 Henry Cohn, 2026, needs more optimization.
18 233 0.239901030381 Henry Cohn, 2026, needs more optimization.
18 234 0.240464162966 Henry Cohn, 2026, needs more optimization.
18 235 0.240752877260 Henry Cohn, 2026, needs more optimization.
18 236 0.241236857485 Henry Cohn, 2026, needs more optimization.
18 237 0.241646826492 Henry Cohn, 2026, needs more optimization.
18 238 0.242117529852 Henry Cohn, 2026, needs more optimization.
18 239 0.242621252118 Henry Cohn, 2026, needs more optimization.
18 240 0.243057068372 Henry Cohn, 2026, needs more optimization.
18 241 0.243350193761 Henry Cohn, 2026, needs more optimization.
18 242 0.243690256316 Henry Cohn, 2026, needs more optimization.
18 243 0.244025383235 Henry Cohn, 2026, needs more optimization.
18 244 0.244381395897 Henry Cohn, 2026, needs more optimization.
18 245 0.244798946761 Henry Cohn, 2026, needs more optimization.
18 246 0.245010374509 Henry Cohn, 2026, needs more optimization.
18 247 0.245331661606 Henry Cohn, 2026, needs more optimization.
18 248 0.245387636514 Henry Cohn, 2026, needs more optimization.
18 249 0.245536656833 Henry Cohn, 2026, needs more optimization.
18 250 0.245627654677 Henry Cohn, 2026, needs more optimization.
18 251 0.245771014639 Henry Cohn, 2026, needs more optimization.
18 252 0.245833399556 Henry Cohn, 2026, needs more optimization.
18 253 0.245966761969 Henry Cohn, 2026, needs more optimization.
18 254 0.245968257244 Henry Cohn, 2026, needs more optimization.
18 255 0.246018610036 Henry Cohn, 2026, needs more optimization.
18 256 0.246066160878 Henry Cohn, 2026, needs more optimization.
18 257 0.246122779266 Henry Cohn, 2026, needs more optimization.
18 258 0.246134895279 Henry Cohn, 2026, needs more optimization.
18 259 0.246241211073 Henry Cohn, 2026, needs more optimization.
18 260 0.246316908953 Henry Cohn, 2026, needs more optimization.
18 261 0.246344426839 Henry Cohn, 2026, needs more optimization.
18 262 0.246402896659 Henry Cohn, 2026, needs more optimization.
18 263 0.246433997538 Henry Cohn, 2026, needs more optimization.
18 264 0.246478751985 Henry Cohn, 2026, needs more optimization.
18 265 0.246918202774 Henry Cohn, 2026, needs more optimization.
18 266 0.246951437831 Henry Cohn, 2026, needs more optimization.
18 267 0.246972072506 Henry Cohn, 2026, needs more optimization.
18 268 0.247076619076 Henry Cohn, 2026, needs more optimization.
18 269 0.247473172015 Henry Cohn, 2026, needs more optimization.
18 270 0.247484780315 Henry Cohn, 2026, needs more optimization.
18 271 0.247527102968 Henry Cohn, 2026, needs more optimization.
18 272 0.247574166690 Henry Cohn, 2026, needs more optimization.
18 273 0.247580687905 Henry Cohn, 2026, needs more optimization.
18 274 0.247594186788 Henry Cohn, 2026, needs more optimization.
18 275 0.247626130923 Henry Cohn, 2026, needs more optimization.
18 276 0.247646419025 Henry Cohn, 2026, needs more optimization.
18 277 0.247700626784 Henry Cohn, 2026, needs more optimization.
18 278 0.247719111937 Henry Cohn, 2026, needs more optimization.
18 279 0.247739345413 Henry Cohn, 2026, needs more optimization.
18 280 0.247741668984 Henry Cohn, 2026, needs more optimization.
18 281 0.247789218250 Henry Cohn, 2026, needs more optimization.
18 282 0.247800395597 Henry Cohn, 2026, needs more optimization.
18 283 0.247855354500 Henry Cohn, 2026, needs more optimization.
18 284 0.247855356407 Henry Cohn, 2026, needs more optimization.
18 285 0.247856117218 Henry Cohn, 2026, needs more optimization.
18 286 0.247856125798 Henry Cohn, 2026, needs more optimization.
18 287 0.248144132866 Henry Cohn, 2026, needs more optimization.
18 288 0.248878267179 Henry Cohn, 2026, needs more optimization.
18 289 0.248922011081 Henry Cohn, 2026, needs more optimization.
18 290 0.249110616061 Henry Cohn, 2026, needs more optimization.
18 291 0.249357451446 Henry Cohn, 2026, needs more optimization.
18 292 0.249395484426 Henry Cohn, 2026, needs more optimization.
18 293 0.249622422237 Henry Cohn, 2026, needs more optimization.
18 294 0.249873845622 Henry Cohn, 2026, needs more optimization.
18 295 0.249874851265 Henry Cohn, 2026, needs more optimization.
18 296 0.249928491455 Henry Cohn, 2026, needs more optimization.
18 297 0.250003000434 Henry Cohn, 2026, needs more optimization.
18 298 0.250003013679 Henry Cohn, 2026, needs more optimization.
18 299 0.250003022488 Henry Cohn, 2026, needs more optimization.
18 300 0.250003629951 Henry Cohn, 2026, needs more optimization.
18 301 0.250003634731 Henry Cohn, 2026, needs more optimization.
18 302 0.250003678229 Henry Cohn, 2026, needs more optimization.
18 303 0.250008678872 Henry Cohn, 2026, needs more optimization.
18 304 0.250009255812 Henry Cohn, 2026, needs more optimization.
18 305 0.250019508673 Henry Cohn, 2026, needs more optimization.
18 306 0.250117452624 Henry Cohn, 2026, needs more optimization.
18 307 0.251207489942 Henry Cohn, 2026, needs more optimization.
18 308 0.251969388095 Henry Cohn, 2026, needs more optimization.
18 309 0.252613053013 Henry Cohn, 2026, needs more optimization.
18 310 0.253759006378 Henry Cohn, 2026, needs more optimization.
18 311 0.254809338887 Henry Cohn, 2026, needs more optimization.
18 312 0.256213816402 Henry Cohn, 2026, needs more optimization.
18 313 0.256826791517 Henry Cohn, 2026, needs more optimization.
18 314 0.258091019543 Henry Cohn, 2026, needs more optimization.
18 315 0.258817632748 Henry Cohn, 2026, needs more optimization.
18 316 0.258834366682 Henry Cohn, 2026, needs more optimization.
18 317 0.258928475395 Henry Cohn, 2026, needs more optimization.
18 318 0.258932597526 Henry Cohn, 2026, needs more optimization.
18 319 0.259041690530 Henry Cohn, 2026, needs more optimization.
18 320 0.259157489174 Henry Cohn, 2026, needs more optimization.
18 321 0.259163156512 Henry Cohn, 2026, needs more optimization.
18 322 0.259173494309 Henry Cohn, 2026, needs more optimization.
18 323 0.259181175220 Henry Cohn, 2026, needs more optimization.
18 324 0.259354188758 Henry Cohn, 2026, needs more optimization.
18 325 0.259840750699 Henry Cohn, 2026, needs more optimization.
18 326 0.259912688869 Henry Cohn, 2026, needs more optimization.
18 327 0.260096832993 Henry Cohn, 2026, needs more optimization.
18 328 0.260214021724 Henry Cohn, 2026, needs more optimization.
18 329 0.260395772961 Henry Cohn, 2026, needs more optimization.
18 330 0.260709405173 Henry Cohn, 2026, needs more optimization.
18 331 0.260710788723 Henry Cohn, 2026, needs more optimization.
18 332 0.260712669593 Henry Cohn, 2026, needs more optimization.
18 333 0.260730743783 Henry Cohn, 2026, needs more optimization.
18 334 0.260749068159 Henry Cohn, 2026, needs more optimization.
18 335 0.260766809809 Henry Cohn, 2026, needs more optimization.
18 336 0.260776237715 Henry Cohn, 2026, needs more optimization.
18 337 0.260822386154 Henry Cohn, 2026, needs more optimization.
18 338 0.260823540313 Henry Cohn, 2026, needs more optimization.
18 339 0.260834749561 Henry Cohn, 2026, needs more optimization.
18 340 0.260836480836 Henry Cohn, 2026, needs more optimization.
18 341 0.260868053514 Henry Cohn, 2026, needs more optimization.
18 342 0.260868798962 Henry Cohn, 2026, needs more optimization.
18 343 0.260878415415 Henry Cohn, 2026, needs more optimization.
18 344 0.260910521139 Henry Cohn, 2026, needs more optimization.
18 345 0.260928271838 Henry Cohn, 2026, needs more optimization.
18 346 0.260938858854 Henry Cohn, 2026, needs more optimization.
18 347 0.260942878345 Henry Cohn, 2026, needs more optimization.
18 348 0.260957767359 Henry Cohn, 2026, needs more optimization.
18 349 0.260961866166 Henry Cohn, 2026, needs more optimization.
18 350 0.260988759179 Henry Cohn, 2026, needs more optimization.
18 351 0.261013576559 Henry Cohn, 2026, needs more optimization.
18 352 0.261013578020 Henry Cohn, 2026, needs more optimization.
18 353 0.262945969973 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 354 0.277835032990 Henry Cohn, 2026, needs more optimization.
18 355 0.280365583999 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 356 0.284677619291 Henry Cohn, 2026, needs more optimization.
18 357 0.287869003393 Henry Cohn, 2026, needs more optimization.
18 358 0.290324074061 Henry Cohn, 2026, needs more optimization.
18 359 0.291541488075 Henry Cohn, 2026, needs more optimization.
18 360 0.292837949312 Henry Cohn, 2026, needs more optimization.
18 366 0.294118349081 Henry Cohn, 2026, needs more optimization.
18 368 0.294118364476 Henry Cohn, 2026, needs more optimization.
18 374 0.294118378911 Henry Cohn, 2026, needs more optimization.
18 379 0.294118399809 Henry Cohn, 2026, needs more optimization.
18 399 0.294118475997 Henry Cohn, 2026, needs more optimization.
18 402 0.294118478695 Henry Cohn, 2026, needs more optimization.
18 411 0.294118496257 Henry Cohn, 2026, needs more optimization.
18 413 0.294119936152 Henry Cohn, 2026, needs more optimization.
18 414 0.294163845247 Henry Cohn, 2026, needs more optimization.
18 415 0.295538239529 Henry Cohn, 2026, needs more optimization.
18 416 0.295538317517 Henry Cohn, 2026, needs more optimization.
18 417 0.295876274618 Henry Cohn, 2026, needs more optimization.
18 419 0.295911304702 Henry Cohn, 2026, needs more optimization.
18 420 0.295923675013 Henry Cohn, 2026, needs more optimization.
18 480 0.296296296297 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
27⁢x−8
18 481 0.298381039896 Henry Cohn, 2026, needs more optimization.
18 482 0.300180850929 Henry Cohn, 2026, needs more optimization.
18 483 0.301456013084 Henry Cohn, 2026, needs more optimization.
18 484 0.302682594026 Henry Cohn, 2026, needs more optimization.
18 485 0.303478200320 Henry Cohn, 2026, needs more optimization.
18 486 0.305662838512 Henry Cohn, 2026, needs more optimization.
18 487 0.307359527544 Henry Cohn, 2026, needs more optimization.
18 488 0.309212791229 Henry Cohn, 2026, needs more optimization.
18 489 0.309480416750 Henry Cohn, 2026, needs more optimization.
18 490 0.309601876583 Henry Cohn, 2026, needs more optimization.
18 491 0.309882098976 Henry Cohn, 2026, needs more optimization.
18 492 0.310035493759 Henry Cohn, 2026, needs more optimization.
18 493 0.311325631241 Henry Cohn, 2026, needs more optimization.
18 494 0.312263559519 Henry Cohn, 2026, needs more optimization.
18 495 0.312956809283 Henry Cohn, 2026, needs more optimization.
18 499 0.313181985173 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 500 0.314687864289 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
18 501 0.315952140128 Henry Cohn, 2026, needs more optimization.
18 502 0.316367524225 Henry Cohn, 2026, needs more optimization.
18 503 0.316619445698 Henry Cohn, 2026, needs more optimization.
18 504 0.316735149492 Henry Cohn, 2026, needs more optimization.
18 505 0.317102993793 Henry Cohn, 2026, needs more optimization.
18 506 0.317419556623 Henry Cohn, 2026, needs more optimization.
18 507 0.317883231222 Henry Cohn, 2026, needs more optimization.
18 508 0.318370576142 Henry Cohn, 2026, needs more optimization.
18 509 0.318705890955 Henry Cohn, 2026, needs more optimization.
18 510 0.318835744273 Henry Cohn, 2026, needs more optimization.
18 511 0.318929642853 Henry Cohn, 2026, needs more optimization.
18 512 0.319257735178 Henry Cohn, 2026, needs more optimization.
18 513 0.319284492363 Henry Cohn, 2026, needs more optimization.
18 514 0.319628971536 Henry Cohn, 2026, needs more optimization.
18 515 0.319681000675 Henry Cohn, 2026, needs more optimization.
18 516 0.320212107772 Henry Cohn, 2026, needs more optimization.
18 517 0.320463264632 Henry Cohn, 2026, needs more optimization.
18 518 0.321004890467 Henry Cohn, 2026, needs more optimization.
18 519 0.321650195650 Henry Cohn, 2026, needs more optimization.
18 520 0.321836381069 Henry Cohn, 2026, needs more optimization.
18 521 0.321862883280 Henry Cohn, 2026, needs more optimization.
18 522 0.323073025853 Henry Cohn, 2026, needs more optimization.
18 523 0.323106569680 Henry Cohn, 2026, needs more optimization.
18 524 0.323167104396 Henry Cohn, 2026, needs more optimization.
18 525 0.323734337408 Henry Cohn, 2026, needs more optimization.
18 526 0.323938628922 Henry Cohn, 2026, needs more optimization.
18 527 0.324353574267 Henry Cohn, 2026, needs more optimization.
18 528 0.324641201384 Henry Cohn, 2026, needs more optimization.
18 529 0.324922154974 Henry Cohn, 2026, needs more optimization.
18 530 0.324930796419 Henry Cohn, 2026, needs more optimization.
18 531 0.325262399933 Henry Cohn, 2026, needs more optimization.
18 532 0.325685907264 Henry Cohn, 2026, needs more optimization.
18 533 0.326007409182 Henry Cohn, 2026, needs more optimization.
18 534 0.326333342710 Henry Cohn, 2026, needs more optimization.
18 535 0.326574834409 Henry Cohn, 2026, needs more optimization.
18 536 0.326875242289 Henry Cohn, 2026, needs more optimization.
18 537 0.327103170148 Henry Cohn, 2026, needs more optimization.
18 538 0.327724004012 Henry Cohn, 2026, needs more optimization.
18 539 0.327903942910 Henry Cohn, 2026, needs more optimization.
18 540 0.328307501962 Henry Cohn, 2026, needs more optimization.
18 541 0.328713435928 Henry Cohn, 2026, needs more optimization.
18 542 0.328990685954 Henry Cohn, 2026, needs more optimization.
18 543 0.329066181401 Henry Cohn, 2026, needs more optimization.
18 544 0.329516122111 Henry Cohn, 2026, needs more optimization.
18 545 0.329665019261 Henry Cohn, 2026, needs more optimization.
18 546 0.330029469640 Henry Cohn, 2026, needs more optimization.
18 547 0.330236319649 Henry Cohn, 2026, needs more optimization.
18 548 0.330494625983 Henry Cohn, 2026, needs more optimization.
18 549 0.330846313400 Henry Cohn, 2026, needs more optimization.
18 550 0.331282401280 Henry Cohn, 2026, needs more optimization.
18 551 0.331636388358 Henry Cohn, 2026, needs more optimization.
18 552 0.331922727941 Henry Cohn, 2026, needs more optimization.
18 553 0.332346155005 Henry Cohn, 2026, needs more optimization.
18 554 0.332422015435 Henry Cohn, 2026, needs more optimization.
18 555 0.332557888131 Henry Cohn, 2026, needs more optimization.
18 556 0.332845475007 Henry Cohn, 2026, needs more optimization.
18 557 0.332965865415 Henry Cohn, 2026, needs more optimization.
18 558 0.333149007154 Henry Cohn, 2026, needs more optimization.
18 672 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
18 704 0.333333333334 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
3⁢x−1
18 705 0.342198337850 Henry Cohn, 2026, needs more optimization.
18 706 0.343271229134 Henry Cohn, 2026, needs more optimization.
18 707 0.344647822940 Henry Cohn, 2026, needs more optimization.
18 708 0.345475300272 Henry Cohn, 2026, needs more optimization.
18 709 0.346116692021 Henry Cohn, 2026, needs more optimization.
18 710 0.346663778384 Henry Cohn, 2026, needs more optimization.
18 711 0.347192024571 Henry Cohn, 2026, needs more optimization.
18 712 0.347589063199 Henry Cohn, 2026, needs more optimization.
18 713 0.348059116204 Henry Cohn, 2026, needs more optimization.
18 714 0.348511022848 Henry Cohn, 2026, needs more optimization.
18 715 0.348818403452 Henry Cohn, 2026, needs more optimization.
18 716 0.348920296127 Henry Cohn, 2026, needs more optimization.
18 717 0.349210271731 Henry Cohn, 2026, needs more optimization.
18 718 0.349479654098 Henry Cohn, 2026, needs more optimization.
18 719 0.349807715286 Henry Cohn, 2026, needs more optimization.
18 720 0.350025353625 Henry Cohn, 2026, needs more optimization.
18 721 0.350297038538 Henry Cohn, 2026, needs more optimization.
18 722 0.350569851137 Henry Cohn, 2026, needs more optimization.
18 723 0.350623937661 Henry Cohn, 2026, needs more optimization.
18 724 0.350843507083 Henry Cohn, 2026, needs more optimization.
18 725 0.350966165023 Henry Cohn, 2026, needs more optimization.
18 726 0.351033977738 Henry Cohn, 2026, needs more optimization.
18 727 0.351243279167 Henry Cohn, 2026, needs more optimization.
18 728 0.351395934656 Henry Cohn, 2026, needs more optimization.
18 729 0.351531824957 Henry Cohn, 2026, needs more optimization.
18 730 0.351721545881 Henry Cohn, 2026, needs more optimization.
18 731 0.351791291828 Henry Cohn, 2026, needs more optimization.
18 733 0.351905748849 Henry Cohn, 2026, needs more optimization.
18 734 0.351912397871 Henry Cohn, 2026, needs more optimization.
18 737 0.351916282364 Henry Cohn, 2026, needs more optimization.
18 740 0.351921797288 Henry Cohn, 2026, needs more optimization.
18 742 0.351922986406 Henry Cohn, 2026, needs more optimization.
18 743 0.351927980828 Henry Cohn, 2026, needs more optimization.
18 744 0.351947300523 Henry Cohn, 2026, needs more optimization.
18 745 0.351949597631 Henry Cohn, 2026, needs more optimization.
18 746 0.351949601515 Henry Cohn, 2026, needs more optimization.
18 747 0.351966481412 Henry Cohn, 2026, needs more optimization.
18 749 0.351979549570 Henry Cohn, 2026, needs more optimization.
18 750 0.351990004419 Henry Cohn, 2026, needs more optimization.
18 752 0.351990421480 Henry Cohn, 2026, needs more optimization.
18 753 0.351995788526 Henry Cohn, 2026, needs more optimization.
18 754 0.352000669145 Henry Cohn, 2026, needs more optimization.
18 755 0.352005786673 Henry Cohn, 2026, needs more optimization.
18 756 0.352007154112 Henry Cohn, 2026, needs more optimization.
18 757 0.352009047128 Henry Cohn, 2026, needs more optimization.
18 758 0.352015933544 Henry Cohn, 2026, needs more optimization.
18 760 0.352019818653 Henry Cohn, 2026, needs more optimization.
18 761 0.352031146913 Henry Cohn, 2026, needs more optimization.
18 762 0.352034967938 Henry Cohn, 2026, needs more optimization.
18 764 0.352035344240 Henry Cohn, 2026, needs more optimization.
18 765 0.352036194317 Henry Cohn, 2026, needs more optimization.
18 767 0.352038821943 Henry Cohn, 2026, needs more optimization.
18 768 0.352039012825 Henry Cohn, 2026, needs more optimization.
18 769 0.352040168730 Henry Cohn, 2026, needs more optimization.
18 771 0.352047287678 Henry Cohn, 2026, needs more optimization.
18 772 0.356479127351 Henry Cohn, 2026, needs more optimization.
18 773 0.356637944288 Henry Cohn, 2026, needs more optimization.
18 774 0.356817948657 Henry Cohn, 2026, needs more optimization.
18 775 0.356968051846 Henry Cohn, 2026, needs more optimization.
18 776 0.357116839303 Henry Cohn, 2026, needs more optimization.
18 867 0.357142857143 Henry Cohn, 2025, by modifying a construction from C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
14⁢x−5
18 868 0.373242601186 Henry Cohn, 2026, needs more optimization.
18 869 0.373254035623 Henry Cohn, 2026, needs more optimization.
18 1024 0.375 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
8⁢x−3
19 39 0.040648168399 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5491⁢x3−361⁢x2−19⁢x+1
19 40 0.047619047620 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
21⁢x−1
19 41 0.053165944699 Henry Cohn, 2023.
19 42 0.053978364917 Henry Cohn, 2025.
19 43 0.058551084358 Henry Cohn, 2025.
19 44 0.059131790994 Henry Cohn, 2023.
19 45 0.059418524383 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
19 48 0.063706690497 Henry Cohn, 2023.
215⁢x2+2⁢x−1
19 50 0.069767441861 Henry Cohn, 2023.
43⁢x−3
19 51 0.075275141543 Henry Cohn, 2025.
19 52 0.077597142083 Henry Cohn, 2026.
19 53 0.080493593475 Henry Cohn, 2026.
19 54 0.081604760576 Henry Cohn, 2026, needs more optimization.
19 55 0.082178889828 Henry Cohn, 2025.
19 56 0.083233613334 Henry Cohn, 2026.
19 57 0.084523221927 Henry Cohn, 2026, needs more optimization.
19 58 0.088502528073 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 60 0.090909090910 Kissing configuration of 81 points in 20 dimensions from A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K.
11⁢x−1
19 62 0.093346164763 Henry Cohn, 2026.
479⁢x2−34⁢x−1
19 66 0.097744360903 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
133⁢x−13
19 69 0.101319957446 Henry Cohn, 2026, needs more optimization.
19 70 0.101392647883 Henry Cohn, 2025, needs more optimization.
19 71 0.101456853395 Henry Cohn, 2026, needs more optimization.
19 72 0.101838513947 Henry Cohn, 2026, needs more optimization.
19 73 0.102201317334 Henry Cohn, 2026.
311⁢x2−22⁢x−1
19 74 0.104236915651 Henry Cohn, 2026, needs more optimization.
19 75 0.107816370262 Henry Cohn, 2026, needs more optimization.
19 76 0.111553284797 Henry Cohn, 2026.
19 77 0.112762714951 Henry Cohn, 2026, needs more optimization.
19 89 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
19 90 0.121308037796 Henry Cohn, 2024.
2809⁢x4−192⁢x3−86⁢x2+1
19 91 0.128902034018 Henry Cohn, 2026, needs more optimization.
19 92 0.133859602915 Henry Cohn, 2026, needs more optimization.
19 93 0.142506259847 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 100 0.142857142858 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
19 102 0.142857142858 Henry Cohn, 2023, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
19 103 0.149928121676 Henry Cohn, 2026.
19 104 0.150748959688 Henry Cohn, 2026.
19 105 0.152679567208 Henry Cohn, 2026, needs more optimization.
19 106 0.152679567278 Henry Cohn, 2026, needs more optimization.
19 107 0.153846307095 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 108 0.156351981287 Henry Cohn, 2026, needs more optimization.
19 132 0.157894736843 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
19⁢x−3
19 133 0.168802199651 Henry Cohn, 2026.
19 134 0.174620105369 Henry Cohn, 2026, needs more optimization.
19 135 0.175005074820 Henry Cohn, 2026, needs more optimization.
19 136 0.175550936424 Henry Cohn, 2026, needs more optimization.
19 137 0.176552070737 Henry Cohn, 2026, needs more optimization.
19 138 0.177160791714 Henry Cohn, 2026, needs more optimization.
19 139 0.177607143476 Henry Cohn, 2026, needs more optimization.
19 140 0.178022647099 Henry Cohn, 2026, needs more optimization.
19 141 0.178306252863 Henry Cohn, 2026, needs more optimization.
19 142 0.178659456328 Henry Cohn, 2026, needs more optimization.
19 143 0.179124256213 Henry Cohn, 2026, needs more optimization.
19 144 0.179750083872 Henry Cohn, 2026, needs more optimization.
19 145 0.180428416940 Henry Cohn, 2026, needs more optimization.
19 146 0.180708617968 Henry Cohn, 2026, needs more optimization.
19 147 0.182330406869 Henry Cohn, 2026, needs more optimization.
19 148 0.183293302259 Henry Cohn, 2026, needs more optimization.
19 149 0.183922068892 Henry Cohn, 2026, needs more optimization.
19 150 0.184646543855 Henry Cohn, 2026, needs more optimization.
19 151 0.186861702854 Henry Cohn, 2026, needs more optimization.
19 166 0.189189189190 Henry Cohn, 2026.
37⁢x−7
19 176 0.191919191920 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
99⁢x−19
19 177 0.193637369253 Henry Cohn, 2026.
19 178 0.194663251780 Henry Cohn, 2026, needs more optimization.
19 179 0.195466927188 Henry Cohn, 2026, needs more optimization.
19 180 0.195821119719 Henry Cohn, 2026, needs more optimization.
19 181 0.196900141851 Henry Cohn, 2026, needs more optimization.
19 182 0.197578676004 Henry Cohn, 2026, needs more optimization.
19 183 0.198453415676 Henry Cohn, 2026, needs more optimization.
19 184 0.199206618091 Henry Cohn, 2026, needs more optimization.
19 185 0.199766908559 Henry Cohn, 2026, needs more optimization.
19 192 0.2 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
19 193 0.203357314598 Henry Cohn, 2026.
19 194 0.205905415936 Henry Cohn, 2026, needs more optimization.
19 195 0.207107868928 Henry Cohn, 2026, needs more optimization.
19 196 0.208039034343 Henry Cohn, 2026, needs more optimization.
19 197 0.208691100249 Henry Cohn, 2026, needs more optimization.
19 198 0.209389191477 Henry Cohn, 2026, needs more optimization.
19 199 0.209806570057 Henry Cohn, 2026, needs more optimization.
19 202 0.210526315790 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
19⁢x−4
19 203 0.212022013149 Henry Cohn, 2026, needs more optimization.
19 204 0.212309120613 Henry Cohn, 2026, needs more optimization.
19 205 0.212684657183 Henry Cohn, 2026, needs more optimization.
19 206 0.212895489764 Henry Cohn, 2026, needs more optimization.
19 207 0.213596185610 Henry Cohn, 2026, needs more optimization.
19 208 0.214189894336 Henry Cohn, 2026, needs more optimization.
19 209 0.214622273360 Henry Cohn, 2026, needs more optimization.
19 210 0.214960658191 Henry Cohn, 2026, needs more optimization.
19 211 0.215403214275 Henry Cohn, 2026, needs more optimization.
19 212 0.215584840980 Henry Cohn, 2026, needs more optimization.
19 213 0.216093435043 Henry Cohn, 2026, needs more optimization.
19 214 0.216350940255 Henry Cohn, 2026, needs more optimization.
19 215 0.216856750032 Henry Cohn, 2026, needs more optimization.
19 216 0.217388127779 Henry Cohn, 2026, needs more optimization.
19 217 0.217552838570 Henry Cohn, 2026, needs more optimization.
19 218 0.218606447010 Henry Cohn, 2026, needs more optimization.
19 219 0.219121056065 Henry Cohn, 2026, needs more optimization.
19 220 0.219981250016 Henry Cohn, 2026, needs more optimization.
19 221 0.221044726230 Henry Cohn, 2026, needs more optimization.
19 222 0.222157280260 Henry Cohn, 2026, needs more optimization.
19 223 0.222363675477 Henry Cohn, 2026, needs more optimization.
19 224 0.222481879575 Henry Cohn, 2026, needs more optimization.
19 225 0.223293094850 Henry Cohn, 2026, needs more optimization.
19 226 0.223540654982 Henry Cohn, 2026, needs more optimization.
19 227 0.223954667135 Henry Cohn, 2026, needs more optimization.
19 228 0.224159411574 Henry Cohn, 2026, needs more optimization.
19 229 0.224194069300 Henry Cohn, 2026, needs more optimization.
19 230 0.224312771130 Henry Cohn, 2026, needs more optimization.
19 231 0.224470118545 Henry Cohn, 2026, needs more optimization.
19 232 0.224533691962 Henry Cohn, 2026, needs more optimization.
19 233 0.224686956127 Henry Cohn, 2026, needs more optimization.
19 234 0.224739916145 Henry Cohn, 2026, needs more optimization.
19 235 0.225173620930 Henry Cohn, 2026, needs more optimization.
19 236 0.225829134010 Henry Cohn, 2026, needs more optimization.
19 237 0.225934294481 Henry Cohn, 2026, needs more optimization.
19 238 0.225960617386 Henry Cohn, 2026, needs more optimization.
19 239 0.225980934094 Henry Cohn, 2026, needs more optimization.
19 240 0.226446633114 Henry Cohn, 2026, needs more optimization.
19 241 0.226625810151 Henry Cohn, 2026, needs more optimization.
19 242 0.226789078341 Henry Cohn, 2026, needs more optimization.
19 243 0.227019622689 Henry Cohn, 2026, needs more optimization.
19 244 0.227635839096 Henry Cohn, 2026, needs more optimization.
19 245 0.228801341042 Henry Cohn, 2026, needs more optimization.
19 246 0.229502786017 Henry Cohn, 2026, needs more optimization.
19 247 0.229935141123 Henry Cohn, 2026, needs more optimization.
19 248 0.230600487646 Henry Cohn, 2026, needs more optimization.
19 277 0.230769230770 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−3
19 278 0.235886984497 Henry Cohn, 2026, needs more optimization.
19 279 0.237011115077 Henry Cohn, 2026, needs more optimization.
19 280 0.237995387901 Henry Cohn, 2026, needs more optimization.
19 291 0.238519273263 Henry Cohn, 2026, needs more optimization.
19 292 0.240704635744 Henry Cohn, 2026, needs more optimization.
19 293 0.242301431280 Henry Cohn, 2026, needs more optimization.
19 294 0.243897269928 Henry Cohn, 2026, needs more optimization.
19 295 0.244482854972 Henry Cohn, 2026, needs more optimization.
19 296 0.244755914623 Henry Cohn, 2026, needs more optimization.
19 297 0.245792686473 Henry Cohn, 2026, needs more optimization.
19 298 0.246151713092 Henry Cohn, 2026, needs more optimization.
19 299 0.246490602624 Henry Cohn, 2026, needs more optimization.
19 300 0.246607929441 Henry Cohn, 2026, needs more optimization.
19 301 0.247839109160 Henry Cohn, 2026, needs more optimization.
19 302 0.248195352330 Henry Cohn, 2026, needs more optimization.
19 303 0.248993938474 Henry Cohn, 2026, needs more optimization.
19 304 0.249236210787 Henry Cohn, 2026, needs more optimization.
19 305 0.249405853754 Henry Cohn, 2026, needs more optimization.
19 306 0.249834392765 Henry Cohn, 2026, needs more optimization.
19 307 0.249929924675 Henry Cohn, 2026, needs more optimization.
19 308 0.249930332971 Henry Cohn, 2026, needs more optimization.
19 309 0.249933195930 Henry Cohn, 2026, needs more optimization.
19 311 0.249935361232 Henry Cohn, 2026, needs more optimization.
19 312 0.249947708810 Henry Cohn, 2026, needs more optimization.
19 313 0.249947790084 Henry Cohn, 2026, needs more optimization.
19 314 0.249950108395 Henry Cohn, 2026, needs more optimization.
19 315 0.249952577353 Henry Cohn, 2026, needs more optimization.
19 318 0.249963764413 Henry Cohn, 2026, needs more optimization.
19 319 0.249967165980 Henry Cohn, 2026, needs more optimization.
19 320 0.249988819083 Henry Cohn, 2026, needs more optimization.
19 321 0.249995104371 Henry Cohn, 2026, needs more optimization.
19 322 0.250000789385 Henry Cohn, 2026, needs more optimization.
19 323 0.250002929300 Henry Cohn, 2026, needs more optimization.
19 324 0.250017872056 Henry Cohn, 2026, needs more optimization.
19 325 0.250054454271 Henry Cohn, 2026, needs more optimization.
19 326 0.250149576999 Henry Cohn, 2026, needs more optimization.
19 327 0.250727023360 Henry Cohn, 2026, needs more optimization.
19 328 0.251781786204 Henry Cohn, 2026, needs more optimization.
19 329 0.252746238548 Henry Cohn, 2026, needs more optimization.
19 330 0.253217192515 Henry Cohn, 2026, needs more optimization.
19 331 0.254209170467 Henry Cohn, 2026, needs more optimization.
19 332 0.255661161903 Henry Cohn, 2026, needs more optimization.
19 333 0.256788881214 Henry Cohn, 2026, needs more optimization.
19 334 0.257980131566 Henry Cohn, 2026, needs more optimization.
19 335 0.258029579372 Henry Cohn, 2026, needs more optimization.
19 336 0.258113644701 Henry Cohn, 2026, needs more optimization.
19 337 0.258203390843 Henry Cohn, 2026, needs more optimization.
19 338 0.258251084814 Henry Cohn, 2026, needs more optimization.
19 339 0.258358001215 Henry Cohn, 2026, needs more optimization.
19 340 0.258480000728 Henry Cohn, 2026, needs more optimization.
19 341 0.258540542868 Henry Cohn, 2026, needs more optimization.
19 342 0.258640462513 Henry Cohn, 2026, needs more optimization.
19 343 0.258804716765 Henry Cohn, 2026, needs more optimization.
19 345 0.258818445340 Henry Cohn, 2026, needs more optimization.
19 346 0.258828529225 Henry Cohn, 2026, needs more optimization.
19 347 0.258869544352 Henry Cohn, 2026, needs more optimization.
19 348 0.258874082690 Henry Cohn, 2026, needs more optimization.
19 349 0.258925944609 Henry Cohn, 2026, needs more optimization.
19 350 0.259055755292 Henry Cohn, 2026, needs more optimization.
19 351 0.259175660992 Henry Cohn, 2026, needs more optimization.
19 352 0.259230367281 Henry Cohn, 2026, needs more optimization.
19 353 0.259307756464 Henry Cohn, 2026, needs more optimization.
19 354 0.259361427094 Henry Cohn, 2026, needs more optimization.
19 355 0.259422779652 Henry Cohn, 2026, needs more optimization.
19 356 0.259507446267 Henry Cohn, 2026, needs more optimization.
19 357 0.259545483839 Henry Cohn, 2026, needs more optimization.
19 358 0.259869359926 Henry Cohn, 2026, needs more optimization.
19 359 0.259957069901 Henry Cohn, 2026, needs more optimization.
19 360 0.260589687809 Henry Cohn, 2026, needs more optimization.
19 361 0.261503047934 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 362 0.263803610833 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 363 0.265639077445 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 364 0.267119347611 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 367 0.268538829782 Henry Cohn, 2026, needs more optimization.
19 368 0.270348137076 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 369 0.271660296784 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 404 0.272727272728 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
11⁢x−3
19 405 0.278180715130 Henry Cohn, 2026, needs more optimization.
19 406 0.279647385064 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 407 0.281131452886 Henry Cohn, 2026, needs more optimization.
19 408 0.281654060252 Henry Cohn, 2026, needs more optimization.
19 409 0.282094571487 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 410 0.282455904294 Henry Cohn, 2026, needs more optimization.
19 411 0.282665893882 Henry Cohn, 2026, needs more optimization.
19 412 0.282900032948 Henry Cohn, 2026, needs more optimization.
19 413 0.283124640223 Henry Cohn, 2026, needs more optimization.
19 414 0.283380491940 Henry Cohn, 2026, needs more optimization.
19 415 0.286038313848 Henry Cohn, 2026, needs more optimization.
19 416 0.286354872971 Henry Cohn, 2026, needs more optimization.
19 417 0.287128783204 Henry Cohn, 2026, needs more optimization.
19 464 0.287671232877 Henry Cohn, 2026.
73⁢x−21
19 465 0.287673623805 Henry Cohn, 2026, needs more optimization.
19 466 0.287758305044 Henry Cohn, 2026, needs more optimization.
19 468 0.287862066704 Henry Cohn, 2026, needs more optimization.
19 469 0.287887488317 Henry Cohn, 2026, needs more optimization.
19 470 0.287889377660 Henry Cohn, 2026, needs more optimization.
19 471 0.287891516177 Henry Cohn, 2026, needs more optimization.
19 472 0.287899511306 Henry Cohn, 2026, needs more optimization.
19 473 0.287901922453 Henry Cohn, 2026, needs more optimization.
19 474 0.287903996769 Henry Cohn, 2026, needs more optimization.
19 476 0.287907345145 Henry Cohn, 2026, needs more optimization.
19 477 0.287908498069 Henry Cohn, 2026, needs more optimization.
19 478 0.287914247274 Henry Cohn, 2026, needs more optimization.
19 479 0.287919663835 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
19 480 0.287925976337 Henry Cohn, 2026, needs more optimization.
19 569 0.294117647059 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
17⁢x−5
19 578 0.294117647059 Henry Cohn, 2026.
17⁢x−5
19 579 0.295154604839 Henry Cohn, 2026, needs more optimization.
19 580 0.296103691093 Henry Cohn, 2026, needs more optimization.
19 581 0.296709917468 Henry Cohn, 2026, needs more optimization.
19 582 0.296711245934 Henry Cohn, 2026, needs more optimization.
19 583 0.296714142923 Henry Cohn, 2026, needs more optimization.
19 584 0.296835018202 Henry Cohn, 2026, needs more optimization.
19 585 0.296934346206 Henry Cohn, 2026, needs more optimization.
19 586 0.297170050634 Henry Cohn, 2026, needs more optimization.
19 587 0.297366008063 Henry Cohn, 2026, needs more optimization.
19 588 0.297835407985 Henry Cohn, 2026, needs more optimization.
19 589 0.298138106644 Henry Cohn, 2026, needs more optimization.
19 590 0.298503962680 Henry Cohn, 2026, needs more optimization.
19 591 0.298843492557 Henry Cohn, 2026, needs more optimization.
19 592 0.299187675968 Henry Cohn, 2026, needs more optimization.
19 593 0.299286049335 Henry Cohn, 2026, needs more optimization.
19 594 0.299540141596 Henry Cohn, 2026, needs more optimization.
19 595 0.299674080628 Henry Cohn, 2026, needs more optimization.
19 596 0.299852844362 Henry Cohn, 2026, needs more optimization.
19 597 0.300024575003 Henry Cohn, 2026, needs more optimization.
19 598 0.300229918437 Henry Cohn, 2026, needs more optimization.
19 599 0.300366911549 Henry Cohn, 2026, needs more optimization.
19 600 0.300489543748 Henry Cohn, 2026, needs more optimization.
19 601 0.300634374335 Henry Cohn, 2026, needs more optimization.
19 602 0.300851164712 Henry Cohn, 2026, needs more optimization.
19 603 0.301013105968 Henry Cohn, 2026, needs more optimization.
19 604 0.301359905204 Henry Cohn, 2026, needs more optimization.
19 605 0.301633289422 Henry Cohn, 2026, needs more optimization.
19 606 0.301896399288 Henry Cohn, 2026, needs more optimization.
19 607 0.302100645815 Henry Cohn, 2026, needs more optimization.
19 608 0.302342661066 Henry Cohn, 2026, needs more optimization.
19 609 0.302592827967 Henry Cohn, 2026, needs more optimization.
19 610 0.302849023780 Henry Cohn, 2026, needs more optimization.
19 611 0.303037642392 Henry Cohn, 2026, needs more optimization.
19 612 0.303234837044 Henry Cohn, 2026, needs more optimization.
19 613 0.303376521901 Henry Cohn, 2026, needs more optimization.
19 614 0.303607879027 Henry Cohn, 2026, needs more optimization.
19 615 0.303762548424 Henry Cohn, 2026, needs more optimization.
19 616 0.303865029483 Henry Cohn, 2026, needs more optimization.
19 617 0.304053326927 Henry Cohn, 2026, needs more optimization.
19 618 0.304180224957 Henry Cohn, 2026, needs more optimization.
19 619 0.304248744166 Henry Cohn, 2026, needs more optimization.
19 620 0.304346550071 Henry Cohn, 2026, needs more optimization.
19 621 0.304449013195 Henry Cohn, 2026, needs more optimization.
19 622 0.304551560703 Henry Cohn, 2026, needs more optimization.
19 623 0.305092665914 Henry Cohn, 2026, needs more optimization.
19 624 0.305096046120 Henry Cohn, 2026, needs more optimization.
19 625 0.305097253201 Henry Cohn, 2026, needs more optimization.
19 626 0.305106741198 Henry Cohn, 2026, needs more optimization.
19 627 0.305114263345 Henry Cohn, 2026, needs more optimization.
19 628 0.305118236805 Henry Cohn, 2026, needs more optimization.
19 629 0.305123988522 Henry Cohn, 2026, needs more optimization.
19 630 0.305129363646 Henry Cohn, 2026, needs more optimization.
19 631 0.305137745883 Henry Cohn, 2026, needs more optimization.
19 632 0.305144684071 Henry Cohn, 2026, needs more optimization.
19 633 0.305147823680 Henry Cohn, 2026, needs more optimization.
19 634 0.305152506937 Henry Cohn, 2026, needs more optimization.
19 635 0.305155445660 Henry Cohn, 2026, needs more optimization.
19 636 0.305160763002 Henry Cohn, 2026, needs more optimization.
19 637 0.305164388065 Henry Cohn, 2026, needs more optimization.
19 638 0.305168568361 Henry Cohn, 2026, needs more optimization.
19 639 0.305172394499 Henry Cohn, 2026, needs more optimization.
19 640 0.305174491984 Henry Cohn, 2026, needs more optimization.
19 642 0.308281130354 Henry Cohn, 2026, needs more optimization.
19 643 0.308281148541 Henry Cohn, 2026, needs more optimization.
19 644 0.309142043362 Henry Cohn, 2026, needs more optimization.
19 645 0.309755517177 Henry Cohn, 2026, needs more optimization.
19 646 0.309756104923 Henry Cohn, 2026, needs more optimization.
19 647 0.310676758229 Henry Cohn, 2026, needs more optimization.
19 648 0.310959399195 Henry Cohn, 2026, needs more optimization.
19 649 0.311339320726 Henry Cohn, 2026, needs more optimization.
19 650 0.311459518255 Henry Cohn, 2026, needs more optimization.
19 651 0.311956750327 Henry Cohn, 2026, needs more optimization.
19 652 0.312211552981 Henry Cohn, 2026, needs more optimization.
19 653 0.312267857760 Henry Cohn, 2026, needs more optimization.
19 654 0.312731783019 Henry Cohn, 2026, needs more optimization.
19 655 0.312977282278 Henry Cohn, 2026, needs more optimization.
19 656 0.313150663275 Henry Cohn, 2026, needs more optimization.
19 657 0.313578744863 Henry Cohn, 2026, needs more optimization.
19 658 0.313799798058 Henry Cohn, 2026, needs more optimization.
19 659 0.314009796646 Henry Cohn, 2026, needs more optimization.
19 660 0.314163237556 Henry Cohn, 2026, needs more optimization.
19 661 0.314393046688 Henry Cohn, 2026, needs more optimization.
19 662 0.314544278692 Henry Cohn, 2026, needs more optimization.
19 663 0.314809479111 Henry Cohn, 2026, needs more optimization.
19 664 0.314972875157 Henry Cohn, 2026, needs more optimization.
19 665 0.315218694413 Henry Cohn, 2026, needs more optimization.
19 666 0.315351818624 Henry Cohn, 2026, needs more optimization.
19 667 0.315390512011 Henry Cohn, 2026, needs more optimization.
19 668 0.315672870063 Henry Cohn, 2026, needs more optimization.
19 669 0.315850907925 Henry Cohn, 2026, needs more optimization.
19 670 0.316102825988 Henry Cohn, 2026, needs more optimization.
19 671 0.316452516039 Henry Cohn, 2026, needs more optimization.
19 672 0.316543787344 Henry Cohn, 2026, needs more optimization.
19 673 0.316700034912 Henry Cohn, 2026, needs more optimization.
19 674 0.316961189468 Henry Cohn, 2026, needs more optimization.
19 675 0.317116593232 Henry Cohn, 2026, needs more optimization.
19 676 0.317245308358 Henry Cohn, 2026, needs more optimization.
19 677 0.317315445763 Henry Cohn, 2026, needs more optimization.
19 678 0.317572746130 Henry Cohn, 2026, needs more optimization.
19 679 0.317927949586 Henry Cohn, 2026, needs more optimization.
19 680 0.318232311007 Henry Cohn, 2026, needs more optimization.
19 681 0.318366697165 Henry Cohn, 2026, needs more optimization.
19 682 0.318722696995 Henry Cohn, 2026, needs more optimization.
19 683 0.318984841612 Henry Cohn, 2026, needs more optimization.
19 684 0.319315874024 Henry Cohn, 2026, needs more optimization.
19 685 0.319451508250 Henry Cohn, 2026, needs more optimization.
19 686 0.319674855634 Henry Cohn, 2026, needs more optimization.
19 687 0.319785960979 Henry Cohn, 2026, needs more optimization.
19 688 0.320173989380 Henry Cohn, 2026, needs more optimization.
19 689 0.320281573300 Henry Cohn, 2026, needs more optimization.
19 690 0.320489396046 Henry Cohn, 2026, needs more optimization.
19 691 0.320723886459 Henry Cohn, 2026, needs more optimization.
19 692 0.321068274264 Henry Cohn, 2026, needs more optimization.
19 693 0.321286831647 Henry Cohn, 2026, needs more optimization.
19 694 0.321406558371 Henry Cohn, 2026, needs more optimization.
19 695 0.321757347113 Henry Cohn, 2026, needs more optimization.
19 696 0.321903770837 Henry Cohn, 2026, needs more optimization.
19 697 0.322133995800 Henry Cohn, 2026, needs more optimization.
19 698 0.322371035084 Henry Cohn, 2026, needs more optimization.
19 699 0.322542447959 Henry Cohn, 2026, needs more optimization.
19 700 0.322608873073 Henry Cohn, 2026, needs more optimization.
19 701 0.322685576352 Henry Cohn, 2026, needs more optimization.
19 702 0.322920340512 Henry Cohn, 2026, needs more optimization.
19 703 0.323187005844 Henry Cohn, 2026, needs more optimization.
19 704 0.323563560313 Henry Cohn, 2026, needs more optimization.
19 705 0.323707250684 Henry Cohn, 2026, needs more optimization.
19 706 0.323801344073 Henry Cohn, 2026, needs more optimization.
19 707 0.323987744311 Henry Cohn, 2026, needs more optimization.
19 708 0.324132806580 Henry Cohn, 2026, needs more optimization.
19 709 0.324304371950 Henry Cohn, 2026, needs more optimization.
19 710 0.324379924468 Henry Cohn, 2026, needs more optimization.
19 711 0.324469677134 Henry Cohn, 2026, needs more optimization.
19 712 0.324548863314 Henry Cohn, 2026, needs more optimization.
19 713 0.324821024014 Henry Cohn, 2026, needs more optimization.
19 714 0.324918596033 Henry Cohn, 2026, needs more optimization.
19 715 0.325139985213 Henry Cohn, 2026, needs more optimization.
19 716 0.325361710505 Henry Cohn, 2026, needs more optimization.
19 717 0.325612435522 Henry Cohn, 2026, needs more optimization.
19 718 0.325804008078 Henry Cohn, 2026, needs more optimization.
19 719 0.326036452428 Henry Cohn, 2026, needs more optimization.
19 720 0.326204001745 Henry Cohn, 2026, needs more optimization.
19 721 0.326323736807 Henry Cohn, 2026, needs more optimization.
19 722 0.326526159507 Henry Cohn, 2026, needs more optimization.
19 723 0.326633835109 Henry Cohn, 2026, needs more optimization.
19 724 0.326711130147 Henry Cohn, 2026, needs more optimization.
19 725 0.326817386423 Henry Cohn, 2026, needs more optimization.
19 726 0.326984997969 Henry Cohn, 2026, needs more optimization.
19 727 0.327093605271 Henry Cohn, 2026, needs more optimization.
19 728 0.327249637102 Henry Cohn, 2026, needs more optimization.
19 729 0.327400830749 Henry Cohn, 2026, needs more optimization.
19 730 0.327702745061 Henry Cohn, 2026, needs more optimization.
19 731 0.327798556541 Henry Cohn, 2026, needs more optimization.
19 732 0.327934625540 Henry Cohn, 2026, needs more optimization.
19 733 0.328128494316 Henry Cohn, 2026, needs more optimization.
19 734 0.328247530257 Henry Cohn, 2026, needs more optimization.
19 735 0.328425130879 Henry Cohn, 2026, needs more optimization.
19 736 0.328566426306 Henry Cohn, 2026, needs more optimization.
19 737 0.328755709499 Henry Cohn, 2026, needs more optimization.
19 738 0.328944346317 Henry Cohn, 2026, needs more optimization.
19 739 0.329136717841 Henry Cohn, 2026, needs more optimization.
19 740 0.329436598150 Henry Cohn, 2026, needs more optimization.
19 741 0.329750901690 Henry Cohn, 2026, needs more optimization.
19 742 0.329870936767 Henry Cohn, 2026, needs more optimization.
19 743 0.330128049316 Henry Cohn, 2026, needs more optimization.
19 744 0.330398505389 Henry Cohn, 2026, needs more optimization.
19 745 0.330484237547 Henry Cohn, 2026, needs more optimization.
19 746 0.330737723386 Henry Cohn, 2026, needs more optimization.
19 747 0.330830517410 Henry Cohn, 2026, needs more optimization.
19 748 0.331084331990 Henry Cohn, 2026, needs more optimization.
19 749 0.331220817909 Henry Cohn, 2026, needs more optimization.
19 750 0.331413079436 Henry Cohn, 2026, needs more optimization.
19 751 0.331645334806 Henry Cohn, 2026, needs more optimization.
19 752 0.331878522456 Henry Cohn, 2026, needs more optimization.
19 753 0.332141168691 Henry Cohn, 2026, needs more optimization.
19 754 0.332340463460 Henry Cohn, 2026, needs more optimization.
19 755 0.332672513649 Henry Cohn, 2026, needs more optimization.
19 756 0.332848025475 Henry Cohn, 2026, needs more optimization.
19 757 0.333055196747 Henry Cohn, 2026, needs more optimization.
19 896 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
19 897 0.339468251558 Henry Cohn, 2026, needs more optimization.
19 898 0.341203627549 Henry Cohn, 2026, needs more optimization.
19 899 0.342630964184 Henry Cohn, 2026, needs more optimization.
19 900 0.344028064773 Henry Cohn, 2026, needs more optimization.
19 901 0.345530981795 Henry Cohn, 2026, needs more optimization.
19 902 0.346047645762 Henry Cohn, 2026, needs more optimization.
19 903 0.346834037764 Henry Cohn, 2026, needs more optimization.
19 904 0.347400478043 Henry Cohn, 2026, needs more optimization.
19 905 0.347928802964 Henry Cohn, 2026, needs more optimization.
19 906 0.348379183141 Henry Cohn, 2026, needs more optimization.
19 907 0.349035503623 Henry Cohn, 2026, needs more optimization.
19 908 0.349287854060 Henry Cohn, 2026, needs more optimization.
19 909 0.349719632465 Henry Cohn, 2026, needs more optimization.
19 910 0.350000023643 Henry Cohn, 2026, needs more optimization.
19 911 0.350105994531 Henry Cohn, 2026, needs more optimization.
19 912 0.350850556494 Henry Cohn, 2026, needs more optimization.
19 913 0.350981132195 Henry Cohn, 2026, needs more optimization.
19 914 0.351378852319 Henry Cohn, 2026, needs more optimization.
19 915 0.351463297623 Henry Cohn, 2026, needs more optimization.
19 916 0.351524280476 Henry Cohn, 2026, needs more optimization.
19 917 0.351612342325 Henry Cohn, 2026, needs more optimization.
19 918 0.351656574496 Henry Cohn, 2026, needs more optimization.
19 919 0.351793160188 Henry Cohn, 2026, needs more optimization.
19 920 0.351910924187 Henry Cohn, 2026, needs more optimization.
19 921 0.352102405786 Henry Cohn, 2026, needs more optimization.
19 922 0.352185282578 Henry Cohn, 2026, needs more optimization.
19 923 0.352263467486 Henry Cohn, 2026, needs more optimization.
19 924 0.352459781541 Henry Cohn, 2026, needs more optimization.
19 925 0.352529661690 Henry Cohn, 2026, needs more optimization.
19 926 0.352730000813 Henry Cohn, 2026, needs more optimization.
19 927 0.352981152327 Henry Cohn, 2026, needs more optimization.
19 928 0.353075868027 Henry Cohn, 2026, needs more optimization.
19 929 0.353213858013 Henry Cohn, 2026, needs more optimization.
19 930 0.353417622759 Henry Cohn, 2026, needs more optimization.
19 931 0.353667827821 Henry Cohn, 2026, needs more optimization.
19 932 0.353766518736 Henry Cohn, 2026, needs more optimization.
19 933 0.353855416031 Henry Cohn, 2026, needs more optimization.
19 934 0.354022190200 Henry Cohn, 2026, needs more optimization.
19 935 0.354183265127 Henry Cohn, 2026, needs more optimization.
19 936 0.354326437281 Henry Cohn, 2026, needs more optimization.
19 937 0.354508380149 Henry Cohn, 2026, needs more optimization.
19 938 0.354673832651 Henry Cohn, 2026, needs more optimization.
19 1024 0.354838709678 Henry Cohn, 2026, subcode of a code of size 1040.
31⁢x−11
20 41 0.038815055717 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6480⁢x3−400⁢x2−20⁢x+1
20 42 0.045454545455 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
22⁢x−1
20 43 0.050117159654 Henry Cohn, 2024.
6493504⁢x6+4442432⁢x5−359919⁢x4−90844⁢x3+13006⁢x2−588⁢x+9
20 44 0.051781487230 Henry Cohn, 2023.
20 45 0.053400898990 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 46 0.053968966531 Henry Cohn, 2025.
20 47 0.053993355922 Henry Cohn, 2023.
120⁢x2−25⁢x+1
20 48 0.055838151510 Henry Cohn, 2023.
464⁢x2−8⁢x−1
20 49 0.060513303142 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 50 0.063702950432 Henry Cohn, 2025.
20 56* 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
15⁢x−1
20 60 0.076923076924 Kissing configuration of 77 points in 21 dimensions.
13⁢x−1
20 63 0.081967213115 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
61⁢x−5
20 64 0.087282748333 Henry Cohn, 2026.
20 65 0.087640553689 Henry Cohn, 2026, needs more optimization.
20 66 0.089602007874 Henry Cohn, 2026.
20 67 0.090150903490 Henry Cohn, 2026.
2103⁢x4−1376⁢x3+230⁢x2−1
20 68 0.092978419163 Henry Cohn, 2026.
20 69 0.096785945467 Henry Cohn, 2026, needs more optimization.
20 70 0.097920843564 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 81 0.1 A. E. Brouwer and W. H. Haemers, Structure and uniqueness of the (81,20,1,6) strongly regular graph, Discrete Math. 106/107 (1992), 77–82, doi:10.1016/0012-365X(92)90532-K.
10⁢x−1
20 82 0.111111111112 Henry Cohn, 2026.
9⁢x−1
20 83 0.112895349919 Henry Cohn, 2026, needs more optimization.
20 84 0.112895349921 Henry Cohn, 2026, needs more optimization.
20 85 0.112902505491 Henry Cohn, 2026, needs more optimization.
20 86 0.112908499193 Henry Cohn, 2026, needs more optimization.
20 87 0.112912074804 Henry Cohn, 2025, needs more optimization.
20 88 0.112912612812 Henry Cohn, 2025, needs more optimization.
20 89 0.112912613185 Henry Cohn, 2025, needs more optimization.
20 92 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
20 93 0.118699001808 Henry Cohn, 2026, needs more optimization.
20 105 0.125 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8⁢x−1
20 106 0.136915269061 Henry Cohn, 2026.
7225⁢x4−990⁢x3−480⁢x2+9
20 120 0.142857142858 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
7⁢x−1
20 124 0.145853791080 Henry Cohn, 2026, needs more optimization.
20 125 0.147670835572 Henry Cohn, 2026.
20 126 0.149455666198 Henry Cohn, 2026, needs more optimization.
20 127 0.149702279507 Henry Cohn, 2026, needs more optimization.
20 128 0.149900399046 Henry Cohn, 2026, needs more optimization.
20 129 0.150190420678 Henry Cohn, 2026, needs more optimization.
20 130 0.150479191679 Henry Cohn, 2026, needs more optimization.
20 131 0.150512837745 Henry Cohn, 2026, needs more optimization.
20 132 0.150513448004 Henry Cohn, 2026, needs more optimization.
20 133 0.151452462029 Henry Cohn, 2026, needs more optimization.
20 135 0.151500526296 Henry Cohn, 2026, needs more optimization.
20 136 0.151500526411 Henry Cohn, 2026, needs more optimization.
20 137 0.153058908365 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 138 0.154375390899 Henry Cohn, 2026, needs more optimization.
20 139 0.154944920631 Henry Cohn, 2026, needs more optimization.
20 140 0.156027125137 Henry Cohn, 2026, needs more optimization.
20 141 0.157229456154 Henry Cohn, 2026, needs more optimization.
20 142 0.161809087523 Henry Cohn, 2026, needs more optimization.
20 143 0.166621463255 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 170 0.166666666667 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
6⁢x−1
20 171 0.181540268746 Henry Cohn, 2026, needs more optimization.
20 172 0.187883200045 Henry Cohn, 2026, needs more optimization.
20 173 0.189189871693 Henry Cohn, 2026, needs more optimization.
20 174 0.189189878780 Henry Cohn, 2026, needs more optimization.
20 175 0.189189887513 Henry Cohn, 2026, needs more optimization.
20 176 0.189189888376 Henry Cohn, 2026, needs more optimization.
20 177 0.189189896011 Henry Cohn, 2026, needs more optimization.
20 178 0.189189900746 Henry Cohn, 2026, needs more optimization.
20 179 0.189189907333 Henry Cohn, 2026, needs more optimization.
