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 0.969909525964 Henry Cohn, 2026, needs more optimization.
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 0.972578596339 Henry Cohn, 2026, needs more optimization.
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 0.973166312973 Henry Cohn, 2026, needs more optimization.
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 0.974246953956 Henry Cohn, 2024.
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 0.976130656685 Henry Cohn, 2024.
3 286 0.976198007997 Henry Cohn, 2026.
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 0.977138858781 Henry Cohn, 2026.
3 299 0.977212814333 Henry Cohn, 2026, needs more optimization.
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 0.979227007488 Henry Cohn, 2024.
3 329 0.979277635210 Henry Cohn, 2024.
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 0.979489586862 Henry Cohn, 2026, needs more optimization.
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 0.981891941481 Henry Cohn, 2024.
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 0.982313990090 Henry Cohn, 2024.
3 387 0.982346497568 Henry Cohn, 2024.
3 388 0.982373183313 Henry Cohn, 2024.
3 389 0.982417056387 Henry Cohn, 2026.
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 0.983168565133 Henry Cohn, 2024.
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 0.983544996006 Henry Cohn, 2026, needs more optimization.
3 416 0.983572356049 Henry Cohn, 2024.
3 417 0.983606337391 Henry Cohn, 2026.
3 418 0.983668285529 Henry Cohn, 2024.
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 0.983874347222 Henry Cohn, 2026.
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 0.983947724258 Henry Cohn, 2024.
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 0.984130874521 Henry Cohn, 2026, needs more optimization.
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 0.984667372266 Henry Cohn, 2024.
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 0.984846922701 Henry Cohn, 2024.
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.
3 474 0.985602045775 Henry Cohn, 2026, needs more optimization.
3 475 0.985602451902 Henry Cohn, 2026, needs more optimization.
3 476 0.985629966650 Henry Cohn, 2026.
3 477 0.985650812703 Henry Cohn, 2026.
3 478 0.985679876222 Henry Cohn, 2026.
3 479 0.985700108040 Henry Cohn, 2026, needs more optimization.
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 0.985924698901 Henry Cohn, 2024.
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 0.986348497971 Henry Cohn, 2026, needs more optimization.
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 0.986479196655 Henry Cohn, 2024.
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 0.986749064827 Henry Cohn, 2024.
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 0.988465092835 Henry Cohn, 2026, needs more optimization.
3 594 0.988487841215 Henry Cohn, 2026, needs more optimization.
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 0.988639847715 Henry Cohn, 2026, needs more optimization.
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 0.988726120936 Henry Cohn, 2026, needs more optimization.
3 608 0.988753049196 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 0.988800912598 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 0.988873099629 Henry Cohn, 2026, needs more optimization.
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 0.989102260067 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 0.989201672529 Henry Cohn, 2026, needs more optimization.
3 635 0.989217714617 Henry Cohn, 2026.
3 636 0.989241817793 Henry Cohn, 2026, needs more optimization.
3 637 0.989258653000 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 0.989370321422 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 0.989432732690 Henry Cohn, 2026, needs more optimization.
3 649 0.989449788085 Henry Cohn, 2026, needs more optimization.
3 650 0.989461679845 Henry Cohn, 2026.
3 651 0.989485039605 Henry Cohn, 2024.
3 652 0.989499769599 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 0.989623972684 Henry Cohn, 2026, needs more optimization.
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 0.989692795388 Henry Cohn, 2026, needs more optimization.
3 666 0.989717351243 Henry Cohn, 2026.
3 667 0.989730982552 Henry Cohn, 2026.
3 668 0.989745107620 Henry Cohn, 2026, needs more optimization.
3 669 0.989759503187 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 0.989846916511 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 0.989918641442 Henry Cohn, 2026, needs more optimization.
3 681 0.989936920244 Henry Cohn, 2024.
3 682 0.989953273780 Henry Cohn, 2026.
3 683 0.989967898498 Henry Cohn, 2026, needs more optimization.
3 684 0.989976775468 Henry Cohn, 2026.
3 685 0.990001194691 Henry Cohn, 2026, needs more optimization.
3 686 0.990006418271 Henry Cohn, 2024.