20 180 0.189189926951 Henry Cohn, 2026, needs more optimization.
20 181 0.189189929061 Henry Cohn, 2026, needs more optimization.
20 182 0.189189931527 Henry Cohn, 2026, needs more optimization.
20 183 0.189189933878 Henry Cohn, 2026, needs more optimization.
20 184 0.189189939309 Henry Cohn, 2026, needs more optimization.
20 185 0.189190082765 Henry Cohn, 2026, needs more optimization.
20 186 0.189190089913 Henry Cohn, 2026, needs more optimization.
20 187 0.189190101038 Henry Cohn, 2026, needs more optimization.
20 188 0.189190792255 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 189 0.189190793043 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 190 0.189190794850 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 191 0.189270510651 Henry Cohn, 2026, needs more optimization.
20 192 0.191919195342 Henry Cohn, 2026, needs more optimization.
20 194 0.191919195347 Henry Cohn, 2026, needs more optimization.
20 195 0.191919195351 Henry Cohn, 2026, needs more optimization.
20 196 0.191919195361 Henry Cohn, 2026, needs more optimization.
20 197 0.191919201142 Henry Cohn, 2026, needs more optimization.
20 198 0.191919201143 Henry Cohn, 2026, needs more optimization.
20 201 0.191919201146 Henry Cohn, 2026, needs more optimization.
20 202 0.191919229689 Henry Cohn, 2026, needs more optimization.
20 203 0.191919308153 Henry Cohn, 2026, needs more optimization.
20 204 0.192060808037 Henry Cohn, 2026, needs more optimization.
20 231 0.192307692308 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
20 256 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
20 257 0.203357314598 Henry Cohn, 2026.
20 258 0.205762326152 Henry Cohn, 2026, needs more optimization.
20 259 0.206639865991 Henry Cohn, 2026, needs more optimization.
20 260 0.208081992550 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 262 0.208386799892 Henry Cohn, 2026, needs more optimization.
20 263 0.208832042722 Henry Cohn, 2026, needs more optimization.
20 264 0.208834164080 Henry Cohn, 2026, needs more optimization.
20 265 0.212156205955 Henry Cohn, 2026, needs more optimization.
20 266 0.212382451039 Henry Cohn, 2026, needs more optimization.
20 267 0.212660728203 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 268 0.212959272996 Henry Cohn, 2026, needs more optimization.
20 269 0.213323553607 Henry Cohn, 2026, needs more optimization.
20 270 0.213404383547 Henry Cohn, 2026, needs more optimization.
20 271 0.213455062263 Henry Cohn, 2026, needs more optimization.
20 272 0.213892868191 Henry Cohn, 2026, needs more optimization.
20 273 0.214294027408 Henry Cohn, 2026, needs more optimization.
20 274 0.214680528003 Henry Cohn, 2026, needs more optimization.
20 275 0.214959036473 Henry Cohn, 2026, needs more optimization.
20 276 0.215444613504 Henry Cohn, 2026, needs more optimization.
20 277 0.215809701847 Henry Cohn, 2026, needs more optimization.
20 278 0.216144510023 Henry Cohn, 2026, needs more optimization.
20 279 0.216302082152 Henry Cohn, 2026, needs more optimization.
20 280 0.216538907953 Henry Cohn, 2026, needs more optimization.
20 281 0.216758866898 Henry Cohn, 2026, needs more optimization.
20 282 0.217056698289 Henry Cohn, 2026, needs more optimization.
20 283 0.217394291648 Henry Cohn, 2026, needs more optimization.
20 284 0.217566873913 Henry Cohn, 2026, needs more optimization.
20 285 0.217796560040 Henry Cohn, 2026, needs more optimization.
20 286 0.217920481049 Henry Cohn, 2026, needs more optimization.
20 287 0.218011370200 Henry Cohn, 2026, needs more optimization.
20 288 0.219342110970 Henry Cohn, 2026, needs more optimization.
20 289 0.219891682055 Henry Cohn, 2026, needs more optimization.
20 290 0.220243098981 Henry Cohn, 2026, needs more optimization.
20 291 0.220614906695 Henry Cohn, 2026, needs more optimization.
20 292 0.220690239766 Henry Cohn, 2026, needs more optimization.
20 293 0.220690240670 Henry Cohn, 2026, needs more optimization.
20 294 0.220691805452 Henry Cohn, 2026, needs more optimization.
20 301 0.222222222223 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−2
20 322 0.222222222223 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−2
20 323 0.232387029873 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 324 0.236122065990 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
20 378 0.236363636364 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
55⁢x−13
20 379 0.242464091180 Henry Cohn, 2026, needs more optimization.
20 380 0.242509745068 Henry Cohn, 2026, needs more optimization.
20 381 0.242573763508 Henry Cohn, 2026, needs more optimization.
20 382 0.242648822467 Henry Cohn, 2026, needs more optimization.
20 383 0.242713791848 Henry Cohn, 2026, needs more optimization.
20 384 0.242785869848 Henry Cohn, 2026, needs more optimization.
20 385 0.242877690448 Henry Cohn, 2026, needs more optimization.
20 386 0.242965624892 Henry Cohn, 2026, needs more optimization.
20 387 0.242987302817 Henry Cohn, 2026, needs more optimization.
20 388 0.243020606257 Henry Cohn, 2026, needs more optimization.
20 389 0.243111653501 Henry Cohn, 2026, needs more optimization.
20 390 0.243171239031 Henry Cohn, 2026, needs more optimization.
20 391 0.243219020327 Henry Cohn, 2026, needs more optimization.
20 392 0.243332229098 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
Minimal polynomial listed in plain text data
20 393 0.247798396078 Henry Cohn, 2026, needs more optimization.
20 405 0.25 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
4⁢x−1
20 406 0.262172700766 Henry Cohn, 2026, needs more optimization.
20 407 0.264976400968 Henry Cohn, 2026, needs more optimization.
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 474 0.269855642213 Henry Cohn, 2026, needs more optimization.
20 475 0.270933959731 Henry Cohn, 2026, needs more optimization.
20 476 0.272595503772 Henry Cohn, 2026, needs more optimization.
20 524 0.272727272728 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
11⁢x−3
20 567 0.273861278753 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
40⁢x2−3
20 568 0.280556241340 Henry Cohn, 2026, needs more optimization.
20 640 0.285714285715 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
7⁢x−2
20 641 0.292028046770 Henry Cohn, 2026, needs more optimization.
20 840 0.3 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
10⁢x−3
20 841 0.303064566389 Henry Cohn, 2026, needs more optimization.
20 1002 0.307692307693 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
13⁢x−4
20 1003 0.315496048152 Henry Cohn, 2026, needs more optimization.
20 1006 0.323084228076 Henry Cohn, 2026, needs more optimization.
20 1007 0.323177154763 Henry Cohn, 2026, needs more optimization.
20 1008 0.323177276700 Henry Cohn, 2026, needs more optimization.
20 1010 0.323472509383 Henry Cohn, 2026, needs more optimization.
20 1011 0.323874765104 Henry Cohn, 2026, needs more optimization.
20 1012 0.323878294021 Henry Cohn, 2026, needs more optimization.
20 1014 0.323878896500 Henry Cohn, 2026, needs more optimization.
20 1015 0.323879471638 Henry Cohn, 2026, needs more optimization.
20 1017 0.323975315787 Henry Cohn, 2026, needs more optimization.
20 1019 0.324106924455 Henry Cohn, 2026, needs more optimization.
20 1020 0.324108277595 Henry Cohn, 2026, needs more optimization.
20 1021 0.324194601360 Henry Cohn, 2026, needs more optimization.
20 1022 0.324194955792 Henry Cohn, 2026, needs more optimization.
20 1023 0.324712538998 Henry Cohn, 2026, needs more optimization.
20 1024 0.324712546319 Henry Cohn, 2026, needs more optimization.
21 43 0.037145782135 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7581⁢x3−441⁢x2−21⁢x+1
21 44 0.043532808199 Henry Cohn, 2023.
21 50* 0.047619047620 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
21⁢x−1
21 51 0.058803648698 Henry Cohn, 2024.
21 52 0.062635030303 Henry Cohn, 2026.
21 53 0.066664743320 Henry Cohn, 2026, needs more optimization.
21 54 0.066665400631 Henry Cohn, 2026, needs more optimization.
21 55 0.066666409280 Henry Cohn, 2025.
21 56 0.066666653891 Henry Cohn, 2025, needs more optimization.
21 57 0.066666662289 Henry Cohn, 2025, needs more optimization.
21 58 0.066666666335 Henry Cohn, 2026, needs more optimization.
21 59 0.072019011748 Henry Cohn, 2025.
21 60 0.074662292991 Henry Cohn, 2026.
21 61 0.076923073145 Henry Cohn, 2025, needs more optimization.
21 62 0.076923075369 Henry Cohn, 2025, needs more optimization.
21 63 0.078689325834 Henry Cohn, 2026.
9⁢x2+12⁢x−1
21 64 0.080216778694 Henry Cohn, 2026.
14481⁢x4−18000⁢x3+4848⁢x2−480⁢x+16
21 65 0.081966984741 Henry Cohn, 2026.
21 77* 0.083333333334 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
12⁢x−1
21 78 0.093247656078 Henry Cohn, 2026.
21 82 0.093297851017 Henry Cohn, 2026.
144⁢x4−840⁢x3+192⁢x2−1
21 83 0.095523255230 Henry Cohn, 2026, needs more optimization.
21 84 0.096073235105 Henry Cohn, 2026, needs more optimization.
21 85 0.097702080330 Henry Cohn, 2026, needs more optimization.
21 87 0.103204295473 Ilmari Vahteristo, 2026.
168⁢x3−156⁢x2+24⁢x−1
21 88 0.106199014100 Henry Cohn, 2026, needs more optimization.
21 89 0.108845760578 Henry Cohn, 2026, needs more optimization.
21 90 0.109639633905 Henry Cohn, 2026, needs more optimization.
21 92 0.109918568059 Henry Cohn, 2026, needs more optimization.
21 93 0.110695598499 Henry Cohn, 2026, needs more optimization.
21 112* 0.111111111112 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
9⁢x−1
21 113 0.127363959709 Henry Cohn, 2026.
21 119 0.131782945737 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
129⁢x−17
21 120 0.139344934125 Henry Cohn, 2026, needs more optimization.
21 121 0.139344936826 Henry Cohn, 2026, needs more optimization.
21 122 0.139344956937 Henry Cohn, 2026, needs more optimization.
21 123 0.139385702154 Henry Cohn, 2026, needs more optimization.
21 124 0.140535690921 Henry Cohn, 2026, needs more optimization.
21 162* 0.142857142858 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
7⁢x−1
21 163 0.153926281042 Henry Cohn, 2026.
21 164 0.160001004624 Henry Cohn, 2026, needs more optimization.
21 165 0.160002652619 Henry Cohn, 2026, needs more optimization.
21 166 0.160894258955 Henry Cohn, 2026, needs more optimization.
21 198 0.161904761905 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
105⁢x−17
21 199 0.172187000249 Henry Cohn, 2026.
21 200 0.174789245948 Henry Cohn, 2026, needs more optimization.
21 201 0.174789523679 Henry Cohn, 2026, needs more optimization.
21 217 0.174875298960 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
119⁢x4+580⁢x3+42⁢x2−20⁢x−1
21 218 0.177286556402 Henry Cohn, 2026, needs more optimization.
21 219 0.177401695417 Henry Cohn, 2026, needs more optimization.
21 220 0.177459656339 Henry Cohn, 2026, needs more optimization.
21 221 0.177479979994 Henry Cohn, 2026, needs more optimization.
21 224 0.177492046263 Henry Cohn, 2026, needs more optimization.
21 225 0.178085751307 Henry Cohn, 2026, needs more optimization.
21 226 0.185484136393 Henry Cohn, 2026.
21 227 0.190599360827 Henry Cohn, 2026, needs more optimization.
21 233 0.192307692308 Code with 231 points in 20 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
21 234 0.192307929309 Henry Cohn, 2026, needs more optimization.
21 235 0.192308006431 Henry Cohn, 2026, needs more optimization.
21 236 0.194538258320 Henry Cohn, 2026, needs more optimization.
21 237 0.195347439018 Henry Cohn, 2026, needs more optimization.
21 336 0.2 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
5⁢x−1
21 352 0.214285714286 Henry Cohn, 2026.
14⁢x−3
21 353 0.222395820677 Henry Cohn, 2026.
21 373 0.227586206897 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
145⁢x−33
21 388 0.227586206897 Antoine Jay, 2026, using the program of A. Jay, M. Poberznik, M. Brut, A. Hemeryck, L.-H. Hoang, M. Gunde, N. Salles, G. Cruchon, and M. Roux, Equidistribution of points on the hypersphere including symmetries, preprint, 2026, doi:0.2139/ssrn.6427919.
145⁢x−33
21 394 0.230769230770 Henry Cohn, 2026.
13⁢x−3
21 395 0.230770690659 Henry Cohn, 2026, needs more optimization.
21 396 0.232285518710 Henry Cohn, 2026, needs more optimization.
21 397 0.237323451236 Henry Cohn, 2026, needs more optimization.
21 554 0.238095238096 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
21⁢x−5
21 567 0.25 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
4⁢x−1
21 568 0.253536497486 Henry Cohn, 2026, needs more optimization.
21 569 0.254499432066 Henry Cohn, 2026, needs more optimization.
21 570 0.255064892889 Henry Cohn, 2026, needs more optimization.
21 571 0.255477419291 Henry Cohn, 2026, needs more optimization.
21 572 0.255805547252 Henry Cohn, 2026, needs more optimization.
21 573 0.256122279505 Henry Cohn, 2026, needs more optimization.
21 574 0.256383937289 Henry Cohn, 2026, needs more optimization.
21 575 0.256601170565 Henry Cohn, 2026, needs more optimization.
21 576 0.256818506238 Henry Cohn, 2026, needs more optimization.
21 577 0.257065132807 Henry Cohn, 2026, needs more optimization.
21 578 0.257277688307 Henry Cohn, 2026, needs more optimization.
21 579 0.257423057186 Henry Cohn, 2026, needs more optimization.
21 580 0.257574573131 Henry Cohn, 2026, needs more optimization.
21 581 0.257695093577 Henry Cohn, 2026, needs more optimization.
21 582 0.257814778789 Henry Cohn, 2026, needs more optimization.
21 583 0.257901495272 Henry Cohn, 2026, needs more optimization.
21 584 0.258015671381 Henry Cohn, 2026, needs more optimization.
21 585 0.258106838858 Henry Cohn, 2026, needs more optimization.
21 586 0.258234373766 Henry Cohn, 2026, needs more optimization.
21 587 0.258300379011 Henry Cohn, 2026, needs more optimization.
21 588 0.258372949610 Henry Cohn, 2026, needs more optimization.
21 589 0.258443901984 Henry Cohn, 2026, needs more optimization.
21 590 0.258598881671 Henry Cohn, 2026, needs more optimization.
21 591 0.258699043381 Henry Cohn, 2026, needs more optimization.
21 592 0.258733582342 Henry Cohn, 2026, needs more optimization.
21 593 0.258970535722 Henry Cohn, 2026, needs more optimization.
21 594 0.259204621950 Henry Cohn, 2026, needs more optimization.
21 595 0.259316080121 Henry Cohn, 2026, needs more optimization.
21 596 0.259390837906 Henry Cohn, 2026, needs more optimization.
21 597 0.259458548077 Henry Cohn, 2026, needs more optimization.
21 598 0.259597267752 Henry Cohn, 2026, needs more optimization.
21 599 0.259670816467 Henry Cohn, 2026, needs more optimization.
21 600 0.259736997734 Henry Cohn, 2026, needs more optimization.
21 601 0.259788364852 Henry Cohn, 2026, needs more optimization.
21 602 0.259827601603 Henry Cohn, 2026, needs more optimization.
21 603 0.259903549146 Henry Cohn, 2026, needs more optimization.
21 604 0.259937018449 Henry Cohn, 2026, needs more optimization.
21 605 0.260041521885 Henry Cohn, 2026, needs more optimization.
21 606 0.260130729137 Henry Cohn, 2026, needs more optimization.
21 607 0.260226383702 Henry Cohn, 2026, needs more optimization.
21 608 0.260272874370 Henry Cohn, 2026, needs more optimization.
21 609 0.260313792225 Henry Cohn, 2026, needs more optimization.
21 610 0.260493677987 Henry Cohn, 2026, needs more optimization.
21 611 0.260597898017 Henry Cohn, 2026, needs more optimization.
21 612 0.260661885670 Henry Cohn, 2026, needs more optimization.
21 613 0.260783569132 Henry Cohn, 2026, needs more optimization.
21 614 0.260874737196 Henry Cohn, 2026, needs more optimization.
21 615 0.260931932061 Henry Cohn, 2026, needs more optimization.
21 616 0.261024544443 Henry Cohn, 2026, needs more optimization.
21 617 0.261082040001 Henry Cohn, 2026, needs more optimization.
21 618 0.261158096530 Henry Cohn, 2026, needs more optimization.
21 619 0.261226651273 Henry Cohn, 2026, needs more optimization.
21 620 0.261266482577 Henry Cohn, 2026, needs more optimization.
21 621 0.261304896176 Henry Cohn, 2026, needs more optimization.
21 622 0.261344833544 Henry Cohn, 2026, needs more optimization.
21 623 0.261388963666 Henry Cohn, 2026, needs more optimization.
21 624 0.261423938954 Henry Cohn, 2026, needs more optimization.
21 625 0.261459559431 Henry Cohn, 2026, needs more optimization.
21 626 0.261499928188 Henry Cohn, 2026, needs more optimization.
21 627 0.261571991993 Henry Cohn, 2026, needs more optimization.
21 628 0.261627095453 Henry Cohn, 2026, needs more optimization.
21 629 0.261682611985 Henry Cohn, 2026, needs more optimization.
21 630 0.262074421160 Henry Cohn, 2026, needs more optimization.
21 631 0.262324770772 Henry Cohn, 2026, needs more optimization.
21 632 0.262514527258 Henry Cohn, 2026, needs more optimization.
21 633 0.262613944524 Henry Cohn, 2026, needs more optimization.
21 634 0.262684551132 Henry Cohn, 2026, needs more optimization.
21 635 0.262734886792 Henry Cohn, 2026, needs more optimization.
21 636 0.262885701968 Henry Cohn, 2026, needs more optimization.
21 637 0.263006192418 Henry Cohn, 2026, needs more optimization.
21 638 0.263137953876 Henry Cohn, 2026, needs more optimization.
21 639 0.263227156199 Henry Cohn, 2026, needs more optimization.
21 640 0.263327545898 Henry Cohn, 2026, needs more optimization.
21 641 0.263415267970 Henry Cohn, 2026, needs more optimization.
21 642 0.263576840460 Henry Cohn, 2026, needs more optimization.
21 643 0.263702462827 Henry Cohn, 2026, needs more optimization.
21 644 0.263824992410 Henry Cohn, 2026, needs more optimization.
21 645 0.263933498380 Henry Cohn, 2026, needs more optimization.
21 646 0.263971430802 Henry Cohn, 2026, needs more optimization.
21 647 0.264048013847 Henry Cohn, 2026, needs more optimization.
21 648 0.264123735401 Henry Cohn, 2026, needs more optimization.
21 649 0.264185348287 Henry Cohn, 2026, needs more optimization.
21 650 0.264291722824 Henry Cohn, 2026, needs more optimization.
21 651 0.264364706503 Henry Cohn, 2026, needs more optimization.
21 652 0.264436384769 Henry Cohn, 2026, needs more optimization.
21 653 0.264503961358 Henry Cohn, 2026, needs more optimization.
21 654 0.264557744558 Henry Cohn, 2026, needs more optimization.
21 655 0.264633939124 Henry Cohn, 2026, needs more optimization.
21 656 0.264732810064 Henry Cohn, 2026, needs more optimization.
21 657 0.264801546539 Henry Cohn, 2026, needs more optimization.
21 658 0.264893789228 Henry Cohn, 2026, needs more optimization.
21 659 0.264987724093 Henry Cohn, 2026, needs more optimization.
21 660 0.265122404177 Henry Cohn, 2026, needs more optimization.
21 661 0.265178183501 Henry Cohn, 2026, needs more optimization.
21 662 0.265230321747 Henry Cohn, 2026, needs more optimization.
21 663 0.265294809766 Henry Cohn, 2026, needs more optimization.
21 664 0.265373972239 Henry Cohn, 2026, needs more optimization.
21 665 0.265446035336 Henry Cohn, 2026, needs more optimization.
21 666 0.265519620637 Henry Cohn, 2026, needs more optimization.
21 667 0.265557375318 Henry Cohn, 2026, needs more optimization.
21 668 0.265602713503 Henry Cohn, 2026, needs more optimization.
21 669 0.265630785091 Henry Cohn, 2026, needs more optimization.
21 670 0.265666524130 Henry Cohn, 2026, needs more optimization.
21 671 0.265729899059 Henry Cohn, 2026, needs more optimization.
21 672 0.265768268354 Henry Cohn, 2026, needs more optimization.
21 673 0.265851480752 Henry Cohn, 2026, needs more optimization.
21 674 0.265900187492 Henry Cohn, 2026, needs more optimization.
21 675 0.265958470836 Henry Cohn, 2026, needs more optimization.
21 676 0.266025713679 Henry Cohn, 2026, needs more optimization.
21 677 0.266078403654 Henry Cohn, 2026, needs more optimization.
21 678 0.266134805860 Henry Cohn, 2026, needs more optimization.
21 679 0.266165728536 Henry Cohn, 2026, needs more optimization.
21 680 0.266222535087 Henry Cohn, 2026, needs more optimization.
21 681 0.266278296080 Henry Cohn, 2026, needs more optimization.
21 682 0.266341767332 Henry Cohn, 2026, needs more optimization.
21 683 0.266503146947 Henry Cohn, 2026, needs more optimization.
21 684 0.266585287587 Henry Cohn, 2026, needs more optimization.
21 715 0.266666666667 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
15⁢x−4
21 728 0.267171850610 Henry Cohn, 2026.
21 729 0.267261241913 Henry Cohn, 2026.
14⁢x2−1
21 730 0.277220609560 Henry Cohn, 2026, needs more optimization.
21 731 0.282339600791 Henry Cohn, 2026, needs more optimization.
21 732 0.284690511848 Henry Cohn, 2026, needs more optimization.
21 850 0.285714285715 Henry Cohn, 2026.
7⁢x−2
21 851 0.290297029223 Henry Cohn, 2026, needs more optimization.
21 852 0.291094896311 Henry Cohn, 2026, needs more optimization.
21 853 0.291722394351 Henry Cohn, 2026, needs more optimization.
21 854 0.292104563824 Henry Cohn, 2026, needs more optimization.
21 855 0.292429826575 Henry Cohn, 2026, needs more optimization.
21 856 0.292762589721 Henry Cohn, 2026, needs more optimization.
21 857 0.293056611922 Henry Cohn, 2026, needs more optimization.
21 858 0.293321668529 Henry Cohn, 2026, needs more optimization.
21 859 0.293634139896 Henry Cohn, 2026, needs more optimization.
21 974 0.294117647059 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
17⁢x−5
21 975 0.299221130573 Henry Cohn, 2026, needs more optimization.
21 1024 0.3 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
10⁢x−3
22 45 0.035618974680 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8800⁢x3−484⁢x2−22⁢x+1
22 46 0.041709010468 Henry Cohn, 2026.
22 47 0.046962270332 Henry Cohn, 2026, continuous family of codes without rattlers.
736⁢x3+236⁢x2−34⁢x+1
22 48 0.047524915294 Henry Cohn, 2025, continuous family of codes without rattlers.
64⁢x2+18⁢x−1
22 49 0.047603596724 Henry Cohn, 2026.
22 50 0.047618606209 Henry Cohn, 2025, needs more optimization.
22 52 0.047619047316 Henry Cohn, 2025, needs more optimization.
22 53 0.057560345703 Henry Cohn, 2024.
22 54 0.060108874148 Henry Cohn, 2025.
22 55 0.064358001899 Henry Cohn, 2026.
22 56 0.066435767847 Henry Cohn, 2026, needs more optimization.
22 57 0.066559109857 Henry Cohn, 2026.
22 58 0.066625280614 Henry Cohn, 2026, needs more optimization.
22 59 0.066652771147 Henry Cohn, 2026, needs more optimization.
22 60 0.066661305531 Henry Cohn, 2026, needs more optimization.
22 61 0.069638781740 Henry Cohn, 2026.
22 62 0.071702992547 Henry Cohn, 2026, needs more optimization.
22 63 0.076903596608 Henry Cohn, 2026, needs more optimization.
22 64 0.076918163613 Henry Cohn, 2026, needs more optimization.
22 65 0.076924075517 Henry Cohn, 2026, needs more optimization.
22 66 0.078243584883 Henry Cohn, 2026.
22 67 0.079295758513 Henry Cohn, 2026, needs more optimization.
22 68 0.080927905651 Henry Cohn, 2026.
22 69 0.083018488572 Henry Cohn, 2026, needs more optimization.
22 70 0.083309827283 Henry Cohn, 2025, needs more optimization.
22 71 0.083331871272 Henry Cohn, 2025, needs more optimization.
22 72 0.083333305430 Henry Cohn, 2026, needs more optimization.
22 73 0.083333332773 Henry Cohn, 2025, needs more optimization.
22 79 0.083333333334 Code with 77 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
12⁢x−1
22 80 0.086876541301 Henry Cohn, 2026.
22 100* 0.090909090910 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
11⁢x−1
22 101 0.109433688331 Henry Cohn, 2026.
6912⁢x4−560⁢x3−272⁢x2+3
22 114 0.111111111112 Code with 112 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
22 115 0.112789665003 Henry Cohn, 2026.
68⁢x2−52⁢x+5
22 116 0.117359909647 Henry Cohn, 2026.
30⁢x2+5⁢x−1
22 117 0.122749957634 Henry Cohn, 2026, needs more optimization.
22 118 0.126503630021 Henry Cohn, 2026, needs more optimization.
22 119 0.126740173095 Henry Cohn, 2026, needs more optimization.
22 120 0.131231549706 Henry Cohn, 2026, needs more optimization.
22 127 0.131782945737 Henry Cohn, 2026.
129⁢x−17
22 136 0.135135135136 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−5
22 141 0.135135135136 Henry Cohn, 2026.
37⁢x−5
22 142 0.135517367774 Henry Cohn, 2026, needs more optimization.
22 143 0.137953427684 Henry Cohn, 2026, needs more optimization.
22 144 0.139623936236 Henry Cohn, 2026, needs more optimization.
22 166 0.142857142858 Henry Cohn, 2026.
7⁢x−1
22 167 0.144948974279 Henry Cohn, 2026.
20⁢x2+4⁢x−1
22 169 0.149071198500 Henry Cohn, 2026.
45⁢x2−1
22 170 0.153808582906 Henry Cohn, 2026.
22 171 0.156572050095 Henry Cohn, 2026.
22 172 0.158304782082 Henry Cohn, 2026, needs more optimization.
22 173 0.159107132818 Henry Cohn, 2026, needs more optimization.
22 174 0.161501328310 Henry Cohn, 2026, needs more optimization.
22 201 0.161904761905 Henry Cohn, 2026.
105⁢x−17
22 202 0.161905113244 Henry Cohn, 2026, needs more optimization.
22 203 0.165615111593 Henry Cohn, 2026, needs more optimization.
22 275* 0.166666666667 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
6⁢x−1
22 276 0.178506323194 Henry Cohn, 2026.
22 277 0.185913607156 Henry Cohn, 2026, needs more optimization.
22 278 0.189283232162 Henry Cohn, 2026, needs more optimization.
22 279 0.191581546361 Henry Cohn, 2026, needs more optimization.
22 280 0.193234499863 Henry Cohn, 2026, needs more optimization.
22 281 0.194512975923 Henry Cohn, 2026, needs more optimization.
22 282 0.195694468102 Henry Cohn, 2026, needs more optimization.
22 283 0.196333225377 Henry Cohn, 2026, needs more optimization.
22 284 0.196353279308 Henry Cohn, 2026, needs more optimization.
22 286 0.196362023436 Henry Cohn, 2026, needs more optimization.
22 287 0.199244817412 Henry Cohn, 2026, needs more optimization.
22 352 0.2 C. Ma, T. Tao Z., P. Li, M. Liu, H. Chen, Z. Mao, Y. Cheng, Y. Qi, and Y. Yang, Finding kissing numbers with game-theoretic reinforcement learning, preprint, 2025, arXiv:2511.13391.
5⁢x−1
22 353 0.201777989818 Henry Cohn, 2026.
22 354 0.202832443486 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
22 355 0.203727072273 Henry Cohn, 2026, needs more optimization.
22 356 0.204034193781 Henry Cohn, 2026, needs more optimization.
22 357 0.204058223592 Henry Cohn, 2026, needs more optimization.
22 358 0.204059171295 Henry Cohn, 2026, needs more optimization.
22 359 0.204488590084 Henry Cohn, 2026, needs more optimization.
22 374 0.204624019941 Henry Cohn, 2026.
22 375 0.205718448770 Henry Cohn, 2026, needs more optimization.
22 376 0.206395598566 Henry Cohn, 2026, needs more optimization.
22 377 0.206695251640 Henry Cohn, 2026, needs more optimization.
22 378 0.206884606303 Henry Cohn, 2026, needs more optimization.
22 379 0.207057776180 Henry Cohn, 2026, needs more optimization.
22 380 0.207118971078 Henry Cohn, 2026, needs more optimization.
22 381 0.207165729959 Henry Cohn, 2026, needs more optimization.
22 383 0.207172060077 Henry Cohn, 2026, needs more optimization.
22 384 0.207172218110 Henry Cohn, 2026, needs more optimization.
22 385 0.207172398061 Henry Cohn, 2026, needs more optimization.
22 387 0.207172542358 Henry Cohn, 2026, needs more optimization.
22 388 0.207172999975 Henry Cohn, 2026, needs more optimization.
22 389 0.207173003748 Henry Cohn, 2026, needs more optimization.
22 390 0.207173532979 Henry Cohn, 2026, needs more optimization.
22 391 0.208463217107 Henry Cohn, 2026, needs more optimization.
22 392 0.208815802216 Henry Cohn, 2026, needs more optimization.
22 393 0.209019444823 Henry Cohn, 2026, needs more optimization.
22 394 0.209060231953 Henry Cohn, 2026, needs more optimization.
22 395 0.209386077957 Henry Cohn, 2026, needs more optimization.
22 396 0.209524317342 Henry Cohn, 2026, needs more optimization.
22 397 0.209574946501 Henry Cohn, 2026, needs more optimization.
22 398 0.209589648533 Henry Cohn, 2026, needs more optimization.
22 399 0.209592406373 Henry Cohn, 2026, needs more optimization.
22 400 0.209594050128 Henry Cohn, 2026, needs more optimization.
22 401 0.209595120004 Henry Cohn, 2026, needs more optimization.
22 402 0.209599157254 Henry Cohn, 2026, needs more optimization.
22 403 0.209600440117 Henry Cohn, 2026, needs more optimization.
22 404 0.209686857106 Henry Cohn, 2026, needs more optimization.
22 405 0.209705577938 Henry Cohn, 2026, needs more optimization.
22 415 0.209711457926 Henry Cohn, 2026, needs more optimization.
22 416 0.209814456873 Henry Cohn, 2026, needs more optimization.
22 430 0.209817069797 Henry Cohn, 2026.
22 431 0.210993089892 Henry Cohn, 2026, needs more optimization.
22 432 0.211661635422 Henry Cohn, 2026, needs more optimization.
22 433 0.212032939829 Henry Cohn, 2026, needs more optimization.
22 436 0.212148697334 Henry Cohn, 2026, needs more optimization.
22 437 0.212406676956 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
22 438 0.212505211637 Henry Cohn, 2026, needs more optimization.
22 439 0.212505214875 Henry Cohn, 2026, needs more optimization.
22 440 0.212505214877 Henry Cohn, 2026, needs more optimization.
22 441 0.212505214879 Henry Cohn, 2026, needs more optimization.
22 442 0.212505214885 Henry Cohn, 2026, needs more optimization.
22 451 0.212653226480 Henry Cohn, 2026.
22 452 0.213200716356 Henry Cohn, 2026.
22⁢x2−1
22 485 0.229650347182 Henry Cohn, 2026, needs more optimization.
22 505 0.229926564594 Henry Cohn, 2026, needs more optimization.
22 506 0.231137104549 Henry Cohn, 2026, needs more optimization.
22 529 0.233333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
30⁢x−7
22 556 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 2 points in 1 dimension.
21⁢x−5
22 557 0.238095351377 Henry Cohn, 2026, needs more optimization.
22 558 0.238097213136 Henry Cohn, 2026, needs more optimization.
22 559 0.238211131327 Henry Cohn, 2026, needs more optimization.
22 560 0.238514727327 Henry Cohn, 2026, needs more optimization.
22 561 0.240687770529 Henry Cohn, 2026, needs more optimization.
22 562 0.244013244622 Henry Cohn, 2026, needs more optimization.
22 563 0.246119690767 Henry Cohn, 2026, needs more optimization.
22 564 0.248007452356 Henry Cohn, 2026, needs more optimization.
22 565 0.249744520705 Henry Cohn, 2026, needs more optimization.
22 891* 0.25 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
4⁢x−1
22 1024 0.272727272728 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
11⁢x−3
23 47 0.034216857253 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10143⁢x3−529⁢x2−23⁢x+1
23 48 0.040044233015 Henry Cohn, 2025.
23 49 0.045954913455 Henry Cohn, 2026.
23 50 0.046749604258 Henry Cohn, 2025, continuous family of codes without rattlers.
713⁢x3+215⁢x2−33⁢x+1
23 51 0.047343031571 Henry Cohn, 2026.
23 52 0.047477902076 Henry Cohn, 2026, needs more optimization.
23 53 0.047579301640 Henry Cohn, 2026, needs more optimization.
23 54 0.047608667748 Henry Cohn, 2026.
23 55 0.055365527542 Henry Cohn, 2026.
23 56 0.057275984127 Henry Cohn, 2025.
23 57 0.061654200859 Henry Cohn, 2026.
23 58 0.064487742711 Henry Cohn, 2026, needs more optimization.
23 59 0.065947075080 Henry Cohn, 2026, needs more optimization.
23 60 0.066273219336 Henry Cohn, 2026, needs more optimization.
23 61 0.066456403785 Henry Cohn, 2026, needs more optimization.
23 62 0.066559757736 Henry Cohn, 2026, needs more optimization.
23 63 0.067249405088 Henry Cohn, 2026.
23 64 0.069716146261 Henry Cohn, 2026.
23 65 0.073130743225 Henry Cohn, 2026.
23 66 0.075359392650 Henry Cohn, 2026, needs more optimization.
23 67 0.076883023372 Henry Cohn, 2026, needs more optimization.
23 68 0.076894792023 Henry Cohn, 2026, needs more optimization.
23 69 0.077605236851 Henry Cohn, 2026, needs more optimization.
23 70 0.077985592951 Henry Cohn, 2026, needs more optimization.
23 71 0.079522620309 Henry Cohn, 2026.
23 72 0.080064660878 Henry Cohn, 2026.
23 73 0.081988639062 Henry Cohn, 2026, needs more optimization.
23 74 0.083305684338 Henry Cohn, 2026, needs more optimization.
23 75 0.083307299784 Henry Cohn, 2026, needs more optimization.
23 76 0.083319579641 Henry Cohn, 2026, needs more optimization.
23 77 0.083330983365 Henry Cohn, 2026, needs more optimization.
23 79 0.083333145471 Henry Cohn, 2026, needs more optimization.
23 81 0.083333222004 Henry Cohn, 2025, needs more optimization.
23 82 0.083365056374 Henry Cohn, 2026, needs more optimization.
23 83 0.087272831288 Henry Cohn, 2026, needs more optimization.
23 84 0.089248231432 Henry Cohn, 2026, needs more optimization.
23 102 0.090909090910 Code with 100 points in 22 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−1
23 103 0.094789393423 Henry Cohn, 2026.
67⁢x2−38⁢x+3
23 104 0.102473100453 Henry Cohn, 2026, needs more optimization.
23 106 0.109392443214 Henry Cohn, 2026.
2175⁢x2+210⁢x−49
23 107 0.111111109507 Henry Cohn, 2026, needs more optimization.
23 108 0.111111109510 Henry Cohn, 2026, needs more optimization.
23 111 0.111111109519 Henry Cohn, 2026, needs more optimization.
23 113 0.111111109682 Henry Cohn, 2026, needs more optimization.
23 115 0.111111109683 Henry Cohn, 2026, needs more optimization.
23 116 0.111111109684 Henry Cohn, 2026, needs more optimization.
23 117 0.111111521995 Henry Cohn, 2026, needs more optimization.
23 118 0.111111531356 Henry Cohn, 2026, needs more optimization.
23 119 0.115910206677 Henry Cohn, 2026, needs more optimization.
23 120 0.119778745349 Henry Cohn, 2026, needs more optimization.
23 121 0.124476981536 Henry Cohn, 2026, needs more optimization.
23 122 0.124526838481 Henry Cohn, 2026, needs more optimization.
23 123 0.130470282744 Henry Cohn, 2026, needs more optimization.
23 129 0.131782945737 Orthogonal union of 127 points in 22 dimensions and 2 points in 1 dimension.
129⁢x−17
23 130 0.131783417809 Henry Cohn, 2026, needs more optimization.
23 131 0.132067114845 Henry Cohn, 2026, needs more optimization.
23 132 0.134161312265 Henry Cohn, 2026, needs more optimization.
23 133 0.134703237183 Henry Cohn, 2026, needs more optimization.
23 134 0.135029155465 Henry Cohn, 2026, needs more optimization.
23 147 0.135135135136 Henry Cohn, 2026.
37⁢x−5
23 148 0.135305743637 Henry Cohn, 2026, needs more optimization.
23 149 0.136611840996 Henry Cohn, 2026, needs more optimization.
23 150 0.136642660470 Henry Cohn, 2026, needs more optimization.
23 151 0.137557808169 Henry Cohn, 2026, needs more optimization.
23 152 0.138673551832 Henry Cohn, 2026, needs more optimization.
23 168 0.142857142858 Orthogonal union of 166 points in 22 dimensions and 2 points in 1 dimension.
7⁢x−1
23 169 0.142857630115 Henry Cohn, 2026, needs more optimization.
23 170 0.142857630117 Henry Cohn, 2026, needs more optimization.
23 171 0.145096803132 Henry Cohn, 2026, needs more optimization.
23 172 0.145383795939 Henry Cohn, 2026, needs more optimization.
23 173 0.145383795957 Henry Cohn, 2026, needs more optimization.
23 174 0.146719214737 Henry Cohn, 2026, needs more optimization.
23 175 0.150592518043 Henry Cohn, 2026, needs more optimization.
23 176 0.153571022662 Henry Cohn, 2026, needs more optimization.
23 177 0.154899102694 Henry Cohn, 2026, needs more optimization.
23 178 0.155965299532 Henry Cohn, 2026, needs more optimization.
23 179 0.156306715649 Henry Cohn, 2026, needs more optimization.
23 180 0.158773056143 Henry Cohn, 2026, needs more optimization.
23 181 0.159255831194 Henry Cohn, 2026, needs more optimization.
23 182 0.160918535525 Henry Cohn, 2026, needs more optimization.
23 183 0.161390084221 Henry Cohn, 2026, needs more optimization.
23 203 0.161904761905 Orthogonal union of 201 points in 22 dimensions and 2 points in 1 dimension.
105⁢x−17
23 204 0.161904891178 Henry Cohn, 2026, needs more optimization.
23 205 0.161904895839 Henry Cohn, 2026, needs more optimization.
23 206 0.161907076292 Henry Cohn, 2026, needs more optimization.
23 207 0.161918513785 Henry Cohn, 2026, needs more optimization.
23 208 0.161957295579 Henry Cohn, 2026, needs more optimization.
23 209 0.164060791591 Henry Cohn, 2026, needs more optimization.
23 210 0.164949113377 Henry Cohn, 2026, needs more optimization.
23 211 0.165496549516 Henry Cohn, 2026, needs more optimization.
23 212 0.166122583399 Henry Cohn, 2026, needs more optimization.
23 213 0.166454985156 Henry Cohn, 2026, needs more optimization.
23 214 0.166587973051 Henry Cohn, 2026, needs more optimization.
23 278 0.166666666667 Henry Cohn, 2026.
6⁢x−1
23 279 0.168164328629 Henry Cohn, 2026, needs more optimization.
23 280 0.174223843259 Henry Cohn, 2026, needs more optimization.
23 281 0.178760839439 Henry Cohn, 2026, needs more optimization.
23 282 0.181917179016 Henry Cohn, 2026, needs more optimization.
23 283 0.183303363511 Henry Cohn, 2026, needs more optimization.
23 284 0.185710494490 Henry Cohn, 2026, needs more optimization.
23 285 0.186029346710 Henry Cohn, 2026, needs more optimization.
23 286 0.187582461543 Henry Cohn, 2026, needs more optimization.
23 287 0.188050784977 Henry Cohn, 2026, needs more optimization.
23 288 0.188291955135 Henry Cohn, 2026, needs more optimization.
23 289 0.189180114939 Henry Cohn, 2026, needs more optimization.
23 290 0.189363556675 Henry Cohn, 2026, needs more optimization.
23 291 0.189500926560 Henry Cohn, 2026, needs more optimization.
23 292 0.189580003335 Henry Cohn, 2026, needs more optimization.
23 293 0.189621926311 Henry Cohn, 2026, needs more optimization.
23 294 0.189656236996 Henry Cohn, 2026, needs more optimization.
23 295 0.189656239065 Henry Cohn, 2026, needs more optimization.
23 296 0.189656254877 Henry Cohn, 2026, needs more optimization.
23 297 0.189656366363 Henry Cohn, 2026, needs more optimization.
23 298 0.189656372879 Henry Cohn, 2026, needs more optimization.
23 299 0.189656379762 Henry Cohn, 2026, needs more optimization.
23 300 0.189657892523 Henry Cohn, 2026, needs more optimization.
23 301 0.190658498794 Henry Cohn, 2026, needs more optimization.
23 302 0.193044183846 Henry Cohn, 2026, needs more optimization.
23 303 0.194180527571 Henry Cohn, 2026, needs more optimization.
23 304 0.195440261896 Henry Cohn, 2026, needs more optimization.
23 305 0.196304794465 Henry Cohn, 2026, needs more optimization.
23 306 0.197473252744 Henry Cohn, 2026, needs more optimization.
23 307 0.198603084621 Henry Cohn, 2026, needs more optimization.
23 308 0.199006017618 Henry Cohn, 2026, needs more optimization.
23 309 0.199259131687 Henry Cohn, 2026, needs more optimization.
23 552* 0.2 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
5⁢x−1
23 553 0.232851959963 Henry Cohn, 2026, needs more optimization.
23 554 0.235338473108 Henry Cohn, 2026, needs more optimization.
23 558 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 4 points in 2 dimensions.
21⁢x−5
23 559 0.238095351377 Orthogonal union of 557 points in 22 dimensions and 2 points in 1 dimension.
23 560 0.238096151989 Henry Cohn, 2026, needs more optimization.
23 562 0.238096283359 Henry Cohn, 2026, needs more optimization.
23 563 0.238096556032 Henry Cohn, 2026, needs more optimization.
23 566 0.238100030295 Henry Cohn, 2026, needs more optimization.
23 568 0.238774166804 Henry Cohn, 2026, needs more optimization.
23 569 0.238777692477 Henry Cohn, 2026, needs more optimization.
23 570 0.238777795398 Henry Cohn, 2026, needs more optimization.
23 571 0.238782912015 Henry Cohn, 2026, needs more optimization.
23 572 0.238783314348 Henry Cohn, 2026, needs more optimization.
23 573 0.239234841906 Henry Cohn, 2026, needs more optimization.
23 574 0.240065393702 Henry Cohn, 2026, needs more optimization.
23 575 0.241013569414 Henry Cohn, 2026, needs more optimization.
23 576 0.241358330015 Henry Cohn, 2026, needs more optimization.
23 577 0.241575117558 Henry Cohn, 2026, needs more optimization.
23 578 0.242523605310 Henry Cohn, 2026, needs more optimization.
23 579 0.242821350954 Henry Cohn, 2026, needs more optimization.
23 581 0.243305829331 Henry Cohn, 2026, needs more optimization.
23 582 0.243557397748 Henry Cohn, 2026, needs more optimization.
23 583 0.244213807943 Henry Cohn, 2026, needs more optimization.
23 584 0.244885272933 Henry Cohn, 2026, needs more optimization.
23 585 0.245311975515 Henry Cohn, 2026, needs more optimization.
23 586 0.245502727058 Henry Cohn, 2026, needs more optimization.
23 587 0.245870907587 Henry Cohn, 2026, needs more optimization.
23 588 0.245918987806 Henry Cohn, 2026, needs more optimization.
23 589 0.246132132955 Henry Cohn, 2026, needs more optimization.
23 590 0.246156080354 Henry Cohn, 2026, needs more optimization.
23 591 0.246456938472 Henry Cohn, 2026, needs more optimization.
23 592 0.246489179786 Henry Cohn, 2026, needs more optimization.
23 593 0.247102863082 Henry Cohn, 2026, needs more optimization.
23 594 0.247156016449 Henry Cohn, 2026, needs more optimization.
23 595 0.247308807453 Henry Cohn, 2026, needs more optimization.
23 596 0.247665344775 Henry Cohn, 2026, needs more optimization.
23 597 0.247973383899 Henry Cohn, 2026, needs more optimization.
23 598 0.248470102387 Henry Cohn, 2026, needs more optimization.
23 599 0.248730793471 Henry Cohn, 2026, needs more optimization.
23 600 0.248899205428 Henry Cohn, 2026, needs more optimization.
23 601 0.249302185503 Henry Cohn, 2026, needs more optimization.
23 602 0.249458836455 Henry Cohn, 2026, needs more optimization.
23 603 0.249617835762 Henry Cohn, 2026, needs more optimization.
23 604 0.249623655938 Henry Cohn, 2026, needs more optimization.
23 605 0.249806507383 Henry Cohn, 2026, needs more optimization.
23 894 0.25 Henry Cohn, 2026.
4⁢x−1
23 895 0.250001006462 Henry Cohn, 2026, needs more optimization.
23 896 0.252693959928 Henry Cohn, 2026, needs more optimization.
23 897 0.254297679216 Henry Cohn, 2026, needs more optimization.
23 898 0.255385789253 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
23 899 0.256375872009 Henry Cohn, 2026, needs more optimization.
23 900 0.256477369157 Henry Cohn, 2026, needs more optimization.
23 901 0.256477369165 Henry Cohn, 2026, needs more optimization.
23 902 0.256932999542 Henry Cohn, 2026, needs more optimization.
23 903 0.257961139445 Henry Cohn, 2026, needs more optimization.
23 904 0.258522625187 Henry Cohn, 2026, needs more optimization.
23 905 0.259254131041 Henry Cohn, 2026, needs more optimization.
23 906 0.259361838791 Henry Cohn, 2026, needs more optimization.
23 907 0.261480085536 Henry Cohn, 2026, needs more optimization.
23 908 0.264857826632 Henry Cohn, 2026, needs more optimization.
23 909 0.265174498054 Henry Cohn, 2026, needs more optimization.
23 910 0.265378339351 Henry Cohn, 2026, needs more optimization.
23 911 0.266013487955 Henry Cohn, 2026, needs more optimization.
23 912 0.267146116078 Henry Cohn, 2026, needs more optimization.
23 913 0.268028956841 Henry Cohn, 2026, needs more optimization.
23 914 0.268685082742 Henry Cohn, 2026, needs more optimization.
23 915 0.268789498377 Henry Cohn, 2026, needs more optimization.
23 916 0.269609695139 Henry Cohn, 2026, needs more optimization.
23 917 0.270148026773 Henry Cohn, 2026, needs more optimization.
23 918 0.270686088284 Henry Cohn, 2026, needs more optimization.
23 919 0.271126062943 Henry Cohn, 2026, needs more optimization.
23 920 0.271420462777 Henry Cohn, 2026, needs more optimization.
23 921 0.272114129023 Henry Cohn, 2026, needs more optimization.
23 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
23 4600* 0.333333333334 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
3⁢x−1
24 49 0.032924519945 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11616⁢x3−576⁢x2−24⁢x+1
24 50 0.038461538462 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
26⁢x−1
24 51 0.045537713846 Henry Cohn, 2025.
24 52 0.046377212908 Henry Cohn, 2025.
24 53 0.046712202497 Henry Cohn, 2025.
24 54 0.047284571428 Henry Cohn, 2025.
24 55 0.047381601960 Henry Cohn, 2024.
24 56 0.047562533008 Henry Cohn, 2026.
24 57 0.053295295011 Henry Cohn, 2026.
24 58 0.054361642549 Henry Cohn, 2026.
24 59 0.057903810057 Henry Cohn, 2026.
24 60 0.061561217808 Henry Cohn, 2026.
24 61 0.064589747421 Henry Cohn, 2026.
24 62 0.065059060069 Henry Cohn, 2026, needs more optimization.
24 63 0.065490775921 Henry Cohn, 2026, needs more optimization.
24 64 0.065895166529 Henry Cohn, 2026, needs more optimization.
24 65 0.066584831638 Henry Cohn, 2026, needs more optimization.
24 66 0.068178739603 Henry Cohn, 2026, needs more optimization.
24 67 0.070762396841 Henry Cohn, 2026.
24 68 0.072116568734 Henry Cohn, 2026.
24 69 0.073247042433 Henry Cohn, 2026.
24 70 0.076551768722 Henry Cohn, 2026, needs more optimization.
24 71 0.076919863254 Henry Cohn, 2026, needs more optimization.
24 72 0.077408479699 Henry Cohn, 2026, needs more optimization.
24 73 0.077739709459 Henry Cohn, 2026, needs more optimization.
24 74 0.077908661685 Henry Cohn, 2026, needs more optimization.
24 75 0.078506895697 Henry Cohn, 2026, needs more optimization.
24 76 0.078850061999 Henry Cohn, 2026, needs more optimization.
24 77 0.081772395483 Henry Cohn, 2026, needs more optimization.
24 78 0.082752960006 Henry Cohn, 2026, needs more optimization.
24 79 0.083132279756 Henry Cohn, 2026, needs more optimization.
24 80 0.083243848155 Henry Cohn, 2026, needs more optimization.
24 81 0.083290446134 Henry Cohn, 2026, needs more optimization.
24 82 0.083315859918 Henry Cohn, 2026, needs more optimization.
24 83 0.083315860155 Henry Cohn, 2026, needs more optimization.
24 84 0.083327201975 Henry Cohn, 2026, needs more optimization.
24 85 0.083328479334 Henry Cohn, 2026, needs more optimization.
24 86 0.086216670296 Henry Cohn, 2026, needs more optimization.
24 87 0.088123581467 Henry Cohn, 2026, needs more optimization.
24 88 0.089529919867 Henry Cohn, 2026, needs more optimization.
24 89 0.090146321658 Henry Cohn, 2026, needs more optimization.
24 90 0.090524183304 Henry Cohn, 2026, needs more optimization.
24 91 0.090706241610 Henry Cohn, 2026, needs more optimization.
24 92 0.090827423226 Henry Cohn, 2026, needs more optimization.
24 93 0.090884056128 Henry Cohn, 2026, needs more optimization.
24 97 0.090909090540 Henry Cohn, 2026, needs more optimization.
24 98 0.090909090556 Henry Cohn, 2026, needs more optimization.
24 99 0.090909090568 Henry Cohn, 2026, needs more optimization.
24 104 0.090909090571 Henry Cohn, 2026, needs more optimization.
24 105 0.091487373996 Henry Cohn, 2026, needs more optimization.
24 106 0.095233114625 Henry Cohn, 2026, needs more optimization.
24 107 0.100951897359 Henry Cohn, 2026, needs more optimization.
24 108 0.105645381061 Henry Cohn, 2026, needs more optimization.
24 109 0.110674437886 Henry Cohn, 2026, needs more optimization.
24 110 0.110674454154 Henry Cohn, 2026, needs more optimization.
24 111 0.110685596623 Henry Cohn, 2026, needs more optimization.
24 112 0.110685654624 Henry Cohn, 2026, needs more optimization.
24 113 0.110865971607 Henry Cohn, 2026, needs more optimization.
24 118 0.111099565428 Henry Cohn, 2025, needs more optimization.
24 121 0.111111111112 Henry Cohn, 2026.
9⁢x−1
24 122 0.112098401211 Henry Cohn, 2026, needs more optimization.
24 123 0.116165160132 Henry Cohn, 2026, needs more optimization.
24 124 0.117892095501 Henry Cohn, 2026, needs more optimization.
24 125 0.122807017544 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
57⁢x−7
24 126 0.131751192408 Henry Cohn, 2026, needs more optimization.
24 127 0.131762642933 Henry Cohn, 2026, needs more optimization.
24 128 0.131762643101 Henry Cohn, 2026, needs more optimization.
24 129 0.131764719093 Henry Cohn, 2026, needs more optimization.
24 130 0.131764720548 Henry Cohn, 2026, needs more optimization.
24 131 0.131774458399 Henry Cohn, 2026, needs more optimization.
24 132 0.131777154590 Henry Cohn, 2026, needs more optimization.
24 133 0.131781799024 Henry Cohn, 2026, needs more optimization.
24 134 0.131784002661 Henry Cohn, 2026, needs more optimization.
24 135 0.131946344782 Henry Cohn, 2026, needs more optimization.
24 136 0.132201445273 Henry Cohn, 2026, needs more optimization.
24 137 0.132919808061 Henry Cohn, 2026, needs more optimization.
24 138 0.133265101145 Henry Cohn, 2026, needs more optimization.
24 139 0.134214454261 Henry Cohn, 2026, needs more optimization.
24 140 0.134394032533 Henry Cohn, 2026, needs more optimization.
24 141 0.134777353034 Henry Cohn, 2026, needs more optimization.
24 142 0.134934448941 Henry Cohn, 2026, needs more optimization.
24 143 0.135094556280 Henry Cohn, 2026, needs more optimization.
24 149 0.135135135136 Orthogonal union of 147 points in 23 dimensions and 2 points in 1 dimension.
37⁢x−5
24 152 0.135135665735 Henry Cohn, 2026, needs more optimization.
24 153 0.136258601804 Henry Cohn, 2026, needs more optimization.
24 154 0.136258667057 Henry Cohn, 2026, needs more optimization.
24 155 0.137111103874 Henry Cohn, 2026, needs more optimization.
24 156 0.139155468816 Henry Cohn, 2026, needs more optimization.
24 157 0.141118833718 Henry Cohn, 2026, needs more optimization.
24 158 0.142857107111 Henry Cohn, 2026, needs more optimization.
24 159 0.142857110816 Henry Cohn, 2026, needs more optimization.
24 161 0.142857110831 Henry Cohn, 2026, needs more optimization.
24 162 0.142857110917 Henry Cohn, 2026, needs more optimization.
24 163 0.142857116250 Henry Cohn, 2026, needs more optimization.
24 164 0.142857116266 Henry Cohn, 2026, needs more optimization.
24 166 0.142857121940 Henry Cohn, 2026, needs more optimization.
24 168 0.142857122001 Henry Cohn, 2026, needs more optimization.
24 171 0.142857138919 Henry Cohn, 2026, needs more optimization.
24 172 0.142857140416 Henry Cohn, 2026, needs more optimization.
24 173 0.142857171592 Henry Cohn, 2026, needs more optimization.
24 174 0.142857172713 Henry Cohn, 2026, needs more optimization.
24 175 0.143408861499 Henry Cohn, 2026, needs more optimization.
24 176 0.145880462849 Henry Cohn, 2026, needs more optimization.
24 177 0.145880465406 Henry Cohn, 2026, needs more optimization.
24 178 0.145883605837 Henry Cohn, 2026, needs more optimization.
24 179 0.146017714533 Henry Cohn, 2026, needs more optimization.
24 181 0.146043295276 Henry Cohn, 2026, needs more optimization.
24 182 0.148037777785 Henry Cohn, 2026, needs more optimization.
24 183 0.148199577722 Henry Cohn, 2026, needs more optimization.
24 184 0.148268864796 Henry Cohn, 2026, needs more optimization.
24 186 0.148728163557 Henry Cohn, 2026, needs more optimization.
24 187 0.152036767098 Henry Cohn, 2026, needs more optimization.
24 188 0.152152499162 Henry Cohn, 2026, needs more optimization.
24 189 0.152169650228 Henry Cohn, 2026, needs more optimization.
24 190 0.153302835990 Henry Cohn, 2026, needs more optimization.
24 191 0.155105463420 Henry Cohn, 2026, needs more optimization.
24 192 0.155157909295 Henry Cohn, 2026, needs more optimization.
24 193 0.155183119903 Henry Cohn, 2026, needs more optimization.
24 194 0.157422031958 Henry Cohn, 2026, needs more optimization.
24 195 0.157763293576 Henry Cohn, 2026, needs more optimization.
24 196 0.159089475700 Henry Cohn, 2026, needs more optimization.
24 197 0.160025558592 Henry Cohn, 2026, needs more optimization.
24 198 0.160191094937 Henry Cohn, 2026, needs more optimization.
24 199 0.161379380895 Henry Cohn, 2026, needs more optimization.
24 200 0.161471603290 Henry Cohn, 2026, needs more optimization.
24 205 0.161904761905 Orthogonal union of 201 points in 22 dimensions and 4 points in 2 dimensions.
105⁢x−17
24 206 0.161904778714 Henry Cohn, 2026, needs more optimization.
24 207 0.161904778979 Henry Cohn, 2026, needs more optimization.
24 208 0.161904789200 Henry Cohn, 2026, needs more optimization.
24 209 0.161904789352 Henry Cohn, 2026, needs more optimization.
24 210 0.161904789382 Henry Cohn, 2026, needs more optimization.
24 212 0.161904799606 Henry Cohn, 2026, needs more optimization.
24 213 0.161905360980 Henry Cohn, 2026, needs more optimization.
24 214 0.161999048216 Henry Cohn, 2026, needs more optimization.
24 215 0.162166530735 Henry Cohn, 2026, needs more optimization.
24 216 0.163079457095 Henry Cohn, 2026, needs more optimization.
24 217 0.163167999522 Henry Cohn, 2026, needs more optimization.
24 218 0.164149337956 Henry Cohn, 2026, needs more optimization.
24 219 0.164900948088 Henry Cohn, 2026, needs more optimization.
24 220 0.165004593298 Henry Cohn, 2026, needs more optimization.
24 221 0.165523001723 Henry Cohn, 2026, needs more optimization.
24 222 0.165837113959 Henry Cohn, 2026, needs more optimization.
24 223 0.166148056284 Henry Cohn, 2026, needs more optimization.
24 224 0.166407995662 Henry Cohn, 2026, needs more optimization.
24 280 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 2 points in 1 dimension.
6⁢x−1
24 281 0.166666872447 Henry Cohn, 2026, needs more optimization.
24 283 0.166666872448 Henry Cohn, 2026, needs more optimization.
24 284 0.166823801363 Henry Cohn, 2026, needs more optimization.
24 285 0.170017845112 Henry Cohn, 2026, needs more optimization.
24 286 0.171353775603 Henry Cohn, 2026, needs more optimization.
24 287 0.174955147244 Henry Cohn, 2026, needs more optimization.
24 288 0.177014115509 Henry Cohn, 2026, needs more optimization.
24 289 0.179237299385 Henry Cohn, 2026, needs more optimization.
24 290 0.181619521359 Henry Cohn, 2026, needs more optimization.
24 297 0.181818181819 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−2
24 313 0.181818181819 Henry Cohn, 2026, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x−2
24 314 0.182026301858 Henry Cohn, 2026, needs more optimization.
24 315 0.186792613971 Henry Cohn, 2026, needs more optimization.
24 316 0.189656736342 Henry Cohn, 2026, needs more optimization.
24 317 0.191040654359 Henry Cohn, 2026, needs more optimization.
24 318 0.192004275444 Henry Cohn, 2026, needs more optimization.
24 330 0.193548387097 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
31⁢x−6
24 555 0.2 Valentin Khrulkov, 2026, using the program of A. Kravatsky, V. Khrulkov, and I. Oseledets, ImprovEvolve: basin-hopping meets LLM-guided evolutionary search, ICML 2026 AI4Math Workshop Poster, https://openreview.net/forum?id=nE1q0gRDNr, arXiv:2602.10233.
5⁢x−1
24 556 0.200810413628 Henry Cohn, 2026, needs more optimization.
24 557 0.206708802860 Henry Cohn, 2026, needs more optimization.
24 558 0.213698067814 Henry Cohn, 2026, needs more optimization.
24 559 0.216965519689 Henry Cohn, 2026, needs more optimization.
24 560 0.219724280030 Henry Cohn, 2026, needs more optimization.
24 561 0.222335414621 Henry Cohn, 2026, needs more optimization.
24 562 0.222631705348 Henry Cohn, 2026, needs more optimization.
24 563 0.224103170529 Henry Cohn, 2026, needs more optimization.
24 564 0.225318836535 Henry Cohn, 2026, needs more optimization.
24 565 0.226555631528 Henry Cohn, 2026, needs more optimization.
24 566 0.228187912751 Henry Cohn, 2026, needs more optimization.
24 567 0.229101528942 Henry Cohn, 2026, needs more optimization.
24 568 0.230489745562 Henry Cohn, 2026, needs more optimization.
24 569 0.231641341855 Henry Cohn, 2026, needs more optimization.
24 570 0.231785572712 Henry Cohn, 2026, needs more optimization.
24 571 0.232153551205 Henry Cohn, 2026, needs more optimization.
24 572 0.232352084172 Henry Cohn, 2026, needs more optimization.
24 573 0.232834746329 Henry Cohn, 2026, needs more optimization.
24 574 0.233340895141 Henry Cohn, 2026, needs more optimization.
24 581 0.233711730709 Numaro AI Autoresearch, 11,000+ New Verified Spherical-Code Records from AI Autoresearch, Numaro Research Report NUMARO-2026-015 (2026), https://numaro.tech/research/spherical-codes-2026/.
160⁢x2−16⁢x−5
24 582 0.234149666387 Henry Cohn, 2026, needs more optimization.
24 583 0.234571789872 Henry Cohn, 2026, needs more optimization.
24 584 0.234981702152 Henry Cohn, 2026, needs more optimization.
24 585 0.235415802070 Henry Cohn, 2026, needs more optimization.
24 586 0.235875663669 Henry Cohn, 2026, needs more optimization.
24 587 0.238314333145 Henry Cohn, 2026, needs more optimization.
24 590 0.238433735775 Henry Cohn, 2026, needs more optimization.
24 592 0.238436357318 Henry Cohn, 2026, needs more optimization.
24 593 0.238462394875 Henry Cohn, 2026, needs more optimization.
24 594 0.238730020024 Henry Cohn, 2026, needs more optimization.
24 595 0.239289090176 Henry Cohn, 2026, needs more optimization.
24 596 0.239314434808 Henry Cohn, 2026, needs more optimization.
24 597 0.239518109186 Henry Cohn, 2026, needs more optimization.
24 598 0.240308959168 Henry Cohn, 2026, needs more optimization.
24 599 0.240488938298 Henry Cohn, 2026, needs more optimization.
24 600 0.241437585180 Henry Cohn, 2026, needs more optimization.
24 603 0.241656465180 Henry Cohn, 2026, needs more optimization.
24 604 0.241725417749 Henry Cohn, 2026, needs more optimization.
24 605 0.241966176227 Henry Cohn, 2026, needs more optimization.
24 606 0.242209503492 Henry Cohn, 2026, needs more optimization.
24 607 0.242711667759 Henry Cohn, 2026, needs more optimization.
24 608 0.243233163962 Henry Cohn, 2026, needs more optimization.
24 609 0.243463942893 Henry Cohn, 2026, needs more optimization.
24 610 0.243644763097 Henry Cohn, 2026, needs more optimization.
24 611 0.244083426429 Henry Cohn, 2026, needs more optimization.
24 612 0.244436019320 Henry Cohn, 2026, needs more optimization.
24 613 0.244963197910 Henry Cohn, 2026, needs more optimization.
24 614 0.245511754509 Henry Cohn, 2026, needs more optimization.
24 615 0.245654594798 Henry Cohn, 2026, needs more optimization.
24 616 0.246255999297 Henry Cohn, 2026, needs more optimization.
24 617 0.246727679861 Henry Cohn, 2026, needs more optimization.
24 618 0.247121047575 Henry Cohn, 2026, needs more optimization.
24 619 0.247248817482 Henry Cohn, 2026, needs more optimization.
24 620 0.247248987877 Henry Cohn, 2026, needs more optimization.
24 621 0.247607651382 Henry Cohn, 2026, needs more optimization.
24 622 0.248141533190 Henry Cohn, 2026, needs more optimization.
24 623 0.248433848604 Henry Cohn, 2026, needs more optimization.
24 624 0.248857940955 Henry Cohn, 2026, needs more optimization.
24 625 0.249071681539 Henry Cohn, 2026, needs more optimization.
24 626 0.249388505332 Henry Cohn, 2026, needs more optimization.
24 627 0.249552413894 Henry Cohn, 2026, needs more optimization.
24 628 0.249616029692 Henry Cohn, 2026, needs more optimization.
24 629 0.249778077628 Henry Cohn, 2026, needs more optimization.
24 896 0.25 Orthogonal union of 894 points in 23 dimensions and 2 points in 1 dimension.
4⁢x−1
24 897 0.250001006462 Orthogonal union of 895 points in 23 dimensions and 2 points in 1 dimension.
24 898 0.250016848122 Henry Cohn, 2026, needs more optimization.
24 899 0.250018154639 Henry Cohn, 2026, needs more optimization.
24 900 0.250026459047 Henry Cohn, 2026, needs more optimization.
24 901 0.250027444738 Henry Cohn, 2026, needs more optimization.
24 903 0.250118983412 Henry Cohn, 2026, needs more optimization.
24 904 0.250119224070 Henry Cohn, 2026, needs more optimization.
24 905 0.250125754699 Henry Cohn, 2026, needs more optimization.
24 906 0.250174633895 Henry Cohn, 2026, needs more optimization.
24 907 0.250242229553 Henry Cohn, 2026, needs more optimization.
24 908 0.251063427438 Henry Cohn, 2026, needs more optimization.
24 909 0.251279908264 Henry Cohn, 2026, needs more optimization.
24 910 0.251724139730 Henry Cohn, 2026, needs more optimization.
24 911 0.254871642763 Henry Cohn, 2026, needs more optimization.
24 912 0.255861411969 Henry Cohn, 2026, needs more optimization.
24 913 0.255943696830 Henry Cohn, 2026, needs more optimization.
24 914 0.256257142704 Henry Cohn, 2026, needs more optimization.
24 915 0.256454397140 Henry Cohn, 2026, needs more optimization.
24 916 0.256459943314 Henry Cohn, 2026, needs more optimization.
24 917 0.256470502772 Henry Cohn, 2026, needs more optimization.
24 918 0.256473260801 Henry Cohn, 2026, needs more optimization.
24 919 0.256751368104 Henry Cohn, 2026, needs more optimization.
24 920 0.257033692826 Henry Cohn, 2026, needs more optimization.
24 921 0.257594059566 Henry Cohn, 2026, needs more optimization.
24 922 0.258303174054 Henry Cohn, 2026, needs more optimization.
24 923 0.258827406898 Henry Cohn, 2026, needs more optimization.
24 924 0.259321902521 Henry Cohn, 2026, needs more optimization.
24 925 0.259346846692 Henry Cohn, 2026, needs more optimization.
24 926 0.261252565324 Henry Cohn, 2026, needs more optimization.
24 927 0.262252469518 Henry Cohn, 2026, needs more optimization.
24 928 0.262599724477 Henry Cohn, 2026, needs more optimization.
24 929 0.263666324862 Henry Cohn, 2026, needs more optimization.
24 930 0.264010259476 Henry Cohn, 2026, needs more optimization.
24 931 0.264463051660 Henry Cohn, 2026, needs more optimization.
24 932 0.265235834632 Henry Cohn, 2026, needs more optimization.
24 933 0.265461422854 Henry Cohn, 2026, needs more optimization.
24 934 0.266492569836 Henry Cohn, 2026, needs more optimization.
24 935 0.266799196662 Henry Cohn, 2026, needs more optimization.
24 936 0.267123502685 Henry Cohn, 2026, needs more optimization.
24 937 0.267156279140 Henry Cohn, 2026, needs more optimization.
24 938 0.267445016225 Henry Cohn, 2026, needs more optimization.
24 939 0.267901406408 Henry Cohn, 2026, needs more optimization.
24 940 0.268407315107 Henry Cohn, 2026, needs more optimization.
24 941 0.268884429652 Henry Cohn, 2026, needs more optimization.
24 942 0.269124707906 Henry Cohn, 2026, needs more optimization.
24 943 0.270068613985 Henry Cohn, 2026, needs more optimization.
24 945 0.270857267931 Henry Cohn, 2026, needs more optimization.
24 946 0.271317551542 Henry Cohn, 2026, needs more optimization.
24 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
24 196560* 0.5 J. Leech, Notes on sphere packings, Canadian J. Math. 19 (1967), 251–267, doi:10.4153/CJM-1967-017-0; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8.
2⁢x−1
25 51 0.031729360276 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13225⁢x3−625⁢x2−25⁢x+1
25 52 0.037068271283 Henry Cohn, 2025.
25 55 0.04 Henry Cohn, 2026.
25⁢x−1
25 56 0.046433703861 Henry Cohn, 2025, needs more optimization.
25 57 0.046835490758 Henry Cohn, 2026, needs more optimization.
25 58 0.046863920964 Henry Cohn, 2025.
25 59 0.051394584232 Henry Cohn, 2024.
25 60 0.052966665528 Henry Cohn, 2026.
25 61 0.056064008005 Henry Cohn, 2026.
25 62 0.060613957797 Henry Cohn, 2026.
25 63 0.062392555280 Henry Cohn, 2026.
25 64 0.064223832775 Henry Cohn, 2026.
25 65 0.065021575237 Henry Cohn, 2026, needs more optimization.
25 66 0.065051275928 Henry Cohn, 2026, needs more optimization.
25 67 0.066210992151 Henry Cohn, 2026, needs more optimization.
25 68 0.066465897930 Henry Cohn, 2026, needs more optimization.
25 69 0.068627707329 Henry Cohn, 2026.
25 70 0.071055411990 Henry Cohn, 2026.
25 71 0.071772043787 Henry Cohn, 2026, needs more optimization.
25 72 0.073324155306 Henry Cohn, 2026, needs more optimization.
25 73 0.076166300235 Henry Cohn, 2026, needs more optimization.
25 74 0.076826407245 Henry Cohn, 2026, needs more optimization.
25 76 0.076922977355 Henry Cohn, 2026, needs more optimization.
25 77 0.077469182907 Henry Cohn, 2026, needs more optimization.
25 78 0.077915334945 Henry Cohn, 2026, needs more optimization.
25 79 0.078551128877 Henry Cohn, 2026, needs more optimization.
25 80 0.080764897911 Henry Cohn, 2026, needs more optimization.
25 81 0.082025427537 Henry Cohn, 2026, needs more optimization.
25 82 0.082586416726 Henry Cohn, 2026, needs more optimization.
25 83 0.082940816507 Henry Cohn, 2026, needs more optimization.
25 85 0.083095965795 Henry Cohn, 2026, needs more optimization.
25 86 0.083268254948 Henry Cohn, 2026, needs more optimization.
25 87 0.083303405556 Henry Cohn, 2026, needs more optimization.
25 88 0.083314404622 Henry Cohn, 2026, needs more optimization.
25 89 0.085157324776 Henry Cohn, 2026, needs more optimization.
25 90 0.087152563830 Henry Cohn, 2026, needs more optimization.
25 91 0.087278836679 Henry Cohn, 2026, needs more optimization.
25 92 0.088760001589 Henry Cohn, 2026, needs more optimization.
25 93 0.089631257128 Henry Cohn, 2026, needs more optimization.
25 94 0.089904490585 Henry Cohn, 2026, needs more optimization.
25 95 0.090423382552 Henry Cohn, 2026, needs more optimization.
25 96 0.090621476881 Henry Cohn, 2026, needs more optimization.
25 97 0.090825310211 Henry Cohn, 2026, needs more optimization.
25 98 0.090826482007 Henry Cohn, 2026, needs more optimization.
25 99 0.090890603300 Henry Cohn, 2026, needs more optimization.
25 100 0.090906141844 Henry Cohn, 2026, needs more optimization.
25 101 0.090908872477 Henry Cohn, 2026, needs more optimization.
25 106 0.090909090571 Henry Cohn, 2026, needs more optimization.
25 107 0.090909344634 Henry Cohn, 2026, needs more optimization.
25 108 0.090910559169 Henry Cohn, 2026, needs more optimization.
25 109 0.095542644965 Henry Cohn, 2026, needs more optimization.
25 110 0.099772180030 Henry Cohn, 2026, needs more optimization.
25 111 0.102626189891 Henry Cohn, 2026, needs more optimization.
25 117 0.105319726475 Henry Cohn, 2026.
375⁢x2−30⁢x−1
25 118 0.107225148391 Henry Cohn, 2026, needs more optimization.
25 119 0.108599687945 Henry Cohn, 2026, needs more optimization.
25 120 0.108643756678 Henry Cohn, 2026, needs more optimization.
25 121 0.109292354357 Henry Cohn, 2026, needs more optimization.
25 122 0.109483241755 Henry Cohn, 2026, needs more optimization.
25 123 0.109834547978 Henry Cohn, 2026, needs more optimization.
25 124 0.111025491684 Henry Cohn, 2026, needs more optimization.
25 125 0.111109577261 Henry Cohn, 2026, needs more optimization.
25 126 0.111115484390 Henry Cohn, 2026, needs more optimization.
25 127 0.111141877697 Henry Cohn, 2026, needs more optimization.
25 128 0.111329528695 Henry Cohn, 2026, needs more optimization.
25 129 0.117076938705 Henry Cohn, 2026, needs more optimization.
25 130 0.119943710439 Henry Cohn, 2026, needs more optimization.
25 131 0.121764571046 Henry Cohn, 2026, needs more optimization.
25 132 0.123580525290 Henry Cohn, 2026, needs more optimization.
25 133 0.124981451545 Henry Cohn, 2026, needs more optimization.
25 134 0.126241839380 Henry Cohn, 2026, needs more optimization.
25 135 0.128185811082 Henry Cohn, 2026, needs more optimization.
25 136 0.129707611770 Henry Cohn, 2026, needs more optimization.
25 137 0.131691144880 Henry Cohn, 2026, needs more optimization.
25 138 0.131739301924 Henry Cohn, 2026, needs more optimization.
25 139 0.131774235336 Henry Cohn, 2026, needs more optimization.
25 140 0.131778436263 Henry Cohn, 2026, needs more optimization.
25 141 0.131805865850 Henry Cohn, 2026, needs more optimization.
25 142 0.132199110869 Henry Cohn, 2026, needs more optimization.
25 143 0.132804817029 Henry Cohn, 2026, needs more optimization.
25 156 0.133333333334 Henry Cohn, 2023. In Ericson and Zinoviev's notation, this code is the union of a code constructed by CW2 from C : (26,6,8,130) and -S25 by CW2.
15⁢x−2
25 157 0.135170715877 Henry Cohn, 2026, needs more optimization.
25 158 0.136963466832 Henry Cohn, 2026, needs more optimization.
25 159 0.138087374340 Henry Cohn, 2026, needs more optimization.
25 160 0.139594340473 Henry Cohn, 2026, needs more optimization.
25 161 0.141378220365 Henry Cohn, 2026, needs more optimization.
25 162 0.142805144270 Henry Cohn, 2026, needs more optimization.
25 163 0.142822030377 Henry Cohn, 2026, needs more optimization.
25 164 0.142832909369 Henry Cohn, 2026, needs more optimization.
25 165 0.142837323020 Henry Cohn, 2026, needs more optimization.
25 166 0.142837331455 Henry Cohn, 2026, needs more optimization.
25 167 0.142838739211 Henry Cohn, 2026, needs more optimization.
25 168 0.142845442260 Henry Cohn, 2026, needs more optimization.
25 169 0.142849944380 Henry Cohn, 2026, needs more optimization.
25 170 0.142850086774 Henry Cohn, 2026, needs more optimization.
25 171 0.142850086865 Henry Cohn, 2026, needs more optimization.
25 172 0.142851003131 Henry Cohn, 2026, needs more optimization.
25 173 0.142855879293 Henry Cohn, 2026, needs more optimization.
25 174 0.142855880069 Henry Cohn, 2026, needs more optimization.
25 175 0.142855940428 Henry Cohn, 2026, needs more optimization.
25 176 0.142855961129 Henry Cohn, 2026, needs more optimization.
25 177 0.142858216513 Henry Cohn, 2026, needs more optimization.
25 178 0.142877360805 Henry Cohn, 2026, needs more optimization.
25 179 0.142898543905 Henry Cohn, 2026, needs more optimization.
25 180 0.143251460698 Henry Cohn, 2026, needs more optimization.
25 181 0.144733173587 Henry Cohn, 2026, needs more optimization.
25 182 0.144739295888 Henry Cohn, 2026, needs more optimization.
25 183 0.145771481499 Henry Cohn, 2026, needs more optimization.
25 184 0.145771483638 Henry Cohn, 2026, needs more optimization.
25 185 0.146029577696 Henry Cohn, 2026, needs more optimization.
25 186 0.146181528682 Henry Cohn, 2026, needs more optimization.
25 187 0.146197142871 Henry Cohn, 2026, needs more optimization.
25 188 0.146793273955 Henry Cohn, 2026, needs more optimization.
25 189 0.147155580015 Henry Cohn, 2026, needs more optimization.
25 190 0.147234993374 Henry Cohn, 2026, needs more optimization.
25 191 0.147332692501 Henry Cohn, 2026, needs more optimization.
25 192 0.147676645805 Henry Cohn, 2026, needs more optimization.
25 193 0.150396955092 Henry Cohn, 2026, needs more optimization.
25 194 0.151345558252 Henry Cohn, 2026, needs more optimization.
25 197 0.151597571160 Henry Cohn, 2026, needs more optimization.
25 198 0.152707409421 Henry Cohn, 2026, needs more optimization.
25 199 0.152729847990 Henry Cohn, 2026, needs more optimization.
25 200 0.153212008046 Henry Cohn, 2026, needs more optimization.
25 201 0.153217082104 Henry Cohn, 2026, needs more optimization.
25 202 0.153708071823 Henry Cohn, 2026, needs more optimization.
25 203 0.153823448220 Henry Cohn, 2026, needs more optimization.
25 204 0.155228358378 Henry Cohn, 2026, needs more optimization.
25 205 0.155228431593 Henry Cohn, 2026, needs more optimization.
25 206 0.155399671701 Henry Cohn, 2026, needs more optimization.
25 207 0.155399682083 Henry Cohn, 2026, needs more optimization.
25 208 0.155399683812 Henry Cohn, 2026, needs more optimization.
25 209 0.156568030323 Henry Cohn, 2026, needs more optimization.
25 210 0.157315917020 Henry Cohn, 2026, needs more optimization.
25 211 0.158563865581 Henry Cohn, 2026, needs more optimization.
25 212 0.158675112057 Henry Cohn, 2026, needs more optimization.
25 213 0.158877482383 Henry Cohn, 2026, needs more optimization.
25 214 0.158878753549 Henry Cohn, 2026, needs more optimization.
25 215 0.158878798921 Robert Dallara, 2026.
25 216 0.159797714184 Henry Cohn, 2026, needs more optimization.
25 217 0.159868880759 Henry Cohn, 2026, needs more optimization.
25 218 0.160701199133 Henry Cohn, 2026, needs more optimization.
25 219 0.160855671732 Henry Cohn, 2026, needs more optimization.
25 220 0.161493982472 Henry Cohn, 2026, needs more optimization.
25 221 0.161923683801 Henry Cohn, 2026, needs more optimization.
25 222 0.161923691371 Henry Cohn, 2026, needs more optimization.
25 223 0.162163211000 Henry Cohn, 2026, needs more optimization.
25 224 0.162625233678 Henry Cohn, 2026, needs more optimization.
25 225 0.162858629181 Henry Cohn, 2026, needs more optimization.
25 226 0.163573460492 Henry Cohn, 2026, needs more optimization.
25 227 0.164285931671 Henry Cohn, 2026, needs more optimization.
25 228 0.164653882126 Henry Cohn, 2026, needs more optimization.
25 229 0.165082928251 Henry Cohn, 2026, needs more optimization.
25 230 0.165409424397 Henry Cohn, 2026, needs more optimization.
25 231 0.165848324413 Henry Cohn, 2026, needs more optimization.
25 232 0.165954615291 Henry Cohn, 2026, needs more optimization.
25 233 0.166177158299 Henry Cohn, 2026, needs more optimization.
25 234 0.166381766757 Henry Cohn, 2026, needs more optimization.
25 235 0.166444771476 Henry Cohn, 2026, needs more optimization.
25 236 0.166531499644 Henry Cohn, 2026, needs more optimization.
25 237 0.166569196343 Henry Cohn, 2026, needs more optimization.
25 238 0.166588557915 Henry Cohn, 2026, needs more optimization.
25 282 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 4 points in 2 dimensions.
6⁢x−1
25 285 0.166666872445 Henry Cohn, 2026, needs more optimization.
25 286 0.166667609218 Henry Cohn, 2026, needs more optimization.
25 287 0.166667609465 Henry Cohn, 2026, needs more optimization.
25 288 0.166667609972 Henry Cohn, 2026, needs more optimization.
25 289 0.166668396516 Henry Cohn, 2026, needs more optimization.
25 290 0.166693644947 Henry Cohn, 2026, needs more optimization.
25 291 0.167643892032 Henry Cohn, 2026, needs more optimization.
25 292 0.169481786538 Henry Cohn, 2026, needs more optimization.
25 293 0.169996117874 Henry Cohn, 2026, needs more optimization.
25 294 0.172043831194 Henry Cohn, 2026, needs more optimization.
25 295 0.173773086917 Henry Cohn, 2026, needs more optimization.
25 296 0.175881260302 Henry Cohn, 2026, needs more optimization.
25 297 0.177343314717 Henry Cohn, 2026, needs more optimization.
25 298 0.178927883944 Henry Cohn, 2026, needs more optimization.
25 299 0.180496403440 Henry Cohn, 2026, needs more optimization.
25 315 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 2 points in 1 dimension.
11⁢x−2
25 318 0.181818678585 Henry Cohn, 2026, needs more optimization.
25 319 0.181819266673 Henry Cohn, 2026, needs more optimization.
25 320 0.181820282642 Henry Cohn, 2026, needs more optimization.
25 321 0.181824326734 Henry Cohn, 2026, needs more optimization.
25 322 0.183669539689 Henry Cohn, 2026, needs more optimization.
25 323 0.184797125679 Henry Cohn, 2026, needs more optimization.
25 324 0.185421054077 Henry Cohn, 2026, needs more optimization.
25 325 0.187069548254 Henry Cohn, 2026, needs more optimization.
25 326 0.187751127096 Henry Cohn, 2026, needs more optimization.
25 327 0.189795555530 Henry Cohn, 2026, needs more optimization.
25 328 0.191162946551 Henry Cohn, 2026, needs more optimization.
25 329 0.192095868404 Henry Cohn, 2026, needs more optimization.
25 332 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 2 points in 1 dimension.
31⁢x−6
25 333 0.193548403014 Henry Cohn, 2026, needs more optimization.
25 334 0.193551665272 Henry Cohn, 2026, needs more optimization.
25 335 0.193891559982 Henry Cohn, 2026, needs more optimization.
25 340 0.194120819402 Henry Cohn, 2026, needs more optimization.
25 341 0.196567236582 Henry Cohn, 2026, needs more optimization.
25 342 0.198076126800 Henry Cohn, 2026, needs more optimization.
25 343 0.199509871327 Henry Cohn, 2026, needs more optimization.
25 557 0.2 Orthogonal union of 555 points in 24 dimensions and 2 points in 1 dimension.
5⁢x−1
25 559 0.200001487222 Henry Cohn, 2026, needs more optimization.
25 560 0.200001493690 Henry Cohn, 2026, needs more optimization.
25 561 0.200001742850 Henry Cohn, 2026, needs more optimization.
25 562 0.200004107004 Henry Cohn, 2026, needs more optimization.
25 563 0.200189841018 Henry Cohn, 2026, needs more optimization.
25 564 0.201394626702 Henry Cohn, 2026, needs more optimization.
25 565 0.203326183201 Henry Cohn, 2026, needs more optimization.
25 566 0.206981620304 Henry Cohn, 2026, needs more optimization.
25 567 0.209904141467 Henry Cohn, 2026, needs more optimization.
25 568 0.211754446603 Henry Cohn, 2026, needs more optimization.
25 569 0.214498154344 Henry Cohn, 2026, needs more optimization.
25 570 0.216470507174 Henry Cohn, 2026, needs more optimization.
25 571 0.217980205855 Henry Cohn, 2026, needs more optimization.
25 572 0.219514094737 Henry Cohn, 2026, needs more optimization.
25 573 0.221344252607 Henry Cohn, 2026, needs more optimization.
25 574 0.222236012315 Henry Cohn, 2026, needs more optimization.
25 575 0.223718323193 Henry Cohn, 2026, needs more optimization.
25 576 0.224654116977 Henry Cohn, 2026, needs more optimization.
25 577 0.226221497788 Henry Cohn, 2026, needs more optimization.
25 578 0.226394090711 Henry Cohn, 2026, needs more optimization.
25 579 0.227363312737 Henry Cohn, 2026, needs more optimization.
25 580 0.228299661563 Henry Cohn, 2026, needs more optimization.
25 581 0.229074267178 Henry Cohn, 2026, needs more optimization.
25 582 0.229574635256 Henry Cohn, 2026, needs more optimization.
25 583 0.230788304044 Henry Cohn, 2026, needs more optimization.
25 584 0.231754086739 Henry Cohn, 2026, needs more optimization.
25 585 0.232042635085 Henry Cohn, 2026, needs more optimization.
25 586 0.232966921991 Henry Cohn, 2026, needs more optimization.
25 587 0.233520245260 Henry Cohn, 2026, needs more optimization.
25 588 0.234186534186 Henry Cohn, 2026, needs more optimization.
25 589 0.235014579710 Henry Cohn, 2026, needs more optimization.
25 590 0.235669563766 Henry Cohn, 2026, needs more optimization.
25 591 0.236457109696 Henry Cohn, 2026, needs more optimization.
25 592 0.237387934837 Henry Cohn, 2026, needs more optimization.
25 593 0.237481663429 Henry Cohn, 2026, needs more optimization.
25 594 0.237736338588 Henry Cohn, 2026, needs more optimization.
25 596 0.238096840109 Henry Cohn, 2026, needs more optimization.
25 599 0.238096841245 Henry Cohn, 2026, needs more optimization.
25 600 0.238097666705 Henry Cohn, 2026, needs more optimization.
25 601 0.238097666708 Henry Cohn, 2026, needs more optimization.
25 602 0.238097666942 Henry Cohn, 2026, needs more optimization.
25 603 0.238097666948 Henry Cohn, 2026, needs more optimization.
25 604 0.238098381076 Henry Cohn, 2026, needs more optimization.
25 605 0.238098381077 Henry Cohn, 2026, needs more optimization.
25 606 0.238098381093 Henry Cohn, 2026, needs more optimization.
25 607 0.238098467518 Henry Cohn, 2026, needs more optimization.
25 608 0.238101588070 Henry Cohn, 2026, needs more optimization.
25 609 0.238104304287 Henry Cohn, 2026, needs more optimization.
25 611 0.238109804579 Henry Cohn, 2026, needs more optimization.
25 612 0.238109809198 Henry Cohn, 2026, needs more optimization.
25 613 0.238126839909 Henry Cohn, 2026, needs more optimization.
25 614 0.238363327802 Henry Cohn, 2026, needs more optimization.
25 615 0.238497981188 Henry Cohn, 2026, needs more optimization.
25 616 0.238626701106 Henry Cohn, 2026, needs more optimization.
25 617 0.238878736753 Henry Cohn, 2026, needs more optimization.
25 618 0.239091956350 Henry Cohn, 2026, needs more optimization.
25 620 0.239321077598 Henry Cohn, 2026, needs more optimization.
25 621 0.239790839790 Henry Cohn, 2026, needs more optimization.
25 622 0.240211140665 Henry Cohn, 2026, needs more optimization.
25 623 0.240851453791 Henry Cohn, 2026, needs more optimization.
25 624 0.241348650007 Henry Cohn, 2026, needs more optimization.
25 625 0.241730929781 Henry Cohn, 2026, needs more optimization.
25 626 0.241902961641 Henry Cohn, 2026, needs more optimization.
25 627 0.247248202427 Henry Cohn, 2026, needs more optimization.
25 628 0.247265292128 Henry Cohn, 2026, needs more optimization.
25 630 0.247449011615 Henry Cohn, 2026, needs more optimization.
25 631 0.247776727701 Henry Cohn, 2026, needs more optimization.
25 632 0.247776800135 Henry Cohn, 2026, needs more optimization.
25 633 0.248005867790 Henry Cohn, 2026, needs more optimization.
25 634 0.248007383859 Henry Cohn, 2026, needs more optimization.
25 637 0.248214980543 Henry Cohn, 2026, needs more optimization.
25 638 0.248433920340 Henry Cohn, 2026, needs more optimization.
25 639 0.248482411398 Henry Cohn, 2026, needs more optimization.
25 640 0.248693076627 Henry Cohn, 2026, needs more optimization.
25 641 0.248703865515 Henry Cohn, 2026, needs more optimization.
25 642 0.248703880007 Henry Cohn, 2026, needs more optimization.
25 645 0.248727513492 Henry Cohn, 2026, needs more optimization.
25 646 0.248826274474 Henry Cohn, 2026, needs more optimization.
25 647 0.248861249135 Henry Cohn, 2026, needs more optimization.
25 648 0.249000649890 Henry Cohn, 2026, needs more optimization.
25 650 0.249059404483 Henry Cohn, 2026, needs more optimization.
25 651 0.249081940555 Henry Cohn, 2026, needs more optimization.
25 652 0.249081941556 Henry Cohn, 2026, needs more optimization.
25 653 0.249109504689 Henry Cohn, 2026, needs more optimization.
25 654 0.249109509915 Henry Cohn, 2026, needs more optimization.
25 655 0.249190814218 Henry Cohn, 2026, needs more optimization.
25 656 0.249247737189 Henry Cohn, 2026, needs more optimization.
25 657 0.249263319322 Henry Cohn, 2026, needs more optimization.
25 658 0.249292729401 Henry Cohn, 2026, needs more optimization.
25 659 0.249401753351 Henry Cohn, 2026, needs more optimization.
25 660 0.249436348671 Henry Cohn, 2026, needs more optimization.
25 661 0.249449563624 Henry Cohn, 2026, needs more optimization.
25 662 0.249486034488 Henry Cohn, 2026, needs more optimization.
25 663 0.249502168221 Henry Cohn, 2026, needs more optimization.
25 664 0.249561878636 Henry Cohn, 2026, needs more optimization.
25 665 0.249588650618 Henry Cohn, 2026, needs more optimization.
25 666 0.249625871969 Henry Cohn, 2026, needs more optimization.
25 667 0.249655508990 Henry Cohn, 2026, needs more optimization.
25 669 0.249710100649 Henry Cohn, 2026, needs more optimization.
25 670 0.249739960505 Henry Cohn, 2026, needs more optimization.
25 671 0.249759819926 Henry Cohn, 2026, needs more optimization.
25 672 0.249783696400 Henry Cohn, 2026, needs more optimization.
25 673 0.249833831537 Henry Cohn, 2026, needs more optimization.
25 674 0.249845505947 Henry Cohn, 2026, needs more optimization.
25 675 0.249865319073 Henry Cohn, 2026, needs more optimization.
25 676 0.249886516568 Henry Cohn, 2026, needs more optimization.
25 677 0.249897425854 Henry Cohn, 2026, needs more optimization.
25 900 0.25 Henry Cohn, 2025.
4⁢x−1
25 901 0.250001996202 Henry Cohn, 2026, needs more optimization.
25 902 0.250002209208 Henry Cohn, 2026, needs more optimization.
25 905 0.250002211933 Henry Cohn, 2026, needs more optimization.
25 908 0.250002217503 Henry Cohn, 2026, needs more optimization.
25 914 0.250002482491 Henry Cohn, 2026, needs more optimization.
25 915 0.250003191892 Henry Cohn, 2026, needs more optimization.
25 916 0.250004659176 Henry Cohn, 2026, needs more optimization.
25 917 0.250011799157 Henry Cohn, 2026, needs more optimization.
25 918 0.250030809075 Henry Cohn, 2026, needs more optimization.
25 919 0.250087781438 Henry Cohn, 2026, needs more optimization.
25 920 0.250244209461 Henry Cohn, 2026, needs more optimization.
25 921 0.250358978716 Henry Cohn, 2026, needs more optimization.
25 922 0.250758608708 Henry Cohn, 2026, needs more optimization.
25 923 0.250979053981 Henry Cohn, 2026, needs more optimization.
25 925 0.251226287779 Henry Cohn, 2026, needs more optimization.
25 926 0.251551486700 Henry Cohn, 2026, needs more optimization.
25 927 0.251780215560 Henry Cohn, 2026, needs more optimization.
25 928 0.252519140461 Henry Cohn, 2026, needs more optimization.
25 929 0.253475912511 Henry Cohn, 2026, needs more optimization.
25 930 0.253742058680 Henry Cohn, 2026, needs more optimization.
25 931 0.254320601119 Henry Cohn, 2026, needs more optimization.
25 932 0.254742979502 Henry Cohn, 2026, needs more optimization.
25 933 0.255066122465 Henry Cohn, 2026, needs more optimization.
25 934 0.255697121448 Henry Cohn, 2026, needs more optimization.
25 935 0.256102664827 Henry Cohn, 2026, needs more optimization.
25 936 0.256829262434 Henry Cohn, 2026, needs more optimization.
25 937 0.257382603386 Henry Cohn, 2026, needs more optimization.
25 938 0.257725254457 Henry Cohn, 2026, needs more optimization.
25 939 0.257998130293 Henry Cohn, 2026, needs more optimization.
25 940 0.258401427644 Henry Cohn, 2026, needs more optimization.
25 941 0.258998486135 Henry Cohn, 2026, needs more optimization.
25 942 0.259698835389 Henry Cohn, 2026, needs more optimization.
25 943 0.259932998932 Henry Cohn, 2026, needs more optimization.
25 944 0.260336139238 Henry Cohn, 2026, needs more optimization.
25 945 0.260786861357 Henry Cohn, 2026, needs more optimization.
25 946 0.261453051245 Henry Cohn, 2026, needs more optimization.
25 947 0.261714905359 Henry Cohn, 2026, needs more optimization.
25 948 0.262039551643 Henry Cohn, 2026, needs more optimization.
25 949 0.262784104438 Henry Cohn, 2026, needs more optimization.
25 950 0.263440570918 Henry Cohn, 2026, needs more optimization.
25 951 0.263587891422 Henry Cohn, 2026, needs more optimization.
25 952 0.263955190896 Henry Cohn, 2026, needs more optimization.
25 953 0.264303257036 Henry Cohn, 2026, needs more optimization.
25 954 0.264470909203 Henry Cohn, 2026, needs more optimization.
25 955 0.265013003623 Henry Cohn, 2026, needs more optimization.
25 956 0.265726538778 Henry Cohn, 2026, needs more optimization.
25 957 0.266135008009 Henry Cohn, 2026, needs more optimization.
25 958 0.266511351948 Henry Cohn, 2026, needs more optimization.
25 959 0.266937165217 Henry Cohn, 2026, needs more optimization.
25 960 0.267275280640 Henry Cohn, 2026, needs more optimization.
25 961 0.267515050021 Henry Cohn, 2026, needs more optimization.
25 962 0.267592500339 Henry Cohn, 2026, needs more optimization.
25 963 0.267822646658 Henry Cohn, 2026, needs more optimization.
25 964 0.268192230351 Henry Cohn, 2026, needs more optimization.
25 965 0.268574102018 Henry Cohn, 2026, needs more optimization.
25 966 0.268912861303 Henry Cohn, 2026, needs more optimization.
25 967 0.269283858709 Henry Cohn, 2026, needs more optimization.
25 968 0.269503522125 Henry Cohn, 2026, needs more optimization.
25 969 0.269811772045 Henry Cohn, 2026, needs more optimization.
25 970 0.269842020955 Henry Cohn, 2026, needs more optimization.
25 971 0.270353900824 Henry Cohn, 2026, needs more optimization.
25 973 0.270644880405 Henry Cohn, 2026, needs more optimization.
25 974 0.270838027746 Henry Cohn, 2026, needs more optimization.
25 975 0.271496905874 Henry Cohn, 2026, needs more optimization.
25 976 0.271758939091 Henry Cohn, 2026, needs more optimization.
25 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
26 53 0.030620650808 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
14976⁢x3−676⁢x2−26⁢x+1
26 54 0.035747861992 Henry Cohn, 2026.
26 55 0.039998970502 Henry Cohn, 2026, needs more optimization.
26 57 0.04 Orthogonal union of 55 points in 25 dimensions and 2 points in 1 dimension.
25⁢x−1
26 58 0.045550434603 Henry Cohn, 2024.
26 59 0.046163974402 Henry Cohn, 2025.
26 60 0.046455966295 Henry Cohn, 2026.
26 61 0.049243792036 Henry Cohn, 2026.
26 62 0.051908007699 Henry Cohn, 2026.
26 63 0.054427947454 Henry Cohn, 2026.
26 64 0.056899291385 Henry Cohn, 2026, needs more optimization.
26 65 0.060274304023 Henry Cohn, 2026, needs more optimization.
26 66 0.062099828320 Henry Cohn, 2026, needs more optimization.
26 67 0.063558077805 Henry Cohn, 2026, needs more optimization.
26 68 0.063599477145 Henry Cohn, 2026, needs more optimization.
26 69 0.064915240899 Henry Cohn, 2026, needs more optimization.
26 70 0.065398731058 Henry Cohn, 2026, needs more optimization.
26 71 0.067315604578 Henry Cohn, 2026.
26 72 0.068297564143 Henry Cohn, 2026, needs more optimization.
26 73 0.070930211069 Henry Cohn, 2026, needs more optimization.
26 74 0.073181771145 Henry Cohn, 2026, needs more optimization.
26 75 0.074026843580 Henry Cohn, 2026, needs more optimization.
26 76 0.075372291887 Henry Cohn, 2026, needs more optimization.
26 77 0.076353856726 Henry Cohn, 2026, needs more optimization.
26 78 0.076846444918 Henry Cohn, 2026, needs more optimization.
26 79 0.076914514483 Henry Cohn, 2026, needs more optimization.
26 80 0.076951826028 Henry Cohn, 2026, needs more optimization.
26 81 0.077575846201 Henry Cohn, 2026, needs more optimization.
26 82 0.077924828163 Henry Cohn, 2026, needs more optimization.
26 83 0.078204418340 Henry Cohn, 2026, needs more optimization.
26 84 0.078381128167 Henry Cohn, 2026, needs more optimization.
26 85 0.078751875327 Henry Cohn, 2026, needs more optimization.
26 86 0.079365739290 Henry Cohn, 2026, needs more optimization.
26 94 0.080685003328 Henry Cohn, 2026.
575⁢x2−34⁢x−1
26 95 0.082980204615 Henry Cohn, 2026, needs more optimization.
26 96 0.085913008595 Henry Cohn, 2026, needs more optimization.
26 97 0.089146467049 Henry Cohn, 2026, needs more optimization.
26 98 0.089647536551 Henry Cohn, 2026, needs more optimization.
26 99 0.090045419523 Henry Cohn, 2026, needs more optimization.
26 100 0.090257601917 Henry Cohn, 2026, needs more optimization.
26 101 0.090489573305 Henry Cohn, 2026, needs more optimization.
26 102 0.090675643519 Henry Cohn, 2026, needs more optimization.
26 103 0.090757055698 Henry Cohn, 2026, needs more optimization.
26 104 0.090837050278 Henry Cohn, 2026, needs more optimization.
26 105 0.090855845834 Henry Cohn, 2026, needs more optimization.
26 106 0.090896205715 Henry Cohn, 2026, needs more optimization.
26 107 0.090897052770 Henry Cohn, 2026, needs more optimization.
26 108 0.090897053128 Henry Cohn, 2026, needs more optimization.
26 109 0.090902499298 Henry Cohn, 2026, needs more optimization.
26 110 0.090908500058 Henry Cohn, 2026, needs more optimization.
26 111 0.091744798003 Henry Cohn, 2026, needs more optimization.
26 112 0.094490093393 Henry Cohn, 2026, needs more optimization.
26 113 0.097426668218 Henry Cohn, 2026, needs more optimization.
26 114 0.100692911134 Henry Cohn, 2026, needs more optimization.
26 120 0.103125332235 Henry Cohn, 2026.
191⁢x2−10⁢x−1
26 121 0.103746590262 Henry Cohn, 2026, needs more optimization.
26 122 0.105407242902 Henry Cohn, 2026, needs more optimization.
26 123 0.106258413462 Henry Cohn, 2026, needs more optimization.
26 124 0.107109897083 Henry Cohn, 2026, needs more optimization.
26 125 0.107664866093 Henry Cohn, 2026, needs more optimization.
26 126 0.108555048971 Henry Cohn, 2026, needs more optimization.
26 127 0.109071030668 Henry Cohn, 2026, needs more optimization.
26 128 0.111056715828 Henry Cohn, 2026, needs more optimization.
26 129 0.111060357622 Henry Cohn, 2026, needs more optimization.
26 130 0.111079881181 Henry Cohn, 2026, needs more optimization.
26 131 0.111105296949 Henry Cohn, 2026, needs more optimization.
26 132 0.112888749630 Henry Cohn, 2026, needs more optimization.
26 133 0.114520694013 Henry Cohn, 2026, needs more optimization.
26 134 0.115288469718 Henry Cohn, 2026, needs more optimization.
26 135 0.116296111054 Henry Cohn, 2026, needs more optimization.
26 136 0.116447579730 Henry Cohn, 2026, needs more optimization.
26 137 0.117070041436 Henry Cohn, 2026, needs more optimization.
26 138 0.118625425485 Henry Cohn, 2026, needs more optimization.
26 139 0.122342178710 Henry Cohn, 2026, needs more optimization.
26 140 0.125308136484 Henry Cohn, 2026, needs more optimization.
26 141 0.127923713142 Henry Cohn, 2026, needs more optimization.
26 142 0.130225464886 Henry Cohn, 2026, needs more optimization.
26 143 0.131429147146 Henry Cohn, 2026, needs more optimization.
26 144 0.131609703130 Henry Cohn, 2026, needs more optimization.
26 145 0.131716478379 Henry Cohn, 2026, needs more optimization.
26 146 0.131773267027 Henry Cohn, 2026, needs more optimization.
26 147 0.131900102114 Henry Cohn, 2026, needs more optimization.
26 148 0.132068104586 Henry Cohn, 2026, needs more optimization.
26 149 0.132340766529 Henry Cohn, 2026, needs more optimization.
26 150 0.132996028776 Henry Cohn, 2026, needs more optimization.
26 158 0.133333333334 Orthogonal union of 156 points in 25 dimensions and 2 points in 1 dimension.
15⁢x−2
26 159 0.133334797041 Henry Cohn, 2026, needs more optimization.
26 160 0.134520569674 Henry Cohn, 2026, needs more optimization.
26 161 0.135127304775 Henry Cohn, 2026, needs more optimization.
26 162 0.135323044627 Henry Cohn, 2026, needs more optimization.
26 163 0.136045768687 Henry Cohn, 2026, needs more optimization.
26 164 0.136696337817 Henry Cohn, 2026, needs more optimization.
26 165 0.137898840479 Henry Cohn, 2026, needs more optimization.
26 166 0.138939476500 Henry Cohn, 2026, needs more optimization.
26 167 0.139937937886 Henry Cohn, 2026, needs more optimization.
26 168 0.141029261735 Henry Cohn, 2026, needs more optimization.
26 169 0.142690551471 Henry Cohn, 2026, needs more optimization.
26 170 0.142703779571 Henry Cohn, 2026, needs more optimization.
26 171 0.142711808922 Henry Cohn, 2026, needs more optimization.
26 172 0.142734181303 Henry Cohn, 2026, needs more optimization.
26 173 0.142744763048 Henry Cohn, 2026, needs more optimization.
26 174 0.142776061082 Henry Cohn, 2026, needs more optimization.
26 175 0.142790163472 Henry Cohn, 2026, needs more optimization.
26 176 0.142796307051 Henry Cohn, 2026, needs more optimization.
26 177 0.142799764498 Henry Cohn, 2026, needs more optimization.
26 178 0.142806203363 Henry Cohn, 2026, needs more optimization.
26 179 0.142809092969 Henry Cohn, 2026, needs more optimization.
26 180 0.142810447747 Henry Cohn, 2026, needs more optimization.
26 181 0.142827166154 Henry Cohn, 2026, needs more optimization.
26 182 0.142846016791 Henry Cohn, 2026, needs more optimization.
26 183 0.142852058760 Henry Cohn, 2026, needs more optimization.
26 184 0.142855876497 Henry Cohn, 2026, needs more optimization.
26 185 0.142893544714 Henry Cohn, 2026, needs more optimization.
26 186 0.143123216807 Henry Cohn, 2026, needs more optimization.
26 187 0.143815489575 Henry Cohn, 2026, needs more optimization.
26 188 0.145213919103 Henry Cohn, 2026, needs more optimization.
26 189 0.145474233780 Henry Cohn, 2026, needs more optimization.
26 190 0.145474578163 Henry Cohn, 2026, needs more optimization.
26 191 0.146049392850 Henry Cohn, 2026, needs more optimization.
26 192 0.146206946104 Henry Cohn, 2026, needs more optimization.
26 193 0.146606562482 Henry Cohn, 2026, needs more optimization.
26 194 0.146820075327 Henry Cohn, 2026, needs more optimization.
26 195 0.146894002780 Henry Cohn, 2026, needs more optimization.
26 196 0.147005890823 Henry Cohn, 2026, needs more optimization.
26 197 0.147007736866 Henry Cohn, 2026, needs more optimization.
26 198 0.147007737578 Henry Cohn, 2026, needs more optimization.
26 199 0.147107313032 Henry Cohn, 2026, needs more optimization.
26 200 0.147149908962 Henry Cohn, 2026, needs more optimization.
26 201 0.147483019988 Henry Cohn, 2026, needs more optimization.
26 202 0.147489694567 Henry Cohn, 2026, needs more optimization.
26 203 0.148133620092 Henry Cohn, 2026, needs more optimization.
26 204 0.148897079839 Henry Cohn, 2026, needs more optimization.
26 205 0.149234992250 Henry Cohn, 2026, needs more optimization.
26 206 0.149249066977 Henry Cohn, 2026, needs more optimization.
26 207 0.149973510361 Henry Cohn, 2026, needs more optimization.
26 208 0.150254635983 Henry Cohn, 2026, needs more optimization.
26 209 0.150309107812 Henry Cohn, 2026, needs more optimization.
26 210 0.150466195104 Henry Cohn, 2026, needs more optimization.
26 211 0.150466305732 Henry Cohn, 2026, needs more optimization.
26 212 0.150998105989 Henry Cohn, 2026, needs more optimization.
26 213 0.151225642605 Henry Cohn, 2026, needs more optimization.
26 214 0.151282747548 Henry Cohn, 2026, needs more optimization.
26 215 0.151282813430 Henry Cohn, 2026, needs more optimization.
26 216 0.151825494436 Henry Cohn, 2026, needs more optimization.
26 217 0.151831386258 Henry Cohn, 2026, needs more optimization.
26 218 0.151923694086 Henry Cohn, 2026, needs more optimization.
26 219 0.151933919868 Henry Cohn, 2026, needs more optimization.
26 220 0.152487301028 Henry Cohn, 2026, needs more optimization.
26 221 0.154073526501 Henry Cohn, 2026, needs more optimization.
26 222 0.154405318702 Henry Cohn, 2026, needs more optimization.
26 223 0.154609706626 Henry Cohn, 2026, needs more optimization.
26 224 0.155109750213 Henry Cohn, 2026, needs more optimization.
26 225 0.156461561148 Henry Cohn, 2026, needs more optimization.
26 226 0.156910135186 Henry Cohn, 2026, needs more optimization.
26 227 0.157287308500 Henry Cohn, 2026, needs more optimization.
26 228 0.158667618708 Henry Cohn, 2026, needs more optimization.
26 229 0.158690917686 Henry Cohn, 2026, needs more optimization.
26 230 0.159329681264 Henry Cohn, 2026, needs more optimization.
26 231 0.160244460829 Henry Cohn, 2026, needs more optimization.
26 232 0.161964032921 Henry Cohn, 2026, needs more optimization.
26 233 0.162060185639 Henry Cohn, 2026, needs more optimization.
26 234 0.162548950717 Henry Cohn, 2026, needs more optimization.
26 235 0.162918726840 Henry Cohn, 2026, needs more optimization.
26 236 0.163196819352 Henry Cohn, 2026, needs more optimization.
26 237 0.163320935704 Henry Cohn, 2026, needs more optimization.
26 238 0.163919712724 Henry Cohn, 2026, needs more optimization.
26 239 0.164438222376 Henry Cohn, 2026, needs more optimization.
26 240 0.164539027057 Henry Cohn, 2026, needs more optimization.
26 241 0.165089061181 Henry Cohn, 2026, needs more optimization.
26 242 0.165311854063 Henry Cohn, 2026, needs more optimization.
26 243 0.165632630316 Henry Cohn, 2026, needs more optimization.
26 244 0.165867659311 Henry Cohn, 2026, needs more optimization.
26 245 0.165984133445 Henry Cohn, 2026, needs more optimization.
26 246 0.166217994226 Henry Cohn, 2026, needs more optimization.
26 247 0.166332349209 Henry Cohn, 2026, needs more optimization.
26 248 0.166407211221 Henry Cohn, 2026, needs more optimization.
26 249 0.166422161013 Henry Cohn, 2026, needs more optimization.
26 250 0.166422350716 Henry Cohn, 2026, needs more optimization.
26 251 0.166466113108 Henry Cohn, 2026, needs more optimization.
26 252 0.166500387621 Henry Cohn, 2026, needs more optimization.
26 253 0.166599819901 Henry Cohn, 2026, needs more optimization.
26 285 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 10 points in 4 dimensions.
6⁢x−1
26 287 0.166666872444 Henry Cohn, 2026, needs more optimization.
26 288 0.166667607421 Henry Cohn, 2026, needs more optimization.
26 289 0.166667608030 Henry Cohn, 2026, needs more optimization.
26 290 0.166667608908 Henry Cohn, 2026, needs more optimization.
26 291 0.166668243729 Henry Cohn, 2026, needs more optimization.
26 292 0.166668243874 Henry Cohn, 2026, needs more optimization.
26 293 0.166669119464 Henry Cohn, 2026, needs more optimization.
26 294 0.166669119777 Henry Cohn, 2026, needs more optimization.
26 295 0.166674813232 Henry Cohn, 2026, needs more optimization.
26 296 0.166693230512 Henry Cohn, 2026, needs more optimization.
26 297 0.166878162768 Henry Cohn, 2026, needs more optimization.
26 298 0.167303726479 Henry Cohn, 2026, needs more optimization.
26 299 0.168423942075 Henry Cohn, 2026, needs more optimization.
26 300 0.169915092151 Henry Cohn, 2026, needs more optimization.
26 301 0.170968845417 Henry Cohn, 2026, needs more optimization.
26 302 0.172059473855 Henry Cohn, 2026, needs more optimization.
26 303 0.173843174757 Henry Cohn, 2026, needs more optimization.
26 304 0.175635071872 Henry Cohn, 2026, needs more optimization.
26 305 0.176542831089 Henry Cohn, 2026, needs more optimization.
26 306 0.178292673718 Henry Cohn, 2026, needs more optimization.
26 307 0.179598662812 Henry Cohn, 2026, needs more optimization.
26 308 0.180436409480 Henry Cohn, 2026, needs more optimization.
26 317 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 4 points in 2 dimensions.
11⁢x−2
26 318 0.181818678585 Orthogonal union of 316 points in 25 dimensions and 2 points in 1 dimension.
26 323 0.181818875487 Henry Cohn, 2026, needs more optimization.
26 325 0.181819027653 Henry Cohn, 2026, needs more optimization.
26 326 0.181819213815 Henry Cohn, 2026, needs more optimization.
26 327 0.181819278045 Henry Cohn, 2026, needs more optimization.
26 328 0.181820171862 Henry Cohn, 2026, needs more optimization.
26 329 0.181820679091 Henry Cohn, 2026, needs more optimization.
26 330 0.181822651156 Henry Cohn, 2026, needs more optimization.
26 331 0.182091887517 Henry Cohn, 2026, needs more optimization.
26 332 0.182702277919 Henry Cohn, 2026, needs more optimization.
26 333 0.184006376631 Henry Cohn, 2026, needs more optimization.
26 334 0.185140009883 Henry Cohn, 2026, needs more optimization.
26 335 0.185776920032 Henry Cohn, 2026, needs more optimization.
26 336 0.187116712734 Henry Cohn, 2026, needs more optimization.
26 337 0.187946318088 Henry Cohn, 2026, needs more optimization.
26 338 0.188837509385 Henry Cohn, 2026, needs more optimization.
26 339 0.189989912016 Henry Cohn, 2026, needs more optimization.
26 340 0.190310773064 Henry Cohn, 2026, needs more optimization.
26 341 0.192155493947 Henry Cohn, 2026, needs more optimization.
26 342 0.192561192879 Henry Cohn, 2026, needs more optimization.
26 343 0.193206828595 Henry Cohn, 2026, needs more optimization.
26 344 0.194463481964 Henry Cohn, 2026, needs more optimization.
26 345 0.195171822308 Henry Cohn, 2026, needs more optimization.
26 346 0.196294150993 Henry Cohn, 2026, needs more optimization.
26 347 0.196433297390 Henry Cohn, 2026, needs more optimization.
26 348 0.196573571974 Henry Cohn, 2026, needs more optimization.
26 349 0.196657862278 Henry Cohn, 2026, needs more optimization.
26 350 0.196894885682 Henry Cohn, 2026, needs more optimization.
26 351 0.196979585488 Henry Cohn, 2026, needs more optimization.
26 352 0.197113339988 Henry Cohn, 2026, needs more optimization.
26 353 0.197248661812 Henry Cohn, 2026, needs more optimization.
26 354 0.197321566972 Henry Cohn, 2026, needs more optimization.
26 355 0.197409252160 Henry Cohn, 2026, needs more optimization.
26 356 0.197669548056 Henry Cohn, 2026, needs more optimization.
26 357 0.197757145949 Henry Cohn, 2026, needs more optimization.
26 358 0.197848624884 Henry Cohn, 2026, needs more optimization.
26 359 0.198030078898 Henry Cohn, 2026, needs more optimization.
26 360 0.198122501785 Henry Cohn, 2026, needs more optimization.
26 361 0.198216489304 Henry Cohn, 2026, needs more optimization.
26 362 0.198267959987 Henry Cohn, 2026, needs more optimization.
26 363 0.198311908610 Henry Cohn, 2026, needs more optimization.
26 364 0.198396800842 Henry Cohn, 2026, needs more optimization.
26 365 0.198493881690 Henry Cohn, 2026, needs more optimization.
26 366 0.198541588007 Henry Cohn, 2026, needs more optimization.
26 367 0.198627875716 Henry Cohn, 2026, needs more optimization.
26 368 0.198686992987 Henry Cohn, 2026, needs more optimization.
26 369 0.198800353821 Henry Cohn, 2026, needs more optimization.
26 370 0.198866480934 Henry Cohn, 2026, needs more optimization.
26 371 0.199006536844 Henry Cohn, 2026, needs more optimization.
26 372 0.199070347430 Henry Cohn, 2026, needs more optimization.
26 373 0.199079492328 Henry Cohn, 2026, needs more optimization.
26 374 0.199181450416 Henry Cohn, 2026, needs more optimization.
26 375 0.199244089968 Henry Cohn, 2026, needs more optimization.
26 376 0.199297325804 Henry Cohn, 2026, needs more optimization.
26 377 0.199332411656 Henry Cohn, 2026, needs more optimization.
26 378 0.199409849164 Henry Cohn, 2026, needs more optimization.
26 379 0.199454395222 Henry Cohn, 2026, needs more optimization.
26 380 0.199492818764 Henry Cohn, 2026, needs more optimization.
26 381 0.199501483942 Henry Cohn, 2026, needs more optimization.
26 382 0.199518637491 Henry Cohn, 2026, needs more optimization.
26 383 0.199528992302 Henry Cohn, 2026, needs more optimization.
26 384 0.199558929657 Henry Cohn, 2026, needs more optimization.
26 385 0.199598368313 Henry Cohn, 2026, needs more optimization.
26 386 0.199651831758 Henry Cohn, 2026, needs more optimization.
26 387 0.199687163933 Henry Cohn, 2026, needs more optimization.
26 388 0.199710352746 Henry Cohn, 2026, needs more optimization.
26 389 0.199750700944 Henry Cohn, 2026, needs more optimization.