3 687 0.990023877788 Henry Cohn, 2026, needs more optimization.
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 0.990078940124 Henry Cohn, 2026, needs more optimization.
3 694 0.990103743152 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.
3 699 0.990191563570 Henry Cohn, 2026, needs more optimization.
3 700 0.990192254287 Henry Cohn, 2026.
3 701 0.990202423105 Henry Cohn, 2026, needs more optimization.
3 702 0.990207507930 Henry Cohn, 2025.
3 703 0.990226501892 Henry Cohn, 2026.
3 704 0.990247522690 Henry Cohn, 2026, needs more optimization.
3 705 0.990263988882 Henry Cohn, 2026, needs more optimization.
3 706 0.990280269273 Henry Cohn, 2026.
3 707 0.990307749113 Henry Cohn, 2024.
3 708 0.990308161383 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 0.990383183548 Henry Cohn, 2026, needs more optimization.
3 714 0.990387021148 Henry Cohn, 2026, needs more optimization.
3 715 0.990399232663 Henry Cohn, 2026, needs more optimization.
3 716 0.990424201178 Henry Cohn, 2024.
3 717 0.990435742039 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 0.990511130593 Henry Cohn, 2026, needs more optimization.
3 724 0.990532198847 Henry Cohn, 2024.
3 725 0.990534529638 Henry Cohn, 2024.
3 726 0.990551400390 Henry Cohn, 2026, needs more optimization.
3 727 0.990566965324 Henry Cohn, 2024.
3 728 0.990571170880 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 0.990635128011 Henry Cohn, 2026, needs more optimization.
3 734 0.990652693601 Henry Cohn, 2026, needs more optimization.
3 735 0.990665859867 Henry Cohn, 2026.
3 736 0.990680033860 Henry Cohn, 2026.
3 737 0.990695306177 Henry Cohn, 2024.
3 738 0.990704677084 Henry Cohn, 2024.
3 739 0.990712804529 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 0.990786255878 Henry Cohn, 2026, needs more optimization.
3 746 0.990800147942 Henry Cohn, 2026, needs more optimization.
3 747 0.990816878553 Henry Cohn, 2024.
3 748 0.990825554974 Henry Cohn, 2026, needs more optimization.
3 749 0.990837968357 Henry Cohn, 2026.
3 750 0.990847475915 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.
3 751 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 0.990899134620 Henry Cohn, 2026, needs more optimization.
3 756 0.990921466258 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 0.991020015136 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 0.991092703929 Henry Cohn, 2026, needs more optimization.
3 772 0.991107834438 Henry Cohn, 2024.
3 773 0.991119133097 Henry Cohn, 2026.
3 774 0.991132071939 Henry Cohn, 2024.
3 775 0.991142880919 Henry Cohn, 2026, needs more optimization.
3 776 0.991154326426 Henry Cohn, 2026, needs more optimization.
3 777 0.991161697853 Henry Cohn, 2024.
3 778 0.991176107049 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 0.991215177221 Henry Cohn, 2026, needs more optimization.
3 783 0.991224998811 Henry Cohn, 2026, needs more optimization.
3 784 0.991237581418 Henry Cohn, 2024.
3 785 0.991246020182 Henry Cohn, 2026, needs more optimization.
3 786 0.991261576581 Henry Cohn, 2026.
3 787 0.991274864071 Henry Cohn, 2026, needs more optimization.
3 788 0.991285577631 Henry Cohn, 2026.
3 789 0.991288796383 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 0.991336046932 Henry Cohn, 2026, needs more optimization.
3 794 0.991351979642 Henry Cohn, 2026, needs more optimization.
3 795 0.991358759051 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 0.991404670857 Henry Cohn, 2026, needs more optimization.
3 800 0.991414851715 Henry Cohn, 2024.
3 801 0.991423316027 Henry Cohn, 2026, needs more optimization.
3 802 0.991434093044 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 0.991477473610 Henry Cohn, 2026, needs more optimization.
3 807 0.991488929993 Henry Cohn, 2024.
3 808 0.991499113412 Henry Cohn, 2026.
3 809 0.991512054441 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 0.991566962007 Henry Cohn, 2026, needs more optimization.