26 390 0.199808935350 Henry Cohn, 2026, needs more optimization.
26 391 0.199820279424 Henry Cohn, 2026, needs more optimization.
26 392 0.199827833474 Henry Cohn, 2026, needs more optimization.
26 393 0.199843806628 Henry Cohn, 2026, needs more optimization.
26 394 0.199859778572 Henry Cohn, 2026, needs more optimization.
26 395 0.199879711560 Henry Cohn, 2026, needs more optimization.
26 396 0.199906892317 Henry Cohn, 2026, needs more optimization.
26 397 0.199936228573 Henry Cohn, 2026, needs more optimization.
26 398 0.199951964267 Henry Cohn, 2026, needs more optimization.
26 399 0.199959039317 Henry Cohn, 2026, needs more optimization.
26 400 0.199966120209 Henry Cohn, 2026, needs more optimization.
26 559 0.2 Orthogonal union of 555 points in 24 dimensions and 4 points in 2 dimensions.
5⁢x−1
26 568 0.200000846007 Henry Cohn, 2026, needs more optimization.
26 569 0.200009771735 Henry Cohn, 2026, needs more optimization.
26 570 0.200042787198 Henry Cohn, 2026, needs more optimization.
26 571 0.200478839313 Henry Cohn, 2026, needs more optimization.
26 572 0.200566780070 Henry Cohn, 2026, needs more optimization.
26 573 0.200959485786 Henry Cohn, 2026, needs more optimization.
26 574 0.202303744927 Henry Cohn, 2026, needs more optimization.
26 575 0.204393048343 Henry Cohn, 2026, needs more optimization.
26 576 0.205509120826 Henry Cohn, 2026, needs more optimization.
26 577 0.208734883897 Henry Cohn, 2026, needs more optimization.
26 578 0.210040074997 Henry Cohn, 2026, needs more optimization.
26 579 0.211454957684 Henry Cohn, 2026, needs more optimization.
26 580 0.212526167208 Henry Cohn, 2026, needs more optimization.
26 581 0.214547030303 Henry Cohn, 2026, needs more optimization.
26 582 0.215937633986 Henry Cohn, 2026, needs more optimization.
26 583 0.216865997638 Henry Cohn, 2026, needs more optimization.
26 584 0.217492933399 Henry Cohn, 2026, needs more optimization.
26 585 0.218831522475 Henry Cohn, 2026, needs more optimization.
26 586 0.219381139654 Henry Cohn, 2026, needs more optimization.
26 587 0.220716308389 Henry Cohn, 2026, needs more optimization.
26 588 0.221594928626 Henry Cohn, 2026, needs more optimization.
26 589 0.222090339987 Henry Cohn, 2026, needs more optimization.
26 590 0.222857330730 Henry Cohn, 2026, needs more optimization.
26 591 0.223959700145 Henry Cohn, 2026, needs more optimization.
26 592 0.224527249743 Henry Cohn, 2026, needs more optimization.
26 593 0.224983073180 Henry Cohn, 2026, needs more optimization.
26 594 0.225937976103 Henry Cohn, 2026, needs more optimization.
26 595 0.226174008057 Henry Cohn, 2026, needs more optimization.
26 596 0.226469090389 Henry Cohn, 2026, needs more optimization.
26 602 0.238096469173 Henry Cohn, 2026, needs more optimization.
26 613 0.238096563601 Henry Cohn, 2026, needs more optimization.
26 614 0.238096570683 Henry Cohn, 2026, needs more optimization.
26 616 0.238096808690 Henry Cohn, 2026, needs more optimization.
26 618 0.238096808741 Henry Cohn, 2026, needs more optimization.
26 619 0.238096808744 Henry Cohn, 2026, needs more optimization.
26 620 0.238097441579 Henry Cohn, 2026, needs more optimization.
26 622 0.238097954250 Henry Cohn, 2026, needs more optimization.
26 623 0.238098599485 Henry Cohn, 2026, needs more optimization.
26 627 0.238104767477 Henry Cohn, 2026, needs more optimization.
26 628 0.238117404763 Henry Cohn, 2026, needs more optimization.
26 629 0.238226639885 Henry Cohn, 2026, needs more optimization.
26 630 0.238349548159 Henry Cohn, 2026, needs more optimization.
26 631 0.238510588094 Henry Cohn, 2026, needs more optimization.
26 632 0.238625321955 Henry Cohn, 2026, needs more optimization.
26 633 0.238829001721 Henry Cohn, 2026, needs more optimization.
26 634 0.239383791990 Henry Cohn, 2026, needs more optimization.
26 635 0.240081609856 Henry Cohn, 2026, needs more optimization.
26 636 0.240726484023 Henry Cohn, 2026, needs more optimization.
26 637 0.240907138105 Henry Cohn, 2026, needs more optimization.
26 638 0.241269960768 Henry Cohn, 2026, needs more optimization.
26 639 0.242152981013 Henry Cohn, 2026, needs more optimization.
26 640 0.242290237645 Henry Cohn, 2026, needs more optimization.
26 641 0.243156267549 Henry Cohn, 2026, needs more optimization.
26 642 0.243306933296 Henry Cohn, 2026, needs more optimization.
26 643 0.243744961313 Henry Cohn, 2026, needs more optimization.
26 644 0.244190977135 Henry Cohn, 2026, needs more optimization.
26 646 0.244852102628 Henry Cohn, 2026, needs more optimization.
26 647 0.245114949041 Henry Cohn, 2026, needs more optimization.
26 648 0.245452379937 Henry Cohn, 2026, needs more optimization.
26 649 0.245758101016 Henry Cohn, 2026, needs more optimization.
26 650 0.245805867258 Henry Cohn, 2026, needs more optimization.
26 651 0.246105719065 Henry Cohn, 2026, needs more optimization.
26 652 0.246411905235 Henry Cohn, 2026, needs more optimization.
26 653 0.246612582921 Henry Cohn, 2026, needs more optimization.
26 654 0.246711383228 Henry Cohn, 2026, needs more optimization.
26 655 0.247051595773 Henry Cohn, 2026, needs more optimization.
26 656 0.247121950953 Henry Cohn, 2026, needs more optimization.
26 657 0.247199174268 Henry Cohn, 2026, needs more optimization.
26 658 0.247200035086 Henry Cohn, 2026, needs more optimization.
26 659 0.247575979582 Henry Cohn, 2026, needs more optimization.
26 660 0.247623368439 Henry Cohn, 2026, needs more optimization.
26 661 0.247780880039 Henry Cohn, 2026, needs more optimization.
26 662 0.247832454045 Henry Cohn, 2026, needs more optimization.
26 663 0.247854085770 Henry Cohn, 2026, needs more optimization.
26 664 0.247854107722 Henry Cohn, 2026, needs more optimization.
26 665 0.248118270769 Henry Cohn, 2026, needs more optimization.
26 666 0.248155617623 Henry Cohn, 2026, needs more optimization.
26 667 0.248155621252 Henry Cohn, 2026, needs more optimization.
26 668 0.248171676182 Henry Cohn, 2026, needs more optimization.
26 670 0.248247523876 Henry Cohn, 2026, needs more optimization.
26 671 0.248364937153 Henry Cohn, 2026, needs more optimization.
26 672 0.248365284169 Henry Cohn, 2026, needs more optimization.
26 673 0.248384989569 Henry Cohn, 2026, needs more optimization.
26 674 0.248405326094 Henry Cohn, 2026, needs more optimization.
26 675 0.248519511292 Henry Cohn, 2026, needs more optimization.
26 676 0.248535467142 Henry Cohn, 2026, needs more optimization.
26 677 0.248661437582 Henry Cohn, 2026, needs more optimization.
26 678 0.248713989853 Henry Cohn, 2026, needs more optimization.
26 679 0.248740977519 Henry Cohn, 2026, needs more optimization.
26 681 0.248784895206 Henry Cohn, 2026, needs more optimization.
26 682 0.248853326140 Henry Cohn, 2026, needs more optimization.
26 683 0.248925080334 Henry Cohn, 2026, needs more optimization.
26 684 0.248929720888 Henry Cohn, 2026, needs more optimization.
26 685 0.248929748187 Henry Cohn, 2026, needs more optimization.
26 686 0.249023093502 Henry Cohn, 2026, needs more optimization.
26 687 0.249096982627 Henry Cohn, 2026, needs more optimization.
26 688 0.249110727404 Henry Cohn, 2026, needs more optimization.
26 689 0.249168545690 Henry Cohn, 2026, needs more optimization.
26 690 0.249195213607 Henry Cohn, 2026, needs more optimization.
26 691 0.249202302988 Henry Cohn, 2026, needs more optimization.
26 692 0.249234173540 Henry Cohn, 2026, needs more optimization.
26 693 0.249354495049 Henry Cohn, 2026, needs more optimization.
26 694 0.249384408628 Henry Cohn, 2026, needs more optimization.
26 695 0.249401359765 Henry Cohn, 2026, needs more optimization.
26 696 0.249411458322 Henry Cohn, 2026, needs more optimization.
26 697 0.249414279861 Henry Cohn, 2026, needs more optimization.
26 698 0.249414361784 Henry Cohn, 2026, needs more optimization.
26 699 0.249427047940 Henry Cohn, 2026, needs more optimization.
26 700 0.249430033441 Henry Cohn, 2026, needs more optimization.
26 701 0.249459652563 Henry Cohn, 2026, needs more optimization.
26 702 0.249481989898 Henry Cohn, 2026, needs more optimization.
26 703 0.249517567864 Henry Cohn, 2026, needs more optimization.
26 704 0.249535177713 Henry Cohn, 2026, needs more optimization.
26 705 0.249541346471 Henry Cohn, 2026, needs more optimization.
26 706 0.249587833328 Henry Cohn, 2026, needs more optimization.
26 707 0.249649641405 Henry Cohn, 2026, needs more optimization.
26 708 0.249658525381 Henry Cohn, 2026, needs more optimization.
26 709 0.249673132133 Henry Cohn, 2026, needs more optimization.
26 710 0.249690669184 Henry Cohn, 2026, needs more optimization.
26 712 0.249716206791 Henry Cohn, 2026, needs more optimization.
26 713 0.249728383944 Henry Cohn, 2026, needs more optimization.
26 714 0.249735342652 Henry Cohn, 2026, needs more optimization.
26 715 0.249752156772 Henry Cohn, 2026, needs more optimization.
26 716 0.249785577966 Henry Cohn, 2026, needs more optimization.
26 717 0.249789535431 Henry Cohn, 2026, needs more optimization.
26 718 0.249809427985 Henry Cohn, 2026, needs more optimization.
26 719 0.249830581203 Henry Cohn, 2026, needs more optimization.
26 720 0.249838724453 Henry Cohn, 2026, needs more optimization.
26 721 0.249850918574 Henry Cohn, 2026, needs more optimization.
26 722 0.249868150809 Henry Cohn, 2026, needs more optimization.
26 723 0.249892884709 Henry Cohn, 2026, needs more optimization.
26 903 0.25 Orthogonal union of 891 points in 22 dimensions and 12 points in 4 dimensions.
4⁢x−1
26 904 0.250001683008 Henry Cohn, 2026, needs more optimization.
26 909 0.250001694407 Henry Cohn, 2026, needs more optimization.
26 910 0.250001694753 Henry Cohn, 2026, needs more optimization.
26 911 0.250001697355 Henry Cohn, 2026, needs more optimization.
26 912 0.250001698163 Henry Cohn, 2026, needs more optimization.
26 913 0.250001698677 Henry Cohn, 2026, needs more optimization.
26 915 0.250001954317 Henry Cohn, 2026, needs more optimization.
26 923 0.250001955161 Henry Cohn, 2026, needs more optimization.
26 924 0.250001958312 Henry Cohn, 2026, needs more optimization.
26 925 0.250002337144 Henry Cohn, 2026, needs more optimization.
26 926 0.250002337205 Henry Cohn, 2026, needs more optimization.
26 927 0.250003138447 Henry Cohn, 2026, needs more optimization.
26 930 0.250004552394 Henry Cohn, 2026, needs more optimization.
26 932 0.250004905545 Henry Cohn, 2026, needs more optimization.
26 933 0.250007258411 Henry Cohn, 2026, needs more optimization.
26 934 0.250010046542 Henry Cohn, 2026, needs more optimization.
26 935 0.250031245764 Henry Cohn, 2026, needs more optimization.
26 936 0.250054891410 Henry Cohn, 2026, needs more optimization.
26 937 0.250111449590 Henry Cohn, 2026, needs more optimization.
26 938 0.250152997890 Henry Cohn, 2026, needs more optimization.
26 939 0.250280279489 Henry Cohn, 2026, needs more optimization.
26 940 0.250291159033 Henry Cohn, 2026, needs more optimization.
26 941 0.250506605278 Henry Cohn, 2026, needs more optimization.
26 942 0.250810633783 Henry Cohn, 2026, needs more optimization.
26 943 0.250936170393 Henry Cohn, 2026, needs more optimization.
26 944 0.251194105983 Henry Cohn, 2026, needs more optimization.
26 945 0.251587015318 Henry Cohn, 2026, needs more optimization.
26 946 0.251968822201 Henry Cohn, 2026, needs more optimization.
26 947 0.252216181686 Henry Cohn, 2026, needs more optimization.
26 948 0.252557406532 Henry Cohn, 2026, needs more optimization.
26 949 0.253088025615 Henry Cohn, 2026, needs more optimization.
26 950 0.253247829808 Henry Cohn, 2026, needs more optimization.
26 951 0.253508199664 Henry Cohn, 2026, needs more optimization.
26 952 0.254011463242 Henry Cohn, 2026, needs more optimization.
26 953 0.254268153201 Henry Cohn, 2026, needs more optimization.
26 954 0.254806950083 Henry Cohn, 2026, needs more optimization.
26 955 0.255170370061 Henry Cohn, 2026, needs more optimization.
26 956 0.255653271764 Henry Cohn, 2026, needs more optimization.
26 957 0.255985324556 Henry Cohn, 2026, needs more optimization.
26 958 0.256157495895 Henry Cohn, 2026, needs more optimization.
26 959 0.256572273338 Henry Cohn, 2026, needs more optimization.
26 960 0.257124921258 Henry Cohn, 2026, needs more optimization.
26 961 0.257203693334 Henry Cohn, 2026, needs more optimization.
26 962 0.257611205991 Henry Cohn, 2026, needs more optimization.
26 963 0.258220562156 Henry Cohn, 2026, needs more optimization.
26 964 0.258521745931 Henry Cohn, 2026, needs more optimization.
26 965 0.258613146274 Henry Cohn, 2026, needs more optimization.
26 966 0.258962082964 Henry Cohn, 2026, needs more optimization.
26 967 0.259413323841 Henry Cohn, 2026, needs more optimization.
26 968 0.259613970759 Henry Cohn, 2026, needs more optimization.
26 969 0.259875517511 Henry Cohn, 2026, needs more optimization.
26 970 0.260085516426 Henry Cohn, 2026, needs more optimization.
26 971 0.260691008989 Henry Cohn, 2026, needs more optimization.
26 972 0.261043483384 Henry Cohn, 2026, needs more optimization.
26 973 0.261252046387 Henry Cohn, 2026, needs more optimization.
26 974 0.261790553290 Henry Cohn, 2026, needs more optimization.
26 975 0.262179342364 Henry Cohn, 2026, needs more optimization.
26 976 0.262785210152 Henry Cohn, 2026, needs more optimization.
26 977 0.263033040287 Henry Cohn, 2026, needs more optimization.
26 978 0.263496551163 Henry Cohn, 2026, needs more optimization.
26 979 0.263613828459 Henry Cohn, 2026, needs more optimization.
26 980 0.263736781404 Henry Cohn, 2026, needs more optimization.
26 981 0.264434487482 Henry Cohn, 2026, needs more optimization.
26 982 0.265000170589 Henry Cohn, 2026, needs more optimization.
26 983 0.265427368773 Henry Cohn, 2026, needs more optimization.
26 984 0.265695816230 Henry Cohn, 2026, needs more optimization.
26 985 0.265957683650 Henry Cohn, 2026, needs more optimization.
26 986 0.266259359607 Henry Cohn, 2026, needs more optimization.
26 987 0.266322190092 Henry Cohn, 2026, needs more optimization.
26 988 0.266584301482 Henry Cohn, 2026, needs more optimization.
26 989 0.266795092042 Henry Cohn, 2026, needs more optimization.
26 990 0.267203300001 Henry Cohn, 2026, needs more optimization.
26 991 0.267262228979 Henry Cohn, 2026, needs more optimization.
26 992 0.267470557917 Henry Cohn, 2026, needs more optimization.
26 993 0.267710432764 Henry Cohn, 2026, needs more optimization.
26 994 0.267941002118 Henry Cohn, 2026, needs more optimization.
26 995 0.268070444531 Henry Cohn, 2026, needs more optimization.
26 996 0.268260509483 Henry Cohn, 2026, needs more optimization.
26 997 0.268561971347 Henry Cohn, 2026, needs more optimization.
26 998 0.268824025729 Henry Cohn, 2026, needs more optimization.
26 999 0.269247639833 Henry Cohn, 2026, needs more optimization.
26 1000 0.269472155462 Henry Cohn, 2026, needs more optimization.
26 1001 0.269823714566 Henry Cohn, 2026, needs more optimization.
26 1002 0.269963634824 Henry Cohn, 2026, needs more optimization.
26 1003 0.270395431229 Henry Cohn, 2026, needs more optimization.
26 1004 0.270492555002 Henry Cohn, 2026, needs more optimization.
26 1005 0.270691287633 Henry Cohn, 2026, needs more optimization.
26 1007 0.271112417086 Henry Cohn, 2026, needs more optimization.
26 1008 0.271266989232 Henry Cohn, 2026, needs more optimization.
26 1009 0.271452362473 Henry Cohn, 2026, needs more optimization.
26 1010 0.271769762707 Henry Cohn, 2026, needs more optimization.
26 1011 0.271920570790 Henry Cohn, 2026, needs more optimization.
26 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
27 55 0.029589200879 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
16875⁢x3−729⁢x2−27⁢x+1
27 56 0.034511432831 Henry Cohn, 2024.
27 58 0.039896885932 Henry Cohn, 2026, needs more optimization.
27 59 0.039967796543 Henry Cohn, 2026.
27 60 0.044786634957 Henry Cohn, 2026, needs more optimization.
27 61 0.045484192884 Henry Cohn, 2026.
27 62 0.046198040189 Henry Cohn, 2025.
27 63 0.047652441689 Henry Cohn, 2026.
27 64 0.050067815256 Henry Cohn, 2026.
27 65 0.054259436682 Henry Cohn, 2026, needs more optimization.
27 66 0.056203231214 Henry Cohn, 2026, needs more optimization.
27 67 0.058358030299 Henry Cohn, 2026, needs more optimization.
27 68 0.060150459250 Henry Cohn, 2026.
27 69 0.061646691897 Henry Cohn, 2026.
27 70 0.062921569653 Henry Cohn, 2026, needs more optimization.
27 71 0.064107005747 Henry Cohn, 2026, needs more optimization.
27 72 0.064938029724 Henry Cohn, 2026, needs more optimization.
27 73 0.065796345165 Henry Cohn, 2026, needs more optimization.
27 74 0.066304723816 Henry Cohn, 2026, needs more optimization.
27 75 0.067944284023 Henry Cohn, 2026, needs more optimization.
27 76 0.069937587917 Henry Cohn, 2026, needs more optimization.
27 77 0.072325859984 Henry Cohn, 2026, needs more optimization.
27 78 0.074623460879 Henry Cohn, 2026, needs more optimization.
27 79 0.075323684066 Henry Cohn, 2026, needs more optimization.
27 80 0.076112429910 Henry Cohn, 2026, needs more optimization.
27 81 0.076614766210 Henry Cohn, 2026, needs more optimization.
27 82 0.076871523192 Henry Cohn, 2026, needs more optimization.
27 83 0.076905074552 Henry Cohn, 2026, needs more optimization.
27 84 0.077004662147 Henry Cohn, 2026, needs more optimization.
27 85 0.077371168618 Henry Cohn, 2026, needs more optimization.
27 86 0.077582864621 Henry Cohn, 2026, needs more optimization.
27 87 0.078368588042 Henry Cohn, 2026, needs more optimization.
27 88 0.078627435630 Henry Cohn, 2026, needs more optimization.
27 89 0.079086004459 Henry Cohn, 2026, needs more optimization.
27 90 0.079547685892 Henry Cohn, 2026, needs more optimization.
27 91 0.080269732744 Henry Cohn, 2026, needs more optimization.
27 92 0.080397348706 Henry Cohn, 2026, needs more optimization.
27 93 0.080670831555 Henry Cohn, 2026, needs more optimization.
27 94 0.080682780934 Henry Cohn, 2026, needs more optimization.
27 95 0.080684833766 Henry Cohn, 2026, needs more optimization.
27 96 0.080685003328 Orthogonal union of 94 points in 26 dimensions and 2 points in 1 dimension.
575⁢x2−34⁢x−1
27 97 0.080685560950 Henry Cohn, 2026, needs more optimization.
27 98 0.080685608415 Henry Cohn, 2026, needs more optimization.
27 99 0.084156893838 Henry Cohn, 2026, needs more optimization.
27 100 0.086566248682 Henry Cohn, 2026, needs more optimization.
27 101 0.088590539850 Henry Cohn, 2026, needs more optimization.
27 102 0.089445510156 Henry Cohn, 2026, needs more optimization.
27 103 0.089766471336 Henry Cohn, 2026, needs more optimization.
27 104 0.089958857629 Henry Cohn, 2026, needs more optimization.
27 105 0.090188784374 Henry Cohn, 2026, needs more optimization.
27 106 0.090273263093 Henry Cohn, 2026, needs more optimization.
27 107 0.090517727351 Henry Cohn, 2026, needs more optimization.
27 108 0.090582128305 Henry Cohn, 2026, needs more optimization.
27 109 0.090630767592 Henry Cohn, 2026, needs more optimization.
27 110 0.090630768950 Henry Cohn, 2026, needs more optimization.
27 111 0.090766764392 Henry Cohn, 2026, needs more optimization.
27 112 0.090858041770 Henry Cohn, 2026, needs more optimization.
27 113 0.090888931763 Henry Cohn, 2026, needs more optimization.
27 114 0.091261776702 Henry Cohn, 2026, needs more optimization.
27 115 0.092923915778 Henry Cohn, 2026, needs more optimization.
27 116 0.095573310182 Henry Cohn, 2026, needs more optimization.
27 117 0.098515838666 Henry Cohn, 2026, needs more optimization.
27 118 0.100950538449 Henry Cohn, 2026, needs more optimization.
27 119 0.102960003963 Henry Cohn, 2026, needs more optimization.
27 120 0.103031478672 Henry Cohn, 2026, needs more optimization.
27 121 0.103031482900 Henry Cohn, 2026, needs more optimization.
27 122 0.103111832623 Henry Cohn, 2026, needs more optimization.
27 125 0.103125332566 Henry Cohn, 2026, needs more optimization.
27 126 0.104301939976 Henry Cohn, 2026, needs more optimization.
27 127 0.105168360577 Henry Cohn, 2026, needs more optimization.
27 128 0.105899010242 Henry Cohn, 2026, needs more optimization.
27 129 0.107226934261 Henry Cohn, 2026, needs more optimization.
27 130 0.107683458458 Henry Cohn, 2026, needs more optimization.
27 131 0.108485255519 Henry Cohn, 2026, needs more optimization.
27 132 0.109597765757 Henry Cohn, 2026, needs more optimization.
27 133 0.110548359620 Henry Cohn, 2026, needs more optimization.
27 134 0.111003552067 Henry Cohn, 2026, needs more optimization.
27 135 0.111009480897 Henry Cohn, 2026, needs more optimization.
27 136 0.111391902487 Henry Cohn, 2026, needs more optimization.
27 137 0.112893701175 Henry Cohn, 2026, needs more optimization.
27 138 0.114326025372 Henry Cohn, 2026, needs more optimization.
27 139 0.114830603053 Henry Cohn, 2026, needs more optimization.
27 140 0.115260406461 Henry Cohn, 2026, needs more optimization.
27 141 0.116308469912 Henry Cohn, 2026, needs more optimization.
27 142 0.117412225121 Henry Cohn, 2026, needs more optimization.
27 143 0.119136293829 Henry Cohn, 2026, needs more optimization.
27 144 0.120994247249 Henry Cohn, 2026, needs more optimization.
27 145 0.123133562978 Henry Cohn, 2026, needs more optimization.
27 146 0.125354279892 Henry Cohn, 2026, needs more optimization.
27 147 0.127230977488 Henry Cohn, 2026, needs more optimization.
27 148 0.128556753093 Henry Cohn, 2026, needs more optimization.
27 149 0.129948130535 Henry Cohn, 2026, needs more optimization.
27 150 0.131242611914 Henry Cohn, 2026, needs more optimization.
27 151 0.131378486798 Henry Cohn, 2026, needs more optimization.
27 152 0.131596524809 Henry Cohn, 2026, needs more optimization.
27 153 0.131753217052 Henry Cohn, 2026, needs more optimization.
27 154 0.132000663779 Henry Cohn, 2026, needs more optimization.
27 155 0.132013973127 Henry Cohn, 2026, needs more optimization.
27 156 0.132208000265 Henry Cohn, 2026, needs more optimization.
27 157 0.132527432325 Henry Cohn, 2026, needs more optimization.
27 158 0.132743404700 Henry Cohn, 2026, needs more optimization.
27 159 0.132998175446 Henry Cohn, 2026, needs more optimization.
27 160 0.133268784549 Henry Cohn, 2026, needs more optimization.
27 161 0.133301301991 Henry Cohn, 2026, needs more optimization.
27 162 0.133316675319 Henry Cohn, 2026, needs more optimization.
27 163 0.133329299979 Henry Cohn, 2026, needs more optimization.
27 164 0.133482387060 Henry Cohn, 2026, needs more optimization.
27 165 0.135017324384 Henry Cohn, 2026, needs more optimization.
27 166 0.135025470029 Henry Cohn, 2026, needs more optimization.
27 167 0.135106302332 Henry Cohn, 2026, needs more optimization.
27 168 0.135124215427 Henry Cohn, 2026, needs more optimization.
27 169 0.135254176819 Henry Cohn, 2026, needs more optimization.
27 170 0.135783814906 Henry Cohn, 2026, needs more optimization.
27 171 0.136291682258 Henry Cohn, 2026, needs more optimization.
27 172 0.137278204277 Henry Cohn, 2026, needs more optimization.
27 173 0.138901423428 Henry Cohn, 2026, needs more optimization.
27 174 0.139554118556 Henry Cohn, 2026, needs more optimization.
27 175 0.140948388679 Henry Cohn, 2026, needs more optimization.
27 176 0.142247701720 Henry Cohn, 2026, needs more optimization.
27 177 0.142295938523 Henry Cohn, 2026, needs more optimization.
27 178 0.142402002795 Henry Cohn, 2026, needs more optimization.
27 179 0.142415775992 Henry Cohn, 2026, needs more optimization.
27 180 0.142492707303 Henry Cohn, 2026, needs more optimization.
27 181 0.142532865957 Henry Cohn, 2026, needs more optimization.
27 182 0.142551646888 Henry Cohn, 2026, needs more optimization.
27 183 0.142568613535 Henry Cohn, 2026, needs more optimization.
27 184 0.142671503908 Henry Cohn, 2026, needs more optimization.
27 185 0.142695872513 Henry Cohn, 2026, needs more optimization.
27 186 0.142745940748 Henry Cohn, 2026, needs more optimization.
27 187 0.142747451282 Henry Cohn, 2026, needs more optimization.
27 188 0.142757547558 Henry Cohn, 2026, needs more optimization.
27 189 0.142758817325 Henry Cohn, 2026, needs more optimization.
27 190 0.142758818541 Henry Cohn, 2026, needs more optimization.
27 191 0.142829523481 Henry Cohn, 2026, needs more optimization.
27 192 0.142968402153 Henry Cohn, 2026, needs more optimization.
27 193 0.142976495474 Henry Cohn, 2026, needs more optimization.
27 194 0.143905862304 Henry Cohn, 2026, needs more optimization.
27 195 0.144424723728 Henry Cohn, 2026, needs more optimization.
27 196 0.145381751663 Henry Cohn, 2026, needs more optimization.
27 197 0.145383227635 Henry Cohn, 2026, needs more optimization.
27 198 0.145413683378 Henry Cohn, 2026, needs more optimization.
27 199 0.145492558159 Henry Cohn, 2026, needs more optimization.
27 200 0.145775085808 Henry Cohn, 2026, needs more optimization.
27 201 0.146083700079 Henry Cohn, 2026, needs more optimization.
27 202 0.146348757929 Henry Cohn, 2026, needs more optimization.
27 203 0.146521214212 Henry Cohn, 2026, needs more optimization.
27 204 0.146942851162 Henry Cohn, 2026, needs more optimization.
27 205 0.147166176182 Henry Cohn, 2026, needs more optimization.
27 206 0.147193434403 Henry Cohn, 2026, needs more optimization.
27 207 0.147328515081 Henry Cohn, 2026, needs more optimization.
27 208 0.147416791519 Henry Cohn, 2026, needs more optimization.
27 209 0.147416907992 Henry Cohn, 2026, needs more optimization.
27 210 0.147418474709 Henry Cohn, 2026, needs more optimization.
27 211 0.147419762480 Henry Cohn, 2026, needs more optimization.
27 212 0.147451744616 Henry Cohn, 2026, needs more optimization.
27 215 0.147651517511 Henry Cohn, 2026.
1655⁢x2−136⁢x−16
27 216 0.147963766104 Henry Cohn, 2026, needs more optimization.
27 217 0.148993501436 Henry Cohn, 2026, needs more optimization.
27 218 0.149003109108 Henry Cohn, 2026, needs more optimization.
27 219 0.149321917273 Henry Cohn, 2026, needs more optimization.
27 220 0.149321952206 Henry Cohn, 2026, needs more optimization.
27 221 0.149323859713 Henry Cohn, 2026, needs more optimization.
27 222 0.149331314255 Henry Cohn, 2026, needs more optimization.
27 223 0.149331314782 Henry Cohn, 2026, needs more optimization.
27 224 0.149331315282 Henry Cohn, 2026, needs more optimization.
27 225 0.149405814802 Henry Cohn, 2026, needs more optimization.
27 226 0.149711238828 Henry Cohn, 2026, needs more optimization.
27 227 0.149742685799 Henry Cohn, 2026, needs more optimization.
27 228 0.150035567819 Henry Cohn, 2026, needs more optimization.
27 229 0.150041532530 Henry Cohn, 2026, needs more optimization.
27 230 0.150314684391 Henry Cohn, 2026, needs more optimization.
27 231 0.150366696050 Henry Cohn, 2026, needs more optimization.
27 232 0.150898838526 Henry Cohn, 2026, needs more optimization.
27 233 0.151548180173 Henry Cohn, 2026, needs more optimization.
27 234 0.152313304765 Henry Cohn, 2026, needs more optimization.
27 235 0.152393427489 Henry Cohn, 2026, needs more optimization.
27 236 0.153632414067 Henry Cohn, 2026, needs more optimization.
27 237 0.155588711370 Henry Cohn, 2026, needs more optimization.
27 238 0.157681448085 Henry Cohn, 2026, needs more optimization.
27 239 0.157707002121 Henry Cohn, 2026, needs more optimization.
27 240 0.158836014255 Henry Cohn, 2026, needs more optimization.
27 241 0.159827406127 Henry Cohn, 2026, needs more optimization.
27 242 0.160381422769 Henry Cohn, 2026, needs more optimization.
27 243 0.161433311724 Henry Cohn, 2026, needs more optimization.
27 244 0.162258872748 Henry Cohn, 2026, needs more optimization.
27 245 0.162284581410 Henry Cohn, 2026, needs more optimization.
27 246 0.162534142922 Henry Cohn, 2026, needs more optimization.
27 247 0.162671344686 Henry Cohn, 2026, needs more optimization.
27 248 0.162721488853 Henry Cohn, 2026, needs more optimization.
27 249 0.162902857497 Henry Cohn, 2026, needs more optimization.
27 250 0.163015096579 Henry Cohn, 2026, needs more optimization.
27 251 0.163638298993 Henry Cohn, 2026, needs more optimization.
27 252 0.163904928226 Henry Cohn, 2026, needs more optimization.
27 253 0.164117185656 Henry Cohn, 2026, needs more optimization.
27 254 0.164161239327 Henry Cohn, 2026, needs more optimization.
27 255 0.164502468171 Henry Cohn, 2026, needs more optimization.
27 256 0.164633166354 Henry Cohn, 2026, needs more optimization.
27 257 0.164806039374 Henry Cohn, 2026, needs more optimization.
27 258 0.165013296342 Henry Cohn, 2026, needs more optimization.
27 259 0.165103299905 Henry Cohn, 2026, needs more optimization.
27 260 0.165244467509 Henry Cohn, 2026, needs more optimization.
27 261 0.165399551794 Henry Cohn, 2026, needs more optimization.
27 262 0.165508480673 Henry Cohn, 2026, needs more optimization.
27 263 0.165596333609 Henry Cohn, 2026, needs more optimization.
27 264 0.165705786574 Henry Cohn, 2026, needs more optimization.
27 265 0.165792320774 Henry Cohn, 2026, needs more optimization.
27 266 0.165856947326 Henry Cohn, 2026, needs more optimization.
27 267 0.165904198033 Henry Cohn, 2026, needs more optimization.
27 268 0.165983465031 Henry Cohn, 2026, needs more optimization.
27 269 0.166049725916 Henry Cohn, 2026, needs more optimization.
27 270 0.166166552600 Henry Cohn, 2026, needs more optimization.
27 271 0.166260604786 Henry Cohn, 2026, needs more optimization.
27 272 0.166309226799 Henry Cohn, 2026, needs more optimization.
27 273 0.166353334090 Henry Cohn, 2026, needs more optimization.
27 274 0.166403870820 Henry Cohn, 2026, needs more optimization.
27 275 0.166440466996 Henry Cohn, 2026, needs more optimization.
27 276 0.166479521226 Henry Cohn, 2026, needs more optimization.
27 277 0.166496244583 Henry Cohn, 2026, needs more optimization.
27 278 0.166545592327 Henry Cohn, 2026, needs more optimization.
27 279 0.166579213740 Henry Cohn, 2026, needs more optimization.
27 280 0.166579219288 Henry Cohn, 2026, needs more optimization.
27 281 0.166608238870 Henry Cohn, 2026, needs more optimization.
27 288 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 10 points in 4 dimensions.
6⁢x−1
27 289 0.166666862675 Henry Cohn, 2026, needs more optimization.
27 290 0.166666863212 Henry Cohn, 2026, needs more optimization.
27 291 0.166666863878 Henry Cohn, 2026, needs more optimization.
27 292 0.166666864054 Henry Cohn, 2026, needs more optimization.
27 293 0.166666864290 Henry Cohn, 2026, needs more optimization.
27 294 0.166667326113 Henry Cohn, 2026, needs more optimization.
27 295 0.166667326327 Henry Cohn, 2026, needs more optimization.
27 296 0.166667326656 Henry Cohn, 2026, needs more optimization.
27 297 0.166668077845 Henry Cohn, 2026, needs more optimization.
27 298 0.166668078565 Henry Cohn, 2026, needs more optimization.
27 299 0.166668154052 Henry Cohn, 2026, needs more optimization.
27 300 0.166668154433 Henry Cohn, 2026, needs more optimization.
27 302 0.166668154586 Henry Cohn, 2026, needs more optimization.
27 303 0.166668637380 Henry Cohn, 2026, needs more optimization.
27 304 0.166686482236 Henry Cohn, 2026, needs more optimization.
27 305 0.166737497896 Henry Cohn, 2026, needs more optimization.
27 306 0.166927909366 Henry Cohn, 2026, needs more optimization.
27 307 0.167298903610 Henry Cohn, 2026, needs more optimization.
27 308 0.168124938638 Henry Cohn, 2026, needs more optimization.
27 309 0.169392554334 Henry Cohn, 2026, needs more optimization.
27 310 0.170450795883 Henry Cohn, 2026, needs more optimization.
27 311 0.171686330557 Henry Cohn, 2026, needs more optimization.
27 312 0.172836709403 Henry Cohn, 2026, needs more optimization.
27 313 0.173872885978 Henry Cohn, 2026, needs more optimization.
27 314 0.174681051170 Henry Cohn, 2026, needs more optimization.
27 315 0.176005212409 Henry Cohn, 2026, needs more optimization.
27 316 0.177382133809 Henry Cohn, 2026, needs more optimization.
27 317 0.178088875505 Henry Cohn, 2026, needs more optimization.
27 318 0.179066387575 Henry Cohn, 2026, needs more optimization.
27 319 0.179745037550 Henry Cohn, 2026, needs more optimization.
27 320 0.180599075065 Henry Cohn, 2026, needs more optimization.
27 321 0.180959904932 Henry Cohn, 2026, needs more optimization.
27 322 0.181002751573 Henry Cohn, 2026, needs more optimization.
27 323 0.181181726906 Henry Cohn, 2026, needs more optimization.
27 324 0.181274317673 Henry Cohn, 2026, needs more optimization.
27 325 0.181377692225 Henry Cohn, 2026, needs more optimization.
27 326 0.181442819309 Henry Cohn, 2026, needs more optimization.
27 327 0.181480474408 Henry Cohn, 2026, needs more optimization.
27 328 0.181483800624 Henry Cohn, 2026, needs more optimization.
27 329 0.181653222895 Henry Cohn, 2026, needs more optimization.
27 330 0.181701471446 Henry Cohn, 2026, needs more optimization.
27 331 0.181711499159 Henry Cohn, 2026, needs more optimization.
27 332 0.181737127335 Henry Cohn, 2026, needs more optimization.
27 333 0.181762154729 Henry Cohn, 2026, needs more optimization.
27 334 0.181815488193 Henry Cohn, 2026, needs more optimization.
27 335 0.181816581427 Henry Cohn, 2026, needs more optimization.
27 336 0.181821004398 Henry Cohn, 2026, needs more optimization.
27 337 0.181830292260 Henry Cohn, 2026, needs more optimization.
27 338 0.181845087566 Henry Cohn, 2026, needs more optimization.
27 339 0.181970100636 Henry Cohn, 2026, needs more optimization.
27 340 0.182285158866 Henry Cohn, 2026, needs more optimization.
27 341 0.182694702220 Henry Cohn, 2026, needs more optimization.
27 342 0.183560656462 Henry Cohn, 2026, needs more optimization.
27 343 0.184170277186 Henry Cohn, 2026, needs more optimization.
27 344 0.184549924828 Henry Cohn, 2026, needs more optimization.
27 345 0.185603640696 Henry Cohn, 2026, needs more optimization.
27 346 0.186389447204 Henry Cohn, 2026, needs more optimization.
27 347 0.186706055139 Henry Cohn, 2026, needs more optimization.
27 348 0.187544265469 Henry Cohn, 2026, needs more optimization.
27 349 0.188104859101 Henry Cohn, 2026, needs more optimization.
27 350 0.188593800875 Henry Cohn, 2026, needs more optimization.
27 351 0.189327138868 Henry Cohn, 2026, needs more optimization.
27 352 0.190307997022 Henry Cohn, 2026, needs more optimization.
27 353 0.191009624211 Henry Cohn, 2026, needs more optimization.
27 354 0.191879999633 Henry Cohn, 2026, needs more optimization.
27 355 0.192677518290 Henry Cohn, 2026, needs more optimization.
27 356 0.193339062064 Henry Cohn, 2026, needs more optimization.
27 357 0.193842135088 Henry Cohn, 2026, needs more optimization.
27 358 0.193886367695 Henry Cohn, 2026, needs more optimization.
27 359 0.194009434960 Henry Cohn, 2026, needs more optimization.
27 360 0.194529400485 Henry Cohn, 2026, needs more optimization.
27 361 0.195806851502 Henry Cohn, 2026, needs more optimization.
27 362 0.195917189814 Henry Cohn, 2026, needs more optimization.
27 363 0.196032159754 Henry Cohn, 2026, needs more optimization.
27 364 0.196209109707 Henry Cohn, 2026, needs more optimization.
27 365 0.196304275578 Henry Cohn, 2026, needs more optimization.
27 366 0.196461049099 Henry Cohn, 2026, needs more optimization.
27 367 0.196499893838 Henry Cohn, 2026, needs more optimization.
27 368 0.196530364519 Henry Cohn, 2026, needs more optimization.
27 369 0.196569832064 Henry Cohn, 2026, needs more optimization.
27 370 0.196646421502 Henry Cohn, 2026, needs more optimization.
27 371 0.196720910826 Henry Cohn, 2026, needs more optimization.
27 372 0.196828472549 Henry Cohn, 2026, needs more optimization.
27 373 0.196971828001 Henry Cohn, 2026, needs more optimization.
27 374 0.197098075062 Henry Cohn, 2026, needs more optimization.
27 375 0.197140244609 Henry Cohn, 2026, needs more optimization.
27 376 0.197252404396 Henry Cohn, 2026, needs more optimization.
27 377 0.197490608766 Henry Cohn, 2026, needs more optimization.
27 378 0.197612450508 Henry Cohn, 2026, needs more optimization.
27 379 0.197718768234 Henry Cohn, 2026, needs more optimization.
27 380 0.197816295046 Henry Cohn, 2026, needs more optimization.
27 381 0.197952193725 Henry Cohn, 2026, needs more optimization.
27 382 0.198017850195 Henry Cohn, 2026, needs more optimization.
27 383 0.198105386175 Henry Cohn, 2026, needs more optimization.
27 384 0.198142881382 Henry Cohn, 2026, needs more optimization.
27 385 0.198262490546 Henry Cohn, 2026, needs more optimization.
27 386 0.198374713783 Henry Cohn, 2026, needs more optimization.
27 387 0.198478590651 Henry Cohn, 2026, needs more optimization.
27 388 0.198538696360 Henry Cohn, 2026, needs more optimization.
27 389 0.198681576295 Henry Cohn, 2026, needs more optimization.
27 390 0.198733626576 Henry Cohn, 2026, needs more optimization.
27 391 0.198777947299 Henry Cohn, 2026, needs more optimization.
27 392 0.198842707227 Henry Cohn, 2026, needs more optimization.
27 393 0.198892185442 Henry Cohn, 2026, needs more optimization.
27 394 0.198995124191 Henry Cohn, 2026, needs more optimization.
27 396 0.199077763707 Henry Cohn, 2026, needs more optimization.
27 397 0.199150007337 Henry Cohn, 2026, needs more optimization.
27 398 0.199187991584 Henry Cohn, 2026, needs more optimization.
27 399 0.199210569496 Henry Cohn, 2026, needs more optimization.
27 400 0.199273770617 Henry Cohn, 2026, needs more optimization.
27 401 0.199273770618 Henry Cohn, 2026, needs more optimization.
27 402 0.199304861515 Henry Cohn, 2026, needs more optimization.
27 403 0.199339546822 Henry Cohn, 2026, needs more optimization.
27 404 0.199385480672 Henry Cohn, 2026, needs more optimization.
27 405 0.199401120910 Henry Cohn, 2026, needs more optimization.
27 406 0.199425377922 Henry Cohn, 2026, needs more optimization.
27 407 0.199487727723 Henry Cohn, 2026, needs more optimization.
27 408 0.199525925197 Henry Cohn, 2026, needs more optimization.
27 410 0.199590644218 Henry Cohn, 2026, needs more optimization.
27 411 0.199620732243 Henry Cohn, 2026, needs more optimization.
27 412 0.199672129470 Henry Cohn, 2026, needs more optimization.
27 413 0.199708289630 Henry Cohn, 2026, needs more optimization.
27 414 0.199734767567 Henry Cohn, 2026, needs more optimization.
27 415 0.199752617296 Henry Cohn, 2026, needs more optimization.
27 416 0.199756910998 Henry Cohn, 2026, needs more optimization.
27 417 0.199784262022 Henry Cohn, 2026, needs more optimization.
27 418 0.199800523935 Henry Cohn, 2026, needs more optimization.
27 419 0.199834773816 Henry Cohn, 2026, needs more optimization.
27 420 0.199857801667 Henry Cohn, 2026, needs more optimization.
27 421 0.199890193271 Henry Cohn, 2026, needs more optimization.
27 422 0.199895855671 Henry Cohn, 2026, needs more optimization.
27 423 0.199921324332 Henry Cohn, 2026, needs more optimization.
27 424 0.199942972283 Henry Cohn, 2026, needs more optimization.
27 425 0.199945679368 Henry Cohn, 2026, needs more optimization.
27 562 0.2 Orthogonal union of 552 points in 23 dimensions and 10 points in 4 dimensions.
5⁢x−1
27 570 0.200000846007 Orthogonal union of 568 points in 26 dimensions and 2 points in 1 dimension.
27 571 0.200001179175 Henry Cohn, 2026, needs more optimization.
27 573 0.200001701385 Henry Cohn, 2026, needs more optimization.
27 574 0.200001701396 Henry Cohn, 2026, needs more optimization.
27 575 0.200001951515 Henry Cohn, 2026, needs more optimization.
27 576 0.200013005061 Henry Cohn, 2026, needs more optimization.
27 577 0.200027325939 Henry Cohn, 2026, needs more optimization.
27 578 0.200051322068 Henry Cohn, 2026, needs more optimization.
27 579 0.200059893877 Henry Cohn, 2026, needs more optimization.
27 580 0.200168849164 Henry Cohn, 2026, needs more optimization.
27 581 0.200213727161 Henry Cohn, 2026, needs more optimization.
27 582 0.200795306210 Henry Cohn, 2026, needs more optimization.
27 583 0.201189414818 Henry Cohn, 2026, needs more optimization.
27 584 0.202586959031 Henry Cohn, 2026, needs more optimization.
27 585 0.203159057534 Henry Cohn, 2026, needs more optimization.
27 586 0.203753274700 Henry Cohn, 2026, needs more optimization.
27 587 0.205325161048 Henry Cohn, 2026, needs more optimization.
27 588 0.206488398199 Henry Cohn, 2026, needs more optimization.
27 589 0.207352434626 Henry Cohn, 2026, needs more optimization.
27 590 0.208835436660 Henry Cohn, 2026, needs more optimization.
27 591 0.209625409490 Henry Cohn, 2026, needs more optimization.
27 592 0.210626953289 Henry Cohn, 2026, needs more optimization.
27 593 0.212043688568 Henry Cohn, 2026, needs more optimization.
27 594 0.212348094417 Henry Cohn, 2026, needs more optimization.
27 595 0.213420584283 Henry Cohn, 2026, needs more optimization.
27 596 0.213972494912 Henry Cohn, 2026, needs more optimization.
27 597 0.214504288288 Henry Cohn, 2026, needs more optimization.
27 598 0.215120291928 Henry Cohn, 2026, needs more optimization.
27 616 0.238095214846 Henry Cohn, 2026, needs more optimization.
27 622 0.238095518372 Henry Cohn, 2026, needs more optimization.
27 631 0.238095829234 Henry Cohn, 2026, needs more optimization.
27 632 0.238095829301 Henry Cohn, 2026, needs more optimization.
27 633 0.238096575545 Henry Cohn, 2026, needs more optimization.
27 634 0.238096575575 Henry Cohn, 2026, needs more optimization.
27 636 0.238098690305 Henry Cohn, 2026, needs more optimization.
27 637 0.238098892524 Henry Cohn, 2026, needs more optimization.
27 639 0.238099055282 Henry Cohn, 2026, needs more optimization.
27 640 0.238099745490 Henry Cohn, 2026, needs more optimization.
27 641 0.238124436375 Henry Cohn, 2026, needs more optimization.
27 642 0.238134061695 Henry Cohn, 2026, needs more optimization.
27 643 0.238140749626 Henry Cohn, 2026, needs more optimization.
27 644 0.238142432926 Henry Cohn, 2026, needs more optimization.
27 645 0.238142433183 Henry Cohn, 2026, needs more optimization.
27 646 0.238142433205 Henry Cohn, 2026, needs more optimization.
27 647 0.238143891455 Henry Cohn, 2026, needs more optimization.
27 648 0.238144176739 Henry Cohn, 2026, needs more optimization.
27 649 0.238144180115 Henry Cohn, 2026, needs more optimization.
27 651 0.238207198692 Henry Cohn, 2026, needs more optimization.
27 652 0.238312643025 Henry Cohn, 2026, needs more optimization.
27 653 0.238313697733 Henry Cohn, 2026, needs more optimization.
27 654 0.238463093655 Henry Cohn, 2026, needs more optimization.
27 655 0.238513080264 Henry Cohn, 2026, needs more optimization.
27 656 0.238575496325 Henry Cohn, 2026, needs more optimization.
27 657 0.238575564454 Henry Cohn, 2026, needs more optimization.
27 658 0.238659196542 Henry Cohn, 2026, needs more optimization.
27 659 0.238990947940 Henry Cohn, 2026, needs more optimization.
27 660 0.239324105610 Henry Cohn, 2026, needs more optimization.
27 661 0.239665996478 Henry Cohn, 2026, needs more optimization.
27 662 0.239896495342 Henry Cohn, 2026, needs more optimization.
27 663 0.240062595791 Henry Cohn, 2026, needs more optimization.
27 664 0.240602226175 Henry Cohn, 2026, needs more optimization.
27 666 0.240918643032 Henry Cohn, 2026, needs more optimization.
27 667 0.240964969002 Henry Cohn, 2026, needs more optimization.
27 668 0.241120997757 Henry Cohn, 2026, needs more optimization.
27 669 0.241153442910 Henry Cohn, 2026, needs more optimization.
27 670 0.241356196196 Henry Cohn, 2026, needs more optimization.
27 671 0.241963350230 Henry Cohn, 2026, needs more optimization.
27 672 0.242087736950 Henry Cohn, 2026, needs more optimization.
27 673 0.242184323433 Henry Cohn, 2026, needs more optimization.
27 674 0.242184345940 Henry Cohn, 2026, needs more optimization.
27 676 0.242845288821 Henry Cohn, 2026, needs more optimization.
27 677 0.242908464000 Henry Cohn, 2026, needs more optimization.
27 678 0.243119153694 Henry Cohn, 2026, needs more optimization.
27 679 0.243307242843 Henry Cohn, 2026, needs more optimization.
27 680 0.243389823836 Henry Cohn, 2026, needs more optimization.
27 681 0.244236625098 Henry Cohn, 2026, needs more optimization.
27 682 0.244475240920 Henry Cohn, 2026, needs more optimization.
27 683 0.244495495115 Henry Cohn, 2026, needs more optimization.
27 684 0.244675563039 Henry Cohn, 2026, needs more optimization.
27 685 0.244951131137 Henry Cohn, 2026, needs more optimization.
27 687 0.244984533803 Henry Cohn, 2026, needs more optimization.
27 688 0.244984685741 Henry Cohn, 2026, needs more optimization.
27 689 0.245089874770 Henry Cohn, 2026, needs more optimization.
27 690 0.245175279268 Henry Cohn, 2026, needs more optimization.
27 691 0.245247665753 Henry Cohn, 2026, needs more optimization.
27 692 0.245270555209 Henry Cohn, 2026, needs more optimization.
27 693 0.245375850648 Henry Cohn, 2026, needs more optimization.
27 695 0.245644162311 Henry Cohn, 2026, needs more optimization.
27 696 0.245829713294 Henry Cohn, 2026, needs more optimization.
27 697 0.245897495047 Henry Cohn, 2026, needs more optimization.
27 698 0.245986360182 Henry Cohn, 2026, needs more optimization.
27 699 0.246193305477 Henry Cohn, 2026, needs more optimization.
27 700 0.246400937295 Henry Cohn, 2026, needs more optimization.
27 701 0.246555783704 Henry Cohn, 2026, needs more optimization.
27 702 0.246671252968 Henry Cohn, 2026, needs more optimization.
27 703 0.246730015946 Henry Cohn, 2026, needs more optimization.
27 704 0.246899939995 Henry Cohn, 2026, needs more optimization.
27 705 0.246945350957 Henry Cohn, 2026, needs more optimization.
27 706 0.247040898627 Henry Cohn, 2026, needs more optimization.
27 707 0.247132931609 Henry Cohn, 2026, needs more optimization.
27 708 0.247338738763 Henry Cohn, 2026, needs more optimization.
27 709 0.247405168953 Henry Cohn, 2026, needs more optimization.
27 710 0.247454431970 Henry Cohn, 2026, needs more optimization.
27 711 0.247486079974 Henry Cohn, 2026, needs more optimization.
27 712 0.247554743602 Henry Cohn, 2026, needs more optimization.
27 713 0.247792244166 Henry Cohn, 2026, needs more optimization.
27 714 0.247792275819 Henry Cohn, 2026, needs more optimization.
27 715 0.247932384564 Henry Cohn, 2026, needs more optimization.
27 716 0.248009150885 Henry Cohn, 2026, needs more optimization.
27 717 0.248033237966 Henry Cohn, 2026, needs more optimization.
27 718 0.248037793959 Henry Cohn, 2026, needs more optimization.
27 719 0.248037939752 Henry Cohn, 2026, needs more optimization.
27 720 0.248105464202 Henry Cohn, 2026, needs more optimization.
27 721 0.248164493932 Henry Cohn, 2026, needs more optimization.
27 722 0.248280317110 Henry Cohn, 2026, needs more optimization.
27 723 0.248287498313 Henry Cohn, 2026, needs more optimization.
27 724 0.248372665020 Henry Cohn, 2026, needs more optimization.
27 725 0.248433629800 Henry Cohn, 2026, needs more optimization.
27 726 0.248551848662 Henry Cohn, 2026, needs more optimization.
27 727 0.248604014594 Henry Cohn, 2026, needs more optimization.
27 728 0.248616681495 Henry Cohn, 2026, needs more optimization.
27 729 0.248674729790 Henry Cohn, 2026, needs more optimization.
27 730 0.248760417667 Henry Cohn, 2026, needs more optimization.
27 731 0.248835573950 Henry Cohn, 2026, needs more optimization.
27 732 0.248838104827 Henry Cohn, 2026, needs more optimization.
27 733 0.248907149245 Henry Cohn, 2026, needs more optimization.
27 734 0.248997847282 Henry Cohn, 2026, needs more optimization.
27 735 0.249011207295 Henry Cohn, 2026, needs more optimization.
27 736 0.249105671854 Henry Cohn, 2026, needs more optimization.
27 737 0.249132413934 Henry Cohn, 2026, needs more optimization.
27 738 0.249202596609 Henry Cohn, 2026, needs more optimization.
27 739 0.249221621908 Henry Cohn, 2026, needs more optimization.
27 740 0.249293007013 Henry Cohn, 2026, needs more optimization.
27 741 0.249335841380 Henry Cohn, 2026, needs more optimization.
27 742 0.249373646438 Henry Cohn, 2026, needs more optimization.
27 743 0.249401182046 Henry Cohn, 2026, needs more optimization.
27 744 0.249407751044 Henry Cohn, 2026, needs more optimization.
27 745 0.249457263441 Henry Cohn, 2026, needs more optimization.
27 746 0.249460548407 Henry Cohn, 2026, needs more optimization.
27 747 0.249467033287 Henry Cohn, 2026, needs more optimization.
27 748 0.249467033320 Henry Cohn, 2026, needs more optimization.
27 749 0.249468962409 Henry Cohn, 2026, needs more optimization.
27 750 0.249469767402 Henry Cohn, 2026, needs more optimization.
27 751 0.249523384948 Henry Cohn, 2026, needs more optimization.
27 752 0.249556675261 Henry Cohn, 2026, needs more optimization.
27 753 0.249557440159 Henry Cohn, 2026, needs more optimization.
27 754 0.249611053527 Henry Cohn, 2026, needs more optimization.
27 755 0.249644201242 Henry Cohn, 2026, needs more optimization.
27 756 0.249685515715 Henry Cohn, 2026, needs more optimization.
27 757 0.249704948228 Henry Cohn, 2026, needs more optimization.
27 758 0.249705008093 Henry Cohn, 2026, needs more optimization.
27 759 0.249747490802 Henry Cohn, 2026, needs more optimization.
27 760 0.249753645890 Henry Cohn, 2026, needs more optimization.
27 761 0.249772662481 Henry Cohn, 2026, needs more optimization.
27 762 0.249794769353 Henry Cohn, 2026, needs more optimization.
27 763 0.249804211046 Henry Cohn, 2026, needs more optimization.
27 764 0.249834399388 Henry Cohn, 2026, needs more optimization.
27 907 0.25 Orthogonal union of 891 points in 22 dimensions and 16 points in 5 dimensions.
4⁢x−1
27 908 0.250000467523 Henry Cohn, 2026, needs more optimization.
27 909 0.250000467974 Henry Cohn, 2026, needs more optimization.
27 916 0.250001190868 Henry Cohn, 2026, needs more optimization.
27 918 0.250001281462 Henry Cohn, 2026, needs more optimization.
27 919 0.250001281946 Henry Cohn, 2026, needs more optimization.
27 924 0.250001336827 Henry Cohn, 2026, needs more optimization.
27 929 0.250001762977 Henry Cohn, 2026, needs more optimization.
27 931 0.250001762978 Henry Cohn, 2026, needs more optimization.
27 932 0.250001762981 Henry Cohn, 2026, needs more optimization.
27 933 0.250001762990 Henry Cohn, 2026, needs more optimization.
27 934 0.250001763074 Henry Cohn, 2026, needs more optimization.
27 935 0.250002244058 Henry Cohn, 2026, needs more optimization.
27 936 0.250002339184 Henry Cohn, 2026, needs more optimization.
27 937 0.250002574837 Henry Cohn, 2026, needs more optimization.
27 939 0.250002577401 Henry Cohn, 2026, needs more optimization.
27 940 0.250003267827 Henry Cohn, 2026, needs more optimization.
27 943 0.250003725054 Henry Cohn, 2026, needs more optimization.
27 944 0.250005992888 Henry Cohn, 2026, needs more optimization.
27 945 0.250005993231 Henry Cohn, 2026, needs more optimization.
27 946 0.250044779276 Henry Cohn, 2026, needs more optimization.
27 947 0.250078674669 Henry Cohn, 2026, needs more optimization.
27 948 0.250084866768 Henry Cohn, 2026, needs more optimization.
27 949 0.250102985206 Henry Cohn, 2026, needs more optimization.
27 950 0.250114198478 Henry Cohn, 2026, needs more optimization.
27 951 0.250153132623 Henry Cohn, 2026, needs more optimization.
27 952 0.250200560471 Henry Cohn, 2026, needs more optimization.
27 956 0.250221295769 Henry Cohn, 2026, needs more optimization.
27 959 0.250296598535 Henry Cohn, 2026, needs more optimization.
27 960 0.250402087721 Henry Cohn, 2026, needs more optimization.
27 961 0.250403057146 Henry Cohn, 2026, needs more optimization.
27 962 0.250509964209 Henry Cohn, 2026, needs more optimization.
27 964 0.250550263448 Henry Cohn, 2026, needs more optimization.
27 965 0.250644389371 Henry Cohn, 2026, needs more optimization.
27 966 0.250923926137 Henry Cohn, 2026, needs more optimization.
27 967 0.250971468460 Henry Cohn, 2026, needs more optimization.
27 968 0.251454957942 Henry Cohn, 2026, needs more optimization.
27 969 0.251781934817 Henry Cohn, 2026, needs more optimization.
27 970 0.251878932640 Henry Cohn, 2026, needs more optimization.
27 971 0.252167481057 Henry Cohn, 2026, needs more optimization.
27 972 0.252474703124 Henry Cohn, 2026, needs more optimization.
27 973 0.252488003188 Henry Cohn, 2026, needs more optimization.
27 974 0.252644759417 Henry Cohn, 2026, needs more optimization.
27 975 0.252908584015 Henry Cohn, 2026, needs more optimization.
27 976 0.253258877769 Henry Cohn, 2026, needs more optimization.
27 977 0.253932530710 Henry Cohn, 2026, needs more optimization.
27 978 0.254120702048 Henry Cohn, 2026, needs more optimization.
27 979 0.254618372369 Henry Cohn, 2026, needs more optimization.
27 980 0.254789207003 Henry Cohn, 2026, needs more optimization.
27 981 0.254971835018 Henry Cohn, 2026, needs more optimization.
27 982 0.255149263604 Henry Cohn, 2026, needs more optimization.
27 983 0.255362330225 Henry Cohn, 2026, needs more optimization.
27 984 0.255509083582 Henry Cohn, 2026, needs more optimization.
27 985 0.257133008540 Henry Cohn, 2026, needs more optimization.
27 986 0.257262295383 Henry Cohn, 2026, needs more optimization.
27 987 0.257452380924 Henry Cohn, 2026, needs more optimization.
27 988 0.257739109762 Henry Cohn, 2026, needs more optimization.
27 989 0.257898087237 Henry Cohn, 2026, needs more optimization.
27 990 0.258036533729 Henry Cohn, 2026, needs more optimization.
27 991 0.258967618439 Henry Cohn, 2026, needs more optimization.
27 992 0.259278317582 Henry Cohn, 2026, needs more optimization.
27 993 0.259650332363 Henry Cohn, 2026, needs more optimization.
27 995 0.260142279655 Henry Cohn, 2026, needs more optimization.
27 996 0.260411924406 Henry Cohn, 2026, needs more optimization.
27 997 0.260602463734 Henry Cohn, 2026, needs more optimization.
27 998 0.260803115346 Henry Cohn, 2026, needs more optimization.
27 999 0.260957668673 Henry Cohn, 2026, needs more optimization.
27 1000 0.261098932782 Henry Cohn, 2026, needs more optimization.
27 1001 0.262221581431 Henry Cohn, 2026, needs more optimization.
27 1002 0.262656139068 Henry Cohn, 2026, needs more optimization.
27 1003 0.263012676116 Henry Cohn, 2026, needs more optimization.
27 1004 0.263209727613 Henry Cohn, 2026, needs more optimization.
27 1005 0.263388795645 Henry Cohn, 2026, needs more optimization.
27 1006 0.263650780305 Henry Cohn, 2026, needs more optimization.
27 1007 0.263872258908 Henry Cohn, 2026, needs more optimization.
27 1008 0.264091996629 Henry Cohn, 2026, needs more optimization.
27 1009 0.264456127602 Henry Cohn, 2026, needs more optimization.
27 1010 0.264523536078 Henry Cohn, 2026, needs more optimization.
27 1011 0.264722456844 Henry Cohn, 2026, needs more optimization.
27 1012 0.264804375696 Henry Cohn, 2026, needs more optimization.
27 1013 0.265010310290 Henry Cohn, 2026, needs more optimization.
27 1014 0.265197175533 Henry Cohn, 2026, needs more optimization.
27 1015 0.265585148630 Henry Cohn, 2026, needs more optimization.
27 1016 0.265880024708 Henry Cohn, 2026, needs more optimization.
27 1017 0.266195483501 Henry Cohn, 2026, needs more optimization.
27 1018 0.266301537328 Henry Cohn, 2026, needs more optimization.
27 1019 0.266534536395 Henry Cohn, 2026, needs more optimization.
27 1020 0.266815363739 Henry Cohn, 2026, needs more optimization.
27 1021 0.267011523837 Henry Cohn, 2026, needs more optimization.
27 1022 0.267218703121 Henry Cohn, 2026, needs more optimization.
27 1023 0.267531446079 Henry Cohn, 2026, needs more optimization.
27 1024 0.267881232602 Henry Cohn, 2026, needs more optimization.
28 57 0.028627089329 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
18928⁢x3−784⁢x2−28⁢x+1
28 58 0.033333333334 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
30⁢x−1
28 59 0.039693085758 Henry Cohn, 2026, needs more optimization.
28 60 0.039703378844 Ilmari Vahteristo, 2026.
584⁢x2+2⁢x−1
28 61 0.039748128111 Henry Cohn, 2026.
28 62 0.044113391839 Henry Cohn, 2026, needs more optimization.
28 63 0.045182094797 Henry Cohn, 2026.
28 64 0.045901657151 Henry Cohn, 2024, needs more optimization.
28 65 0.046144411319 Henry Cohn, 2026.
28 66 0.047459655815 Henry Cohn, 2026.
28 67 0.052249912377 Henry Cohn, 2026.
28 68 0.054257387201 Henry Cohn, 2026.
28 69 0.055901485675 Henry Cohn, 2026, needs more optimization.
28 70 0.058160698453 Henry Cohn, 2026, needs more optimization.
28 71 0.059586716587 Henry Cohn, 2026.
28 72 0.061336054837 Henry Cohn, 2026.
28 73 0.063218203873 Henry Cohn, 2026, needs more optimization.
28 74 0.063890993439 Henry Cohn, 2026, needs more optimization.
28 75 0.064434723528 Henry Cohn, 2026, needs more optimization.
28 76 0.064717246550 Henry Cohn, 2026, needs more optimization.
28 77 0.065922150488 Henry Cohn, 2026, needs more optimization.
28 78 0.067448950547 Henry Cohn, 2026, needs more optimization.
28 79 0.069479904842 Henry Cohn, 2026, needs more optimization.
28 80 0.070910361010 Henry Cohn, 2026, needs more optimization.
28 81 0.072768932730 Henry Cohn, 2026, needs more optimization.
28 82 0.074527160008 Henry Cohn, 2026, needs more optimization.
28 83 0.074837400917 Henry Cohn, 2026, needs more optimization.
28 84 0.075982718924 Henry Cohn, 2026, needs more optimization.
28 85 0.076676421267 Henry Cohn, 2026, needs more optimization.
28 86 0.076860469423 Henry Cohn, 2026, needs more optimization.
28 87 0.076905025239 Henry Cohn, 2026, needs more optimization.
28 88 0.076923523265 Henry Cohn, 2026, needs more optimization.
28 89 0.077231165095 Henry Cohn, 2026, needs more optimization.
28 90 0.077490902162 Henry Cohn, 2026, needs more optimization.
28 91 0.078290621537 Henry Cohn, 2026, needs more optimization.
28 92 0.078673308119 Henry Cohn, 2026, needs more optimization.
28 93 0.079213328317 Henry Cohn, 2026, needs more optimization.
28 94 0.079375589319 Henry Cohn, 2026, needs more optimization.
28 95 0.079798732407 Henry Cohn, 2026, needs more optimization.
28 96 0.080118152192 Henry Cohn, 2026, needs more optimization.
28 97 0.080241544630 Henry Cohn, 2026, needs more optimization.
28 98 0.080465071802 Henry Cohn, 2026, needs more optimization.
28 99 0.080634601073 Henry Cohn, 2026, needs more optimization.
28 100 0.080685071015 Henry Cohn, 2026, needs more optimization.
28 101 0.080685483983 Henry Cohn, 2026, needs more optimization.
28 102 0.080896644757 Henry Cohn, 2026, needs more optimization.
28 103 0.083869984062 Henry Cohn, 2026, needs more optimization.
28 104 0.085671112573 Henry Cohn, 2026, needs more optimization.
28 105 0.086914857469 Henry Cohn, 2026, needs more optimization.
28 106 0.088256958777 Henry Cohn, 2026, needs more optimization.
28 107 0.088683065182 Henry Cohn, 2026, needs more optimization.
28 108 0.089272753571 Henry Cohn, 2026, needs more optimization.
28 109 0.089566492197 Henry Cohn, 2026, needs more optimization.
28 110 0.089694207701 Henry Cohn, 2026, needs more optimization.
28 111 0.089783488253 Henry Cohn, 2026, needs more optimization.
28 112 0.090075961563 Henry Cohn, 2026, needs more optimization.
28 113 0.090252038409 Henry Cohn, 2026, needs more optimization.
28 114 0.090520288043 Henry Cohn, 2026, needs more optimization.
28 115 0.090761770952 Henry Cohn, 2026, needs more optimization.
28 116 0.090836279862 Henry Cohn, 2026, needs more optimization.
28 117 0.090872947016 Henry Cohn, 2026, needs more optimization.
28 118 0.091674121810 Henry Cohn, 2026, needs more optimization.
28 119 0.093902195332 Henry Cohn, 2026, needs more optimization.
28 120 0.096028110307 Henry Cohn, 2026, needs more optimization.
28 121 0.098093425958 Henry Cohn, 2026, needs more optimization.
28 122 0.099649898981 Henry Cohn, 2026, needs more optimization.
28 123 0.101610350028 Henry Cohn, 2026, needs more optimization.
28 124 0.102422525656 Henry Cohn, 2026, needs more optimization.
28 125 0.102478286466 Henry Cohn, 2026, needs more optimization.
28 126 0.102882694622 Henry Cohn, 2026, needs more optimization.
28 127 0.102892414490 Henry Cohn, 2026, needs more optimization.
28 128 0.103048201428 Henry Cohn, 2026, needs more optimization.
28 129 0.103102420760 Henry Cohn, 2026, needs more optimization.
28 130 0.103120602186 Henry Cohn, 2026, needs more optimization.
28 131 0.104307859918 Henry Cohn, 2026, needs more optimization.
28 132 0.105404226358 Henry Cohn, 2026, needs more optimization.
28 133 0.106248432417 Henry Cohn, 2026, needs more optimization.
28 134 0.107850774232 Henry Cohn, 2026, needs more optimization.
28 135 0.108597892729 Henry Cohn, 2026, needs more optimization.
28 136 0.109042524185 Henry Cohn, 2026, needs more optimization.
28 137 0.109744748052 Henry Cohn, 2026, needs more optimization.
28 138 0.110880680286 Henry Cohn, 2026, needs more optimization.
28 139 0.110913416971 Henry Cohn, 2026, needs more optimization.
28 140 0.110988688770 Henry Cohn, 2026, needs more optimization.
28 150 0.111111111112 Henry Cohn, 2026.
9⁢x−1
28 151 0.111556075883 Henry Cohn, 2026.
73⁢x2−44⁢x+4
28 152 0.116948610781 Henry Cohn, 2026.
28 153 0.119770665777 Henry Cohn, 2026, needs more optimization.
28 154 0.122975008722 Henry Cohn, 2026, needs more optimization.
28 155 0.125261837176 Henry Cohn, 2026, needs more optimization.
28 156 0.126321828355 Henry Cohn, 2026, needs more optimization.
28 157 0.127118914492 Henry Cohn, 2026, needs more optimization.
28 158 0.127740446526 Henry Cohn, 2026, needs more optimization.
28 159 0.128111923863 Henry Cohn, 2026, needs more optimization.
28 182 0.128238684469 Henry Cohn, 2026.
92⁢x2−4⁢x−1
28 183 0.130665724291 Henry Cohn, 2026.
28 184 0.141612906936 Henry Cohn, 2026, needs more optimization.
28 185 0.142134532059 Henry Cohn, 2026, needs more optimization.
28 186 0.142160290116 Henry Cohn, 2026, needs more optimization.
28 187 0.142165771689 Henry Cohn, 2026, needs more optimization.
28 188 0.142186231875 Henry Cohn, 2026, needs more optimization.
28 189 0.142222201521 Henry Cohn, 2026, needs more optimization.
28 190 0.142238597623 Henry Cohn, 2026, needs more optimization.
28 191 0.142253079928 Henry Cohn, 2026, needs more optimization.
28 192 0.142393049499 Henry Cohn, 2026, needs more optimization.
28 193 0.142482287295 Henry Cohn, 2026, needs more optimization.
28 194 0.142529315834 Henry Cohn, 2026, needs more optimization.
28 195 0.142599780681 Henry Cohn, 2026, needs more optimization.
28 196 0.142694692986 Henry Cohn, 2026, needs more optimization.
28 197 0.142754910361 Henry Cohn, 2026, needs more optimization.
28 198 0.142783065214 Henry Cohn, 2026, needs more optimization.
28 199 0.142878379722 Henry Cohn, 2026, needs more optimization.
28 200 0.143368709231 Henry Cohn, 2026, needs more optimization.
28 201 0.143695954980 Henry Cohn, 2026, needs more optimization.
28 202 0.144186926754 Henry Cohn, 2026, needs more optimization.
28 203 0.145065819579 Henry Cohn, 2026, needs more optimization.
28 204 0.145910817835 Henry Cohn, 2026, needs more optimization.
28 205 0.145967727193 Henry Cohn, 2026, needs more optimization.
28 206 0.145967758719 Henry Cohn, 2026, needs more optimization.
28 207 0.145967788188 Henry Cohn, 2026, needs more optimization.
28 208 0.146064111607 Henry Cohn, 2026, needs more optimization.
28 209 0.146131405998 Henry Cohn, 2026, needs more optimization.
28 210 0.146202039968 Henry Cohn, 2026, needs more optimization.
28 211 0.146290567773 Henry Cohn, 2026, needs more optimization.
28 212 0.146444911161 Henry Cohn, 2026, needs more optimization.
28 213 0.146890415008 Henry Cohn, 2026, needs more optimization.
28 214 0.147041532764 Henry Cohn, 2026, needs more optimization.
28 215 0.147122271497 Henry Cohn, 2026, needs more optimization.
28 216 0.147126965399 Henry Cohn, 2026, needs more optimization.
28 217 0.147212220855 Henry Cohn, 2026, needs more optimization.
28 218 0.147330630304 Henry Cohn, 2026, needs more optimization.
28 219 0.147390844399 Henry Cohn, 2026, needs more optimization.
28 220 0.147494289076 Henry Cohn, 2026, needs more optimization.
28 221 0.147570500102 Henry Cohn, 2026, needs more optimization.
28 222 0.147654285208 Henry Cohn, 2026, needs more optimization.
28 223 0.147655355138 Henry Cohn, 2026, needs more optimization.
28 224 0.147655355597 Henry Cohn, 2026, needs more optimization.
28 225 0.147664586346 Henry Cohn, 2026, needs more optimization.
28 226 0.147673588694 Henry Cohn, 2026, needs more optimization.
28 227 0.147747039976 Henry Cohn, 2026, needs more optimization.
28 228 0.147894784271 Henry Cohn, 2026, needs more optimization.
28 229 0.148221535729 Henry Cohn, 2026, needs more optimization.
28 230 0.148960789435 Henry Cohn, 2026, needs more optimization.
28 231 0.149101617767 Henry Cohn, 2026, needs more optimization.
28 232 0.149210289434 Henry Cohn, 2026, needs more optimization.
28 233 0.149282990658 Henry Cohn, 2026, needs more optimization.
28 234 0.149287516689 Henry Cohn, 2026, needs more optimization.
28 235 0.149313500350 Henry Cohn, 2026, needs more optimization.
28 236 0.149321971060 Henry Cohn, 2026, needs more optimization.
28 237 0.149321973593 Henry Cohn, 2026, needs more optimization.
28 238 0.149323891619 Henry Cohn, 2026, needs more optimization.
28 239 0.149422635895 Henry Cohn, 2026, needs more optimization.
28 240 0.150164163244 Henry Cohn, 2026, needs more optimization.
28 241 0.150635161099 Henry Cohn, 2026, needs more optimization.
28 242 0.151813774863 Henry Cohn, 2026, needs more optimization.
28 243 0.152630073808 Henry Cohn, 2026, needs more optimization.
28 244 0.154126393955 Henry Cohn, 2026, needs more optimization.
28 245 0.155239042555 Henry Cohn, 2026, needs more optimization.
28 246 0.156941061729 Henry Cohn, 2026, needs more optimization.
28 247 0.157034934875 Henry Cohn, 2026, needs more optimization.
28 248 0.157636036474 Henry Cohn, 2026, needs more optimization.
28 249 0.158610062466 Henry Cohn, 2026, needs more optimization.
28 250 0.160096623357 Henry Cohn, 2026, needs more optimization.
28 251 0.161289119695 Henry Cohn, 2026, needs more optimization.
28 252 0.162023964712 Henry Cohn, 2026, needs more optimization.
28 253 0.162048300500 Henry Cohn, 2026, needs more optimization.
28 254 0.162087893063 Henry Cohn, 2026, needs more optimization.
28 255 0.162159450238 Henry Cohn, 2026, needs more optimization.
28 256 0.162395258852 Henry Cohn, 2026, needs more optimization.
28 257 0.162657806121 Henry Cohn, 2026, needs more optimization.
28 258 0.162868770352 Henry Cohn, 2026, needs more optimization.
28 259 0.163030883245 Henry Cohn, 2026, needs more optimization.
28 260 0.163399111746 Henry Cohn, 2026, needs more optimization.
28 261 0.163581236765 Henry Cohn, 2026, needs more optimization.
28 262 0.163784047484 Henry Cohn, 2026, needs more optimization.
28 263 0.163903063244 Henry Cohn, 2026, needs more optimization.
28 264 0.164106471212 Henry Cohn, 2026, needs more optimization.
28 265 0.164309900357 Henry Cohn, 2026, needs more optimization.
28 266 0.164635947112 Henry Cohn, 2026, needs more optimization.
28 267 0.164742838540 Henry Cohn, 2026, needs more optimization.
28 268 0.164799549539 Henry Cohn, 2026, needs more optimization.
28 269 0.164799646238 Henry Cohn, 2026, needs more optimization.
28 270 0.164892388055 Henry Cohn, 2026, needs more optimization.
28 271 0.164945456190 Henry Cohn, 2026, needs more optimization.
28 272 0.165059723139 Henry Cohn, 2026, needs more optimization.
28 273 0.165217970169 Henry Cohn, 2026, needs more optimization.
28 274 0.165332505036 Henry Cohn, 2026, needs more optimization.
28 275 0.165345947813 Henry Cohn, 2026, needs more optimization.
28 276 0.165429936723 Henry Cohn, 2026, needs more optimization.
28 277 0.165459046738 Henry Cohn, 2026, needs more optimization.
28 278 0.165571544562 Henry Cohn, 2026, needs more optimization.
28 279 0.165623480934 Henry Cohn, 2026, needs more optimization.
28 280 0.165653504645 Henry Cohn, 2026, needs more optimization.
28 281 0.165680158698 Henry Cohn, 2026, needs more optimization.
28 282 0.165744877366 Henry Cohn, 2026, needs more optimization.
28 283 0.165839608627 Henry Cohn, 2026, needs more optimization.
28 284 0.165871957081 Henry Cohn, 2026, needs more optimization.
28 285 0.165912911336 Henry Cohn, 2026, needs more optimization.
28 286 0.166030763611 Henry Cohn, 2026, needs more optimization.
28 287 0.166106284501 Henry Cohn, 2026, needs more optimization.
28 288 0.166165576207 Henry Cohn, 2026, needs more optimization.
28 289 0.166282636381 Henry Cohn, 2026, needs more optimization.
28 290 0.166327179849 Henry Cohn, 2026, needs more optimization.
28 291 0.166351696717 Henry Cohn, 2026, needs more optimization.
28 292 0.166365389602 Henry Cohn, 2026, needs more optimization.
28 293 0.166408602399 Henry Cohn, 2026, needs more optimization.
28 294 0.166454320839 Henry Cohn, 2026, needs more optimization.
28 295 0.166461650188 Henry Cohn, 2026, needs more optimization.
28 296 0.166472421667 Henry Cohn, 2026, needs more optimization.
28 297 0.166488081357 Henry Cohn, 2026, needs more optimization.
28 298 0.166507043925 Henry Cohn, 2026, needs more optimization.
28 299 0.166524202060 Henry Cohn, 2026, needs more optimization.
28 300 0.166555714553 Henry Cohn, 2026, needs more optimization.
28 301 0.166578498571 Henry Cohn, 2026, needs more optimization.
28 302 0.166594403052 Henry Cohn, 2026, needs more optimization.
28 305 0.166664601532 Henry Cohn, 2026, needs more optimization.
28 306 0.166664853656 Henry Cohn, 2026, needs more optimization.
28 307 0.166665061912 Henry Cohn, 2026, needs more optimization.
28 309 0.166667684933 Henry Cohn, 2026, needs more optimization.
28 311 0.166675263896 Henry Cohn, 2026, needs more optimization.
28 312 0.166678670896 Henry Cohn, 2026, needs more optimization.
28 313 0.166710367107 Henry Cohn, 2026, needs more optimization.
28 314 0.167083014087 Henry Cohn, 2026, needs more optimization.
28 315 0.167156886828 Henry Cohn, 2026, needs more optimization.
28 316 0.167668304190 Henry Cohn, 2026, needs more optimization.
28 317 0.168016455194 Henry Cohn, 2026, needs more optimization.
28 318 0.168664679821 Henry Cohn, 2026, needs more optimization.
28 319 0.169467859465 Henry Cohn, 2026, needs more optimization.
28 320 0.170175271796 Henry Cohn, 2026, needs more optimization.
28 321 0.171459699247 Henry Cohn, 2026, needs more optimization.
28 322 0.171962510728 Henry Cohn, 2026, needs more optimization.
28 323 0.172993681824 Henry Cohn, 2026, needs more optimization.
28 324 0.173490189655 Henry Cohn, 2026, needs more optimization.
28 325 0.174925621269 Henry Cohn, 2026, needs more optimization.
28 326 0.175613097170 Henry Cohn, 2026, needs more optimization.
28 327 0.176198749505 Henry Cohn, 2026, needs more optimization.
28 328 0.177114761462 Henry Cohn, 2026, needs more optimization.
28 329 0.178572130574 Henry Cohn, 2026, needs more optimization.
28 330 0.178572529269 Henry Cohn, 2026, needs more optimization.
28 331 0.178574790785 Henry Cohn, 2026, needs more optimization.
28 332 0.178626349962 Henry Cohn, 2026, needs more optimization.
28 333 0.178879419467 Henry Cohn, 2026, needs more optimization.
28 334 0.178890611591 Henry Cohn, 2026, needs more optimization.
28 335 0.179502185510 Henry Cohn, 2026, needs more optimization.
28 336 0.180152541440 Henry Cohn, 2026, needs more optimization.
28 337 0.180154451498 Henry Cohn, 2026, needs more optimization.
28 338 0.180528943429 Henry Cohn, 2026, needs more optimization.
28 339 0.181434975933 Henry Cohn, 2026, needs more optimization.
28 340 0.181478349918 Henry Cohn, 2026, needs more optimization.
28 341 0.181558621537 Henry Cohn, 2026, needs more optimization.
28 342 0.181625773825 Henry Cohn, 2026, needs more optimization.
28 343 0.181657039724 Henry Cohn, 2026, needs more optimization.
28 344 0.181736943140 Henry Cohn, 2026, needs more optimization.
28 345 0.181778943187 Henry Cohn, 2026, needs more optimization.
28 346 0.181804786234 Henry Cohn, 2026, needs more optimization.
28 347 0.181821081974 Henry Cohn, 2026, needs more optimization.
28 348 0.181827373674 Henry Cohn, 2026, needs more optimization.
28 349 0.181838848178 Henry Cohn, 2026, needs more optimization.
28 350 0.181871377889 Henry Cohn, 2026, needs more optimization.
28 351 0.182080956376 Henry Cohn, 2026, needs more optimization.
28 352 0.182373425246 Henry Cohn, 2026, needs more optimization.
28 353 0.182641908631 Henry Cohn, 2026, needs more optimization.
28 354 0.183646465383 Henry Cohn, 2026, needs more optimization.
28 355 0.184384517990 Henry Cohn, 2026, needs more optimization.
28 356 0.184954483762 Henry Cohn, 2026, needs more optimization.
28 357 0.185207190386 Henry Cohn, 2026, needs more optimization.
28 358 0.185760621601 Henry Cohn, 2026, needs more optimization.
28 359 0.186352225993 Henry Cohn, 2026, needs more optimization.
28 360 0.186521045250 Henry Cohn, 2026, needs more optimization.
28 361 0.191559270389 Henry Cohn, 2026, needs more optimization.
28 362 0.191806250951 Henry Cohn, 2026, needs more optimization.
28 363 0.192269130099 Henry Cohn, 2026, needs more optimization.
28 364 0.192378316359 Henry Cohn, 2026, needs more optimization.
28 365 0.192450824779 Henry Cohn, 2026, needs more optimization.
28 366 0.192548051540 Henry Cohn, 2026, needs more optimization.
28 367 0.192831871255 Henry Cohn, 2026, needs more optimization.
28 368 0.192977705975 Henry Cohn, 2026, needs more optimization.
28 369 0.193181456239 Henry Cohn, 2026, needs more optimization.
28 370 0.193377452998 Henry Cohn, 2026, needs more optimization.
28 371 0.193718412876 Henry Cohn, 2026, needs more optimization.
28 372 0.193815493299 Henry Cohn, 2026, needs more optimization.
28 373 0.193986316452 Henry Cohn, 2026, needs more optimization.
28 374 0.194190904616 Henry Cohn, 2026, needs more optimization.
28 375 0.194392513938 Henry Cohn, 2026, needs more optimization.
28 376 0.194594616192 Henry Cohn, 2026, needs more optimization.
28 377 0.194704398385 Henry Cohn, 2026, needs more optimization.
28 378 0.194949370950 Henry Cohn, 2026, needs more optimization.
28 379 0.195078347786 Henry Cohn, 2026, needs more optimization.
28 380 0.195360983337 Henry Cohn, 2026, needs more optimization.
28 381 0.195575679113 Henry Cohn, 2026, needs more optimization.
28 382 0.195677088974 Henry Cohn, 2026, needs more optimization.
28 383 0.195873606950 Henry Cohn, 2026, needs more optimization.
28 384 0.195998945633 Henry Cohn, 2026, needs more optimization.
28 385 0.196171898822 Henry Cohn, 2026, needs more optimization.
28 386 0.196195748490 Henry Cohn, 2026, needs more optimization.
28 387 0.196364420611 Henry Cohn, 2026, needs more optimization.
28 388 0.196487868042 Henry Cohn, 2026, needs more optimization.
28 389 0.196674644647 Henry Cohn, 2026, needs more optimization.
28 390 0.196819305163 Henry Cohn, 2026, needs more optimization.
28 391 0.196851276296 Henry Cohn, 2026, needs more optimization.
28 392 0.196985210655 Henry Cohn, 2026, needs more optimization.
28 393 0.197067697745 Henry Cohn, 2026, needs more optimization.
28 394 0.197171194291 Henry Cohn, 2026, needs more optimization.
28 395 0.197348467188 Henry Cohn, 2026, needs more optimization.
28 396 0.197414067720 Henry Cohn, 2026, needs more optimization.
28 397 0.197439053835 Henry Cohn, 2026, needs more optimization.
28 398 0.197529936392 Henry Cohn, 2026, needs more optimization.
28 399 0.197603310768 Henry Cohn, 2026, needs more optimization.
28 400 0.197756081302 Henry Cohn, 2026, needs more optimization.
28 401 0.197846176821 Henry Cohn, 2026, needs more optimization.
28 402 0.197894608873 Henry Cohn, 2026, needs more optimization.
28 403 0.198081137210 Henry Cohn, 2026, needs more optimization.
28 404 0.198148368017 Henry Cohn, 2026, needs more optimization.
28 405 0.198153741061 Henry Cohn, 2026, needs more optimization.
28 406 0.198246163663 Henry Cohn, 2026, needs more optimization.
28 407 0.198250982325 Henry Cohn, 2026, needs more optimization.
28 408 0.198460492208 Henry Cohn, 2026, needs more optimization.
28 409 0.198527860533 Henry Cohn, 2026, needs more optimization.
28 410 0.198550887129 Henry Cohn, 2026, needs more optimization.
28 411 0.198616696170 Henry Cohn, 2026, needs more optimization.
28 412 0.198629682921 Henry Cohn, 2026, needs more optimization.
28 413 0.198672015307 Henry Cohn, 2026, needs more optimization.
28 414 0.198757314373 Henry Cohn, 2026, needs more optimization.
28 415 0.198792608458 Henry Cohn, 2026, needs more optimization.
28 416 0.198886161686 Henry Cohn, 2026, needs more optimization.
28 417 0.198920838927 Henry Cohn, 2026, needs more optimization.
28 418 0.199021592370 Henry Cohn, 2026, needs more optimization.
28 419 0.199041731969 Henry Cohn, 2026, needs more optimization.
28 420 0.199049115241 Henry Cohn, 2026, needs more optimization.
28 421 0.199121950351 Henry Cohn, 2026, needs more optimization.
28 422 0.199137813620 Henry Cohn, 2026, needs more optimization.
28 423 0.199202229489 Henry Cohn, 2026, needs more optimization.
28 424 0.199223681470 Henry Cohn, 2026, needs more optimization.
28 425 0.199255848218 Henry Cohn, 2026, needs more optimization.
28 426 0.199345140031 Henry Cohn, 2026, needs more optimization.
28 427 0.199363023289 Henry Cohn, 2026, needs more optimization.
28 428 0.199382349622 Henry Cohn, 2026, needs more optimization.
28 429 0.199424928864 Henry Cohn, 2026, needs more optimization.
28 430 0.199468080103 Henry Cohn, 2026, needs more optimization.
28 431 0.199485512593 Henry Cohn, 2026, needs more optimization.
28 432 0.199502762686 Henry Cohn, 2026, needs more optimization.
28 433 0.199503700832 Henry Cohn, 2026, needs more optimization.
28 434 0.199536598144 Henry Cohn, 2026, needs more optimization.
28 435 0.199556771214 Henry Cohn, 2026, needs more optimization.
28 436 0.199599099874 Henry Cohn, 2026, needs more optimization.
28 437 0.199615157218 Henry Cohn, 2026, needs more optimization.
28 438 0.199660914097 Henry Cohn, 2026, needs more optimization.
28 439 0.199671909014 Henry Cohn, 2026, needs more optimization.
28 440 0.199678704198 Henry Cohn, 2026, needs more optimization.
28 441 0.199685366067 Henry Cohn, 2026, needs more optimization.
28 442 0.199699724551 Henry Cohn, 2026, needs more optimization.
28 443 0.199710086728 Henry Cohn, 2026, needs more optimization.
28 444 0.199736130625 Henry Cohn, 2026, needs more optimization.
28 445 0.199751565789 Henry Cohn, 2026, needs more optimization.
28 446 0.199798465333 Henry Cohn, 2026, needs more optimization.
28 447 0.199816595491 Henry Cohn, 2026, needs more optimization.
28 448 0.199840647110 Henry Cohn, 2026, needs more optimization.
28 449 0.199841358762 Henry Cohn, 2026, needs more optimization.
28 450 0.199852446718 Henry Cohn, 2026, needs more optimization.
28 451 0.199860753095 Henry Cohn, 2026, needs more optimization.
28 452 0.199869501057 Henry Cohn, 2026, needs more optimization.
28 453 0.199877908208 Henry Cohn, 2026, needs more optimization.
28 454 0.199900917959 Henry Cohn, 2026, needs more optimization.
28 455 0.199900918041 Henry Cohn, 2026, needs more optimization.
28 456 0.199909449249 Henry Cohn, 2026, needs more optimization.
28 457 0.199914652829 Henry Cohn, 2026, needs more optimization.
28 458 0.199921835987 Henry Cohn, 2026, needs more optimization.
28 459 0.199926430405 Henry Cohn, 2026, needs more optimization.
28 460 0.199950308174 Henry Cohn, 2026, needs more optimization.
28 568 0.2 Orthogonal union of 552 points in 23 dimensions and 16 points in 5 dimensions.
5⁢x−1
28 572 0.200000846007 Orthogonal union of 568 points in 26 dimensions and 4 points in 2 dimensions.
28 573 0.200001179175 Orthogonal union of 571 points in 27 dimensions and 2 points in 1 dimension.
28 577 0.200001476330 Henry Cohn, 2026, needs more optimization.
28 579 0.200001949497 Henry Cohn, 2026, needs more optimization.
28 580 0.200001949503 Henry Cohn, 2026, needs more optimization.
28 581 0.200003602991 Henry Cohn, 2026, needs more optimization.
28 582 0.200003603050 Henry Cohn, 2026, needs more optimization.
28 583 0.200004240918 Henry Cohn, 2026, needs more optimization.
28 584 0.200005318297 Henry Cohn, 2026, needs more optimization.
28 585 0.200006658516 Henry Cohn, 2026, needs more optimization.
28 586 0.200011230870 Henry Cohn, 2026, needs more optimization.
28 587 0.200033985736 Henry Cohn, 2026, needs more optimization.
28 588 0.200064018850 Henry Cohn, 2026, needs more optimization.
28 589 0.200073403596 Henry Cohn, 2026, needs more optimization.
28 590 0.200214120226 Henry Cohn, 2026, needs more optimization.
28 591 0.200332156677 Henry Cohn, 2026, needs more optimization.
28 592 0.200469484067 Henry Cohn, 2026, needs more optimization.
28 593 0.200830095239 Henry Cohn, 2026, needs more optimization.
28 594 0.200944392907 Henry Cohn, 2026, needs more optimization.
28 595 0.201673745727 Henry Cohn, 2026, needs more optimization.
28 596 0.202222292483 Henry Cohn, 2026, needs more optimization.
28 597 0.202945668792 Henry Cohn, 2026, needs more optimization.
28 598 0.203368447768 Henry Cohn, 2026, needs more optimization.
28 599 0.203956663801 Henry Cohn, 2026, needs more optimization.
28 600 0.204521115658 Henry Cohn, 2026, needs more optimization.
28 601 0.237151971594 Henry Cohn, 2026, needs more optimization.
28 602 0.237187902194 Henry Cohn, 2026, needs more optimization.
28 604 0.237202700341 Henry Cohn, 2026, needs more optimization.
28 606 0.237215782315 Henry Cohn, 2026, needs more optimization.
28 608 0.237440192686 Henry Cohn, 2026, needs more optimization.
28 609 0.237514627277 Henry Cohn, 2026, needs more optimization.
28 610 0.237514824638 Henry Cohn, 2026, needs more optimization.
28 612 0.237541666905 Henry Cohn, 2026, needs more optimization.
28 613 0.237661521378 Henry Cohn, 2026, needs more optimization.
28 614 0.237689016273 Henry Cohn, 2026, needs more optimization.
28 619 0.238007376092 Henry Cohn, 2026, needs more optimization.
28 632 0.238024752037 Henry Cohn, 2026, needs more optimization.
28 633 0.238027854046 Henry Cohn, 2026, needs more optimization.
28 636 0.238027856184 Henry Cohn, 2026, needs more optimization.
28 637 0.238027872379 Henry Cohn, 2026, needs more optimization.
28 651 0.238090107250 Henry Cohn, 2026, needs more optimization.
28 652 0.238090115666 Henry Cohn, 2026, needs more optimization.
28 653 0.238090124742 Henry Cohn, 2026, needs more optimization.
28 660 0.238090138289 Henry Cohn, 2026, needs more optimization.
28 661 0.238092754783 Henry Cohn, 2026, needs more optimization.
28 662 0.238098230532 Henry Cohn, 2026, needs more optimization.
28 665 0.238114278514 Henry Cohn, 2026, needs more optimization.
28 666 0.238114293660 Henry Cohn, 2026, needs more optimization.
28 667 0.238117975721 Henry Cohn, 2026, needs more optimization.
28 669 0.238132813918 Henry Cohn, 2026, needs more optimization.
28 670 0.238132813966 Henry Cohn, 2026, needs more optimization.
28 671 0.238132915882 Henry Cohn, 2026, needs more optimization.
28 673 0.238149940822 Henry Cohn, 2026, needs more optimization.
28 674 0.238153101253 Henry Cohn, 2026, needs more optimization.
28 675 0.238153236247 Henry Cohn, 2026, needs more optimization.
28 676 0.238153241376 Henry Cohn, 2026, needs more optimization.
28 677 0.238153241383 Henry Cohn, 2026, needs more optimization.
28 678 0.238181522534 Henry Cohn, 2026, needs more optimization.
28 680 0.238217248663 Henry Cohn, 2026, needs more optimization.
28 682 0.238317196343 Henry Cohn, 2026, needs more optimization.
28 683 0.238318469400 Henry Cohn, 2026, needs more optimization.
28 684 0.238324987451 Henry Cohn, 2026, needs more optimization.
28 685 0.238325032847 Henry Cohn, 2026, needs more optimization.
28 686 0.238337192476 Henry Cohn, 2026, needs more optimization.
28 687 0.238615422379 Henry Cohn, 2026, needs more optimization.
28 688 0.238705690392 Henry Cohn, 2026, needs more optimization.
28 689 0.238916978597 Henry Cohn, 2026, needs more optimization.
28 690 0.238917183380 Henry Cohn, 2026, needs more optimization.
28 691 0.238917197457 Henry Cohn, 2026, needs more optimization.
28 692 0.239039005582 Henry Cohn, 2026, needs more optimization.
28 693 0.239594620784 Henry Cohn, 2026, needs more optimization.
28 694 0.239610954558 Henry Cohn, 2026, needs more optimization.
28 695 0.239864679832 Henry Cohn, 2026, needs more optimization.
28 696 0.240284910591 Henry Cohn, 2026, needs more optimization.
28 697 0.240302970194 Henry Cohn, 2026, needs more optimization.
28 698 0.240625741012 Henry Cohn, 2026, needs more optimization.
28 699 0.240712597487 Henry Cohn, 2026, needs more optimization.
28 700 0.241103875302 Henry Cohn, 2026, needs more optimization.
28 701 0.241215155455 Henry Cohn, 2026, needs more optimization.
28 702 0.241317341093 Henry Cohn, 2026, needs more optimization.
28 703 0.241343945263 Henry Cohn, 2026, needs more optimization.
28 704 0.241422343782 Henry Cohn, 2026, needs more optimization.
28 705 0.241517928572 Henry Cohn, 2026, needs more optimization.
28 707 0.241641327075 Henry Cohn, 2026, needs more optimization.
28 708 0.241894510046 Henry Cohn, 2026, needs more optimization.
28 709 0.242079359537 Henry Cohn, 2026, needs more optimization.
28 710 0.242093595039 Henry Cohn, 2026, needs more optimization.
28 711 0.242608365084 Henry Cohn, 2026, needs more optimization.
28 712 0.242810451532 Henry Cohn, 2026, needs more optimization.
28 713 0.242876154207 Henry Cohn, 2026, needs more optimization.
28 714 0.243031843707 Henry Cohn, 2026, needs more optimization.
28 715 0.243238902702 Henry Cohn, 2026, needs more optimization.
28 716 0.243239602625 Henry Cohn, 2026, needs more optimization.
28 717 0.243805420007 Henry Cohn, 2026, needs more optimization.
28 718 0.247479828995 Henry Cohn, 2026, needs more optimization.
28 719 0.247515471399 Henry Cohn, 2026, needs more optimization.
28 720 0.247515503264 Henry Cohn, 2026, needs more optimization.
28 721 0.247572191618 Henry Cohn, 2026, needs more optimization.
28 722 0.247610878198 Henry Cohn, 2026, needs more optimization.
28 723 0.247628232340 Henry Cohn, 2026, needs more optimization.
28 724 0.247633171078 Henry Cohn, 2026, needs more optimization.
28 725 0.247638840646 Henry Cohn, 2026, needs more optimization.
28 726 0.247689483499 Henry Cohn, 2026, needs more optimization.
28 727 0.247711310932 Henry Cohn, 2026, needs more optimization.
28 728 0.247781244493 Henry Cohn, 2026, needs more optimization.
28 730 0.247845689710 Henry Cohn, 2026, needs more optimization.
28 731 0.247845721486 Henry Cohn, 2026, needs more optimization.
28 732 0.247875573551 Henry Cohn, 2026, needs more optimization.
28 733 0.247949220804 Henry Cohn, 2026, needs more optimization.
28 734 0.247952912318 Henry Cohn, 2026, needs more optimization.
28 735 0.247952912320 Henry Cohn, 2026, needs more optimization.
28 736 0.248038449073 Henry Cohn, 2026, needs more optimization.
28 737 0.248091038101 Henry Cohn, 2026, needs more optimization.
28 738 0.248126837704 Henry Cohn, 2026, needs more optimization.
28 739 0.248161028137 Henry Cohn, 2026, needs more optimization.
28 740 0.248183363299 Henry Cohn, 2026, needs more optimization.
28 741 0.248214557335 Henry Cohn, 2026, needs more optimization.
28 742 0.248295228637 Henry Cohn, 2026, needs more optimization.
28 743 0.248300520350 Henry Cohn, 2026, needs more optimization.
28 744 0.248303009343 Henry Cohn, 2026, needs more optimization.
28 745 0.248374519915 Henry Cohn, 2026, needs more optimization.
28 746 0.248374523143 Henry Cohn, 2026, needs more optimization.
28 747 0.248438616287 Henry Cohn, 2026, needs more optimization.
28 748 0.248461438970 Henry Cohn, 2026, needs more optimization.
28 749 0.248492409926 Henry Cohn, 2026, needs more optimization.
28 750 0.248565356393 Henry Cohn, 2026, needs more optimization.
28 751 0.248606707223 Henry Cohn, 2026, needs more optimization.
28 752 0.248650088057 Henry Cohn, 2026, needs more optimization.
28 753 0.248686380523 Henry Cohn, 2026, needs more optimization.
28 754 0.248738275367 Henry Cohn, 2026, needs more optimization.
28 755 0.248779138884 Henry Cohn, 2026, needs more optimization.
28 756 0.248819840647 Henry Cohn, 2026, needs more optimization.
28 757 0.248865302337 Henry Cohn, 2026, needs more optimization.
28 759 0.248910013595 Henry Cohn, 2026, needs more optimization.
28 760 0.248918128567 Henry Cohn, 2026, needs more optimization.
28 761 0.248971037506 Henry Cohn, 2026, needs more optimization.
28 762 0.249000637519 Henry Cohn, 2026, needs more optimization.
28 763 0.249005728340 Henry Cohn, 2026, needs more optimization.
28 764 0.249044404230 Henry Cohn, 2026, needs more optimization.
28 765 0.249059658954 Henry Cohn, 2026, needs more optimization.
28 766 0.249099378375 Henry Cohn, 2026, needs more optimization.
28 767 0.249126847735 Henry Cohn, 2026, needs more optimization.
28 768 0.249158204434 Henry Cohn, 2026, needs more optimization.
28 769 0.249184429622 Henry Cohn, 2026, needs more optimization.
28 770 0.249204751861 Henry Cohn, 2026, needs more optimization.
28 771 0.249234699650 Henry Cohn, 2026, needs more optimization.
28 772 0.249250311103 Henry Cohn, 2026, needs more optimization.
28 773 0.249270305176 Henry Cohn, 2026, needs more optimization.
28 774 0.249302296023 Henry Cohn, 2026, needs more optimization.
28 775 0.249318230603 Henry Cohn, 2026, needs more optimization.
28 776 0.249351437198 Henry Cohn, 2026, needs more optimization.
28 777 0.249378486555 Henry Cohn, 2026, needs more optimization.
28 778 0.249396098415 Henry Cohn, 2026, needs more optimization.
28 779 0.249401662562 Henry Cohn, 2026, needs more optimization.
28 780 0.249404513540 Henry Cohn, 2026, needs more optimization.
28 781 0.249419905075 Henry Cohn, 2026, needs more optimization.
28 782 0.249442050096 Henry Cohn, 2026, needs more optimization.
28 783 0.249458333015 Henry Cohn, 2026, needs more optimization.
28 784 0.249482036045 Henry Cohn, 2026, needs more optimization.
28 785 0.249516483846 Henry Cohn, 2026, needs more optimization.
28 786 0.249533108197 Henry Cohn, 2026, needs more optimization.
28 787 0.249533108246 Henry Cohn, 2026, needs more optimization.
28 788 0.249533873136 Henry Cohn, 2026, needs more optimization.
28 789 0.249543834095 Henry Cohn, 2026, needs more optimization.
28 790 0.249546464404 Henry Cohn, 2026, needs more optimization.
28 791 0.249557056950 Henry Cohn, 2026, needs more optimization.
28 792 0.249563958245 Henry Cohn, 2026, needs more optimization.
28 793 0.249588465785 Henry Cohn, 2026, needs more optimization.
28 794 0.249596311501 Henry Cohn, 2026, needs more optimization.
28 795 0.249614502773 Henry Cohn, 2026, needs more optimization.
28 796 0.249616780615 Henry Cohn, 2026, needs more optimization.
28 797 0.249628105292 Henry Cohn, 2026, needs more optimization.
28 798 0.249644838655 Henry Cohn, 2026, needs more optimization.
28 799 0.249645619923 Henry Cohn, 2026, needs more optimization.
28 800 0.249674268124 Henry Cohn, 2026, needs more optimization.
28 801 0.249674268504 Henry Cohn, 2026, needs more optimization.
28 802 0.249682276831 Henry Cohn, 2026, needs more optimization.
28 803 0.249682623538 Henry Cohn, 2026, needs more optimization.
28 804 0.249682980727 Henry Cohn, 2026, needs more optimization.
28 805 0.249698988103 Henry Cohn, 2026, needs more optimization.
28 806 0.249711057701 Henry Cohn, 2026, needs more optimization.
28 807 0.249726887314 Henry Cohn, 2026, needs more optimization.
28 808 0.249726895124 Henry Cohn, 2026, needs more optimization.
28 809 0.249741690726 Henry Cohn, 2026, needs more optimization.
28 810 0.249746603534 Henry Cohn, 2026, needs more optimization.
28 811 0.249759509539 Henry Cohn, 2026, needs more optimization.
28 814 0.249790807535 Henry Cohn, 2026, needs more optimization.
28 815 0.249804369326 Henry Cohn, 2026, needs more optimization.
28 816 0.249813792252 Henry Cohn, 2026, needs more optimization.
28 817 0.249832675878 Henry Cohn, 2026, needs more optimization.
28 818 0.249852702340 Henry Cohn, 2026, needs more optimization.
28 819 0.249863356879 Henry Cohn, 2026, needs more optimization.
28 820 0.249867434562 Henry Cohn, 2026, needs more optimization.
28 821 0.249869356992 Henry Cohn, 2026, needs more optimization.
28 822 0.249878481390 Henry Cohn, 2026, needs more optimization.
28 823 0.249885170447 Henry Cohn, 2026, needs more optimization.
28 825 0.249899927913 Henry Cohn, 2026, needs more optimization.
28 976 0.25 Henry Cohn, 2026.
4⁢x−1
28 977 0.250002251778 Henry Cohn, 2026, needs more optimization.
28 980 0.250003378755 Henry Cohn, 2026, needs more optimization.
28 981 0.250003378756 Henry Cohn, 2026, needs more optimization.
28 983 0.250003378759 Henry Cohn, 2026, needs more optimization.
28 984 0.250003378761 Henry Cohn, 2026, needs more optimization.
28 985 0.250003378773 Henry Cohn, 2026, needs more optimization.
28 986 0.250003378872 Henry Cohn, 2026, needs more optimization.
28 987 0.250004823553 Henry Cohn, 2026, needs more optimization.
28 989 0.250005861757 Henry Cohn, 2026, needs more optimization.
28 993 0.250009835234 Henry Cohn, 2026, needs more optimization.
28 994 0.250012612574 Henry Cohn, 2026, needs more optimization.
28 997 0.250012902626 Henry Cohn, 2026, needs more optimization.
28 998 0.250015036501 Henry Cohn, 2026, needs more optimization.
28 1002 0.250027274311 Henry Cohn, 2026, needs more optimization.
28 1004 0.250048779957 Henry Cohn, 2026, needs more optimization.
28 1005 0.250077005092 Henry Cohn, 2026, needs more optimization.
28 1006 0.250095237787 Henry Cohn, 2026, needs more optimization.
28 1009 0.250237612115 Henry Cohn, 2026, needs more optimization.
28 1010 0.250481600559 Henry Cohn, 2026, needs more optimization.
28 1011 0.250597478643 Henry Cohn, 2026, needs more optimization.
28 1012 0.250700831352 Henry Cohn, 2026, needs more optimization.
28 1013 0.250988036118 Henry Cohn, 2026, needs more optimization.
28 1014 0.251281301899 Henry Cohn, 2026, needs more optimization.
28 1015 0.251346903654 Henry Cohn, 2026, needs more optimization.
28 1016 0.251681994214 Henry Cohn, 2026, needs more optimization.
28 1017 0.251999109818 Henry Cohn, 2026, needs more optimization.
28 1018 0.252289792452 Henry Cohn, 2026, needs more optimization.
28 1019 0.252562535448 Henry Cohn, 2026, needs more optimization.
28 1020 0.252836171540 Henry Cohn, 2026, needs more optimization.
28 1021 0.252983767032 Henry Cohn, 2026, needs more optimization.
28 1022 0.253121249634 Henry Cohn, 2026, needs more optimization.
28 1023 0.253441284748 Henry Cohn, 2026, needs more optimization.
28 1024 0.253782836455 Henry Cohn, 2026, needs more optimization.
29 59 0.027727451354 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
21141⁢x3−841⁢x2−29⁢x+1
29 60 0.032283994156 Henry Cohn, 2024.
29 61 0.038074677873 Henry Cohn, 2026, needs more optimization.
29 62 0.039037971400 Henry Cohn, 2026.
29 63 0.039552183365 Henry Cohn, 2026.
29 64 0.043272075045 Henry Cohn, 2026.
29 65 0.044603988536 Henry Cohn, 2026.
29 66 0.044603988567 Henry Cohn, 2026, needs more optimization.
29 67 0.044634924295 Henry Cohn, 2026, needs more optimization.
29 68 0.046023717623 Henry Cohn, 2026.
29 69 0.050837623819 Henry Cohn, 2026.
29 70 0.052553724164 Henry Cohn, 2026, needs more optimization.
29 71 0.054294428466 Henry Cohn, 2026, needs more optimization.
29 72 0.056102523445 Henry Cohn, 2026, needs more optimization.
29 73 0.057718814631 Henry Cohn, 2026, needs more optimization.
29 74 0.059424876151 Henry Cohn, 2026, needs more optimization.
29 75 0.060942469759 Henry Cohn, 2026, needs more optimization.
29 76 0.062589505963 Henry Cohn, 2026, needs more optimization.
29 77 0.063095785535 Henry Cohn, 2026, needs more optimization.
29 78 0.063573775486 Henry Cohn, 2026, needs more optimization.
29 79 0.064129345779 Henry Cohn, 2026, needs more optimization.
29 80 0.065728963669 Henry Cohn, 2026, needs more optimization.
29 81 0.066915471276 Henry Cohn, 2026, needs more optimization.
29 82 0.068550020005 Henry Cohn, 2026, needs more optimization.
29 83 0.070356706903 Henry Cohn, 2026, needs more optimization.
29 84 0.072177323531 Henry Cohn, 2026, needs more optimization.
29 85 0.073569994527 Henry Cohn, 2026, needs more optimization.
29 86 0.074833529393 Henry Cohn, 2026, needs more optimization.
29 87 0.075739731307 Henry Cohn, 2026, needs more optimization.
29 88 0.075918571464 Henry Cohn, 2026, needs more optimization.
29 89 0.076439766734 Henry Cohn, 2026, needs more optimization.
29 90 0.076764556665 Henry Cohn, 2026, needs more optimization.
29 91 0.076968466086 Henry Cohn, 2026, needs more optimization.
29 92 0.077166103115 Henry Cohn, 2026, needs more optimization.
29 93 0.077365642128 Henry Cohn, 2026, needs more optimization.
29 94 0.077814567529 Henry Cohn, 2026, needs more optimization.
29 95 0.078076689798 Henry Cohn, 2026, needs more optimization.
29 96 0.078170510074 Henry Cohn, 2026, needs more optimization.
29 97 0.078815333094 Henry Cohn, 2026, needs more optimization.
29 98 0.078869685099 Henry Cohn, 2026, needs more optimization.
29 99 0.079107931114 Henry Cohn, 2026, needs more optimization.
29 100 0.079418975654 Henry Cohn, 2026, needs more optimization.
29 101 0.080105790459 Henry Cohn, 2026, needs more optimization.
29 102 0.080261661364 Henry Cohn, 2026, needs more optimization.
29 103 0.080656467551 Henry Cohn, 2026, needs more optimization.
29 104 0.080670490863 Henry Cohn, 2026, needs more optimization.
29 105 0.080715141879 Henry Cohn, 2026, needs more optimization.
29 106 0.081955712523 Henry Cohn, 2026, needs more optimization.
29 107 0.082789537521 Henry Cohn, 2026, needs more optimization.
29 108 0.084736287858 Henry Cohn, 2026, needs more optimization.
29 112 0.086333380579 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001, Example 5.10.1.
111⁢x2+2⁢x−1
29 113 0.089539183458 Henry Cohn, 2026, needs more optimization.
29 114 0.089789905514 Henry Cohn, 2026, needs more optimization.
29 115 0.089892503387 Henry Cohn, 2026, needs more optimization.
29 116 0.090009275497 Henry Cohn, 2026, needs more optimization.
29 117 0.090278423087 Henry Cohn, 2026, needs more optimization.
29 118 0.090535433494 Henry Cohn, 2026, needs more optimization.
29 119 0.090606913490 Henry Cohn, 2026, needs more optimization.
29 120 0.090737926341 Henry Cohn, 2026, needs more optimization.
29 121 0.091120660928 Henry Cohn, 2026, needs more optimization.
29 122 0.091808200267 Henry Cohn, 2026, needs more optimization.
29 123 0.093248983122 Henry Cohn, 2026, needs more optimization.
29 124 0.094247398808 Henry Cohn, 2026, needs more optimization.
29 125 0.096609333829 Henry Cohn, 2026, needs more optimization.
29 126 0.098256838980 Henry Cohn, 2026, needs more optimization.
29 127 0.099852823985 Henry Cohn, 2026, needs more optimization.
29 128 0.101502374570 Henry Cohn, 2026, needs more optimization.
29 129 0.102412993835 Henry Cohn, 2026, needs more optimization.
29 130 0.102428811745 Henry Cohn, 2026, needs more optimization.
29 131 0.102515270842 Henry Cohn, 2026, needs more optimization.
29 132 0.102549509937 Henry Cohn, 2026, needs more optimization.
29 133 0.102589089468 Henry Cohn, 2026, needs more optimization.
29 134 0.102712388450 Henry Cohn, 2026, needs more optimization.
29 135 0.103126795112 Henry Cohn, 2026, needs more optimization.
29 136 0.103823445421 Henry Cohn, 2026, needs more optimization.
29 137 0.105087339837 Henry Cohn, 2026, needs more optimization.
29 138 0.106289224032 Henry Cohn, 2026, needs more optimization.
29 139 0.107430911660 Henry Cohn, 2026, needs more optimization.
29 140 0.108105107626 Henry Cohn, 2026, needs more optimization.
29 141 0.108720007972 Henry Cohn, 2026, needs more optimization.
29 142 0.109452223399 Henry Cohn, 2026, needs more optimization.
29 143 0.110245263299 Henry Cohn, 2026, needs more optimization.
29 144 0.110691892505 Henry Cohn, 2026, needs more optimization.
29 145 0.110900523767 Henry Cohn, 2026, needs more optimization.
29 146 0.111108989109 Henry Cohn, 2026, needs more optimization.
29 147 0.111109114582 Henry Cohn, 2026, needs more optimization.
29 149 0.111110832778 Henry Cohn, 2026, needs more optimization.
29 152 0.111111111112 Orthogonal union of 150 points in 28 dimensions and 2 points in 1 dimension.
9⁢x−1
29 153 0.111111607703 Henry Cohn, 2026, needs more optimization.
29 154 0.111111607832 Henry Cohn, 2026, needs more optimization.
29 155 0.112103329788 Henry Cohn, 2026, needs more optimization.
29 156 0.113936469058 Henry Cohn, 2026, needs more optimization.
29 157 0.117883178393 Henry Cohn, 2026, needs more optimization.
29 158 0.119120559327 Henry Cohn, 2026, needs more optimization.
29 159 0.121143556984 Henry Cohn, 2026, needs more optimization.
29 160 0.121313581477 Henry Cohn, 2026, needs more optimization.
29 161 0.122573263458 Henry Cohn, 2026, needs more optimization.
29 162 0.124337217517 Henry Cohn, 2026, needs more optimization.
29 163 0.125681517860 Henry Cohn, 2026, needs more optimization.
29 164 0.126053972746 Henry Cohn, 2026, needs more optimization.
29 165 0.126265388962 Henry Cohn, 2026, needs more optimization.
29 166 0.128052854857 Henry Cohn, 2026, needs more optimization.
29 184 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 2 points in 1 dimension.
92⁢x2−4⁢x−1
29 185 0.128239416803 Henry Cohn, 2026, needs more optimization.
29 186 0.129288753337 Henry Cohn, 2026, needs more optimization.
29 187 0.131022623458 Henry Cohn, 2026, needs more optimization.
29 188 0.131505456681 Henry Cohn, 2026, needs more optimization.
29 189 0.131505460020 Henry Cohn, 2026, needs more optimization.
29 190 0.138788773216 Henry Cohn, 2026, needs more optimization.
29 191 0.139943483988 Henry Cohn, 2026, needs more optimization.
29 192 0.140857715918 Henry Cohn, 2026, needs more optimization.
29 193 0.141711949800 Henry Cohn, 2026, needs more optimization.
29 194 0.141834584611 Henry Cohn, 2026, needs more optimization.
29 195 0.141861701053 Henry Cohn, 2026, needs more optimization.
29 196 0.142025288448 Henry Cohn, 2026, needs more optimization.
29 197 0.142070042087 Henry Cohn, 2026, needs more optimization.
29 198 0.142134300691 Henry Cohn, 2026, needs more optimization.
29 199 0.142183121670 Henry Cohn, 2026, needs more optimization.
29 200 0.142256303547 Henry Cohn, 2026, needs more optimization.
29 201 0.142312679359 Henry Cohn, 2026, needs more optimization.
29 202 0.142361555724 Henry Cohn, 2026, needs more optimization.
29 203 0.142392344727 Henry Cohn, 2026, needs more optimization.
29 204 0.142430117652 Henry Cohn, 2026, needs more optimization.
29 205 0.142532461483 Henry Cohn, 2026, needs more optimization.
29 206 0.142683554884 Henry Cohn, 2026, needs more optimization.
29 207 0.142856046790 Henry Cohn, 2026, needs more optimization.
29 208 0.142989342416 Henry Cohn, 2026, needs more optimization.
29 209 0.143544725402 Henry Cohn, 2026, needs more optimization.
29 210 0.143761526148 Henry Cohn, 2026, needs more optimization.
29 211 0.144242298137 Henry Cohn, 2026, needs more optimization.
29 212 0.144975790091 Henry Cohn, 2026, needs more optimization.
29 213 0.145546804335 Henry Cohn, 2026, needs more optimization.
29 214 0.145769608640 Henry Cohn, 2026, needs more optimization.
29 215 0.145788184000 Henry Cohn, 2026, needs more optimization.
29 216 0.145792655654 Henry Cohn, 2026, needs more optimization.
29 217 0.145798457300 Henry Cohn, 2026, needs more optimization.
29 218 0.145977264066 Henry Cohn, 2026, needs more optimization.
29 219 0.146190340214 Henry Cohn, 2026, needs more optimization.
29 220 0.146331680357 Henry Cohn, 2026, needs more optimization.
29 221 0.146473497736 Henry Cohn, 2026, needs more optimization.
29 222 0.146589262872 Henry Cohn, 2026, needs more optimization.
29 223 0.146691448258 Henry Cohn, 2026, needs more optimization.
29 224 0.146838629739 Henry Cohn, 2026, needs more optimization.
29 225 0.146903652209 Henry Cohn, 2026, needs more optimization.
29 235 0.147102976680 Henry Cohn, 2026.
87⁢x2−6⁢x−1
29 236 0.147877025647 Henry Cohn, 2026, needs more optimization.
29 237 0.147913491605 Henry Cohn, 2026, needs more optimization.
29 238 0.147915823049 Henry Cohn, 2026, needs more optimization.
29 239 0.147982610080 Henry Cohn, 2026.
29 240 0.147998129200 Henry Cohn, 2026, needs more optimization.
29 241 0.148132442489 Henry Cohn, 2026, needs more optimization.
29 242 0.148370703422 Henry Cohn, 2026, needs more optimization.
29 243 0.148710748288 Henry Cohn, 2026, needs more optimization.
29 244 0.148924100048 Henry Cohn, 2026, needs more optimization.
29 245 0.149384821708 Henry Cohn, 2026, needs more optimization.
29 246 0.149964647173 Henry Cohn, 2026, needs more optimization.
29 247 0.150235337915 Henry Cohn, 2026, needs more optimization.
29 248 0.150623776693 Henry Cohn, 2026, needs more optimization.
29 249 0.151075975632 Henry Cohn, 2026, needs more optimization.
29 250 0.151758313418 Henry Cohn, 2026, needs more optimization.
29 251 0.152194777858 Henry Cohn, 2026, needs more optimization.
29 252 0.153232376076 Henry Cohn, 2026, needs more optimization.
29 253 0.153815142924 Henry Cohn, 2026, needs more optimization.
29 254 0.155245005969 Henry Cohn, 2026, needs more optimization.
29 255 0.156025162653 Henry Cohn, 2026, needs more optimization.
29 256 0.156620748155 Henry Cohn, 2026, needs more optimization.
29 257 0.157577210491 Henry Cohn, 2026, needs more optimization.
29 258 0.158307793722 Henry Cohn, 2026, needs more optimization.
29 259 0.159040268353 Henry Cohn, 2026, needs more optimization.
29 260 0.159327210902 Henry Cohn, 2026, needs more optimization.
29 261 0.159977336444 Henry Cohn, 2026, needs more optimization.
29 262 0.160794529724 Henry Cohn, 2026, needs more optimization.
29 263 0.161860757472 Henry Cohn, 2026, needs more optimization.
29 264 0.162281401511 Henry Cohn, 2026, needs more optimization.
29 265 0.162289966943 Henry Cohn, 2026, needs more optimization.
29 266 0.162358038089 Henry Cohn, 2026, needs more optimization.
29 267 0.162360895849 Henry Cohn, 2026, needs more optimization.
29 268 0.162405856771 Henry Cohn, 2026, needs more optimization.
29 269 0.162797113139 Henry Cohn, 2026, needs more optimization.
29 270 0.162802440820 Henry Cohn, 2026, needs more optimization.
29 271 0.162829723392 Henry Cohn, 2026, needs more optimization.
29 272 0.162940084710 Henry Cohn, 2026, needs more optimization.
29 273 0.163363837084 Henry Cohn, 2026, needs more optimization.
29 274 0.163425403135 Henry Cohn, 2026, needs more optimization.
29 275 0.163506441451 Henry Cohn, 2026, needs more optimization.
29 276 0.163574904203 Henry Cohn, 2026, needs more optimization.
29 277 0.163657633244 Henry Cohn, 2026, needs more optimization.
29 278 0.163799069446 Henry Cohn, 2026, needs more optimization.
29 279 0.163876453491 Henry Cohn, 2026, needs more optimization.
29 280 0.163963884400 Henry Cohn, 2026, needs more optimization.
29 281 0.164117075861 Henry Cohn, 2026, needs more optimization.
29 282 0.164306417170 Henry Cohn, 2026, needs more optimization.
29 283 0.164454997426 Henry Cohn, 2026, needs more optimization.
29 284 0.164565543426 Henry Cohn, 2026, needs more optimization.
29 285 0.164647362981 Henry Cohn, 2026, needs more optimization.
29 286 0.164687689115 Henry Cohn, 2026, needs more optimization.
29 287 0.164790102627 Henry Cohn, 2026, needs more optimization.
29 288 0.164943796747 Henry Cohn, 2026, needs more optimization.
29 289 0.165031942623 Henry Cohn, 2026, needs more optimization.
29 290 0.165057082177 Henry Cohn, 2026, needs more optimization.
29 291 0.165109308802 Henry Cohn, 2026, needs more optimization.
29 292 0.165131854529 Henry Cohn, 2026, needs more optimization.
29 293 0.165171696835 Henry Cohn, 2026, needs more optimization.
29 294 0.165219951172 Henry Cohn, 2026, needs more optimization.
29 295 0.165239965144 Henry Cohn, 2026, needs more optimization.
29 296 0.165273778525 Henry Cohn, 2026, needs more optimization.
29 297 0.165327078818 Henry Cohn, 2026, needs more optimization.
29 298 0.165363624354 Henry Cohn, 2026, needs more optimization.
29 299 0.165457998848 Henry Cohn, 2026, needs more optimization.
29 300 0.165541768745 Henry Cohn, 2026, needs more optimization.
29 301 0.165583822211 Henry Cohn, 2026, needs more optimization.
29 302 0.165659386797 Henry Cohn, 2026, needs more optimization.
29 303 0.165738876365 Henry Cohn, 2026, needs more optimization.
29 304 0.165801439554 Henry Cohn, 2026, needs more optimization.
29 305 0.165849217686 Henry Cohn, 2026, needs more optimization.
29 306 0.165943973101 Henry Cohn, 2026, needs more optimization.
29 307 0.165997683033 Henry Cohn, 2026, needs more optimization.
29 308 0.166129131989 Henry Cohn, 2026, needs more optimization.
29 309 0.166155495113 Henry Cohn, 2026, needs more optimization.
29 310 0.166308374369 Henry Cohn, 2026, needs more optimization.
29 311 0.166340499342 Henry Cohn, 2026, needs more optimization.
29 312 0.166459874297 Henry Cohn, 2026, needs more optimization.
29 314 0.166516534126 Henry Cohn, 2026, needs more optimization.
29 315 0.166601124840 Henry Cohn, 2026, needs more optimization.
29 316 0.166658742587 Henry Cohn, 2026, needs more optimization.
29 317 0.166660068150 Henry Cohn, 2026, needs more optimization.
29 319 0.166662932661 Henry Cohn, 2026, needs more optimization.
29 320 0.166666909115 Henry Cohn, 2026, needs more optimization.
29 321 0.166681481455 Henry Cohn, 2026, needs more optimization.
29 322 0.166687616025 Henry Cohn, 2026, needs more optimization.
29 323 0.166880255530 Henry Cohn, 2026, needs more optimization.
29 324 0.166941921085 Henry Cohn, 2026, needs more optimization.
29 325 0.167098796348 Henry Cohn, 2026, needs more optimization.
29 326 0.167183400003 Henry Cohn, 2026, needs more optimization.
29 327 0.167419806742 Henry Cohn, 2026, needs more optimization.
29 328 0.167840324487 Henry Cohn, 2026, needs more optimization.
29 329 0.168244666833 Henry Cohn, 2026, needs more optimization.
29 330 0.168897122935 Henry Cohn, 2026, needs more optimization.
29 331 0.169499902446 Henry Cohn, 2026, needs more optimization.
29 332 0.170965719899 Henry Cohn, 2026, needs more optimization.
29 333 0.171163335352 Henry Cohn, 2026, needs more optimization.
29 334 0.172410921732 Henry Cohn, 2026, needs more optimization.
29 335 0.172776747154 Henry Cohn, 2026, needs more optimization.
29 336 0.173853274006 Henry Cohn, 2026, needs more optimization.
29 337 0.174595319918 Henry Cohn, 2026, needs more optimization.
29 338 0.175318766585 Henry Cohn, 2026, needs more optimization.
29 339 0.175812333033 Henry Cohn, 2026, needs more optimization.
29 340 0.176272808068 Henry Cohn, 2026, needs more optimization.
29 341 0.177195339704 Henry Cohn, 2026, needs more optimization.
29 342 0.177768001648 Henry Cohn, 2026, needs more optimization.
29 343 0.178568657811 Henry Cohn, 2026, needs more optimization.
29 344 0.178608331364 Henry Cohn, 2026, needs more optimization.
29 345 0.178633183680 Henry Cohn, 2026, needs more optimization.
29 346 0.178928239521 Henry Cohn, 2026, needs more optimization.
29 347 0.179099918062 Henry Cohn, 2026, needs more optimization.
29 348 0.179888969787 Henry Cohn, 2026, needs more optimization.
29 349 0.179996181032 Henry Cohn, 2026, needs more optimization.
29 350 0.180374503091 Henry Cohn, 2026, needs more optimization.
29 351 0.180474888176 Henry Cohn, 2026, needs more optimization.
29 352 0.180485297069 Henry Cohn, 2026, needs more optimization.
29 353 0.180526830060 Henry Cohn, 2026, needs more optimization.
29 354 0.180980095543 Henry Cohn, 2026, needs more optimization.
29 355 0.181044511252 Henry Cohn, 2026, needs more optimization.
29 356 0.181102782673 Henry Cohn, 2026, needs more optimization.
29 357 0.181249989246 Henry Cohn, 2026, needs more optimization.
29 358 0.181444131118 Henry Cohn, 2026, needs more optimization.
29 359 0.181615098229 Henry Cohn, 2026, needs more optimization.
29 360 0.181651211674 Henry Cohn, 2026, needs more optimization.
29 361 0.184781518349 Henry Cohn, 2026, needs more optimization.
29 362 0.185276684216 Henry Cohn, 2026, needs more optimization.
29 363 0.185866440759 Henry Cohn, 2026, needs more optimization.
29 364 0.186077556551 Henry Cohn, 2026, needs more optimization.
29 365 0.186243205531 Henry Cohn, 2026, needs more optimization.
29 366 0.186784810914 Henry Cohn, 2026, needs more optimization.
29 367 0.187148627799 Henry Cohn, 2026, needs more optimization.
29 368 0.187284767867 Henry Cohn, 2026, needs more optimization.
29 369 0.187685856721 Henry Cohn, 2026, needs more optimization.
29 370 0.187936752517 Henry Cohn, 2026, needs more optimization.
29 371 0.188345506111 Henry Cohn, 2026, needs more optimization.
29 372 0.188562323502 Henry Cohn, 2026, needs more optimization.
29 373 0.188941896274 Henry Cohn, 2026, needs more optimization.
29 374 0.189280825633 Henry Cohn, 2026, needs more optimization.
29 375 0.189526278710 Henry Cohn, 2026, needs more optimization.
29 376 0.189645602974 Henry Cohn, 2026, needs more optimization.
29 377 0.189960155603 Henry Cohn, 2026, needs more optimization.
29 378 0.190246487540 Henry Cohn, 2026, needs more optimization.
29 379 0.190362410841 Henry Cohn, 2026, needs more optimization.
29 380 0.190789557313 Henry Cohn, 2026, needs more optimization.
29 381 0.191118488926 Henry Cohn, 2026, needs more optimization.
29 382 0.191172993674 Henry Cohn, 2026, needs more optimization.
29 383 0.191403339665 Henry Cohn, 2026, needs more optimization.
29 384 0.191567361586 Henry Cohn, 2026, needs more optimization.
29 385 0.191821809169 Henry Cohn, 2026, needs more optimization.
29 386 0.192000974338 Henry Cohn, 2026, needs more optimization.
29 387 0.192175716606 Henry Cohn, 2026, needs more optimization.
29 388 0.192283745329 Henry Cohn, 2026, needs more optimization.
29 389 0.192769658485 Henry Cohn, 2026, needs more optimization.
29 390 0.192913656076 Henry Cohn, 2026, needs more optimization.
29 391 0.193245039742 Henry Cohn, 2026, needs more optimization.
29 392 0.193553163334 Henry Cohn, 2026, needs more optimization.
29 393 0.193895342209 Henry Cohn, 2026, needs more optimization.
29 394 0.194025585932 Henry Cohn, 2026, needs more optimization.
29 395 0.194288265015 Henry Cohn, 2026, needs more optimization.
29 396 0.194374453167 Henry Cohn, 2026, needs more optimization.
29 451 0.194630872484 Henry Cohn, 2026, needs more optimization.
149⁢x−29
29 452 0.196846963825 Henry Cohn, 2026, needs more optimization.
29 453 0.199323950304 Henry Cohn, 2026, needs more optimization.
29 454 0.199323950362 Henry Cohn, 2026, needs more optimization.
29 455 0.199337698761 Henry Cohn, 2026, needs more optimization.
29 456 0.199346743133 Henry Cohn, 2026, needs more optimization.
29 457 0.199378686326 Henry Cohn, 2026, needs more optimization.
29 458 0.199402323494 Henry Cohn, 2026, needs more optimization.
29 459 0.199431209929 Henry Cohn, 2026, needs more optimization.
29 460 0.199439189329 Henry Cohn, 2026, needs more optimization.
29 461 0.199439189359 Henry Cohn, 2026, needs more optimization.
29 462 0.199456864117 Henry Cohn, 2026, needs more optimization.
29 463 0.199487987357 Henry Cohn, 2026, needs more optimization.
29 464 0.199500163147 Henry Cohn, 2026, needs more optimization.
29 465 0.199535154880 Henry Cohn, 2026, needs more optimization.
29 466 0.199556945504 Henry Cohn, 2026, needs more optimization.
29 467 0.199596520058 Henry Cohn, 2026, needs more optimization.
29 468 0.199598979352 Henry Cohn, 2026, needs more optimization.
29 469 0.199622220878 Henry Cohn, 2026, needs more optimization.
29 470 0.199634231165 Henry Cohn, 2026, needs more optimization.
29 471 0.199658700274 Henry Cohn, 2026, needs more optimization.
29 472 0.199665736300 Henry Cohn, 2026, needs more optimization.
29 473 0.199676709894 Henry Cohn, 2026, needs more optimization.
29 474 0.199683387271 Henry Cohn, 2026, needs more optimization.
29 475 0.199683387362 Henry Cohn, 2026, needs more optimization.
29 476 0.199686822925 Henry Cohn, 2026, needs more optimization.
29 477 0.199695239870 Henry Cohn, 2026, needs more optimization.
29 478 0.199712181967 Henry Cohn, 2026, needs more optimization.
29 479 0.199726057659 Henry Cohn, 2026, needs more optimization.
29 480 0.199731813574 Henry Cohn, 2026, needs more optimization.
29 481 0.199739652637 Henry Cohn, 2026, needs more optimization.
29 482 0.199751027183 Henry Cohn, 2026, needs more optimization.
29 483 0.199766829277 Henry Cohn, 2026, needs more optimization.
29 484 0.199778876616 Henry Cohn, 2026, needs more optimization.
29 485 0.199802973562 Henry Cohn, 2026, needs more optimization.
29 486 0.199818163736 Henry Cohn, 2026, needs more optimization.
29 487 0.199838828355 Henry Cohn, 2026, needs more optimization.
29 488 0.199849217998 Henry Cohn, 2026, needs more optimization.
29 489 0.199863644112 Henry Cohn, 2026, needs more optimization.
29 490 0.199865272855 Henry Cohn, 2026, needs more optimization.
29 491 0.199870295669 Henry Cohn, 2026, needs more optimization.
29 492 0.199889618345 Henry Cohn, 2026, needs more optimization.
29 493 0.199896146853 Henry Cohn, 2026, needs more optimization.
29 494 0.199900546059 Henry Cohn, 2026, needs more optimization.
29 495 0.199915074868 Henry Cohn, 2026, needs more optimization.
29 496 0.199939889116 Henry Cohn, 2026, needs more optimization.
29 576 0.2 Henry Cohn, 2026.
5⁢x−1
29 577 0.200000936716 Henry Cohn, 2026, needs more optimization.
29 579 0.200000936717 Henry Cohn, 2026, needs more optimization.
29 580 0.200000936720 Henry Cohn, 2026, needs more optimization.
29 581 0.200000936734 Henry Cohn, 2026, needs more optimization.
29 582 0.200000936801 Henry Cohn, 2026, needs more optimization.
29 586 0.200001264089 Henry Cohn, 2026, needs more optimization.
29 587 0.200001264095 Henry Cohn, 2026, needs more optimization.
29 588 0.200001501741 Henry Cohn, 2026, needs more optimization.
29 592 0.200002050017 Henry Cohn, 2026, needs more optimization.
29 593 0.200002050071 Henry Cohn, 2026, needs more optimization.
29 594 0.200002772871 Henry Cohn, 2026, needs more optimization.
29 595 0.200006671900 Henry Cohn, 2026, needs more optimization.
29 596 0.200006671952 Henry Cohn, 2026, needs more optimization.
29 597 0.200007130914 Henry Cohn, 2026, needs more optimization.
29 599 0.200011608127 Henry Cohn, 2026, needs more optimization.
29 600 0.200018133546 Henry Cohn, 2026, needs more optimization.
29 601 0.200025403903 Henry Cohn, 2026, needs more optimization.
29 602 0.200048367895 Henry Cohn, 2026, needs more optimization.
29 603 0.200335658601 Henry Cohn, 2026, needs more optimization.
29 604 0.234493590452 Henry Cohn, 2026, needs more optimization.
29 605 0.234600549895 Henry Cohn, 2026, needs more optimization.
29 606 0.234672404348 Henry Cohn, 2026, needs more optimization.
29 609 0.234855934908 Henry Cohn, 2026, needs more optimization.
29 610 0.235102001989 Henry Cohn, 2026, needs more optimization.
29 611 0.235110150098 Henry Cohn, 2026, needs more optimization.
29 612 0.235264631878 Henry Cohn, 2026, needs more optimization.
29 613 0.235265508124 Henry Cohn, 2026, needs more optimization.
29 617 0.235463426987 Henry Cohn, 2026, needs more optimization.
29 620 0.235769083261 Henry Cohn, 2026, needs more optimization.
29 621 0.235810185143 Henry Cohn, 2026, needs more optimization.
29 622 0.235867391692 Henry Cohn, 2026, needs more optimization.
29 623 0.235885897732 Henry Cohn, 2026, needs more optimization.
29 627 0.236176046647 Henry Cohn, 2026, needs more optimization.
29 628 0.236190274050 Henry Cohn, 2026, needs more optimization.
29 629 0.236255596286 Henry Cohn, 2026, needs more optimization.
29 630 0.236347381102 Henry Cohn, 2026, needs more optimization.
29 631 0.236357811887 Henry Cohn, 2026, needs more optimization.
29 633 0.236358593868 Henry Cohn, 2026, needs more optimization.
29 634 0.237040806802 Henry Cohn, 2026, needs more optimization.
29 636 0.237336870707 Henry Cohn, 2026, needs more optimization.
29 637 0.237435465502 Henry Cohn, 2026, needs more optimization.
29 639 0.237455624026 Henry Cohn, 2026, needs more optimization.
29 640 0.237455624346 Henry Cohn, 2026, needs more optimization.
29 641 0.237455743157 Henry Cohn, 2026, needs more optimization.
29 646 0.237516038565 Henry Cohn, 2026, needs more optimization.
29 647 0.237529918593 Henry Cohn, 2026, needs more optimization.
29 653 0.237578606227 Henry Cohn, 2026, needs more optimization.
29 655 0.237578681987 Henry Cohn, 2026, needs more optimization.
29 657 0.237639367925 Henry Cohn, 2026, needs more optimization.
29 658 0.237639475735 Henry Cohn, 2026, needs more optimization.
29 661 0.237968634936 Henry Cohn, 2026, needs more optimization.
29 662 0.237973522219 Henry Cohn, 2026, needs more optimization.
29 663 0.237973545241 Henry Cohn, 2026, needs more optimization.
29 669 0.237973545244 Henry Cohn, 2026, needs more optimization.
29 673 0.237984554783 Henry Cohn, 2026, needs more optimization.
29 677 0.237984573470 Henry Cohn, 2026, needs more optimization.
29 679 0.237984576584 Henry Cohn, 2026, needs more optimization.
29 683 0.237995287343 Henry Cohn, 2026, needs more optimization.
29 684 0.237999028766 Henry Cohn, 2026, needs more optimization.
29 685 0.238005875636 Henry Cohn, 2026, needs more optimization.
29 688 0.238016291358 Henry Cohn, 2026, needs more optimization.
29 689 0.238020428914 Henry Cohn, 2026, needs more optimization.
29 690 0.238020637389 Henry Cohn, 2026, needs more optimization.
29 691 0.238026326988 Henry Cohn, 2026, needs more optimization.
29 692 0.238046967052 Henry Cohn, 2026, needs more optimization.
29 699 0.238071379519 Henry Cohn, 2026, needs more optimization.
29 700 0.238071664053 Henry Cohn, 2026, needs more optimization.
29 702 0.238085200216 Henry Cohn, 2026, needs more optimization.
29 705 0.238088760560 Henry Cohn, 2026, needs more optimization.
29 707 0.238093701602 Henry Cohn, 2026, needs more optimization.
29 710 0.238100183709 Henry Cohn, 2026, needs more optimization.
29 711 0.238100183721 Henry Cohn, 2026, needs more optimization.
29 712 0.238115125115 Henry Cohn, 2026, needs more optimization.
29 713 0.238185572432 Henry Cohn, 2026, needs more optimization.
29 715 0.238225507404 Henry Cohn, 2026, needs more optimization.
29 716 0.238255051723 Henry Cohn, 2026, needs more optimization.
29 717 0.238270912089 Henry Cohn, 2026, needs more optimization.
29 718 0.238324849677 Henry Cohn, 2026, needs more optimization.
29 719 0.240932863677 Henry Cohn, 2026, needs more optimization.
29 720 0.241045325882 Henry Cohn, 2026, needs more optimization.
29 721 0.241114752659 Henry Cohn, 2026, needs more optimization.
29 722 0.241114876164 Henry Cohn, 2026, needs more optimization.
29 723 0.241114934200 Henry Cohn, 2026, needs more optimization.
29 724 0.241228154728 Henry Cohn, 2026, needs more optimization.
29 728 0.241476137586 Henry Cohn, 2026, needs more optimization.
29 729 0.241748594162 Henry Cohn, 2026, needs more optimization.
29 730 0.241891013449 Henry Cohn, 2026, needs more optimization.
29 731 0.241903723109 Henry Cohn, 2026, needs more optimization.
29 733 0.241937274701 Henry Cohn, 2026, needs more optimization.
29 735 0.242133165880 Henry Cohn, 2026, needs more optimization.
29 736 0.242223811722 Henry Cohn, 2026, needs more optimization.
29 737 0.242435011798 Henry Cohn, 2026, needs more optimization.
29 738 0.242553696392 Henry Cohn, 2026, needs more optimization.
29 739 0.242764437568 Henry Cohn, 2026, needs more optimization.
29 740 0.242859634484 Henry Cohn, 2026, needs more optimization.
29 741 0.242859977311 Henry Cohn, 2026, needs more optimization.
29 742 0.242991559043 Henry Cohn, 2026, needs more optimization.
29 743 0.242992968771 Henry Cohn, 2026, needs more optimization.
29 744 0.243006398155 Henry Cohn, 2026, needs more optimization.
29 745 0.243132695570 Henry Cohn, 2026, needs more optimization.
29 746 0.243140729494 Henry Cohn, 2026, needs more optimization.
29 747 0.243253422132 Henry Cohn, 2026, needs more optimization.
29 748 0.243412096502 Henry Cohn, 2026, needs more optimization.
29 749 0.243649466017 Henry Cohn, 2026, needs more optimization.
29 750 0.243728665049 Henry Cohn, 2026, needs more optimization.
29 751 0.243829067408 Henry Cohn, 2026, needs more optimization.
29 753 0.243889793729 Henry Cohn, 2026, needs more optimization.
29 755 0.243889908998 Henry Cohn, 2026, needs more optimization.
29 756 0.243889924755 Henry Cohn, 2026, needs more optimization.
29 760 0.244225268173 Henry Cohn, 2026, needs more optimization.
29 761 0.244354139232 Henry Cohn, 2026, needs more optimization.
29 762 0.244524930113 Henry Cohn, 2026, needs more optimization.
29 763 0.244647833710 Henry Cohn, 2026, needs more optimization.
29 764 0.244656702495 Henry Cohn, 2026, needs more optimization.
29 765 0.244889902900 Henry Cohn, 2026, needs more optimization.
29 766 0.244992389628 Henry Cohn, 2026, needs more optimization.
29 767 0.244992892321 Henry Cohn, 2026, needs more optimization.
29 769 0.245125119557 Henry Cohn, 2026, needs more optimization.
29 770 0.245219280961 Henry Cohn, 2026, needs more optimization.
29 771 0.245307332322 Henry Cohn, 2026, needs more optimization.
29 772 0.245519629404 Henry Cohn, 2026, needs more optimization.
29 773 0.245654506642 Henry Cohn, 2026, needs more optimization.
29 774 0.245809413255 Henry Cohn, 2026, needs more optimization.
29 775 0.245863795284 Henry Cohn, 2026, needs more optimization.
29 776 0.245920242410 Henry Cohn, 2026, needs more optimization.
29 778 0.245960132206 Henry Cohn, 2026, needs more optimization.
29 779 0.246073077331 Henry Cohn, 2026, needs more optimization.
29 780 0.246226166518 Henry Cohn, 2026, needs more optimization.
29 781 0.246297384436 Henry Cohn, 2026, needs more optimization.
29 782 0.246387053675 Henry Cohn, 2026, needs more optimization.
29 785 0.246434487563 Henry Cohn, 2026, needs more optimization.
29 786 0.246482650255 Henry Cohn, 2026, needs more optimization.
29 787 0.246553244896 Henry Cohn, 2026, needs more optimization.
29 788 0.246643418901 Henry Cohn, 2026, needs more optimization.
29 789 0.246742965038 Henry Cohn, 2026, needs more optimization.
29 790 0.246742971357 Henry Cohn, 2026, needs more optimization.
29 791 0.246787934734 Henry Cohn, 2026, needs more optimization.
29 792 0.246840521578 Henry Cohn, 2026, needs more optimization.
29 796 0.246996637820 Henry Cohn, 2026, needs more optimization.
29 797 0.247148228009 Henry Cohn, 2026, needs more optimization.
29 798 0.247196586814 Henry Cohn, 2026, needs more optimization.
29 799 0.247305728396 Henry Cohn, 2026, needs more optimization.
29 800 0.247401603477 Henry Cohn, 2026, needs more optimization.
29 801 0.247457060803 Henry Cohn, 2026, needs more optimization.
29 803 0.247524764676 Henry Cohn, 2026, needs more optimization.
29 804 0.247546243230 Henry Cohn, 2026, needs more optimization.
29 805 0.247662084848 Henry Cohn, 2026, needs more optimization.
29 806 0.247744785370 Henry Cohn, 2026, needs more optimization.
29 807 0.247774647858 Henry Cohn, 2026, needs more optimization.
29 808 0.247867546288 Henry Cohn, 2026, needs more optimization.
29 809 0.247931915572 Henry Cohn, 2026, needs more optimization.
29 810 0.247940910327 Henry Cohn, 2026, needs more optimization.
29 811 0.247940966490 Henry Cohn, 2026, needs more optimization.
29 812 0.248025420322 Henry Cohn, 2026, needs more optimization.
29 813 0.248109841805 Henry Cohn, 2026, needs more optimization.
29 815 0.248146757268 Henry Cohn, 2026, needs more optimization.
29 816 0.248147010851 Henry Cohn, 2026, needs more optimization.
29 817 0.248151222272 Henry Cohn, 2026, needs more optimization.
29 818 0.248192626099 Henry Cohn, 2026, needs more optimization.
29 819 0.248192665673 Henry Cohn, 2026, needs more optimization.
29 820 0.248250532911 Henry Cohn, 2026, needs more optimization.
29 822 0.248274144691 Henry Cohn, 2026, needs more optimization.
29 824 0.248389171281 Henry Cohn, 2026, needs more optimization.
29 825 0.248408421304 Henry Cohn, 2026, needs more optimization.
29 826 0.248419080882 Henry Cohn, 2026, needs more optimization.
29 827 0.248420311645 Henry Cohn, 2026, needs more optimization.
29 829 0.248511782532 Henry Cohn, 2026, needs more optimization.
29 830 0.248651475863 Henry Cohn, 2026, needs more optimization.
29 832 0.248688649931 Henry Cohn, 2026, needs more optimization.
29 833 0.248730839493 Henry Cohn, 2026, needs more optimization.
29 834 0.248735592594 Henry Cohn, 2026, needs more optimization.
29 835 0.248735663873 Henry Cohn, 2026, needs more optimization.
29 836 0.248775323080 Henry Cohn, 2026, needs more optimization.
29 837 0.248789199742 Henry Cohn, 2026, needs more optimization.
29 838 0.248895890431 Henry Cohn, 2026, needs more optimization.
29 839 0.248895891117 Henry Cohn, 2026, needs more optimization.
29 840 0.248895894449 Henry Cohn, 2026, needs more optimization.
29 842 0.248906178555 Henry Cohn, 2026, needs more optimization.
29 843 0.248906190170 Henry Cohn, 2026, needs more optimization.
29 844 0.248926865056 Henry Cohn, 2026, needs more optimization.
29 847 0.248952119703 Henry Cohn, 2026, needs more optimization.
29 850 0.249027864243 Henry Cohn, 2026, needs more optimization.
29 851 0.249068954529 Henry Cohn, 2026, needs more optimization.
29 852 0.249102561627 Henry Cohn, 2026, needs more optimization.
29 853 0.249102636966 Henry Cohn, 2026, needs more optimization.
29 854 0.249131519777 Henry Cohn, 2026, needs more optimization.
29 855 0.249147268057 Henry Cohn, 2026, needs more optimization.
29 856 0.249194811431 Henry Cohn, 2026, needs more optimization.
29 857 0.249194811479 Henry Cohn, 2026, needs more optimization.
29 858 0.249194811554 Henry Cohn, 2026, needs more optimization.
29 859 0.249194812003 Henry Cohn, 2026, needs more optimization.
29 860 0.249194817751 Henry Cohn, 2026, needs more optimization.
29 861 0.249223536034 Henry Cohn, 2026, needs more optimization.
29 862 0.249254765736 Henry Cohn, 2026, needs more optimization.
29 863 0.249291569237 Henry Cohn, 2026, needs more optimization.
29 868 0.249364810434 Henry Cohn, 2026, needs more optimization.
29 869 0.249365822936 Henry Cohn, 2026, needs more optimization.
29 873 0.249458464392 Henry Cohn, 2026, needs more optimization.
29 874 0.249520189539 Henry Cohn, 2026, needs more optimization.
29 875 0.249520189608 Henry Cohn, 2026, needs more optimization.
29 876 0.249520190494 Henry Cohn, 2026, needs more optimization.
29 877 0.249520201495 Henry Cohn, 2026, needs more optimization.
29 878 0.249534802957 Henry Cohn, 2026, needs more optimization.
29 881 0.249541021368 Henry Cohn, 2026, needs more optimization.
29 882 0.249541436534 Henry Cohn, 2026, needs more optimization.
29 884 0.249561500789 Henry Cohn, 2026, needs more optimization.
29 885 0.249611550458 Henry Cohn, 2026, needs more optimization.
29 886 0.249611550459 Henry Cohn, 2026, needs more optimization.
29 887 0.249611550468 Henry Cohn, 2026, needs more optimization.
29 888 0.249611550579 Henry Cohn, 2026, needs more optimization.
29 889 0.249611551981 Henry Cohn, 2026, needs more optimization.
29 890 0.249614333133 Henry Cohn, 2026, needs more optimization.
29 891 0.249615931574 Henry Cohn, 2026, needs more optimization.
29 893 0.249632808619 Henry Cohn, 2026, needs more optimization.
29 894 0.249649708975 Henry Cohn, 2026, needs more optimization.
29 895 0.249661732791 Henry Cohn, 2026, needs more optimization.
29 897 0.249686974570 Henry Cohn, 2026, needs more optimization.
29 898 0.249695907152 Henry Cohn, 2026, needs more optimization.
29 899 0.249710099696 Henry Cohn, 2026, needs more optimization.
29 900 0.249727548749 Henry Cohn, 2026, needs more optimization.
29 901 0.249733333162 Henry Cohn, 2026, needs more optimization.
29 902 0.249746572156 Henry Cohn, 2026, needs more optimization.
29 903 0.249751722114 Henry Cohn, 2026, needs more optimization.
29 904 0.249764232722 Henry Cohn, 2026, needs more optimization.
29 905 0.249780448242 Henry Cohn, 2026, needs more optimization.
29 979 0.249999623216 Henry Cohn, 2026, needs more optimization.
29 982 0.249999623291 Henry Cohn, 2026, needs more optimization.
29 988 0.249999841322 Henry Cohn, 2026, needs more optimization.
29 999 0.250000660564 Henry Cohn, 2026, needs more optimization.
29 1000 0.250001133570 Henry Cohn, 2026, needs more optimization.
29 1006 0.250001322518 Henry Cohn, 2026, needs more optimization.
29 1010 0.250004353378 Henry Cohn, 2026, needs more optimization.
29 1011 0.250004894942 Henry Cohn, 2026, needs more optimization.
29 1013 0.250007648948 Henry Cohn, 2026, needs more optimization.
29 1015 0.250008339875 Henry Cohn, 2026, needs more optimization.
29 1016 0.250011619147 Henry Cohn, 2026, needs more optimization.
29 1018 0.250015249958 Henry Cohn, 2026, needs more optimization.
29 1019 0.250022903850 Henry Cohn, 2026, needs more optimization.
29 1022 0.250023070471 Henry Cohn, 2026, needs more optimization.
29 1024 0.250024040108 Henry Cohn, 2026, needs more optimization.
30 61 0.026884307091 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23520⁢x3−900⁢x2−30⁢x+1
30 62 0.031274698397 Henry Cohn, 2026.
30 63 0.037893320316 Henry Cohn, 2026.
30 64 0.038348157236 Henry Cohn, 2026.
30 65 0.038479664975 Henry Cohn, 2026.
30 66 0.042441820097 Henry Cohn, 2026, needs more optimization.
30 67 0.043917025854 Henry Cohn, 2026, needs more optimization.
30 68 0.044555720231 Henry Cohn, 2026, needs more optimization.
30 69 0.044563591251 Henry Cohn, 2026, needs more optimization.
30 70 0.044757397041 Henry Cohn, 2026.
30 71 0.049847164675 Henry Cohn, 2026.
30 72 0.051255762852 Henry Cohn, 2026, needs more optimization.
30 73 0.052421148036 Henry Cohn, 2026, needs more optimization.
30 74 0.054131831046 Henry Cohn, 2026, needs more optimization.
30 75 0.056243908098 Henry Cohn, 2026, needs more optimization.
30 76 0.057552662592 Henry Cohn, 2026, needs more optimization.
30 77 0.059053175344 Henry Cohn, 2026, needs more optimization.
30 78 0.060498966169 Henry Cohn, 2026, needs more optimization.
30 79 0.062140014429 Henry Cohn, 2026, needs more optimization.
30 80 0.062583983396 Henry Cohn, 2026, needs more optimization.
30 81 0.062832417000 Henry Cohn, 2026, needs more optimization.
30 82 0.064272763647 Henry Cohn, 2026, needs more optimization.
30 83 0.065104551118 Henry Cohn, 2026, needs more optimization.
30 84 0.066453447921 Henry Cohn, 2026, needs more optimization.
30 85 0.068027668364 Henry Cohn, 2026, needs more optimization.
30 86 0.069487665016 Henry Cohn, 2026, needs more optimization.
30 87 0.070938292076 Henry Cohn, 2026, needs more optimization.
30 88 0.072505464092 Henry Cohn, 2026, needs more optimization.
30 89 0.073901964491 Henry Cohn, 2026, needs more optimization.
30 90 0.074428780023 Henry Cohn, 2026, needs more optimization.
30 91 0.075426915233 Henry Cohn, 2026, needs more optimization.
30 92 0.076276608691 Henry Cohn, 2026, needs more optimization.
30 93 0.076879520399 Henry Cohn, 2026, needs more optimization.
30 94 0.076887747790 Henry Cohn, 2026, needs more optimization.
30 95 0.076930063922 Henry Cohn, 2026, needs more optimization.
30 96 0.077017059478 Henry Cohn, 2026, needs more optimization.
30 97 0.077172780788 Henry Cohn, 2026, needs more optimization.
30 98 0.077272033141 Henry Cohn, 2026, needs more optimization.
30 99 0.077380619812 Henry Cohn, 2026, needs more optimization.
30 100 0.077768396634 Henry Cohn, 2026, needs more optimization.
30 101 0.077928680999 Henry Cohn, 2026, needs more optimization.
30 102 0.078182373591 Henry Cohn, 2026, needs more optimization.
30 103 0.078810395981 Henry Cohn, 2026, needs more optimization.
30 104 0.079143972293 Henry Cohn, 2026, needs more optimization.
30 105 0.079624845233 Henry Cohn, 2026, needs more optimization.
30 106 0.080489219121 Henry Cohn, 2026, needs more optimization.
30 107 0.080664882892 Henry Cohn, 2026, needs more optimization.
30 108 0.080812788550 Henry Cohn, 2026, needs more optimization.
30 109 0.081520874857 Henry Cohn, 2026, needs more optimization.
30 110 0.082107993393 Henry Cohn, 2026, needs more optimization.
30 111 0.082302651647 Henry Cohn, 2026, needs more optimization.
30 112 0.083254192309 Henry Cohn, 2026, needs more optimization.
30 113 0.085102366471 Henry Cohn, 2026, needs more optimization.
30 114 0.086333380579 Orthogonal union of 112 points in 29 dimensions and 2 points in 1 dimension.
111⁢x2+2⁢x−1
30 115 0.087944972140 Henry Cohn, 2026, needs more optimization.
30 116 0.088185354180 Henry Cohn, 2026, needs more optimization.
30 117 0.088551274735 Henry Cohn, 2026, needs more optimization.
30 118 0.089018459174 Henry Cohn, 2026, needs more optimization.
30 119 0.089353692852 Henry Cohn, 2026, needs more optimization.
30 120 0.089662040608 Henry Cohn, 2026, needs more optimization.
30 121 0.089965207633 Henry Cohn, 2026, needs more optimization.
30 122 0.090222719560 Henry Cohn, 2026, needs more optimization.
30 123 0.090518046518 Henry Cohn, 2026, needs more optimization.
30 124 0.090775949301 Henry Cohn, 2026, needs more optimization.
30 125 0.090956360885 Henry Cohn, 2026, needs more optimization.
30 126 0.091623895675 Henry Cohn, 2026, needs more optimization.
30 127 0.092700883208 Henry Cohn, 2026, needs more optimization.
30 128 0.094001976904 Henry Cohn, 2026, needs more optimization.
30 129 0.095273773315 Henry Cohn, 2026, needs more optimization.
30 130 0.097292741745 Henry Cohn, 2026, needs more optimization.
30 131 0.098503012276 Henry Cohn, 2026, needs more optimization.
30 132 0.099543739855 Henry Cohn, 2026, needs more optimization.
30 133 0.100616779557 Henry Cohn, 2026, needs more optimization.
30 134 0.102003243221 Henry Cohn, 2026, needs more optimization.
30 135 0.102471619887 Henry Cohn, 2026, needs more optimization.
30 136 0.102542990215 Henry Cohn, 2026, needs more optimization.
30 137 0.102565187971 Henry Cohn, 2026, needs more optimization.
30 138 0.102572132552 Henry Cohn, 2026, needs more optimization.
30 139 0.102602939419 Henry Cohn, 2026, needs more optimization.
30 140 0.102650767805 Henry Cohn, 2026, needs more optimization.
30 141 0.102665225101 Henry Cohn, 2026, needs more optimization.
30 142 0.103623366513 Henry Cohn, 2026, needs more optimization.
30 143 0.105315794439 Henry Cohn, 2026, needs more optimization.
30 144 0.106156523366 Henry Cohn, 2026, needs more optimization.
30 145 0.107192819937 Henry Cohn, 2026, needs more optimization.
30 146 0.108220462246 Henry Cohn, 2026, needs more optimization.
30 147 0.108866104718 Henry Cohn, 2026, needs more optimization.
30 148 0.109073451910 Henry Cohn, 2026, needs more optimization.
30 149 0.109649934835 Henry Cohn, 2026, needs more optimization.
30 150 0.110161291638 Henry Cohn, 2026, needs more optimization.
30 151 0.110742417431 Henry Cohn, 2026, needs more optimization.
30 152 0.111073040361 Henry Cohn, 2026, needs more optimization.
30 153 0.111086787875 Henry Cohn, 2026, needs more optimization.
30 154 0.111092292250 Henry Cohn, 2026, needs more optimization.
30 155 0.111099609597 Henry Cohn, 2026, needs more optimization.
30 156 0.111108882890 Henry Cohn, 2026, needs more optimization.
30 157 0.111112454427 Henry Cohn, 2026, needs more optimization.
30 158 0.111113469944 Henry Cohn, 2026, needs more optimization.
30 159 0.112281091460 Henry Cohn, 2026, needs more optimization.
30 160 0.113646286827 Henry Cohn, 2026, needs more optimization.
30 161 0.115772980440 Henry Cohn, 2026, needs more optimization.
30 162 0.117269804499 Henry Cohn, 2026, needs more optimization.
30 163 0.118948034170 Henry Cohn, 2026, needs more optimization.
30 164 0.120039011294 Henry Cohn, 2026, needs more optimization.
30 165 0.120962183309 Henry Cohn, 2026, needs more optimization.
30 166 0.121723175750 Henry Cohn, 2026, needs more optimization.
30 167 0.121975467578 Henry Cohn, 2026, needs more optimization.
30 168 0.122829219265 Henry Cohn, 2026, needs more optimization.
30 169 0.123550450680 Henry Cohn, 2026, needs more optimization.
30 170 0.124634171762 Henry Cohn, 2026, needs more optimization.
30 171 0.126575955819 Henry Cohn, 2026, needs more optimization.
30 172 0.127612427241 Henry Cohn, 2026, needs more optimization.
30 173 0.128233379956 Henry Cohn, 2026, needs more optimization.
30 186 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 4 points in 2 dimensions.
92⁢x2−4⁢x−1
30 187 0.128239137542 Henry Cohn, 2026, needs more optimization.
30 188 0.128240363758 Henry Cohn, 2026, needs more optimization.
30 189 0.128372008394 Henry Cohn, 2026, needs more optimization.
30 190 0.129244287921 Henry Cohn, 2026, needs more optimization.
30 191 0.130279030276 Henry Cohn, 2026, needs more optimization.
30 192 0.131434492282 Henry Cohn, 2026, needs more optimization.
30 193 0.131434505580 Henry Cohn, 2026, needs more optimization.
30 194 0.131434545247 Henry Cohn, 2026, needs more optimization.
30 195 0.131439454734 Henry Cohn, 2026, needs more optimization.
30 196 0.131439456905 Henry Cohn, 2026, needs more optimization.
30 197 0.137956899713 Henry Cohn, 2026, needs more optimization.
30 198 0.138516887389 Henry Cohn, 2026, needs more optimization.
30 199 0.139404127172 Henry Cohn, 2026, needs more optimization.
30 200 0.140306305032 Henry Cohn, 2026, needs more optimization.
30 201 0.141134664739 Henry Cohn, 2026, needs more optimization.
30 202 0.141166519428 Henry Cohn, 2026, needs more optimization.
30 203 0.141261027556 Henry Cohn, 2026, needs more optimization.
30 204 0.141300081098 Henry Cohn, 2026, needs more optimization.
30 205 0.141396228737 Henry Cohn, 2026, needs more optimization.
30 206 0.141502680925 Henry Cohn, 2026, needs more optimization.
30 207 0.141550252856 Henry Cohn, 2026, needs more optimization.
30 208 0.141631166375 Henry Cohn, 2026, needs more optimization.
30 209 0.141826677930 Henry Cohn, 2026, needs more optimization.
30 210 0.141962951441 Henry Cohn, 2026, needs more optimization.
30 211 0.142150680498 Henry Cohn, 2026, needs more optimization.
30 212 0.142275735400 Henry Cohn, 2026, needs more optimization.
30 213 0.142289964793 Henry Cohn, 2026, needs more optimization.
30 214 0.142343718221 Henry Cohn, 2026, needs more optimization.
30 215 0.142505263858 Henry Cohn, 2026, needs more optimization.
30 216 0.142825560467 Henry Cohn, 2026, needs more optimization.
30 217 0.142863777535 Henry Cohn, 2026, needs more optimization.
30 218 0.143126452309 Henry Cohn, 2026, needs more optimization.
30 219 0.143708247244 Henry Cohn, 2026, needs more optimization.
30 220 0.143959826273 Henry Cohn, 2026, needs more optimization.
30 221 0.144389951345 Henry Cohn, 2026, needs more optimization.
30 222 0.144502006287 Henry Cohn, 2026, needs more optimization.
30 223 0.144842053131 Henry Cohn, 2026, needs more optimization.
30 224 0.144975393241 Henry Cohn, 2026, needs more optimization.
30 225 0.145185464733 Henry Cohn, 2026, needs more optimization.
30 226 0.145340460905 Henry Cohn, 2026, needs more optimization.
30 227 0.145537734973 Henry Cohn, 2026, needs more optimization.
30 228 0.145892366388 Henry Cohn, 2026, needs more optimization.
30 229 0.146409377934 Henry Cohn, 2026, needs more optimization.
30 230 0.146480798606 Henry Cohn, 2026, needs more optimization.
30 231 0.146581188543 Henry Cohn, 2026, needs more optimization.
30 232 0.146724304333 Henry Cohn, 2026, needs more optimization.
30 233 0.146881222332 Henry Cohn, 2026, needs more optimization.
30 234 0.146881225863 Henry Cohn, 2026, needs more optimization.
30 235 0.147028389721 Henry Cohn, 2026, needs more optimization.
30 237 0.147102976680 Orthogonal union of 235 points in 29 dimensions and 2 points in 1 dimension.
87⁢x2−6⁢x−1
30 238 0.147103933710 Henry Cohn, 2026, needs more optimization.
30 239 0.147104260631 Henry Cohn, 2026, needs more optimization.
30 240 0.147117548693 Henry Cohn, 2026, needs more optimization.
30 241 0.147141475438 Henry Cohn, 2026, needs more optimization.
30 242 0.147806946366 Henry Cohn, 2026, needs more optimization.
30 243 0.147824466203 Henry Cohn, 2026, needs more optimization.
30 244 0.147861212655 Henry Cohn, 2026, needs more optimization.
30 245 0.147868976907 Henry Cohn, 2026, needs more optimization.
30 246 0.147915135037 Henry Cohn, 2026, needs more optimization.
30 247 0.147928698206 Henry Cohn, 2026, needs more optimization.
30 248 0.147978290524 Henry Cohn, 2026, needs more optimization.
30 249 0.147984192506 Henry Cohn, 2026, needs more optimization.
30 250 0.148001468858 Henry Cohn, 2026, needs more optimization.
30 251 0.148065491259 Henry Cohn, 2026, needs more optimization.
30 252 0.148301544057 Henry Cohn, 2026, needs more optimization.
30 253 0.148454666386 Henry Cohn, 2026, needs more optimization.
30 254 0.148937544380 Henry Cohn, 2026, needs more optimization.
30 255 0.149525161824 Henry Cohn, 2026, needs more optimization.
30 256 0.149894773132 Henry Cohn, 2026, needs more optimization.
30 257 0.150623197065 Henry Cohn, 2026, needs more optimization.
30 258 0.150831487218 Henry Cohn, 2026, needs more optimization.
30 259 0.151539375594 Henry Cohn, 2026, needs more optimization.
30 260 0.152168171510 Henry Cohn, 2026, needs more optimization.
30 261 0.153123037251 Henry Cohn, 2026, needs more optimization.
30 262 0.153629792396 Henry Cohn, 2026, needs more optimization.
30 263 0.154172219338 Henry Cohn, 2026, needs more optimization.
30 264 0.154824200852 Henry Cohn, 2026, needs more optimization.
30 265 0.155268729763 Henry Cohn, 2026, needs more optimization.
30 266 0.155974625954 Henry Cohn, 2026, needs more optimization.
30 267 0.156631899381 Henry Cohn, 2026, needs more optimization.
30 268 0.157437124961 Henry Cohn, 2026, needs more optimization.
30 269 0.158209122035 Henry Cohn, 2026, needs more optimization.
30 270 0.158917559018 Henry Cohn, 2026, needs more optimization.
30 271 0.159528439160 Henry Cohn, 2026, needs more optimization.
30 272 0.160092996355 Henry Cohn, 2026, needs more optimization.
30 273 0.160707311291 Henry Cohn, 2026, needs more optimization.
30 274 0.161440709594 Henry Cohn, 2026, needs more optimization.
30 275 0.161772830089 Henry Cohn, 2026, needs more optimization.
30 276 0.161814118449 Henry Cohn, 2026, needs more optimization.
30 277 0.161835074567 Henry Cohn, 2026, needs more optimization.
30 278 0.161878900263 Henry Cohn, 2026, needs more optimization.
30 279 0.161882550762 Henry Cohn, 2026, needs more optimization.
30 280 0.161910357816 Henry Cohn, 2026, needs more optimization.
30 281 0.161971517531 Henry Cohn, 2026, needs more optimization.
30 282 0.162004909717 Henry Cohn, 2026, needs more optimization.
30 283 0.162120342249 Henry Cohn, 2026, needs more optimization.
30 284 0.162252610367 Henry Cohn, 2026, needs more optimization.
30 285 0.162388890817 Henry Cohn, 2026, needs more optimization.
30 286 0.162526273597 Henry Cohn, 2026, needs more optimization.
30 287 0.162774918848 Henry Cohn, 2026, needs more optimization.
30 288 0.162877500343 Henry Cohn, 2026, needs more optimization.
30 289 0.163000497696 Henry Cohn, 2026, needs more optimization.
30 290 0.163066514455 Henry Cohn, 2026, needs more optimization.
30 291 0.163189246366 Henry Cohn, 2026, needs more optimization.
30 292 0.163330297238 Henry Cohn, 2026, needs more optimization.
30 293 0.163352802884 Henry Cohn, 2026, needs more optimization.
30 294 0.163441575573 Henry Cohn, 2026, needs more optimization.
30 295 0.163568322461 Henry Cohn, 2026, needs more optimization.
30 296 0.163586521817 Henry Cohn, 2026, needs more optimization.
30 297 0.163650978615 Henry Cohn, 2026, needs more optimization.
30 298 0.163738338199 Henry Cohn, 2026, needs more optimization.
30 299 0.163838280080 Henry Cohn, 2026, needs more optimization.
30 300 0.163913581149 Henry Cohn, 2026, needs more optimization.
30 301 0.164030128810 Henry Cohn, 2026, needs more optimization.
30 302 0.164122063369 Henry Cohn, 2026, needs more optimization.
30 303 0.164386398485 Henry Cohn, 2026, needs more optimization.
30 304 0.164523195656 Henry Cohn, 2026, needs more optimization.
30 305 0.164619849647 Henry Cohn, 2026, needs more optimization.
30 306 0.164709296137 Henry Cohn, 2026, needs more optimization.
30 307 0.164774093713 Henry Cohn, 2026, needs more optimization.
30 308 0.164917482249 Henry Cohn, 2026, needs more optimization.
30 309 0.164991851434 Henry Cohn, 2026, needs more optimization.
30 310 0.165062688399 Henry Cohn, 2026, needs more optimization.
30 311 0.165159340799 Henry Cohn, 2026, needs more optimization.
30 312 0.165196985121 Henry Cohn, 2026, needs more optimization.
30 313 0.165258613213 Henry Cohn, 2026, needs more optimization.
30 314 0.165327145331 Henry Cohn, 2026, needs more optimization.
30 315 0.165451135155 Henry Cohn, 2026, needs more optimization.
30 316 0.165536157506 Henry Cohn, 2026, needs more optimization.
30 317 0.165624354120 Henry Cohn, 2026, needs more optimization.
30 318 0.165648874613 Henry Cohn, 2026, needs more optimization.
30 319 0.165729688858 Henry Cohn, 2026, needs more optimization.
30 321 0.165845204854 Henry Cohn, 2026, needs more optimization.
30 322 0.166042547614 Henry Cohn, 2026, needs more optimization.
30 323 0.166143604073 Henry Cohn, 2026, needs more optimization.
30 324 0.166213090942 Henry Cohn, 2026, needs more optimization.
30 325 0.166351765326 Henry Cohn, 2026, needs more optimization.
30 326 0.166504365512 Henry Cohn, 2026, needs more optimization.
30 327 0.166560227017 Henry Cohn, 2026, needs more optimization.
30 329 0.166609038212 Henry Cohn, 2026, needs more optimization.
30 330 0.166611770448 Henry Cohn, 2026, needs more optimization.
30 331 0.166649261013 Henry Cohn, 2026, needs more optimization.
30 332 0.166671998690 Henry Cohn, 2026, needs more optimization.
30 333 0.166677400861 Henry Cohn, 2026, needs more optimization.
30 334 0.166744090538 Henry Cohn, 2026, needs more optimization.
30 335 0.166831976744 Henry Cohn, 2026, needs more optimization.
30 336 0.167007779116 Henry Cohn, 2026, needs more optimization.
30 337 0.167169825568 Henry Cohn, 2026, needs more optimization.
30 338 0.167259558723 Henry Cohn, 2026, needs more optimization.
30 339 0.167372026900 Henry Cohn, 2026, needs more optimization.
30 340 0.167744703322 Henry Cohn, 2026, needs more optimization.
30 341 0.168059918925 Henry Cohn, 2026, needs more optimization.
30 342 0.168366509985 Henry Cohn, 2026, needs more optimization.
30 343 0.169668683852 Henry Cohn, 2026, needs more optimization.
30 344 0.170174922586 Henry Cohn, 2026, needs more optimization.
30 345 0.171255624013 Henry Cohn, 2026, needs more optimization.
30 346 0.171706970072 Henry Cohn, 2026, needs more optimization.
30 347 0.172541623002 Henry Cohn, 2026, needs more optimization.
30 348 0.172767920575 Henry Cohn, 2026, needs more optimization.
30 349 0.173907885259 Henry Cohn, 2026, needs more optimization.
30 350 0.174539092867 Henry Cohn, 2026, needs more optimization.
30 351 0.174828529035 Henry Cohn, 2026, needs more optimization.
30 352 0.175785611396 Henry Cohn, 2026, needs more optimization.
30 353 0.176381222125 Henry Cohn, 2026, needs more optimization.
30 354 0.176987078232 Henry Cohn, 2026, needs more optimization.
30 355 0.177440833596 Henry Cohn, 2026, needs more optimization.
30 356 0.178184486796 Henry Cohn, 2026, needs more optimization.
30 357 0.178682227660 Henry Cohn, 2026, needs more optimization.
30 358 0.179180903171 Henry Cohn, 2026, needs more optimization.
30 359 0.179789470582 Henry Cohn, 2026, needs more optimization.
30 360 0.180414553640 Henry Cohn, 2026, needs more optimization.
30 361 0.180672413600 Henry Cohn, 2026, needs more optimization.
30 362 0.181130389089 Henry Cohn, 2026, needs more optimization.
30 363 0.181411087235 Henry Cohn, 2026, needs more optimization.
30 364 0.181866360304 Henry Cohn, 2026, needs more optimization.
30 365 0.182221045799 Henry Cohn, 2026, needs more optimization.
30 366 0.182770773532 Henry Cohn, 2026, needs more optimization.
30 367 0.183023057260 Henry Cohn, 2026, needs more optimization.
30 368 0.183257844109 Henry Cohn, 2026, needs more optimization.
30 369 0.183482426664 Henry Cohn, 2026, needs more optimization.
30 370 0.184940911031 Henry Cohn, 2026, needs more optimization.
30 371 0.185088292720 Henry Cohn, 2026, needs more optimization.
30 372 0.185429901412 Henry Cohn, 2026, needs more optimization.
30 373 0.185539158058 Henry Cohn, 2026, needs more optimization.
30 374 0.185576241200 Henry Cohn, 2026, needs more optimization.
30 375 0.186704644017 Henry Cohn, 2026, needs more optimization.
30 376 0.186916018798 Henry Cohn, 2026, needs more optimization.
30 377 0.187073298327 Henry Cohn, 2026, needs more optimization.
30 378 0.187111888225 Henry Cohn, 2026, needs more optimization.
30 379 0.187284166837 Henry Cohn, 2026, needs more optimization.
30 380 0.187343423125 Henry Cohn, 2026, needs more optimization.
30 381 0.187353919740 Henry Cohn, 2026, needs more optimization.
30 382 0.187362726679 Henry Cohn, 2026, needs more optimization.
30 383 0.187504664655 Henry Cohn, 2026, needs more optimization.
30 384 0.187803524230 Henry Cohn, 2026, needs more optimization.
30 385 0.187865195121 Henry Cohn, 2026, needs more optimization.
30 386 0.187889931950 Henry Cohn, 2026, needs more optimization.
30 387 0.187973587824 Henry Cohn, 2026, needs more optimization.
30 388 0.188519911436 Henry Cohn, 2026, needs more optimization.
30 389 0.188596232193 Henry Cohn, 2026, needs more optimization.
30 390 0.188607785974 Henry Cohn, 2026, needs more optimization.
30 391 0.189078920101 Henry Cohn, 2026, needs more optimization.
30 392 0.189127362657 Henry Cohn, 2026, needs more optimization.
30 393 0.189242582479 Henry Cohn, 2026, needs more optimization.
30 394 0.189274657532 Henry Cohn, 2026, needs more optimization.
30 395 0.189834720230 Henry Cohn, 2026, needs more optimization.
30 396 0.190019053032 Henry Cohn, 2026, needs more optimization.
30 397 0.190080518545 Henry Cohn, 2026, needs more optimization.
30 398 0.190651273766 Henry Cohn, 2026, needs more optimization.
30 399 0.190726337523 Henry Cohn, 2026, needs more optimization.
30 400 0.191105248715 Henry Cohn, 2026, needs more optimization.
30 401 0.191439829322 Henry Cohn, 2026, needs more optimization.
30 402 0.191643718422 Henry Cohn, 2026, needs more optimization.
30 403 0.192137799452 Henry Cohn, 2026, needs more optimization.
30 404 0.192280006737 Henry Cohn, 2026, needs more optimization.
30 405 0.192491141995 Henry Cohn, 2026, needs more optimization.
30 406 0.192799595526 Henry Cohn, 2026, needs more optimization.
30 407 0.193006096567 Henry Cohn, 2026, needs more optimization.
30 408 0.193159302949 Henry Cohn, 2026, needs more optimization.
30 409 0.193539483309 Henry Cohn, 2026, needs more optimization.
30 410 0.193832425109 Henry Cohn, 2026, needs more optimization.
30 411 0.194074940565 Henry Cohn, 2026, needs more optimization.
30 412 0.194348007030 Henry Cohn, 2026, needs more optimization.
30 453 0.194630872484 Orthogonal union of 451 points in 29 dimensions and 2 points in 1 dimension.
149⁢x−29
30 454 0.194633481928 Henry Cohn, 2026, needs more optimization.
30 455 0.197953181751 Henry Cohn, 2026, needs more optimization.
30 456 0.197994734589 Henry Cohn, 2026, needs more optimization.
30 457 0.198028667398 Henry Cohn, 2026, needs more optimization.
30 458 0.198059734217 Henry Cohn, 2026, needs more optimization.
30 459 0.198079685609 Henry Cohn, 2026, needs more optimization.
30 460 0.198161375362 Henry Cohn, 2026, needs more optimization.
30 461 0.198173824141 Henry Cohn, 2026, needs more optimization.
30 462 0.198318874100 Henry Cohn, 2026, needs more optimization.
30 463 0.198420905192 Henry Cohn, 2026, needs more optimization.
30 464 0.198465078397 Henry Cohn, 2026, needs more optimization.
30 465 0.198489340925 Henry Cohn, 2026, needs more optimization.
30 466 0.198512555271 Henry Cohn, 2026, needs more optimization.
30 467 0.198575187240 Henry Cohn, 2026, needs more optimization.
30 468 0.198594489708 Henry Cohn, 2026, needs more optimization.
30 469 0.198637768374 Henry Cohn, 2026, needs more optimization.
30 470 0.198712165269 Henry Cohn, 2026, needs more optimization.
30 471 0.198747102163 Henry Cohn, 2026, needs more optimization.
30 472 0.198818342816 Henry Cohn, 2026, needs more optimization.
30 473 0.198863633177 Henry Cohn, 2026, needs more optimization.
30 474 0.198921262988 Henry Cohn, 2026, needs more optimization.
30 475 0.198981888519 Henry Cohn, 2026, needs more optimization.
30 476 0.199001231893 Henry Cohn, 2026, needs more optimization.
30 477 0.199075497146 Henry Cohn, 2026, needs more optimization.
30 478 0.199105121415 Henry Cohn, 2026, needs more optimization.
30 479 0.199132460598 Henry Cohn, 2026, needs more optimization.
30 480 0.199160766471 Henry Cohn, 2026, needs more optimization.
30 481 0.199199045220 Henry Cohn, 2026, needs more optimization.
30 482 0.199227770039 Henry Cohn, 2026, needs more optimization.
30 483 0.199259806971 Henry Cohn, 2026, needs more optimization.
30 484 0.199261955007 Henry Cohn, 2026, needs more optimization.
30 485 0.199294311150 Henry Cohn, 2026, needs more optimization.
30 486 0.199303262444 Henry Cohn, 2026, needs more optimization.
30 487 0.199326976187 Henry Cohn, 2026, needs more optimization.
30 488 0.199364865791 Henry Cohn, 2026, needs more optimization.
30 489 0.199365817318 Henry Cohn, 2026, needs more optimization.
30 490 0.199371526489 Henry Cohn, 2026, needs more optimization.
30 491 0.199371526543 Henry Cohn, 2026, needs more optimization.
30 492 0.199389102694 Henry Cohn, 2026, needs more optimization.
30 493 0.199402409268 Henry Cohn, 2026, needs more optimization.
30 494 0.199424755230 Henry Cohn, 2026, needs more optimization.
30 495 0.199432716982 Henry Cohn, 2026, needs more optimization.
30 496 0.199446246444 Henry Cohn, 2026, needs more optimization.
30 497 0.199453208295 Henry Cohn, 2026, needs more optimization.
30 498 0.199454115754 Henry Cohn, 2026, needs more optimization.
30 499 0.199470153046 Henry Cohn, 2026, needs more optimization.
30 500 0.199489293902 Henry Cohn, 2026, needs more optimization.
30 501 0.199497722499 Henry Cohn, 2026, needs more optimization.
30 502 0.199540642555 Henry Cohn, 2026, needs more optimization.
30 503 0.199553874759 Henry Cohn, 2026, needs more optimization.
30 504 0.199568210616 Henry Cohn, 2026, needs more optimization.
30 505 0.199573158217 Henry Cohn, 2026, needs more optimization.
30 506 0.199577468939 Henry Cohn, 2026, needs more optimization.
30 507 0.199596277582 Henry Cohn, 2026, needs more optimization.
30 508 0.199615715429 Henry Cohn, 2026, needs more optimization.
30 509 0.199646327085 Henry Cohn, 2026, needs more optimization.
30 510 0.199655099660 Henry Cohn, 2026, needs more optimization.
30 511 0.199674421957 Henry Cohn, 2026, needs more optimization.
30 512 0.199721936386 Henry Cohn, 2026, needs more optimization.
30 513 0.199738498520 Henry Cohn, 2026, needs more optimization.
30 514 0.199746506819 Henry Cohn, 2026, needs more optimization.
30 515 0.199756381507 Henry Cohn, 2026, needs more optimization.
30 516 0.199765424324 Henry Cohn, 2026, needs more optimization.
30 518 0.199771404776 Henry Cohn, 2026, needs more optimization.
30 519 0.199793882191 Henry Cohn, 2026, needs more optimization.
30 520 0.199797025824 Henry Cohn, 2026, needs more optimization.
30 521 0.199809404577 Henry Cohn, 2026, needs more optimization.
30 522 0.199817094064 Henry Cohn, 2026, needs more optimization.
30 523 0.199824481966 Henry Cohn, 2026, needs more optimization.
30 524 0.199837256607 Henry Cohn, 2026, needs more optimization.
30 525 0.199856409109 Henry Cohn, 2026, needs more optimization.
30 526 0.199868712766 Henry Cohn, 2026, needs more optimization.
30 528 0.199879024000 Henry Cohn, 2026, needs more optimization.
30 529 0.199884309934 Henry Cohn, 2026, needs more optimization.
30 530 0.199893023909 Henry Cohn, 2026, needs more optimization.
30 531 0.199899408786 Henry Cohn, 2026, needs more optimization.
30 532 0.199913122585 Henry Cohn, 2026, needs more optimization.
30 533 0.199913122595 Henry Cohn, 2026, needs more optimization.
30 534 0.199916930066 Henry Cohn, 2026, needs more optimization.
30 536 0.199926435997 Henry Cohn, 2026, needs more optimization.
30 537 0.199929622863 Henry Cohn, 2026, needs more optimization.
30 538 0.199943211666 Henry Cohn, 2026, needs more optimization.
30 539 0.199957802363 Henry Cohn, 2026, needs more optimization.
30 540 0.199965424354 Henry Cohn, 2026, needs more optimization.
30 656 0.2 Henry Cohn, 2026.
5⁢x−1
30 657 0.203357314611 Henry Cohn, 2026, needs more optimization.
30 660 0.236180145082 Henry Cohn, 2026, needs more optimization.
30 668 0.236305750514 Henry Cohn, 2026, needs more optimization.
30 669 0.236366177088 Henry Cohn, 2026, needs more optimization.
30 671 0.236376814890 Henry Cohn, 2026, needs more optimization.
30 672 0.236376914481 Henry Cohn, 2026, needs more optimization.
30 674 0.236740466462 Henry Cohn, 2026, needs more optimization.
30 682 0.236740496611 Henry Cohn, 2026, needs more optimization.
30 683 0.236874594202 Henry Cohn, 2026, needs more optimization.
30 684 0.236951194294 Henry Cohn, 2026, needs more optimization.
30 687 0.236989509830 Henry Cohn, 2026, needs more optimization.
30 693 0.236999289825 Henry Cohn, 2026, needs more optimization.
30 696 0.237087159364 Henry Cohn, 2026, needs more optimization.
30 697 0.237183415111 Henry Cohn, 2026, needs more optimization.
30 700 0.237184285362 Henry Cohn, 2026, needs more optimization.
30 701 0.237221455985 Henry Cohn, 2026, needs more optimization.
30 702 0.237287770479 Henry Cohn, 2026, needs more optimization.
30 703 0.237435369883 Henry Cohn, 2026, needs more optimization.
30 704 0.237458733094 Henry Cohn, 2026, needs more optimization.
30 705 0.237458787613 Henry Cohn, 2026, needs more optimization.
30 706 0.237475197822 Henry Cohn, 2026, needs more optimization.
30 710 0.237728035893 Henry Cohn, 2026, needs more optimization.
30 713 0.237756914083 Henry Cohn, 2026, needs more optimization.
30 714 0.237756921835 Henry Cohn, 2026, needs more optimization.
30 717 0.237775308784 Henry Cohn, 2026, needs more optimization.
30 719 0.237776142046 Henry Cohn, 2026, needs more optimization.
30 720 0.237865135977 Henry Cohn, 2026, needs more optimization.
30 721 0.238735839750 Henry Cohn, 2026, needs more optimization.
30 722 0.238756714897 Henry Cohn, 2026, needs more optimization.
30 723 0.238759427943 Henry Cohn, 2026, needs more optimization.
30 724 0.238760451103 Henry Cohn, 2026, needs more optimization.
30 727 0.239064186529 Henry Cohn, 2026, needs more optimization.
30 728 0.239066510048 Henry Cohn, 2026, needs more optimization.
30 730 0.239094284762 Henry Cohn, 2026, needs more optimization.
30 731 0.239165921771 Henry Cohn, 2026, needs more optimization.
30 732 0.239206072763 Henry Cohn, 2026, needs more optimization.
30 733 0.239480927576 Henry Cohn, 2026, needs more optimization.
30 734 0.239487784298 Henry Cohn, 2026, needs more optimization.
30 735 0.239520414112 Henry Cohn, 2026, needs more optimization.
30 736 0.239589184013 Henry Cohn, 2026, needs more optimization.
30 737 0.239590609572 Henry Cohn, 2026, needs more optimization.
30 738 0.239758214306 Henry Cohn, 2026, needs more optimization.
30 742 0.239836300028 Henry Cohn, 2026, needs more optimization.
30 743 0.239836438308 Henry Cohn, 2026, needs more optimization.
30 744 0.239836441782 Henry Cohn, 2026, needs more optimization.
30 745 0.239836448621 Henry Cohn, 2026, needs more optimization.
30 747 0.239836492256 Henry Cohn, 2026, needs more optimization.
30 748 0.239836516394 Henry Cohn, 2026, needs more optimization.
30 750 0.239836535679 Henry Cohn, 2026, needs more optimization.
30 751 0.240021244004 Henry Cohn, 2026, needs more optimization.
30 752 0.240108061073 Henry Cohn, 2026, needs more optimization.
30 753 0.240151553587 Henry Cohn, 2026, needs more optimization.
30 756 0.240353315565 Henry Cohn, 2026, needs more optimization.
30 757 0.240526401257 Henry Cohn, 2026, needs more optimization.
30 759 0.240623392032 Henry Cohn, 2026, needs more optimization.
30 760 0.240626010189 Henry Cohn, 2026, needs more optimization.
30 761 0.240645156464 Henry Cohn, 2026, needs more optimization.
30 762 0.240684756464 Henry Cohn, 2026, needs more optimization.
30 763 0.240701100302 Henry Cohn, 2026, needs more optimization.
30 770 0.241342059248 Henry Cohn, 2026, needs more optimization.
30 773 0.241530605398 Henry Cohn, 2026, needs more optimization.
30 776 0.241976656171 Henry Cohn, 2026, needs more optimization.
30 777 0.242106632623 Henry Cohn, 2026, needs more optimization.
30 778 0.242359543363 Henry Cohn, 2026, needs more optimization.
30 779 0.242429936648 Henry Cohn, 2026, needs more optimization.
30 780 0.242509802227 Henry Cohn, 2026, needs more optimization.
30 781 0.242601766106 Henry Cohn, 2026, needs more optimization.
30 783 0.242700144221 Henry Cohn, 2026, needs more optimization.
30 784 0.242700159569 Henry Cohn, 2026, needs more optimization.
30 785 0.242798640535 Henry Cohn, 2026, needs more optimization.
30 786 0.242887695988 Henry Cohn, 2026, needs more optimization.
30 789 0.242968116390 Henry Cohn, 2026, needs more optimization.
30 790 0.243021963281 Henry Cohn, 2026, needs more optimization.
30 791 0.243077694858 Henry Cohn, 2026, needs more optimization.
30 792 0.243105152220 Henry Cohn, 2026, needs more optimization.
30 793 0.243245199442 Henry Cohn, 2026, needs more optimization.
30 794 0.243348345196 Henry Cohn, 2026, needs more optimization.
30 795 0.243388453486 Henry Cohn, 2026, needs more optimization.
30 796 0.243529404539 Henry Cohn, 2026, needs more optimization.
30 797 0.243624355293 Henry Cohn, 2026, needs more optimization.
30 798 0.243798574357 Henry Cohn, 2026, needs more optimization.
30 799 0.243809411575 Henry Cohn, 2026, needs more optimization.
30 801 0.243890408104 Henry Cohn, 2026, needs more optimization.
30 802 0.244015387219 Henry Cohn, 2026, needs more optimization.
30 803 0.244170022749 Henry Cohn, 2026, needs more optimization.
30 804 0.244325262382 Henry Cohn, 2026, needs more optimization.
30 805 0.244447300801 Henry Cohn, 2026, needs more optimization.
30 806 0.244573339412 Henry Cohn, 2026, needs more optimization.
30 808 0.244690303762 Henry Cohn, 2026, needs more optimization.
30 809 0.244779388210 Henry Cohn, 2026, needs more optimization.
30 811 0.244914114733 Henry Cohn, 2026, needs more optimization.
30 812 0.244964666551 Henry Cohn, 2026, needs more optimization.
30 813 0.245155889908 Henry Cohn, 2026, needs more optimization.
30 814 0.245186443040 Henry Cohn, 2026, needs more optimization.
30 815 0.245239319122 Henry Cohn, 2026, needs more optimization.
30 816 0.245324147506 Henry Cohn, 2026, needs more optimization.
30 817 0.245366141992 Henry Cohn, 2026, needs more optimization.
30 820 0.245522045755 Henry Cohn, 2026, needs more optimization.
30 822 0.245668009512 Henry Cohn, 2026, needs more optimization.
30 823 0.245746943226 Henry Cohn, 2026, needs more optimization.
30 824 0.245786377008 Henry Cohn, 2026, needs more optimization.
30 825 0.245791888722 Henry Cohn, 2026, needs more optimization.
30 826 0.245933190946 Henry Cohn, 2026, needs more optimization.
30 827 0.246073717987 Henry Cohn, 2026, needs more optimization.
30 828 0.246117759678 Henry Cohn, 2026, needs more optimization.
30 829 0.246117762869 Henry Cohn, 2026, needs more optimization.
30 830 0.246177173483 Henry Cohn, 2026, needs more optimization.
30 831 0.246177186561 Henry Cohn, 2026, needs more optimization.
30 832 0.246347379290 Henry Cohn, 2026, needs more optimization.
30 833 0.246359169582 Henry Cohn, 2026, needs more optimization.
30 834 0.246398246213 Henry Cohn, 2026, needs more optimization.
30 835 0.246403106693 Henry Cohn, 2026, needs more optimization.
30 836 0.246449902884 Henry Cohn, 2026, needs more optimization.
30 837 0.246533402052 Henry Cohn, 2026, needs more optimization.
30 838 0.246617384509 Henry Cohn, 2026, needs more optimization.
30 839 0.246628916999 Henry Cohn, 2026, needs more optimization.
30 840 0.246645237001 Henry Cohn, 2026, needs more optimization.
30 841 0.246685692668 Henry Cohn, 2026, needs more optimization.
30 842 0.246715086208 Henry Cohn, 2026, needs more optimization.
30 843 0.246814354845 Henry Cohn, 2026, needs more optimization.
30 844 0.246878964132 Henry Cohn, 2026, needs more optimization.
30 845 0.247040472522 Henry Cohn, 2026, needs more optimization.
30 846 0.247125462720 Henry Cohn, 2026, needs more optimization.
30 847 0.247195277100 Henry Cohn, 2026, needs more optimization.
30 848 0.247287965019 Henry Cohn, 2026, needs more optimization.
30 849 0.247292171916 Henry Cohn, 2026, needs more optimization.
30 850 0.247363061090 Henry Cohn, 2026, needs more optimization.
30 851 0.247425084295 Henry Cohn, 2026, needs more optimization.
30 853 0.247425086643 Henry Cohn, 2026, needs more optimization.
30 854 0.247502763991 Henry Cohn, 2026, needs more optimization.
30 855 0.247502765808 Henry Cohn, 2026, needs more optimization.
30 856 0.247541168457 Henry Cohn, 2026, needs more optimization.
30 857 0.247541211136 Henry Cohn, 2026, needs more optimization.
30 858 0.247585076405 Henry Cohn, 2026, needs more optimization.
30 861 0.247652671035 Henry Cohn, 2026, needs more optimization.
30 862 0.247691980845 Henry Cohn, 2026, needs more optimization.
30 863 0.247769680262 Henry Cohn, 2026, needs more optimization.
30 864 0.247823787342 Henry Cohn, 2026, needs more optimization.
30 865 0.247894515305 Henry Cohn, 2026, needs more optimization.
30 866 0.247944624316 Henry Cohn, 2026, needs more optimization.
30 867 0.247948545052 Henry Cohn, 2026, needs more optimization.
30 868 0.247967024212 Henry Cohn, 2026, needs more optimization.
30 869 0.247976024177 Henry Cohn, 2026, needs more optimization.
30 870 0.248018174505 Henry Cohn, 2026, needs more optimization.
30 871 0.248081452775 Henry Cohn, 2026, needs more optimization.
30 872 0.248127671356 Henry Cohn, 2026, needs more optimization.
30 873 0.248145872746 Henry Cohn, 2026, needs more optimization.
30 874 0.248157517129 Henry Cohn, 2026, needs more optimization.
30 876 0.248189507700 Henry Cohn, 2026, needs more optimization.
30 877 0.248191408147 Henry Cohn, 2026, needs more optimization.
30 878 0.248248574160 Henry Cohn, 2026, needs more optimization.
30 879 0.248297433291 Henry Cohn, 2026, needs more optimization.
30 880 0.248346877762 Henry Cohn, 2026, needs more optimization.
30 881 0.248346929000 Henry Cohn, 2026, needs more optimization.
30 883 0.248386502947 Henry Cohn, 2026, needs more optimization.
30 884 0.248437622178 Henry Cohn, 2026, needs more optimization.
30 886 0.248465047417 Henry Cohn, 2026, needs more optimization.
30 887 0.248499109163 Henry Cohn, 2026, needs more optimization.
30 888 0.248547795071 Henry Cohn, 2026, needs more optimization.
30 889 0.248586741785 Henry Cohn, 2026, needs more optimization.
30 891 0.248608240335 Henry Cohn, 2026, needs more optimization.
30 892 0.248611301246 Henry Cohn, 2026, needs more optimization.
30 893 0.248617908114 Henry Cohn, 2026, needs more optimization.
30 894 0.248635953728 Henry Cohn, 2026, needs more optimization.
30 896 0.248692740944 Henry Cohn, 2026, needs more optimization.
30 897 0.248712088137 Henry Cohn, 2026, needs more optimization.
30 898 0.248736725993 Henry Cohn, 2026, needs more optimization.
30 899 0.248764479679 Henry Cohn, 2026, needs more optimization.
30 900 0.248777096869 Henry Cohn, 2026, needs more optimization.
30 901 0.248817566504 Henry Cohn, 2026, needs more optimization.
30 902 0.248859835726 Henry Cohn, 2026, needs more optimization.
30 904 0.248893140007 Henry Cohn, 2026, needs more optimization.
30 905 0.248894545679 Henry Cohn, 2026, needs more optimization.
30 906 0.248917153078 Henry Cohn, 2026, needs more optimization.
30 907 0.248925286024 Henry Cohn, 2026, needs more optimization.
30 908 0.248928709320 Henry Cohn, 2026, needs more optimization.
30 909 0.248965905070 Henry Cohn, 2026, needs more optimization.
30 910 0.249002529584 Henry Cohn, 2026, needs more optimization.
30 911 0.249017060064 Henry Cohn, 2026, needs more optimization.
30 915 0.249020169486 Henry Cohn, 2026, needs more optimization.
30 916 0.249027344517 Henry Cohn, 2026, needs more optimization.
30 917 0.249053934677 Henry Cohn, 2026, needs more optimization.
30 918 0.249063132364 Henry Cohn, 2026, needs more optimization.
30 922 0.249134157858 Henry Cohn, 2026, needs more optimization.
30 923 0.249178790365 Henry Cohn, 2026, needs more optimization.
30 926 0.249185559133 Henry Cohn, 2026, needs more optimization.
30 927 0.249185627788 Henry Cohn, 2026, needs more optimization.
30 928 0.249205452859 Henry Cohn, 2026, needs more optimization.
30 929 0.249226085048 Henry Cohn, 2026, needs more optimization.
30 930 0.249243396084 Henry Cohn, 2026, needs more optimization.
30 934 0.249243920903 Henry Cohn, 2026, needs more optimization.
30 935 0.249274652244 Henry Cohn, 2026, needs more optimization.
30 936 0.249277085325 Henry Cohn, 2026, needs more optimization.
30 937 0.249277085331 Henry Cohn, 2026, needs more optimization.
30 938 0.249277085403 Henry Cohn, 2026, needs more optimization.
30 939 0.249277086302 Henry Cohn, 2026, needs more optimization.
30 940 0.249277098276 Henry Cohn, 2026, needs more optimization.
30 941 0.249284842167 Henry Cohn, 2026, needs more optimization.
30 942 0.249284920516 Henry Cohn, 2026, needs more optimization.
30 945 0.249341397827 Henry Cohn, 2026, needs more optimization.
30 946 0.249358880326 Henry Cohn, 2026, needs more optimization.
30 947 0.249395668167 Henry Cohn, 2026, needs more optimization.
30 951 0.249403785867 Henry Cohn, 2026, needs more optimization.
30 954 0.249409975711 Henry Cohn, 2026, needs more optimization.
30 955 0.249413058218 Henry Cohn, 2026, needs more optimization.
30 956 0.249413058300 Henry Cohn, 2026, needs more optimization.
30 957 0.249413059208 Henry Cohn, 2026, needs more optimization.
30 958 0.249413063041 Henry Cohn, 2026, needs more optimization.
30 967 0.249519051822 Henry Cohn, 2026, needs more optimization.
30 968 0.249519051823 Henry Cohn, 2026, needs more optimization.
30 969 0.249519051831 Henry Cohn, 2026, needs more optimization.
30 970 0.249519051913 Henry Cohn, 2026, needs more optimization.
30 971 0.249519052859 Henry Cohn, 2026, needs more optimization.
30 972 0.249519065242 Henry Cohn, 2026, needs more optimization.
30 973 0.249524521763 Henry Cohn, 2026, needs more optimization.
30 977 0.249582488496 Henry Cohn, 2026, needs more optimization.
30 978 0.249589455218 Henry Cohn, 2026, needs more optimization.
30 980 0.249603779380 Henry Cohn, 2026, needs more optimization.
30 981 0.249603859093 Henry Cohn, 2026, needs more optimization.
30 982 0.249608401851 Henry Cohn, 2026, needs more optimization.
30 983 0.249612255947 Henry Cohn, 2026, needs more optimization.
30 984 0.249619930637 Henry Cohn, 2026, needs more optimization.
30 985 0.249655967003 Henry Cohn, 2026, needs more optimization.
30 986 0.249656852763 Henry Cohn, 2026, needs more optimization.
30 987 0.249665680591 Henry Cohn, 2026, needs more optimization.
30 988 0.249684187917 Henry Cohn, 2026, needs more optimization.
30 993 0.249715544814 Henry Cohn, 2026, needs more optimization.
30 994 0.249715559739 Henry Cohn, 2026, needs more optimization.
30 995 0.249715560692 Henry Cohn, 2026, needs more optimization.
30 996 0.249715573150 Henry Cohn, 2026, needs more optimization.
30 997 0.249763504331 Henry Cohn, 2026, needs more optimization.
30 998 0.249774449817 Henry Cohn, 2026, needs more optimization.
30 999 0.249775649081 Henry Cohn, 2026, needs more optimization.
30 1000 0.249775649753 Henry Cohn, 2026, needs more optimization.
30 1001 0.249775654763 Henry Cohn, 2026, needs more optimization.
30 1024 0.249928119104 Henry Cohn, 2026, needs more optimization.
31 63 0.026092422671 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26071⁢x3−961⁢x2−31⁢x+1
31 64 0.030325190881 Henry Cohn, 2026.
31 65 0.037285566163 Henry Cohn, 2026.
31 66 0.037768798212 Henry Cohn, 2026.
31 67 0.038109705066 Henry Cohn, 2026, needs more optimization.
31 68 0.041215744341 Henry Cohn, 2026, needs more optimization.
31 69 0.043538391987 Henry Cohn, 2026.
31 70 0.043787493764 Henry Cohn, 2026, needs more optimization.
31 71 0.044034146739 Henry Cohn, 2026, needs more optimization.
31 72 0.044582818397 Henry Cohn, 2026, needs more optimization.
31 73 0.048631532114 Henry Cohn, 2026, needs more optimization.
31 74 0.050062100096 Henry Cohn, 2026, needs more optimization.
31 75 0.051024214945 Henry Cohn, 2026, needs more optimization.
31 76 0.052577056816 Henry Cohn, 2026, needs more optimization.
31 77 0.054426883628 Henry Cohn, 2026, needs more optimization.
31 78 0.055755020834 Henry Cohn, 2026, needs more optimization.
31 79 0.057284623728 Henry Cohn, 2026, needs more optimization.
31 80 0.058637531392 Henry Cohn, 2026, needs more optimization.
31 81 0.060011299846 Henry Cohn, 2026, needs more optimization.
31 82 0.061357116921 Henry Cohn, 2026, needs more optimization.
31 83 0.061674399958 Henry Cohn, 2026, needs more optimization.
31 84 0.062330749112 Henry Cohn, 2026, needs more optimization.
31 85 0.063445922615 Henry Cohn, 2026, needs more optimization.
31 86 0.064362380190 Henry Cohn, 2026, needs more optimization.
31 87 0.065615618975 Henry Cohn, 2026, needs more optimization.
31 88 0.067039609619 Henry Cohn, 2026, needs more optimization.
31 89 0.068506494757 Henry Cohn, 2026, needs more optimization.
31 90 0.069720921068 Henry Cohn, 2026, needs more optimization.
31 91 0.071598803746 Henry Cohn, 2026, needs more optimization.
31 92 0.072712083105 Henry Cohn, 2026, needs more optimization.
31 93 0.074055368184 Henry Cohn, 2026, needs more optimization.
31 94 0.074942100090 Henry Cohn, 2026, needs more optimization.
31 95 0.075273135809 Henry Cohn, 2026, needs more optimization.
31 96 0.075939747317 Henry Cohn, 2026, needs more optimization.
31 97 0.076159912689 Henry Cohn, 2026, needs more optimization.
31 98 0.076805759109 Henry Cohn, 2026, needs more optimization.
31 99 0.076860730306 Henry Cohn, 2026, needs more optimization.
31 100 0.076921146539 Henry Cohn, 2026, needs more optimization.
31 101 0.076984635647 Henry Cohn, 2026, needs more optimization.
31 102 0.077145699289 Henry Cohn, 2026, needs more optimization.
31 103 0.077287795351 Henry Cohn, 2026, needs more optimization.
31 104 0.077395981267 Henry Cohn, 2026, needs more optimization.
31 105 0.077813784053 Henry Cohn, 2026, needs more optimization.
31 106 0.078225853997 Henry Cohn, 2026, needs more optimization.
31 107 0.078676677442 Henry Cohn, 2026, needs more optimization.
31 108 0.079518380678 Henry Cohn, 2026, needs more optimization.
31 109 0.079832475378 Henry Cohn, 2026, needs more optimization.
31 110 0.080290685774 Henry Cohn, 2026, needs more optimization.
31 111 0.080622729367 Henry Cohn, 2026, needs more optimization.
31 112 0.080735256913 Henry Cohn, 2026, needs more optimization.
31 113 0.081335624528 Henry Cohn, 2026, needs more optimization.
31 114 0.081692979562 Henry Cohn, 2026, needs more optimization.
31 115 0.082453702481 Henry Cohn, 2026, needs more optimization.
31 116 0.083365407104 Henry Cohn, 2026, needs more optimization.
31 117 0.084477617091 Henry Cohn, 2026, needs more optimization.
31 120 0.084959387951 Henry Cohn, 2026.
115⁢x2+2⁢x−1
31 121 0.088280522434 Henry Cohn, 2026, needs more optimization.
31 122 0.088681590092 Henry Cohn, 2026, needs more optimization.
31 123 0.088839360211 Henry Cohn, 2026, needs more optimization.
31 124 0.089147389665 Henry Cohn, 2026, needs more optimization.
31 125 0.089579238973 Henry Cohn, 2026, needs more optimization.
31 126 0.089915473986 Henry Cohn, 2026, needs more optimization.
31 127 0.090288078824 Henry Cohn, 2026, needs more optimization.
31 128 0.090373079991 Henry Cohn, 2026, needs more optimization.
31 129 0.090746278632 Henry Cohn, 2026, needs more optimization.
31 130 0.091274921879 Henry Cohn, 2026, needs more optimization.
31 131 0.092148790402 Henry Cohn, 2026, needs more optimization.
31 132 0.093185733990 Henry Cohn, 2026, needs more optimization.
31 133 0.094603416465 Henry Cohn, 2026, needs more optimization.
31 134 0.095446492345 Henry Cohn, 2026, needs more optimization.
31 135 0.096343270797 Henry Cohn, 2026, needs more optimization.
31 136 0.097754469560 Henry Cohn, 2026, needs more optimization.
31 137 0.098799749603 Henry Cohn, 2026, needs more optimization.
31 138 0.099759168906 Henry Cohn, 2026, needs more optimization.
31 139 0.100441857370 Henry Cohn, 2026, needs more optimization.
31 140 0.101617334460 Henry Cohn, 2026, needs more optimization.
31 141 0.102422088921 Henry Cohn, 2026, needs more optimization.
31 142 0.102449892044 Henry Cohn, 2026, needs more optimization.
31 143 0.102497370179 Henry Cohn, 2026, needs more optimization.
31 144 0.102555107515 Henry Cohn, 2026, needs more optimization.
31 145 0.102555110754 Henry Cohn, 2026, needs more optimization.
31 146 0.102846172996 Henry Cohn, 2026, needs more optimization.
31 147 0.103818599556 Henry Cohn, 2026, needs more optimization.
31 148 0.104750072085 Henry Cohn, 2026, needs more optimization.
31 149 0.105239923774 Henry Cohn, 2026, needs more optimization.
31 150 0.106265187433 Henry Cohn, 2026, needs more optimization.
31 151 0.106990228860 Henry Cohn, 2026, needs more optimization.
31 152 0.107761951714 Henry Cohn, 2026, needs more optimization.
31 153 0.108593087454 Henry Cohn, 2026, needs more optimization.
31 154 0.109323202154 Henry Cohn, 2026, needs more optimization.
31 155 0.109955077135 Henry Cohn, 2026, needs more optimization.
31 156 0.110150186701 Henry Cohn, 2026, needs more optimization.
31 157 0.110354588223 Henry Cohn, 2026, needs more optimization.
31 158 0.110456169014 Henry Cohn, 2026, needs more optimization.
31 159 0.110681326396 Henry Cohn, 2026, needs more optimization.
31 160 0.111016675626 Henry Cohn, 2026, needs more optimization.
31 161 0.111512858029 Henry Cohn, 2026, needs more optimization.
31 162 0.111966055312 Henry Cohn, 2026, needs more optimization.
31 163 0.113070676059 Henry Cohn, 2026, needs more optimization.
31 164 0.113822127952 Henry Cohn, 2026, needs more optimization.
31 165 0.114366610289 Henry Cohn, 2026, needs more optimization.
31 166 0.115472339177 Henry Cohn, 2026, needs more optimization.
31 167 0.116367688187 Henry Cohn, 2026, needs more optimization.
31 168 0.117334606586 Henry Cohn, 2026, needs more optimization.
31 169 0.118278595838 Henry Cohn, 2026, needs more optimization.
31 170 0.119300570890 Henry Cohn, 2026, needs more optimization.
31 171 0.120183440460 Henry Cohn, 2026, needs more optimization.
31 172 0.121257618483 Henry Cohn, 2026, needs more optimization.
31 173 0.122372782253 Henry Cohn, 2026, needs more optimization.
31 174 0.123654081020 Henry Cohn, 2026, needs more optimization.
31 175 0.124761086836 Henry Cohn, 2026, needs more optimization.
31 176 0.125711816539 Henry Cohn, 2026, needs more optimization.
31 177 0.126360256261 Henry Cohn, 2026, needs more optimization.
31 178 0.127052817926 Henry Cohn, 2026, needs more optimization.
31 179 0.127663955028 Henry Cohn, 2026, needs more optimization.
31 180 0.127816143487 Henry Cohn, 2026, needs more optimization.
31 181 0.128013698434 Henry Cohn, 2026, needs more optimization.
31 182 0.128094033378 Henry Cohn, 2026, needs more optimization.
31 183 0.128107987643 Henry Cohn, 2026, needs more optimization.
31 184 0.128170516890 Henry Cohn, 2026, needs more optimization.
31 188 0.128237513434 Henry Cohn, 2026, needs more optimization.
31 189 0.128239137542 Orthogonal union of 187 points in 30 dimensions and 2 points in 1 dimension.
31 190 0.128239923410 Henry Cohn, 2026, needs more optimization.
31 191 0.128239923506 Henry Cohn, 2026, needs more optimization.
31 192 0.128240630947 Henry Cohn, 2026, needs more optimization.
31 193 0.128253077683 Henry Cohn, 2026, needs more optimization.
31 194 0.128419107189 Henry Cohn, 2026, needs more optimization.
31 195 0.128954799387 Henry Cohn, 2026, needs more optimization.
31 196 0.129728967130 Henry Cohn, 2026, needs more optimization.
31 197 0.130244241155 Henry Cohn, 2026, needs more optimization.
31 198 0.130246430011 Henry Cohn, 2026, needs more optimization.
31 199 0.131370210066 Henry Cohn, 2026, needs more optimization.
31 200 0.131390928930 Henry Cohn, 2026, needs more optimization.
31 201 0.135033233543 Henry Cohn, 2026, needs more optimization.
31 202 0.135898554595 Henry Cohn, 2026, needs more optimization.
31 203 0.136747422367 Henry Cohn, 2026, needs more optimization.
31 204 0.137361485639 Henry Cohn, 2026, needs more optimization.
31 205 0.137534137818 Henry Cohn, 2026, needs more optimization.
31 206 0.138236204700 Henry Cohn, 2026, needs more optimization.
31 207 0.138689257898 Henry Cohn, 2026, needs more optimization.
31 208 0.138972513872 Henry Cohn, 2026, needs more optimization.
31 209 0.139726801846 Henry Cohn, 2026, needs more optimization.
31 210 0.140499366111 Henry Cohn, 2026, needs more optimization.
31 211 0.140534128460 Henry Cohn, 2026, needs more optimization.
31 212 0.140643801324 Henry Cohn, 2026, needs more optimization.
31 213 0.140685796109 Henry Cohn, 2026, needs more optimization.
31 214 0.140906166908 Henry Cohn, 2026, needs more optimization.
31 215 0.141002098471 Henry Cohn, 2026, needs more optimization.
31 216 0.141043511381 Henry Cohn, 2026, needs more optimization.
31 217 0.141194302184 Henry Cohn, 2026, needs more optimization.
31 218 0.141299435216 Henry Cohn, 2026, needs more optimization.
31 219 0.141535545063 Henry Cohn, 2026, needs more optimization.
31 220 0.141898190120 Henry Cohn, 2026, needs more optimization.
31 221 0.141960972018 Henry Cohn, 2026, needs more optimization.
31 222 0.142036793708 Henry Cohn, 2026, needs more optimization.
31 223 0.142087134696 Henry Cohn, 2026, needs more optimization.
31 224 0.142157246088 Henry Cohn, 2026, needs more optimization.
31 225 0.142402586842 Henry Cohn, 2026, needs more optimization.
31 226 0.142820242868 Henry Cohn, 2026, needs more optimization.
31 227 0.142970277168 Henry Cohn, 2026, needs more optimization.
31 228 0.143197406301 Henry Cohn, 2026, needs more optimization.
31 229 0.143790628677 Henry Cohn, 2026, needs more optimization.
31 230 0.144361508585 Henry Cohn, 2026, needs more optimization.
31 231 0.144763465014 Henry Cohn, 2026, needs more optimization.
31 232 0.144900582615 Henry Cohn, 2026, needs more optimization.
31 233 0.145126148643 Henry Cohn, 2026, needs more optimization.
31 234 0.145322340473 Henry Cohn, 2026, needs more optimization.
31 235 0.145397169248 Henry Cohn, 2026, needs more optimization.
31 236 0.145513681463 Henry Cohn, 2026, needs more optimization.
31 237 0.145627493562 Henry Cohn, 2026, needs more optimization.
31 238 0.145772154163 Henry Cohn, 2026, needs more optimization.
31 239 0.145895462205 Henry Cohn, 2026, needs more optimization.
31 240 0.146019524524 Henry Cohn, 2026, needs more optimization.
31 241 0.146039831597 Henry Cohn, 2026, needs more optimization.
31 242 0.146205978649 Henry Cohn, 2026, needs more optimization.
31 243 0.146415039569 Henry Cohn, 2026, needs more optimization.
31 244 0.146528394014 Henry Cohn, 2026, needs more optimization.
31 245 0.146619486712 Henry Cohn, 2026, needs more optimization.
31 246 0.146732052835 Henry Cohn, 2026, needs more optimization.
31 247 0.146831709873 Henry Cohn, 2026, needs more optimization.
31 248 0.146902593649 Henry Cohn, 2026, needs more optimization.
31 249 0.147158442742 Henry Cohn, 2026, needs more optimization.
31 250 0.147195417344 Henry Cohn, 2026, needs more optimization.
31 251 0.147268143596 Henry Cohn, 2026, needs more optimization.
31 252 0.147328226511 Henry Cohn, 2026, needs more optimization.
31 253 0.147507515523 Henry Cohn, 2026, needs more optimization.
31 254 0.147571626635 Henry Cohn, 2026, needs more optimization.
31 255 0.147651849818 Henry Cohn, 2026, needs more optimization.
31 256 0.147825242292 Henry Cohn, 2026, needs more optimization.
31 257 0.147968343544 Henry Cohn, 2026, needs more optimization.
31 258 0.148277752857 Henry Cohn, 2026, needs more optimization.
31 259 0.148601520814 Henry Cohn, 2026, needs more optimization.
31 260 0.148609273166 Henry Cohn, 2026, needs more optimization.
31 261 0.148644947970 Henry Cohn, 2026, needs more optimization.
31 262 0.149117514640 Henry Cohn, 2026, needs more optimization.
31 263 0.149287089344 Henry Cohn, 2026, needs more optimization.
31 264 0.149732554657 Henry Cohn, 2026, needs more optimization.
31 265 0.150237758787 Henry Cohn, 2026, needs more optimization.
31 266 0.150573891824 Henry Cohn, 2026, needs more optimization.
31 267 0.150843934984 Henry Cohn, 2026, needs more optimization.
31 268 0.151041962608 Henry Cohn, 2026, needs more optimization.
31 269 0.151401411286 Henry Cohn, 2026, needs more optimization.
31 270 0.152144475851 Henry Cohn, 2026, needs more optimization.
31 271 0.152742121421 Henry Cohn, 2026, needs more optimization.
31 272 0.153078145507 Henry Cohn, 2026, needs more optimization.
31 273 0.154341271102 Henry Cohn, 2026, needs more optimization.
31 274 0.154503287181 Henry Cohn, 2026, needs more optimization.
31 275 0.154679067439 Henry Cohn, 2026, needs more optimization.
31 276 0.155433821334 Henry Cohn, 2026, needs more optimization.
31 277 0.156130778496 Henry Cohn, 2026, needs more optimization.
31 278 0.156473175762 Henry Cohn, 2026, needs more optimization.
31 279 0.156888404522 Henry Cohn, 2026, needs more optimization.
31 280 0.157536636716 Henry Cohn, 2026, needs more optimization.
31 281 0.158305019527 Henry Cohn, 2026, needs more optimization.
31 282 0.158882809063 Henry Cohn, 2026, needs more optimization.
31 283 0.159178182974 Henry Cohn, 2026, needs more optimization.
31 284 0.159667077926 Henry Cohn, 2026, needs more optimization.
31 285 0.160163304028 Henry Cohn, 2026, needs more optimization.
31 286 0.160550518765 Henry Cohn, 2026, needs more optimization.
31 287 0.161062424696 Henry Cohn, 2026, needs more optimization.
31 288 0.161639996773 Henry Cohn, 2026, needs more optimization.
31 289 0.161672540965 Henry Cohn, 2026, needs more optimization.
31 290 0.161714379210 Henry Cohn, 2026, needs more optimization.
31 291 0.161717419769 Henry Cohn, 2026, needs more optimization.
31 292 0.161780918868 Henry Cohn, 2026, needs more optimization.
31 293 0.161793752529 Henry Cohn, 2026, needs more optimization.
31 294 0.161803345953 Henry Cohn, 2026, needs more optimization.
31 295 0.161828083232 Henry Cohn, 2026, needs more optimization.
31 296 0.161854089199 Henry Cohn, 2026, needs more optimization.
31 297 0.161903000289 Henry Cohn, 2026, needs more optimization.
31 298 0.161947055242 Henry Cohn, 2026, needs more optimization.
31 299 0.162050182988 Henry Cohn, 2026, needs more optimization.
31 300 0.162139783066 Henry Cohn, 2026, needs more optimization.
31 301 0.162180867947 Henry Cohn, 2026, needs more optimization.
31 302 0.162344475435 Henry Cohn, 2026, needs more optimization.
31 303 0.162477759244 Henry Cohn, 2026, needs more optimization.
31 304 0.162502032770 Henry Cohn, 2026, needs more optimization.
31 305 0.162794689884 Henry Cohn, 2026, needs more optimization.
31 306 0.162957076224 Henry Cohn, 2026, needs more optimization.
31 307 0.163097732869 Henry Cohn, 2026, needs more optimization.
31 308 0.163196549645 Henry Cohn, 2026, needs more optimization.
31 309 0.163319038105 Henry Cohn, 2026, needs more optimization.
31 310 0.163523401836 Henry Cohn, 2026, needs more optimization.
31 311 0.163679022034 Henry Cohn, 2026, needs more optimization.
31 312 0.163772037050 Henry Cohn, 2026, needs more optimization.
31 313 0.163844546699 Henry Cohn, 2026, needs more optimization.
31 314 0.163936502297 Henry Cohn, 2026, needs more optimization.
31 315 0.163988052466 Henry Cohn, 2026, needs more optimization.
31 316 0.164101363662 Henry Cohn, 2026, needs more optimization.
31 317 0.164202130529 Henry Cohn, 2026, needs more optimization.
31 318 0.164239867782 Henry Cohn, 2026, needs more optimization.
31 319 0.164364098599 Henry Cohn, 2026, needs more optimization.
31 320 0.164494123494 Henry Cohn, 2026, needs more optimization.
31 321 0.164510294354 Henry Cohn, 2026, needs more optimization.
31 322 0.164584566293 Henry Cohn, 2026, needs more optimization.
31 323 0.164627942038 Henry Cohn, 2026, needs more optimization.
31 324 0.164697518698 Henry Cohn, 2026, needs more optimization.
31 325 0.164758630234 Henry Cohn, 2026, needs more optimization.
31 326 0.164851633698 Henry Cohn, 2026, needs more optimization.
31 327 0.164924205070 Henry Cohn, 2026, needs more optimization.
31 328 0.165066856975 Henry Cohn, 2026, needs more optimization.
31 329 0.165191479746 Henry Cohn, 2026, needs more optimization.
31 330 0.165224750477 Henry Cohn, 2026, needs more optimization.
31 331 0.165337012034 Henry Cohn, 2026, needs more optimization.
31 332 0.165411260299 Henry Cohn, 2026, needs more optimization.
31 333 0.165495767805 Henry Cohn, 2026, needs more optimization.
31 334 0.165552825138 Henry Cohn, 2026, needs more optimization.
31 335 0.165655138250 Henry Cohn, 2026, needs more optimization.
31 336 0.165725231605 Henry Cohn, 2026, needs more optimization.
31 337 0.165883408305 Henry Cohn, 2026, needs more optimization.
31 338 0.165960119802 Henry Cohn, 2026, needs more optimization.
31 339 0.166127688506 Henry Cohn, 2026, needs more optimization.
31 340 0.166253238175 Henry Cohn, 2026, needs more optimization.
31 341 0.166460538403 Henry Cohn, 2026, needs more optimization.
31 342 0.166524636125 Henry Cohn, 2026, needs more optimization.
31 343 0.166600432488 Henry Cohn, 2026, needs more optimization.
31 344 0.166649100310 Henry Cohn, 2026, needs more optimization.
31 345 0.166719326405 Henry Cohn, 2026, needs more optimization.
31 346 0.166763153372 Henry Cohn, 2026, needs more optimization.
31 347 0.166810946867 Henry Cohn, 2026, needs more optimization.
31 348 0.166916663515 Henry Cohn, 2026, needs more optimization.
31 349 0.166992619107 Henry Cohn, 2026, needs more optimization.
31 350 0.167094080064 Henry Cohn, 2026, needs more optimization.
31 351 0.167464534458 Henry Cohn, 2026, needs more optimization.
31 352 0.168440258142 Henry Cohn, 2026, needs more optimization.
31 353 0.168658409065 Henry Cohn, 2026, needs more optimization.
31 354 0.168922665001 Henry Cohn, 2026, needs more optimization.
31 355 0.169151217088 Henry Cohn, 2026, needs more optimization.
31 356 0.170040634690 Henry Cohn, 2026, needs more optimization.
31 357 0.170376166481 Henry Cohn, 2026, needs more optimization.
31 358 0.171054617681 Henry Cohn, 2026, needs more optimization.
31 359 0.171408214243 Henry Cohn, 2026, needs more optimization.
31 360 0.171764538850 Henry Cohn, 2026, needs more optimization.
31 361 0.178319833929 Henry Cohn, 2026, needs more optimization.
31 362 0.178329383049 Henry Cohn, 2026, needs more optimization.
31 363 0.178371171093 Henry Cohn, 2026, needs more optimization.
31 364 0.178417908349 Henry Cohn, 2026, needs more optimization.
31 365 0.178425302730 Henry Cohn, 2026, needs more optimization.
31 366 0.178548106238 Henry Cohn, 2026, needs more optimization.
31 367 0.178605678121 Henry Cohn, 2026, needs more optimization.
31 368 0.178651470590 Henry Cohn, 2026, needs more optimization.
31 369 0.178729520542 Henry Cohn, 2026, needs more optimization.
31 370 0.178887320262 Henry Cohn, 2026, needs more optimization.
31 371 0.179043140813 Henry Cohn, 2026, needs more optimization.
31 372 0.179378004276 Henry Cohn, 2026, needs more optimization.
31 373 0.179465711182 Henry Cohn, 2026, needs more optimization.
31 374 0.180091710426 Henry Cohn, 2026, needs more optimization.
31 375 0.180427609865 Henry Cohn, 2026, needs more optimization.
31 376 0.180594629109 Henry Cohn, 2026, needs more optimization.
31 377 0.180975589370 Henry Cohn, 2026, needs more optimization.
31 378 0.181566594200 Henry Cohn, 2026, needs more optimization.
31 379 0.181681663799 Henry Cohn, 2026, needs more optimization.
31 380 0.181722542287 Henry Cohn, 2026, needs more optimization.
31 381 0.181729933735 Henry Cohn, 2026, needs more optimization.
31 382 0.181959724833 Henry Cohn, 2026, needs more optimization.
31 383 0.182001575716 Henry Cohn, 2026, needs more optimization.
31 384 0.182083094122 Henry Cohn, 2026, needs more optimization.
31 386 0.182270253513 Henry Cohn, 2026, needs more optimization.
31 387 0.182290833537 Henry Cohn, 2026, needs more optimization.
31 388 0.182550455260 Henry Cohn, 2026, needs more optimization.
31 389 0.182699074023 Henry Cohn, 2026, needs more optimization.
31 390 0.182824479789 Henry Cohn, 2026, needs more optimization.
31 391 0.182978885338 Henry Cohn, 2026, needs more optimization.
31 392 0.183417424933 Henry Cohn, 2026, needs more optimization.
31 393 0.183584398350 Henry Cohn, 2026, needs more optimization.
31 394 0.183813928507 Henry Cohn, 2026, needs more optimization.
31 395 0.183962740190 Henry Cohn, 2026, needs more optimization.
31 396 0.184406357510 Henry Cohn, 2026, needs more optimization.
31 397 0.184692991859 Henry Cohn, 2026, needs more optimization.
31 398 0.184914433207 Henry Cohn, 2026, needs more optimization.
31 399 0.185369806248 Henry Cohn, 2026, needs more optimization.
31 400 0.185889495023 Henry Cohn, 2026, needs more optimization.
31 401 0.185990918151 Henry Cohn, 2026, needs more optimization.
31 402 0.186071192065 Henry Cohn, 2026, needs more optimization.
31 403 0.186295528499 Henry Cohn, 2026, needs more optimization.
31 404 0.186514623225 Henry Cohn, 2026, needs more optimization.
31 405 0.186920008289 Henry Cohn, 2026, needs more optimization.
31 406 0.187157188413 Henry Cohn, 2026, needs more optimization.
31 407 0.187355234048 Henry Cohn, 2026, needs more optimization.
31 408 0.187622622566 Henry Cohn, 2026, needs more optimization.
31 409 0.187718251444 Henry Cohn, 2026, needs more optimization.
31 410 0.187904273227 Henry Cohn, 2026, needs more optimization.
31 411 0.188184703767 Henry Cohn, 2026, needs more optimization.
31 412 0.188486858996 Henry Cohn, 2026, needs more optimization.
31 413 0.188687298798 Henry Cohn, 2026, needs more optimization.
31 414 0.188972756617 Henry Cohn, 2026, needs more optimization.
31 415 0.189140025551 Henry Cohn, 2026, needs more optimization.
31 416 0.189281408460 Henry Cohn, 2026, needs more optimization.
31 417 0.189533556074 Henry Cohn, 2026, needs more optimization.
31 418 0.189706953421 Henry Cohn, 2026, needs more optimization.
31 419 0.190032528147 Henry Cohn, 2026, needs more optimization.
31 420 0.190197525457 Henry Cohn, 2026, needs more optimization.
31 421 0.190395042959 Henry Cohn, 2026, needs more optimization.
31 422 0.190604587096 Henry Cohn, 2026, needs more optimization.
31 423 0.190842204497 Henry Cohn, 2026, needs more optimization.
31 424 0.191095062034 Henry Cohn, 2026, needs more optimization.
31 425 0.191324513750 Henry Cohn, 2026, needs more optimization.
31 426 0.191621738697 Henry Cohn, 2026, needs more optimization.
31 427 0.191784617587 Henry Cohn, 2026, needs more optimization.
31 428 0.191812659421 Henry Cohn, 2026, needs more optimization.
31 429 0.192009728110 Henry Cohn, 2026, needs more optimization.
31 430 0.192133421981 Henry Cohn, 2026, needs more optimization.
31 431 0.192427068651 Henry Cohn, 2026, needs more optimization.
31 432 0.192643525484 Henry Cohn, 2026, needs more optimization.
31 433 0.192956451073 Henry Cohn, 2026, needs more optimization.
31 434 0.193164264819 Henry Cohn, 2026, needs more optimization.
31 435 0.193251445094 Henry Cohn, 2026, needs more optimization.
31 436 0.193423193667 Henry Cohn, 2026, needs more optimization.
31 437 0.193684748281 Henry Cohn, 2026, needs more optimization.
31 438 0.193800115023 Henry Cohn, 2026, needs more optimization.
31 439 0.193999145246 Henry Cohn, 2026, needs more optimization.
31 455 0.194630872484 Orthogonal union of 451 points in 29 dimensions and 4 points in 2 dimensions.
149⁢x−29
31 456 0.194631802692 Henry Cohn, 2026, needs more optimization.
31 457 0.195834894170 Henry Cohn, 2026, needs more optimization.
31 458 0.195921494995 Henry Cohn, 2026, needs more optimization.
31 459 0.195979173425 Henry Cohn, 2026, needs more optimization.
31 460 0.196177940391 Henry Cohn, 2026, needs more optimization.
31 461 0.196384288480 Henry Cohn, 2026, needs more optimization.
31 462 0.196473506598 Henry Cohn, 2026, needs more optimization.
31 463 0.196641203864 Henry Cohn, 2026, needs more optimization.
31 464 0.196728770616 Henry Cohn, 2026, needs more optimization.
31 465 0.196885289892 Henry Cohn, 2026, needs more optimization.
31 466 0.196958470121 Henry Cohn, 2026, needs more optimization.
31 467 0.197130194939 Henry Cohn, 2026, needs more optimization.
31 468 0.197274958480 Henry Cohn, 2026, needs more optimization.
31 469 0.197347480470 Henry Cohn, 2026, needs more optimization.
31 470 0.197428610303 Henry Cohn, 2026, needs more optimization.
31 471 0.197503021491 Henry Cohn, 2026, needs more optimization.
31 472 0.197573506533 Henry Cohn, 2026, needs more optimization.
31 473 0.197607489555 Henry Cohn, 2026, needs more optimization.
31 474 0.197609938123 Henry Cohn, 2026, needs more optimization.
31 475 0.197722787378 Henry Cohn, 2026, needs more optimization.
31 476 0.197793173153 Henry Cohn, 2026, needs more optimization.
31 477 0.197857428633 Henry Cohn, 2026, needs more optimization.
31 478 0.197894494928 Henry Cohn, 2026, needs more optimization.
31 479 0.197906315798 Henry Cohn, 2026, needs more optimization.
31 480 0.197906617001 Henry Cohn, 2026, needs more optimization.
31 481 0.198003770715 Henry Cohn, 2026, needs more optimization.
31 482 0.198007951362 Henry Cohn, 2026, needs more optimization.
31 484 0.198137288768 Henry Cohn, 2026, needs more optimization.
31 485 0.198193489748 Henry Cohn, 2026, needs more optimization.
31 486 0.198229099344 Henry Cohn, 2026, needs more optimization.
31 487 0.198337658635 Henry Cohn, 2026, needs more optimization.
31 488 0.198357278570 Henry Cohn, 2026, needs more optimization.
31 489 0.198479458061 Henry Cohn, 2026, needs more optimization.
31 490 0.198486353052 Henry Cohn, 2026, needs more optimization.
31 491 0.198560323691 Henry Cohn, 2026, needs more optimization.
31 492 0.198591566132 Henry Cohn, 2026, needs more optimization.
31 493 0.198635962240 Henry Cohn, 2026, needs more optimization.
31 494 0.198665794604 Henry Cohn, 2026, needs more optimization.
31 496 0.198748436767 Henry Cohn, 2026, needs more optimization.
31 498 0.198770741487 Henry Cohn, 2026, needs more optimization.
31 499 0.198804759776 Henry Cohn, 2026, needs more optimization.
31 500 0.198834347420 Henry Cohn, 2026, needs more optimization.
31 501 0.198900253018 Henry Cohn, 2026, needs more optimization.
31 502 0.198937763076 Henry Cohn, 2026, needs more optimization.
31 503 0.198982399194 Henry Cohn, 2026, needs more optimization.
31 504 0.199004171236 Henry Cohn, 2026, needs more optimization.
31 505 0.199022916517 Henry Cohn, 2026, needs more optimization.
31 506 0.199058616426 Henry Cohn, 2026, needs more optimization.
31 507 0.199063255879 Henry Cohn, 2026, needs more optimization.
31 509 0.199089171758 Henry Cohn, 2026, needs more optimization.
31 510 0.199104567191 Henry Cohn, 2026, needs more optimization.
31 511 0.199128044946 Henry Cohn, 2026, needs more optimization.
31 512 0.199141259760 Henry Cohn, 2026, needs more optimization.
31 513 0.199195461556 Henry Cohn, 2026, needs more optimization.
31 514 0.199217208806 Henry Cohn, 2026, needs more optimization.
31 515 0.199248679483 Henry Cohn, 2026, needs more optimization.
31 516 0.199284255609 Henry Cohn, 2026, needs more optimization.
31 517 0.199312734671 Henry Cohn, 2026, needs more optimization.
31 518 0.199345792719 Henry Cohn, 2026, needs more optimization.
31 519 0.199381331157 Henry Cohn, 2026, needs more optimization.
31 520 0.199381331166 Henry Cohn, 2026, needs more optimization.
31 521 0.199404005339 Henry Cohn, 2026, needs more optimization.
31 522 0.199426021051 Henry Cohn, 2026, needs more optimization.
31 523 0.199454056792 Henry Cohn, 2026, needs more optimization.
31 524 0.199463418779 Henry Cohn, 2026, needs more optimization.
31 525 0.199472798793 Henry Cohn, 2026, needs more optimization.
31 527 0.199500024869 Henry Cohn, 2026, needs more optimization.
31 529 0.199508169801 Henry Cohn, 2026, needs more optimization.
31 530 0.199534323333 Henry Cohn, 2026, needs more optimization.
31 531 0.199555204260 Henry Cohn, 2026, needs more optimization.
31 533 0.199558183765 Henry Cohn, 2026, needs more optimization.
31 534 0.199559977100 Henry Cohn, 2026, needs more optimization.
31 537 0.199563028801 Henry Cohn, 2026, needs more optimization.
31 538 0.199573855102 Henry Cohn, 2026, needs more optimization.
31 539 0.199588560237 Henry Cohn, 2026, needs more optimization.
31 540 0.199596718732 Henry Cohn, 2026, needs more optimization.
31 541 0.199609475008 Henry Cohn, 2026, needs more optimization.
31 542 0.199634267398 Henry Cohn, 2026, needs more optimization.
31 543 0.199642360844 Henry Cohn, 2026, needs more optimization.
31 544 0.199663284110 Henry Cohn, 2026, needs more optimization.
31 545 0.199668152381 Henry Cohn, 2026, needs more optimization.
31 547 0.199680085981 Henry Cohn, 2026, needs more optimization.
31 548 0.199689737903 Henry Cohn, 2026, needs more optimization.
31 549 0.199702121107 Henry Cohn, 2026, needs more optimization.
31 550 0.199705512889 Henry Cohn, 2026, needs more optimization.
31 551 0.199716928955 Henry Cohn, 2026, needs more optimization.
31 552 0.199726417732 Henry Cohn, 2026, needs more optimization.
31 554 0.199757755177 Henry Cohn, 2026, needs more optimization.
31 555 0.199757823983 Henry Cohn, 2026, needs more optimization.
31 557 0.199776089957 Henry Cohn, 2026, needs more optimization.
31 559 0.199783894033 Henry Cohn, 2026, needs more optimization.
31 561 0.199803120983 Henry Cohn, 2026, needs more optimization.
31 562 0.199815329346 Henry Cohn, 2026, needs more optimization.
31 563 0.199820172912 Henry Cohn, 2026, needs more optimization.
31 564 0.199820176284 Henry Cohn, 2026, needs more optimization.
31 565 0.199826075092 Henry Cohn, 2026, needs more optimization.
31 566 0.199840582715 Henry Cohn, 2026, needs more optimization.
31 568 0.199857507423 Henry Cohn, 2026, needs more optimization.
31 569 0.199867799461 Henry Cohn, 2026, needs more optimization.
31 570 0.199871420775 Henry Cohn, 2026, needs more optimization.
31 572 0.199902312203 Henry Cohn, 2026, needs more optimization.
31 573 0.199902332570 Henry Cohn, 2026, needs more optimization.
31 574 0.199903065274 Henry Cohn, 2026, needs more optimization.
31 575 0.199906144247 Henry Cohn, 2026, needs more optimization.
31 576 0.199908077452 Henry Cohn, 2026, needs more optimization.
31 577 0.199915683183 Henry Cohn, 2026, needs more optimization.
31 578 0.199917605228 Henry Cohn, 2026, needs more optimization.
31 579 0.199917632756 Henry Cohn, 2026, needs more optimization.
31 580 0.199923901853 Henry Cohn, 2026, needs more optimization.
31 581 0.199923901866 Henry Cohn, 2026, needs more optimization.
31 583 0.199929203044 Henry Cohn, 2026, needs more optimization.
31 584 0.199930758533 Henry Cohn, 2026, needs more optimization.
31 585 0.199956045781 Henry Cohn, 2026, needs more optimization.
31 688 0.2 Henry Cohn, 2026.
5⁢x−1
31 689 0.206391133129 Henry Cohn, 2026, needs more optimization.
31 690 0.216286111683 Henry Cohn, 2026, needs more optimization.
31 691 0.216526127647 Henry Cohn, 2026, needs more optimization.
31 692 0.216916180905 Henry Cohn, 2026, needs more optimization.
31 693 0.217258718744 Henry Cohn, 2026, needs more optimization.
31 694 0.217627995929 Henry Cohn, 2026, needs more optimization.
31 695 0.217855164543 Henry Cohn, 2026, needs more optimization.
31 696 0.218026647098 Henry Cohn, 2026, needs more optimization.
31 697 0.218249048213 Henry Cohn, 2026, needs more optimization.
31 698 0.218486468123 Henry Cohn, 2026, needs more optimization.
31 699 0.218747309179 Henry Cohn, 2026, needs more optimization.
31 700 0.219009493633 Henry Cohn, 2026, needs more optimization.
31 701 0.219254955103 Henry Cohn, 2026, needs more optimization.
31 702 0.219575186911 Henry Cohn, 2026, needs more optimization.
31 703 0.219876172193 Henry Cohn, 2026, needs more optimization.
31 704 0.220176888158 Henry Cohn, 2026, needs more optimization.
31 705 0.220463473981 Henry Cohn, 2026, needs more optimization.
31 706 0.220603758873 Henry Cohn, 2026, needs more optimization.
31 707 0.220851768500 Henry Cohn, 2026, needs more optimization.
31 708 0.221098471618 Henry Cohn, 2026, needs more optimization.
31 709 0.221385680106 Henry Cohn, 2026, needs more optimization.
31 710 0.221689378114 Henry Cohn, 2026, needs more optimization.
31 711 0.221975650100 Henry Cohn, 2026, needs more optimization.
31 712 0.222186512437 Henry Cohn, 2026, needs more optimization.
31 713 0.222469122870 Henry Cohn, 2026, needs more optimization.
31 714 0.222681141571 Henry Cohn, 2026, needs more optimization.
31 715 0.222986540428 Henry Cohn, 2026, needs more optimization.
31 716 0.223217265964 Henry Cohn, 2026, needs more optimization.
31 717 0.223531889503 Henry Cohn, 2026, needs more optimization.
31 718 0.223808729960 Henry Cohn, 2026, needs more optimization.
31 719 0.224078152518 Henry Cohn, 2026, needs more optimization.
31 720 0.224354087707 Henry Cohn, 2026, needs more optimization.
31 721 0.224510672863 Henry Cohn, 2026, needs more optimization.
31 722 0.224832927993 Henry Cohn, 2026, needs more optimization.
31 723 0.225070008243 Henry Cohn, 2026, needs more optimization.
31 724 0.225325806677 Henry Cohn, 2026, needs more optimization.
31 725 0.225444405247 Henry Cohn, 2026, needs more optimization.
31 726 0.225764443287 Henry Cohn, 2026, needs more optimization.
31 727 0.225980715786 Henry Cohn, 2026, needs more optimization.
31 728 0.226187641777 Henry Cohn, 2026, needs more optimization.
31 729 0.226498844215 Henry Cohn, 2026, needs more optimization.
31 730 0.226608528168 Henry Cohn, 2026, needs more optimization.
31 731 0.226871996144 Henry Cohn, 2026, needs more optimization.
31 732 0.227122975581 Henry Cohn, 2026, needs more optimization.
31 733 0.227300629571 Henry Cohn, 2026, needs more optimization.
31 734 0.227572939729 Henry Cohn, 2026, needs more optimization.
31 735 0.227745098113 Henry Cohn, 2026, needs more optimization.
31 736 0.228022163360 Henry Cohn, 2026, needs more optimization.
31 737 0.228250994837 Henry Cohn, 2026, needs more optimization.
31 738 0.228548721553 Henry Cohn, 2026, needs more optimization.
31 739 0.228768039646 Henry Cohn, 2026, needs more optimization.
31 740 0.228988824228 Henry Cohn, 2026, needs more optimization.
31 741 0.229182994957 Henry Cohn, 2026, needs more optimization.
31 742 0.229389053689 Henry Cohn, 2026, needs more optimization.
31 743 0.229682611986 Henry Cohn, 2026, needs more optimization.
31 744 0.229916418739 Henry Cohn, 2026, needs more optimization.
31 745 0.230172710204 Henry Cohn, 2026, needs more optimization.
31 746 0.230387861741 Henry Cohn, 2026, needs more optimization.
31 747 0.230622107600 Henry Cohn, 2026, needs more optimization.
31 748 0.230841467383 Henry Cohn, 2026, needs more optimization.
31 749 0.230991794525 Henry Cohn, 2026, needs more optimization.
31 750 0.231237313199 Henry Cohn, 2026, needs more optimization.
31 751 0.231454138920 Henry Cohn, 2026, needs more optimization.
31 752 0.231681677866 Henry Cohn, 2026, needs more optimization.
31 753 0.231899584739 Henry Cohn, 2026, needs more optimization.
31 754 0.232064789574 Henry Cohn, 2026, needs more optimization.
31 755 0.232232252993 Henry Cohn, 2026, needs more optimization.
31 756 0.232386718402 Henry Cohn, 2026, needs more optimization.
31 757 0.232528929934 Henry Cohn, 2026, needs more optimization.
31 758 0.232722726727 Henry Cohn, 2026, needs more optimization.
31 759 0.232996432912 Henry Cohn, 2026, needs more optimization.
31 760 0.233175074995 Henry Cohn, 2026, needs more optimization.
31 761 0.233412871555 Henry Cohn, 2026, needs more optimization.
31 762 0.233519067146 Henry Cohn, 2026, needs more optimization.
31 763 0.233793187775 Henry Cohn, 2026, needs more optimization.
31 764 0.233954253239 Henry Cohn, 2026, needs more optimization.
31 765 0.234112402849 Henry Cohn, 2026, needs more optimization.
31 766 0.234307359655 Henry Cohn, 2026, needs more optimization.
31 767 0.234500386048 Henry Cohn, 2026, needs more optimization.
31 768 0.234691543210 Henry Cohn, 2026, needs more optimization.
31 769 0.234830835576 Henry Cohn, 2026, needs more optimization.
31 770 0.234982862133 Henry Cohn, 2026, needs more optimization.
31 771 0.235144654665 Henry Cohn, 2026, needs more optimization.
31 772 0.235389397974 Henry Cohn, 2026, needs more optimization.
31 773 0.235589049463 Henry Cohn, 2026, needs more optimization.
31 774 0.235731798572 Henry Cohn, 2026, needs more optimization.
31 775 0.235973024756 Henry Cohn, 2026, needs more optimization.
31 776 0.236118707929 Henry Cohn, 2026, needs more optimization.
31 777 0.236295646610 Henry Cohn, 2026, needs more optimization.
31 778 0.236511786055 Henry Cohn, 2026, needs more optimization.
31 779 0.236691953618 Henry Cohn, 2026, needs more optimization.
31 780 0.236920263867 Henry Cohn, 2026, needs more optimization.
31 781 0.237086610216 Henry Cohn, 2026, needs more optimization.
31 782 0.237289221663 Henry Cohn, 2026, needs more optimization.
31 783 0.237479666948 Henry Cohn, 2026, needs more optimization.
31 784 0.237711460911 Henry Cohn, 2026, needs more optimization.
31 1024 0.238095238096 Henry Cohn, 2026.
21⁢x−5
32 65 0.025347196752 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
28800⁢x3−1024⁢x2−32⁢x+1
32 66 0.029441153101 Henry Cohn, 2026.
32 67 0.036059544373 Henry Cohn, 2026, needs more optimization.
32 68 0.036921898559 Henry Cohn, 2026.
32 69 0.037652090605 Henry Cohn, 2026.
32 70 0.040284452403 Henry Cohn, 2026, needs more optimization.
32 71 0.043041700377 Henry Cohn, 2026, needs more optimization.
32 72 0.043340506635 Henry Cohn, 2026, needs more optimization.
32 73 0.043635192354 Henry Cohn, 2026, needs more optimization.
32 74 0.044312064799 Henry Cohn, 2026, needs more optimization.
32 75 0.046969454295 Henry Cohn, 2026, needs more optimization.
32 76 0.048914802229 Henry Cohn, 2026, needs more optimization.
32 77 0.049877266445 Henry Cohn, 2026, needs more optimization.
32 78 0.051358756718 Henry Cohn, 2026, needs more optimization.
32 79 0.053163782305 Henry Cohn, 2026, needs more optimization.
32 80 0.054716199890 Henry Cohn, 2026, needs more optimization.
32 81 0.055651582257 Henry Cohn, 2026, needs more optimization.
32 82 0.056964486782 Henry Cohn, 2026, needs more optimization.
32 83 0.058223867562 Henry Cohn, 2026, needs more optimization.
32 84 0.059654559208 Henry Cohn, 2026, needs more optimization.
32 85 0.060923962302 Henry Cohn, 2026, needs more optimization.
32 86 0.061924997346 Henry Cohn, 2026, needs more optimization.
32 87 0.063171707740 Henry Cohn, 2026, needs more optimization.
32 88 0.064356779926 Henry Cohn, 2026, needs more optimization.
32 89 0.065580030175 Henry Cohn, 2026, needs more optimization.
32 90 0.066403448391 Henry Cohn, 2026, needs more optimization.
32 91 0.067770523192 Henry Cohn, 2026, needs more optimization.
32 92 0.068706407912 Henry Cohn, 2026, needs more optimization.
32 93 0.069828448713 Henry Cohn, 2026, needs more optimization.
32 94 0.070634404780 Henry Cohn, 2026, needs more optimization.
32 95 0.071715164404 Henry Cohn, 2026, needs more optimization.
32 96 0.072860230514 Henry Cohn, 2026, needs more optimization.
32 97 0.073896151958 Henry Cohn, 2026, needs more optimization.
32 98 0.073972144719 Henry Cohn, 2026, needs more optimization.
32 99 0.074680739138 Henry Cohn, 2026, needs more optimization.
32 100 0.075274765234 Henry Cohn, 2026, needs more optimization.
32 101 0.075926597268 Henry Cohn, 2026, needs more optimization.
32 102 0.076145068417 Henry Cohn, 2026, needs more optimization.
32 103 0.076760108485 Henry Cohn, 2026, needs more optimization.
32 104 0.076940555636 Henry Cohn, 2026, needs more optimization.
32 105 0.077067682374 Henry Cohn, 2026, needs more optimization.
32 106 0.077277282825 Henry Cohn, 2026, needs more optimization.
32 107 0.077416298855 Henry Cohn, 2026, needs more optimization.
32 108 0.077639661809 Henry Cohn, 2026, needs more optimization.
32 109 0.077719064956 Henry Cohn, 2026, needs more optimization.
32 110 0.078036300489 Henry Cohn, 2026, needs more optimization.
32 111 0.078886903815 Henry Cohn, 2026, needs more optimization.
32 112 0.079491974951 Henry Cohn, 2026, needs more optimization.
32 113 0.079891939284 Henry Cohn, 2026, needs more optimization.
32 114 0.080450152324 Henry Cohn, 2026, needs more optimization.
32 115 0.080598496147 Henry Cohn, 2026, needs more optimization.
32 116 0.080906179783 Henry Cohn, 2026, needs more optimization.
32 117 0.080987078245 Henry Cohn, 2026, needs more optimization.
32 118 0.081654858152 Henry Cohn, 2026, needs more optimization.
32 119 0.082498968579 Henry Cohn, 2026, needs more optimization.
32 120 0.083463741126 Henry Cohn, 2026, needs more optimization.
32 121 0.084405217293 Henry Cohn, 2026, needs more optimization.
32 122 0.084959387951 Orthogonal union of 120 points in 31 dimensions and 2 points in 1 dimension.
115⁢x2+2⁢x−1
32 123 0.085677620041 Henry Cohn, 2026, needs more optimization.
32 124 0.086091243393 Henry Cohn, 2026, needs more optimization.
32 125 0.086493345699 Henry Cohn, 2026, needs more optimization.
32 126 0.086717021952 Henry Cohn, 2026, needs more optimization.
32 127 0.088524788865 Henry Cohn, 2026, needs more optimization.
32 128 0.088868266117 Henry Cohn, 2026, needs more optimization.
32 129 0.089185302726 Henry Cohn, 2026, needs more optimization.
32 130 0.089563921083 Henry Cohn, 2026, needs more optimization.
32 131 0.089730949904 Henry Cohn, 2026, needs more optimization.
32 132 0.089779523605 Henry Cohn, 2026, needs more optimization.
32 133 0.089985163363 Henry Cohn, 2026, needs more optimization.
32 134 0.090080011995 Henry Cohn, 2026, needs more optimization.
32 135 0.090186844277 Henry Cohn, 2026, needs more optimization.
32 136 0.090738654271 Henry Cohn, 2026, needs more optimization.
32 137 0.091844011563 Henry Cohn, 2026, needs more optimization.
32 138 0.092897411236 Henry Cohn, 2026, needs more optimization.
32 139 0.093783657395 Henry Cohn, 2026, needs more optimization.
32 140 0.094487231284 Henry Cohn, 2026, needs more optimization.
32 141 0.095595397855 Henry Cohn, 2026, needs more optimization.
32 142 0.096711206336 Henry Cohn, 2026, needs more optimization.
32 143 0.097517187312 Henry Cohn, 2026, needs more optimization.
32 144 0.098659674917 Henry Cohn, 2026, needs more optimization.
32 145 0.099651216156 Henry Cohn, 2026, needs more optimization.
32 146 0.100378533555 Henry Cohn, 2026, needs more optimization.
32 147 0.101193884282 Henry Cohn, 2026, needs more optimization.
32 148 0.101934590215 Henry Cohn, 2026, needs more optimization.
32 149 0.102441529765 Henry Cohn, 2026, needs more optimization.
32 150 0.102441530837 Henry Cohn, 2026, needs more optimization.
32 151 0.102468675548 Henry Cohn, 2026, needs more optimization.
32 152 0.102597777800 Henry Cohn, 2026, needs more optimization.
32 153 0.103070450074 Henry Cohn, 2026, needs more optimization.
32 154 0.103775244423 Henry Cohn, 2026, needs more optimization.
32 155 0.104391906101 Henry Cohn, 2026, needs more optimization.
32 156 0.104392119427 Henry Cohn, 2026, needs more optimization.
32 157 0.104392251376 Henry Cohn, 2026, needs more optimization.
32 158 0.106941442306 Henry Cohn, 2026, needs more optimization.
32 159 0.107167315114 Henry Cohn, 2026, needs more optimization.
32 160 0.107543191141 Henry Cohn, 2026, needs more optimization.
32 161 0.107900949679 Henry Cohn, 2026, needs more optimization.
32 162 0.108437898188 Henry Cohn, 2026, needs more optimization.
32 163 0.108908183662 Henry Cohn, 2026, needs more optimization.
32 164 0.109508631941 Henry Cohn, 2026, needs more optimization.
32 165 0.110128675814 Henry Cohn, 2026, needs more optimization.
32 166 0.110630112456 Henry Cohn, 2026, needs more optimization.
32 167 0.111438960617 Henry Cohn, 2026, needs more optimization.
32 168 0.112093551090 Henry Cohn, 2026, needs more optimization.
32 169 0.112755671556 Henry Cohn, 2026, needs more optimization.
32 170 0.113526852778 Henry Cohn, 2026, needs more optimization.
32 171 0.114538873881 Henry Cohn, 2026, needs more optimization.
32 172 0.115404888684 Henry Cohn, 2026, needs more optimization.
32 173 0.116308201126 Henry Cohn, 2026, needs more optimization.
32 174 0.117063736843 Henry Cohn, 2026, needs more optimization.
32 175 0.118176053684 Henry Cohn, 2026, needs more optimization.
32 176 0.119017839533 Henry Cohn, 2026, needs more optimization.
32 177 0.119551831748 Henry Cohn, 2026, needs more optimization.
32 178 0.120416228528 Henry Cohn, 2026, needs more optimization.
32 179 0.121440619030 Henry Cohn, 2026, needs more optimization.
32 180 0.121964898574 Henry Cohn, 2026, needs more optimization.
32 181 0.122750344329 Henry Cohn, 2026, needs more optimization.
32 182 0.123469211836 Henry Cohn, 2026, needs more optimization.
32 183 0.124134672330 Henry Cohn, 2026, needs more optimization.
32 184 0.125017504223 Henry Cohn, 2026, needs more optimization.
32 185 0.125748231640 Henry Cohn, 2026, needs more optimization.
32 186 0.126200027650 Henry Cohn, 2026, needs more optimization.
32 187 0.126978061285 Henry Cohn, 2026, needs more optimization.
32 188 0.127635652497 Henry Cohn, 2026, needs more optimization.
32 189 0.128170896515 Henry Cohn, 2026, needs more optimization.
32 190 0.128170896807 Henry Cohn, 2026, needs more optimization.
32 191 0.128221973311 Henry Cohn, 2026, needs more optimization.
32 192 0.128221975294 Henry Cohn, 2026, needs more optimization.
32 193 0.128227291460 Henry Cohn, 2026, needs more optimization.
32 194 0.128227292562 Henry Cohn, 2026, needs more optimization.
32 195 0.128227293653 Henry Cohn, 2026, needs more optimization.
32 196 0.128239011136 Henry Cohn, 2026, needs more optimization.
32 197 0.128241131392 Henry Cohn, 2026, needs more optimization.
32 198 0.128276913702 Henry Cohn, 2026, needs more optimization.
32 199 0.128647086844 Henry Cohn, 2026, needs more optimization.
32 200 0.128809313404 Henry Cohn, 2026, needs more optimization.
32 201 0.129240737592 Henry Cohn, 2026, needs more optimization.
32 202 0.129908034134 Henry Cohn, 2026, needs more optimization.
32 203 0.129979539861 Henry Cohn, 2026, needs more optimization.
32 204 0.130294030048 Henry Cohn, 2026, needs more optimization.
32 205 0.130673651914 Henry Cohn, 2026, needs more optimization.
32 206 0.130936381349 Henry Cohn, 2026, needs more optimization.
32 207 0.131055175175 Henry Cohn, 2026, needs more optimization.
32 208 0.131208107798 Henry Cohn, 2026, needs more optimization.
32 209 0.134558127391 Henry Cohn, 2026, needs more optimization.
32 210 0.134990230091 Henry Cohn, 2026, needs more optimization.
32 211 0.135570882548 Henry Cohn, 2026, needs more optimization.
32 212 0.135898854633 Henry Cohn, 2026, needs more optimization.
32 213 0.136447858461 Henry Cohn, 2026, needs more optimization.
32 214 0.136787578286 Henry Cohn, 2026, needs more optimization.
32 215 0.137422336857 Henry Cohn, 2026, needs more optimization.
32 216 0.137930063425 Henry Cohn, 2026, needs more optimization.
32 217 0.138566505569 Henry Cohn, 2026, needs more optimization.
32 218 0.138892547837 Henry Cohn, 2026, needs more optimization.
32 219 0.139252729426 Henry Cohn, 2026, needs more optimization.
32 220 0.139857416233 Henry Cohn, 2026, needs more optimization.
32 221 0.140286283640 Henry Cohn, 2026, needs more optimization.
32 222 0.140444061524 Henry Cohn, 2026, needs more optimization.
32 223 0.140533107493 Henry Cohn, 2026, needs more optimization.
32 224 0.140645443854 Henry Cohn, 2026, needs more optimization.
32 225 0.140750645589 Henry Cohn, 2026, needs more optimization.
32 226 0.140890284125 Henry Cohn, 2026, needs more optimization.
32 227 0.141124011678 Henry Cohn, 2026, needs more optimization.
32 228 0.141238322833 Henry Cohn, 2026, needs more optimization.
32 229 0.141407753681 Henry Cohn, 2026, needs more optimization.
32 230 0.141498663240 Henry Cohn, 2026, needs more optimization.
32 231 0.141747246927 Henry Cohn, 2026, needs more optimization.
32 232 0.141895008454 Henry Cohn, 2026, needs more optimization.
32 233 0.142027324453 Henry Cohn, 2026, needs more optimization.
32 234 0.142127192003 Henry Cohn, 2026, needs more optimization.
32 235 0.142432182897 Henry Cohn, 2026, needs more optimization.
32 236 0.142695343032 Henry Cohn, 2026, needs more optimization.
32 237 0.142773756967 Henry Cohn, 2026, needs more optimization.
32 238 0.142896366559 Henry Cohn, 2026, needs more optimization.
32 239 0.143074610925 Henry Cohn, 2026, needs more optimization.
32 240 0.143623933513 Henry Cohn, 2026, needs more optimization.
32 241 0.143692917357 Henry Cohn, 2026, needs more optimization.
32 242 0.143877714215 Henry Cohn, 2026, needs more optimization.
32 243 0.144042140496 Henry Cohn, 2026, needs more optimization.
32 244 0.144427571799 Henry Cohn, 2026, needs more optimization.
32 245 0.144865965282 Henry Cohn, 2026, needs more optimization.
32 246 0.144955062699 Henry Cohn, 2026, needs more optimization.
32 247 0.145047334887 Henry Cohn, 2026, needs more optimization.
32 248 0.145378902881 Henry Cohn, 2026, needs more optimization.
32 249 0.145533041100 Henry Cohn, 2026, needs more optimization.
32 250 0.145788809232 Henry Cohn, 2026, needs more optimization.
32 251 0.146001260530 Henry Cohn, 2026, needs more optimization.
32 252 0.146049322075 Henry Cohn, 2026, needs more optimization.
32 253 0.146254432158 Henry Cohn, 2026, needs more optimization.
32 254 0.146390897060 Henry Cohn, 2026, needs more optimization.
32 255 0.146478957383 Henry Cohn, 2026, needs more optimization.
32 256 0.146601800049 Henry Cohn, 2026, needs more optimization.
32 257 0.146610014325 Henry Cohn, 2026, needs more optimization.
32 258 0.146718802263 Henry Cohn, 2026, needs more optimization.
32 259 0.146900776762 Henry Cohn, 2026, needs more optimization.
32 260 0.147186753554 Henry Cohn, 2026, needs more optimization.
32 261 0.147463808517 Henry Cohn, 2026, needs more optimization.
32 262 0.147608387749 Henry Cohn, 2026, needs more optimization.
32 263 0.147942506226 Henry Cohn, 2026, needs more optimization.
32 264 0.148056565238 Henry Cohn, 2026, needs more optimization.
32 265 0.148190092101 Henry Cohn, 2026, needs more optimization.
32 266 0.148396069400 Henry Cohn, 2026, needs more optimization.
32 267 0.148456932888 Henry Cohn, 2026, needs more optimization.
32 268 0.148650253572 Henry Cohn, 2026, needs more optimization.
32 269 0.148945392277 Henry Cohn, 2026, needs more optimization.
32 270 0.149150118802 Henry Cohn, 2026, needs more optimization.
32 271 0.149376465782 Henry Cohn, 2026, needs more optimization.
32 272 0.149822112496 Henry Cohn, 2026, needs more optimization.
32 273 0.150466804758 Henry Cohn, 2026, needs more optimization.
32 274 0.150786840689 Henry Cohn, 2026, needs more optimization.
32 275 0.151447469928 Henry Cohn, 2026, needs more optimization.
32 276 0.151945116900 Henry Cohn, 2026, needs more optimization.
32 277 0.152544322059 Henry Cohn, 2026, needs more optimization.
32 278 0.152859377570 Henry Cohn, 2026, needs more optimization.
32 279 0.153125078778 Henry Cohn, 2026, needs more optimization.
32 280 0.153233666254 Henry Cohn, 2026, needs more optimization.
32 281 0.153722923184 Henry Cohn, 2026, needs more optimization.
32 282 0.153938402854 Henry Cohn, 2026, needs more optimization.
32 283 0.154411845085 Henry Cohn, 2026, needs more optimization.
32 284 0.154941752742 Henry Cohn, 2026, needs more optimization.
32 285 0.155406578393 Henry Cohn, 2026, needs more optimization.
32 286 0.155879478349 Henry Cohn, 2026, needs more optimization.
32 287 0.156410989342 Henry Cohn, 2026, needs more optimization.
32 288 0.156713802423 Henry Cohn, 2026, needs more optimization.
32 289 0.157123086760 Henry Cohn, 2026, needs more optimization.
32 290 0.157504915660 Henry Cohn, 2026, needs more optimization.
32 291 0.157659752230 Henry Cohn, 2026, needs more optimization.
32 292 0.158268030810 Henry Cohn, 2026, needs more optimization.
32 293 0.158555283880 Henry Cohn, 2026, needs more optimization.
32 294 0.159028230526 Henry Cohn, 2026, needs more optimization.
32 295 0.159368028099 Henry Cohn, 2026, needs more optimization.
32 296 0.159863940141 Henry Cohn, 2026, needs more optimization.
32 297 0.160120566386 Henry Cohn, 2026, needs more optimization.
32 298 0.160639912503 Henry Cohn, 2026, needs more optimization.
32 299 0.160940852824 Henry Cohn, 2026, needs more optimization.
32 300 0.160956016967 Henry Cohn, 2026, needs more optimization.
32 301 0.160991503394 Henry Cohn, 2026, needs more optimization.
32 302 0.161093822951 Henry Cohn, 2026, needs more optimization.
32 303 0.161257155707 Henry Cohn, 2026, needs more optimization.
32 304 0.161405374033 Henry Cohn, 2026, needs more optimization.
32 306 0.161492280659 Henry Cohn, 2026, needs more optimization.
32 307 0.161609401432 Henry Cohn, 2026, needs more optimization.
32 308 0.161675009189 Henry Cohn, 2026, needs more optimization.
32 309 0.161763359110 Henry Cohn, 2026, needs more optimization.
32 310 0.161817311278 Henry Cohn, 2026, needs more optimization.
32 311 0.161874296641 Henry Cohn, 2026, needs more optimization.
32 312 0.161924417419 Henry Cohn, 2026, needs more optimization.
32 313 0.161972636060 Henry Cohn, 2026, needs more optimization.
32 314 0.162025456302 Henry Cohn, 2026, needs more optimization.
32 315 0.162061367051 Henry Cohn, 2026, needs more optimization.
32 316 0.162149311445 Henry Cohn, 2026, needs more optimization.
32 317 0.162241314921 Henry Cohn, 2026, needs more optimization.
32 318 0.162288103877 Henry Cohn, 2026, needs more optimization.
32 319 0.162381523994 Henry Cohn, 2026, needs more optimization.
32 320 0.162451436133 Henry Cohn, 2026, needs more optimization.
32 321 0.162523577097 Henry Cohn, 2026, needs more optimization.
32 322 0.162598055620 Henry Cohn, 2026, needs more optimization.
32 323 0.162690547950 Henry Cohn, 2026, needs more optimization.
32 324 0.162799778904 Henry Cohn, 2026, needs more optimization.
32 325 0.162936504959 Henry Cohn, 2026, needs more optimization.
32 326 0.163041685656 Henry Cohn, 2026, needs more optimization.
32 327 0.163127129741 Henry Cohn, 2026, needs more optimization.
32 328 0.163179527766 Henry Cohn, 2026, needs more optimization.
32 329 0.163290943273 Henry Cohn, 2026, needs more optimization.
32 330 0.163373386854 Henry Cohn, 2026, needs more optimization.
32 331 0.163465998735 Henry Cohn, 2026, needs more optimization.
32 332 0.163556154907 Henry Cohn, 2026, needs more optimization.
32 333 0.163706291675 Henry Cohn, 2026, needs more optimization.
32 334 0.163800739882 Henry Cohn, 2026, needs more optimization.
32 335 0.163868623674 Henry Cohn, 2026, needs more optimization.
32 336 0.163978741348 Henry Cohn, 2026, needs more optimization.
32 337 0.164101805356 Henry Cohn, 2026, needs more optimization.
32 338 0.164213724283 Henry Cohn, 2026, needs more optimization.
32 339 0.164413774703 Henry Cohn, 2026, needs more optimization.
32 340 0.164482994105 Henry Cohn, 2026, needs more optimization.
32 341 0.164568222475 Henry Cohn, 2026, needs more optimization.
32 342 0.164634649726 Henry Cohn, 2026, needs more optimization.
32 343 0.164791079883 Henry Cohn, 2026, needs more optimization.
32 344 0.164875943725 Henry Cohn, 2026, needs more optimization.
32 345 0.164882837203 Henry Cohn, 2026, needs more optimization.
32 346 0.165026534349 Henry Cohn, 2026, needs more optimization.
32 347 0.165162777109 Henry Cohn, 2026, needs more optimization.
32 348 0.165272290212 Henry Cohn, 2026, needs more optimization.
32 349 0.165386714757 Henry Cohn, 2026, needs more optimization.
32 350 0.165562676935 Henry Cohn, 2026, needs more optimization.
32 351 0.165671913390 Henry Cohn, 2026, needs more optimization.
32 352 0.165837135226 Henry Cohn, 2026, needs more optimization.
32 353 0.165955670398 Henry Cohn, 2026, needs more optimization.
32 354 0.166162671711 Henry Cohn, 2026, needs more optimization.
32 355 0.166339846752 Henry Cohn, 2026, needs more optimization.
32 356 0.166691844955 Henry Cohn, 2026, needs more optimization.
32 357 0.166708364482 Henry Cohn, 2026, needs more optimization.
32 358 0.166717828161 Henry Cohn, 2026, needs more optimization.
32 359 0.166803333500 Henry Cohn, 2026, needs more optimization.
32 360 0.167057636266 Henry Cohn, 2026, needs more optimization.
32 361 0.167365071151 Henry Cohn, 2026, needs more optimization.
32 362 0.167416115684 Henry Cohn, 2026, needs more optimization.
32 363 0.177216215153 Henry Cohn, 2026, needs more optimization.
32 364 0.177279736755 Henry Cohn, 2026, needs more optimization.
32 365 0.177302911380 Henry Cohn, 2026, needs more optimization.
32 366 0.177330022025 Henry Cohn, 2026, needs more optimization.
32 367 0.177358988609 Henry Cohn, 2026, needs more optimization.
32 368 0.177836914618 Henry Cohn, 2026, needs more optimization.
32 369 0.177857503797 Henry Cohn, 2026, needs more optimization.
32 370 0.177888780235 Henry Cohn, 2026, needs more optimization.
32 371 0.177916123709 Henry Cohn, 2026, needs more optimization.
32 372 0.177941613685 Henry Cohn, 2026, needs more optimization.
32 373 0.178054259734 Henry Cohn, 2026, needs more optimization.
32 374 0.178103808130 Henry Cohn, 2026, needs more optimization.
32 375 0.178152858681 Henry Cohn, 2026, needs more optimization.
32 376 0.178210687967 Henry Cohn, 2026, needs more optimization.
32 377 0.178235145283 Henry Cohn, 2026, needs more optimization.
32 378 0.178255122880 Henry Cohn, 2026, needs more optimization.
32 379 0.178302899915 Henry Cohn, 2026, needs more optimization.
32 380 0.178494693287 Henry Cohn, 2026, needs more optimization.
32 381 0.178506253554 Henry Cohn, 2026, needs more optimization.
32 382 0.178510268603 Henry Cohn, 2026, needs more optimization.
32 383 0.178533256254 Henry Cohn, 2026, needs more optimization.
32 384 0.178538037096 Henry Cohn, 2026, needs more optimization.
32 385 0.178564390435 Henry Cohn, 2026, needs more optimization.
32 386 0.178572647208 Henry Cohn, 2026, needs more optimization.
32 387 0.178580597093 Henry Cohn, 2026, needs more optimization.
32 388 0.178621560317 Henry Cohn, 2026, needs more optimization.
32 389 0.178634483823 Henry Cohn, 2026, needs more optimization.
32 390 0.178657903025 Henry Cohn, 2026, needs more optimization.
32 391 0.178701982913 Henry Cohn, 2026, needs more optimization.
32 392 0.178754059835 Henry Cohn, 2026, needs more optimization.
32 393 0.178802981062 Henry Cohn, 2026, needs more optimization.
32 394 0.178821005461 Henry Cohn, 2026, needs more optimization.
32 395 0.178860870732 Henry Cohn, 2026, needs more optimization.
32 396 0.178916901376 Henry Cohn, 2026, needs more optimization.
32 397 0.179054893904 Henry Cohn, 2026, needs more optimization.
32 398 0.179453431339 Henry Cohn, 2026, needs more optimization.
32 399 0.179601586535 Henry Cohn, 2026, needs more optimization.
32 400 0.180078286055 Henry Cohn, 2026, needs more optimization.
32 401 0.180207981458 Henry Cohn, 2026, needs more optimization.
32 402 0.180431542796 Henry Cohn, 2026, needs more optimization.
32 403 0.180888392957 Henry Cohn, 2026, needs more optimization.
32 404 0.180951319314 Henry Cohn, 2026, needs more optimization.
32 405 0.181292744314 Henry Cohn, 2026, needs more optimization.
32 406 0.181426376636 Henry Cohn, 2026, needs more optimization.
32 407 0.181603489358 Henry Cohn, 2026, needs more optimization.
32 408 0.182298802401 Henry Cohn, 2026, needs more optimization.
32 409 0.182402791437 Henry Cohn, 2026, needs more optimization.
32 410 0.182605479501 Henry Cohn, 2026, needs more optimization.
32 411 0.182893592194 Henry Cohn, 2026, needs more optimization.
32 412 0.183002474558 Henry Cohn, 2026, needs more optimization.
32 413 0.183171099377 Henry Cohn, 2026, needs more optimization.
32 414 0.183297736281 Henry Cohn, 2026, needs more optimization.
32 415 0.183589114587 Henry Cohn, 2026, needs more optimization.
32 416 0.183966545292 Henry Cohn, 2026, needs more optimization.
32 417 0.184152461656 Henry Cohn, 2026, needs more optimization.
32 418 0.184665459785 Henry Cohn, 2026, needs more optimization.
32 419 0.184985712180 Henry Cohn, 2026, needs more optimization.
32 420 0.185145410353 Henry Cohn, 2026, needs more optimization.
32 421 0.185688127258 Henry Cohn, 2026, needs more optimization.
32 422 0.185928577779 Henry Cohn, 2026, needs more optimization.
32 423 0.186164694568 Henry Cohn, 2026, needs more optimization.
32 424 0.186187181592 Henry Cohn, 2026, needs more optimization.
32 425 0.186275929950 Henry Cohn, 2026, needs more optimization.
32 426 0.186369317799 Henry Cohn, 2026, needs more optimization.
32 427 0.186623315134 Henry Cohn, 2026, needs more optimization.
32 428 0.187138818741 Henry Cohn, 2026, needs more optimization.
32 429 0.187390314273 Henry Cohn, 2026, needs more optimization.
32 430 0.187570791994 Henry Cohn, 2026, needs more optimization.
32 431 0.187726788700 Henry Cohn, 2026, needs more optimization.
32 432 0.188167766710 Henry Cohn, 2026, needs more optimization.
32 433 0.188288341977 Henry Cohn, 2026, needs more optimization.
32 434 0.188480383673 Henry Cohn, 2026, needs more optimization.
32 435 0.188567700002 Henry Cohn, 2026, needs more optimization.
32 436 0.188896479497 Henry Cohn, 2026, needs more optimization.
32 437 0.188923688082 Henry Cohn, 2026, needs more optimization.
32 438 0.189099316230 Henry Cohn, 2026, needs more optimization.
32 439 0.189253179239 Henry Cohn, 2026, needs more optimization.
32 440 0.189490651122 Henry Cohn, 2026, needs more optimization.
32 441 0.189609321460 Henry Cohn, 2026, needs more optimization.
32 442 0.189864505322 Henry Cohn, 2026, needs more optimization.
32 443 0.189950480894 Henry Cohn, 2026, needs more optimization.
32 444 0.189950480895 Henry Cohn, 2026, needs more optimization.
32 445 0.190051715594 Henry Cohn, 2026, needs more optimization.
32 446 0.190164133123 Henry Cohn, 2026, needs more optimization.
32 447 0.190433004533 Henry Cohn, 2026, needs more optimization.
32 448 0.190659158996 Henry Cohn, 2026, needs more optimization.
32 449 0.191111383710 Henry Cohn, 2026, needs more optimization.
32 450 0.191244006723 Henry Cohn, 2026, needs more optimization.
32 451 0.191452888278 Henry Cohn, 2026, needs more optimization.
32 452 0.191538845768 Henry Cohn, 2026, needs more optimization.
32 453 0.191627691490 Henry Cohn, 2026, needs more optimization.
32 454 0.191668255196 Henry Cohn, 2026, needs more optimization.
32 455 0.191831319986 Henry Cohn, 2026, needs more optimization.
32 456 0.192062561648 Henry Cohn, 2026, needs more optimization.
32 457 0.192143544723 Henry Cohn, 2026, needs more optimization.
32 458 0.192186733395 Henry Cohn, 2026, needs more optimization.
32 459 0.192448381059 Henry Cohn, 2026, needs more optimization.
32 460 0.192590592560 Henry Cohn, 2026, needs more optimization.
32 461 0.192657774975 Henry Cohn, 2026, needs more optimization.
32 462 0.192893824714 Henry Cohn, 2026, needs more optimization.
32 463 0.192987912682 Henry Cohn, 2026, needs more optimization.
32 464 0.193174395525 Henry Cohn, 2026, needs more optimization.
32 465 0.193255993890 Henry Cohn, 2026, needs more optimization.
32 466 0.193498079868 Henry Cohn, 2026, needs more optimization.
32 467 0.193642629965 Henry Cohn, 2026, needs more optimization.
32 468 0.193742993703 Henry Cohn, 2026, needs more optimization.
32 469 0.194025290243 Henry Cohn, 2026, needs more optimization.
32 470 0.194083964168 Henry Cohn, 2026, needs more optimization.
32 471 0.194132752208 Henry Cohn, 2026, needs more optimization.
32 472 0.194143893814 Henry Cohn, 2026, needs more optimization.
32 473 0.194323681689 Henry Cohn, 2026, needs more optimization.
32 474 0.194413623793 Henry Cohn, 2026, needs more optimization.
32 475 0.194467349191 Henry Cohn, 2026, needs more optimization.
32 476 0.194529824458 Henry Cohn, 2026, needs more optimization.
32 477 0.194696548001 Henry Cohn, 2026, needs more optimization.
32 478 0.194790627472 Henry Cohn, 2026, needs more optimization.
32 479 0.194902166617 Henry Cohn, 2026, needs more optimization.
32 528 0.195121951220 Henry Cohn, 2026.
41⁢x−8
32 529 0.199360610378 Henry Cohn, 2026, needs more optimization.
32 530 0.199368297307 Henry Cohn, 2026, needs more optimization.
32 531 0.199373053332 Henry Cohn, 2026, needs more optimization.
32 532 0.199373177268 Henry Cohn, 2026, needs more optimization.
32 533 0.199379230943 Henry Cohn, 2026, needs more optimization.
32 534 0.199379238867 Henry Cohn, 2026, needs more optimization.
32 535 0.199388031783 Henry Cohn, 2026, needs more optimization.
32 536 0.199402779487 Henry Cohn, 2026, needs more optimization.
32 537 0.199404019584 Henry Cohn, 2026, needs more optimization.
32 538 0.199418248578 Henry Cohn, 2026, needs more optimization.
32 539 0.199424419385 Henry Cohn, 2026, needs more optimization.
32 540 0.199434827213 Henry Cohn, 2026, needs more optimization.
32 541 0.199446525204 Henry Cohn, 2026, needs more optimization.
32 542 0.199512624914 Henry Cohn, 2026, needs more optimization.
32 543 0.199517436835 Henry Cohn, 2026, needs more optimization.
32 544 0.199587108532 Henry Cohn, 2026, needs more optimization.
32 545 0.199601525370 Henry Cohn, 2026, needs more optimization.
32 546 0.199606655669 Henry Cohn, 2026, needs more optimization.
32 547 0.199610093037 Henry Cohn, 2026, needs more optimization.
32 548 0.199610269087 Henry Cohn, 2026, needs more optimization.
32 549 0.199614320776 Henry Cohn, 2026, needs more optimization.
32 550 0.199621362304 Henry Cohn, 2026, needs more optimization.
32 551 0.199621362326 Henry Cohn, 2026, needs more optimization.
32 552 0.199627071174 Henry Cohn, 2026, needs more optimization.
32 553 0.199630802725 Henry Cohn, 2026, needs more optimization.
32 554 0.199632034209 Henry Cohn, 2026, needs more optimization.
32 556 0.199635385008 Henry Cohn, 2026, needs more optimization.
32 557 0.199635385055 Henry Cohn, 2026, needs more optimization.
32 558 0.199638496705 Henry Cohn, 2026, needs more optimization.
32 560 0.199641177441 Henry Cohn, 2026, needs more optimization.
32 561 0.199649256960 Henry Cohn, 2026, needs more optimization.
32 562 0.199649257010 Henry Cohn, 2026, needs more optimization.
32 563 0.199663295243 Henry Cohn, 2026, needs more optimization.
32 564 0.199672595298 Henry Cohn, 2026, needs more optimization.
32 565 0.199705140900 Henry Cohn, 2026, needs more optimization.
32 566 0.199708201180 Henry Cohn, 2026, needs more optimization.
32 567 0.199716385726 Henry Cohn, 2026, needs more optimization.
32 568 0.199720473451 Henry Cohn, 2026, needs more optimization.
32 569 0.199721505559 Henry Cohn, 2026, needs more optimization.
32 570 0.199721611487 Henry Cohn, 2026, needs more optimization.
32 571 0.199727008219 Henry Cohn, 2026, needs more optimization.
32 572 0.199728529775 Henry Cohn, 2026, needs more optimization.
32 573 0.199728529776 Henry Cohn, 2026, needs more optimization.
32 574 0.199743809395 Henry Cohn, 2026, needs more optimization.
32 575 0.199743888224 Henry Cohn, 2026, needs more optimization.
32 576 0.199744015100 Henry Cohn, 2026, needs more optimization.
32 577 0.199752923455 Henry Cohn, 2026, needs more optimization.
32 578 0.199761252647 Henry Cohn, 2026, needs more optimization.
32 579 0.199765189922 Henry Cohn, 2026, needs more optimization.
32 580 0.199768479915 Henry Cohn, 2026, needs more optimization.
32 581 0.199768482125 Henry Cohn, 2026, needs more optimization.
32 582 0.199773175621 Henry Cohn, 2026, needs more optimization.
32 583 0.199811015443 Henry Cohn, 2026, needs more optimization.
32 584 0.199811114732 Henry Cohn, 2026, needs more optimization.
32 585 0.199811114737 Henry Cohn, 2026, needs more optimization.
32 586 0.199818903429 Henry Cohn, 2026, needs more optimization.
32 587 0.199818909953 Henry Cohn, 2026, needs more optimization.
32 588 0.199822195134 Henry Cohn, 2026, needs more optimization.
32 589 0.199830497034 Henry Cohn, 2026, needs more optimization.
32 590 0.199830497121 Henry Cohn, 2026, needs more optimization.
32 591 0.199840220947 Henry Cohn, 2026, needs more optimization.
32 592 0.199859514689 Henry Cohn, 2026, needs more optimization.
32 594 0.199859525899 Henry Cohn, 2026, needs more optimization.
32 595 0.199873055470 Henry Cohn, 2026, needs more optimization.
32 596 0.199881053207 Henry Cohn, 2026, needs more optimization.
32 597 0.199963378943 Henry Cohn, 2026, needs more optimization.
32 598 0.199964987104 Henry Cohn, 2026, needs more optimization.
32 599 0.199964993070 Henry Cohn, 2026, needs more optimization.
32 601 0.199965317842 Henry Cohn, 2026, needs more optimization.
32 602 0.199966473793 Henry Cohn, 2026, needs more optimization.
32 603 0.199966473802 Henry Cohn, 2026, needs more optimization.
32 605 0.199966473963 Henry Cohn, 2026, needs more optimization.
32 608 0.199967075888 Henry Cohn, 2026, needs more optimization.
32 609 0.199969947935 Henry Cohn, 2026, needs more optimization.
32 610 0.199971610402 Henry Cohn, 2026, needs more optimization.
32 611 0.199972609435 Henry Cohn, 2026, needs more optimization.
32 612 0.199976460696 Henry Cohn, 2026, needs more optimization.
32 613 0.199977503091 Henry Cohn, 2026, needs more optimization.
32 615 0.199977514086 Henry Cohn, 2026, needs more optimization.
32 616 0.199980748464 Henry Cohn, 2026, needs more optimization.
32 617 0.199984936542 Henry Cohn, 2026, needs more optimization.
32 618 0.199984937565 Henry Cohn, 2026, needs more optimization.
32 619 0.199986634216 Henry Cohn, 2026, needs more optimization.
32 620 0.199987300304 Henry Cohn, 2026, needs more optimization.
32 704 0.2 Henry Cohn, 2026.
5⁢x−1
32 705 0.209391128561 Henry Cohn, 2026, needs more optimization.
32 706 0.212767228407 Henry Cohn, 2026, needs more optimization.
32 707 0.212849373144 Henry Cohn, 2026, needs more optimization.
32 708 0.213123570032 Henry Cohn, 2026, needs more optimization.
32 709 0.213215219246 Henry Cohn, 2026, needs more optimization.
32 710 0.214317762757 Henry Cohn, 2026, needs more optimization.
32 711 0.214542002500 Henry Cohn, 2026, needs more optimization.
32 712 0.214635627818 Henry Cohn, 2026, needs more optimization.
32 713 0.214756617578 Henry Cohn, 2026, needs more optimization.
32 714 0.214925576459 Henry Cohn, 2026, needs more optimization.
32 715 0.214974327313 Henry Cohn, 2026, needs more optimization.
32 716 0.215218387274 Henry Cohn, 2026, needs more optimization.
32 717 0.215315376120 Henry Cohn, 2026, needs more optimization.
32 718 0.216495344074 Henry Cohn, 2026, needs more optimization.
32 719 0.216567025161 Henry Cohn, 2026, needs more optimization.
32 720 0.216718690452 Henry Cohn, 2026, needs more optimization.
32 721 0.216782302222 Henry Cohn, 2026, needs more optimization.
32 722 0.217151636835 Henry Cohn, 2026, needs more optimization.
32 723 0.217241621310 Henry Cohn, 2026, needs more optimization.
32 724 0.217652652410 Henry Cohn, 2026, needs more optimization.
32 725 0.217748226101 Henry Cohn, 2026, needs more optimization.
32 726 0.218096956514 Henry Cohn, 2026, needs more optimization.
32 727 0.218157392072 Henry Cohn, 2026, needs more optimization.
32 728 0.218179160659 Henry Cohn, 2026, needs more optimization.
32 729 0.218265866280 Henry Cohn, 2026, needs more optimization.
32 730 0.218322879849 Henry Cohn, 2026, needs more optimization.
32 731 0.219193540793 Henry Cohn, 2026, needs more optimization.
32 732 0.219373202833 Henry Cohn, 2026, needs more optimization.
32 733 0.219472669588 Henry Cohn, 2026, needs more optimization.
32 734 0.219725053185 Henry Cohn, 2026, needs more optimization.
32 735 0.219760040362 Henry Cohn, 2026, needs more optimization.
32 736 0.220109924834 Henry Cohn, 2026, needs more optimization.
32 737 0.220230457092 Henry Cohn, 2026, needs more optimization.
32 738 0.220448876389 Henry Cohn, 2026, needs more optimization.
32 739 0.220559585232 Henry Cohn, 2026, needs more optimization.
32 740 0.220651468721 Henry Cohn, 2026, needs more optimization.
32 741 0.221516641222 Henry Cohn, 2026, needs more optimization.
32 742 0.221617591797 Henry Cohn, 2026, needs more optimization.
32 743 0.221721498367 Henry Cohn, 2026, needs more optimization.
32 744 0.221787757682 Henry Cohn, 2026, needs more optimization.
32 745 0.221950949177 Henry Cohn, 2026, needs more optimization.
32 746 0.222000973133 Henry Cohn, 2026, needs more optimization.
32 747 0.222152622355 Henry Cohn, 2026, needs more optimization.
32 748 0.222200461090 Henry Cohn, 2026, needs more optimization.
32 749 0.222268865420 Henry Cohn, 2026, needs more optimization.
32 750 0.223390141614 Henry Cohn, 2026, needs more optimization.
32 751 0.223458143224 Henry Cohn, 2026, needs more optimization.
32 752 0.223580919803 Henry Cohn, 2026, needs more optimization.
32 753 0.223703855372 Henry Cohn, 2026, needs more optimization.
32 754 0.223771666295 Henry Cohn, 2026, needs more optimization.
32 755 0.223922959611 Henry Cohn, 2026, needs more optimization.
32 756 0.223995661927 Henry Cohn, 2026, needs more optimization.
32 757 0.224154632560 Henry Cohn, 2026, needs more optimization.
32 758 0.224355564540 Henry Cohn, 2026, needs more optimization.
32 759 0.225181967296 Henry Cohn, 2026, needs more optimization.
32 760 0.225268507833 Henry Cohn, 2026, needs more optimization.
32 761 0.225404962166 Henry Cohn, 2026, needs more optimization.
32 762 0.225419120171 Henry Cohn, 2026, needs more optimization.
32 763 0.225598745100 Henry Cohn, 2026, needs more optimization.
32 764 0.225650942308 Henry Cohn, 2026, needs more optimization.
32 765 0.225712697442 Henry Cohn, 2026, needs more optimization.
32 766 0.226335637841 Henry Cohn, 2026, needs more optimization.
32 767 0.226445845720 Henry Cohn, 2026, needs more optimization.
32 768 0.226512595025 Henry Cohn, 2026, needs more optimization.
32 769 0.226692586374 Henry Cohn, 2026, needs more optimization.
32 770 0.226764992186 Henry Cohn, 2026, needs more optimization.
32 771 0.227733959759 Henry Cohn, 2026, needs more optimization.
32 772 0.227780180125 Henry Cohn, 2026, needs more optimization.
32 773 0.227915760145 Henry Cohn, 2026, needs more optimization.
32 774 0.227953330665 Henry Cohn, 2026, needs more optimization.
32 775 0.227980652131 Henry Cohn, 2026, needs more optimization.
32 776 0.228169548686 Henry Cohn, 2026, needs more optimization.
32 777 0.228348070323 Henry Cohn, 2026, needs more optimization.
32 778 0.228400737176 Henry Cohn, 2026, needs more optimization.
32 779 0.228638142510 Henry Cohn, 2026, needs more optimization.
32 780 0.228769669586 Henry Cohn, 2026, needs more optimization.
32 781 0.228878769457 Henry Cohn, 2026, needs more optimization.
32 782 0.228920934408 Henry Cohn, 2026, needs more optimization.
32 783 0.228960178111 Henry Cohn, 2026, needs more optimization.
32 784 0.229059814437 Henry Cohn, 2026, needs more optimization.
32 785 0.229217350668 Henry Cohn, 2026, needs more optimization.
32 786 0.231309286831 Henry Cohn, 2026, needs more optimization.
32 787 0.231508561471 Henry Cohn, 2026, needs more optimization.
32 788 0.231576302664 Henry Cohn, 2026, needs more optimization.
32 789 0.231718020184 Henry Cohn, 2026, needs more optimization.
32 790 0.231812831156 Henry Cohn, 2026, needs more optimization.
32 791 0.231943967063 Henry Cohn, 2026, needs more optimization.
32 792 0.231991108245 Henry Cohn, 2026, needs more optimization.
32 793 0.232037465560 Henry Cohn, 2026, needs more optimization.
32 794 0.232101123298 Henry Cohn, 2026, needs more optimization.
32 795 0.232222647510 Henry Cohn, 2026, needs more optimization.
32 796 0.232320043534 Henry Cohn, 2026, needs more optimization.
32 797 0.232404090365 Henry Cohn, 2026, needs more optimization.
32 798 0.232550467084 Henry Cohn, 2026, needs more optimization.
32 799 0.232664096768 Henry Cohn, 2026, needs more optimization.
32 800 0.232820696838 Henry Cohn, 2026, needs more optimization.
32 801 0.232950829665 Henry Cohn, 2026, needs more optimization.
32 802 0.233137044265 Henry Cohn, 2026, needs more optimization.
32 803 0.233248337124 Henry Cohn, 2026, needs more optimization.
32 804 0.233416684080 Henry Cohn, 2026, needs more optimization.
32 805 0.233540416410 Henry Cohn, 2026, needs more optimization.
32 806 0.233705981252 Henry Cohn, 2026, needs more optimization.
32 807 0.233852458447 Henry Cohn, 2026, needs more optimization.
32 808 0.234058897531 Henry Cohn, 2026, needs more optimization.
32 809 0.234201517663 Henry Cohn, 2026, needs more optimization.
32 810 0.234413079020 Henry Cohn, 2026, needs more optimization.
32 811 0.234543254269 Henry Cohn, 2026, needs more optimization.
32 812 0.234706301163 Henry Cohn, 2026, needs more optimization.
32 813 0.234817608417 Henry Cohn, 2026, needs more optimization.
32 814 0.235003535610 Henry Cohn, 2026, needs more optimization.
32 815 0.235161979557 Henry Cohn, 2026, needs more optimization.
32 816 0.235298882344 Henry Cohn, 2026, needs more optimization.
32 817 0.235520384577 Henry Cohn, 2026, needs more optimization.
32 818 0.235660483589 Henry Cohn, 2026, needs more optimization.
32 819 0.235782682890 Henry Cohn, 2026, needs more optimization.
32 820 0.235924959512 Henry Cohn, 2026, needs more optimization.
32 821 0.236069502555 Henry Cohn, 2026, needs more optimization.
32 822 0.236227895118 Henry Cohn, 2026, needs more optimization.
32 823 0.236338364335 Henry Cohn, 2026, needs more optimization.
32 824 0.236471925150 Henry Cohn, 2026, needs more optimization.
32 825 0.236677015277 Henry Cohn, 2026, needs more optimization.
32 826 0.236809257631 Henry Cohn, 2026, needs more optimization.
32 827 0.236970413461 Henry Cohn, 2026, needs more optimization.
32 828 0.237159280237 Henry Cohn, 2026, needs more optimization.
32 829 0.237343176166 Henry Cohn, 2026, needs more optimization.
32 830 0.237473427338 Henry Cohn, 2026, needs more optimization.
32 831 0.237655225757 Henry Cohn, 2026, needs more optimization.
32 832 0.237704739395 Henry Cohn, 2026, needs more optimization.
32 833 0.237895584714 Henry Cohn, 2026, needs more optimization.
32 1024 0.238095238096 Code with 1024 points in 31 dimensions.
21⁢x−5
52 325* 0.0625 P. J. Cameron, J. M. Goethals, and J. J. Seidel, Strongly regular graphs having strongly regular subconstituents, J. Algebra 55 (1978), 257–280, doi:10.1016/0021-8693(78)90220-X; V. I. Levenshtein, Designs as maximum codes in polynomial metric spaces, Acta Appl. Math. 29 (1992), 1–82, doi:10.1007/BF00053379.
16⁢x−1
64 4224* 0.125 V. I. Levenšteĭn, Bounds for the maximal cardinality of a code with bounded modulus of the inner product (Russian), Dokl. Akad. Nauk SSSR 263 (1982), 1303–1308, English translation in Soviet Math. Dokl. 25 (1982), 526–531; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
8⁢x−1