3 816 0.991580342934 Henry Cohn, 2024.
3 817 0.991591011326 Henry Cohn, 2024.
3 818 0.991597091498 Henry Cohn, 2026, needs more optimization.
3 819 0.991609552901 Henry Cohn, 2026, needs more optimization.
3 820 0.991624044122 Henry Cohn, 2024.
3 821 0.991630142697 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 0.991668700784 Henry Cohn, 2026, needs more optimization.
3 826 0.991679203409 Henry Cohn, 2026, needs more optimization.
3 827 0.991687082167 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 0.991746497985 Henry Cohn, 2026, needs more optimization.
3 834 0.991758792862 Henry Cohn, 2026.
3 835 0.991760362693 Henry Cohn, 2026, needs more optimization.
3 836 0.991770171617 Henry Cohn, 2026, needs more optimization.
3 837 0.991780503947 Henry Cohn, 2026.
3 838 0.991796901496 Henry Cohn, 2026, needs more optimization.
3 839 0.991804758597 Henry Cohn, 2026, needs more optimization.
3 840 0.991804766960 Henry Cohn, 2026, needs more optimization.
3 841 0.991814443516 Henry Cohn, 2026, needs more optimization.
3 842 0.991823489583 Henry Cohn, 2026, needs more optimization.
3 843 0.991831838925 Henry Cohn, 2026, needs more optimization.
3 844 0.991847905567 Henry Cohn, 2026, needs more optimization.
3 845 0.991854773658 Henry Cohn, 2026.
3 846 0.991861925048 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 0.991891189264 Henry Cohn, 2026, needs more optimization.
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 0.991917993656 Henry Cohn, 2026, needs more optimization.
3 854 0.991934894060 Henry Cohn, 2026, needs more optimization.
3 855 0.991948423912 Henry Cohn, 2026.
3 856 0.991959732459 Henry Cohn, 2026, needs more optimization.
3 857 0.991976233079 Henry Cohn, 2026, needs more optimization.
3 858 0.991987713948 Henry Cohn, 2026.
3 859 0.991994871145 Henry Cohn, 2026, needs more optimization.
3 860 0.992000220754 Henry Cohn, 2026.
3 861 0.992009501248 Henry Cohn, 2026, needs more optimization.
3 862 0.992019498595 Henry Cohn, 2026, needs more optimization.
3 863 0.992030946047 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 0.992079945563 Henry Cohn, 2026, needs more optimization.
3 869 0.992081499989 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 0.992124799921 Henry Cohn, 2026, needs more optimization.
3 875 0.992137558500 Henry Cohn, 2026.
3 876 0.992144394016 Henry Cohn, 2026, needs more optimization.
3 877 0.992154329715 Henry Cohn, 2025.
3 878 0.992163497065 Henry Cohn, 2026, needs more optimization.
3 879 0.992169048805 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 0.992205243450 Henry Cohn, 2026, needs more optimization.
3 884 0.992213792229 Henry Cohn, 2026, needs more optimization.
3 885 0.992223430817 Henry Cohn, 2026, needs more optimization.
3 886 0.992236374298 Henry Cohn, 2026.
3 887 0.992242382220 Henry Cohn, 2025.
3 888 0.992254765797 Henry Cohn, 2026, needs more optimization.
3 889 0.992263158186 Henry Cohn, 2026, needs more optimization.
3 890 0.992270277564 Henry Cohn, 2026, needs more optimization.
3 891 0.992282228896 Henry Cohn, 2026, needs more optimization.
3 892 0.992285856055 Henry Cohn, 2026.
3 893 0.992295938617 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 0.992359380332 Henry Cohn, 2026, needs more optimization.
3 902 0.992371998120 Henry Cohn, 2026, needs more optimization.
3 903 0.992381167272 Henry Cohn, 2026, needs more optimization.
3 904 0.992389884610 Henry Cohn, 2026, needs more optimization.
3 905 0.992399600923 Henry Cohn, 2026, needs more optimization.
3 906 0.992403008027 Henry Cohn, 2026, needs more optimization.
3 907 0.992414671348 Henry Cohn, 2026, needs more optimization.
3 908 0.992421147752 Henry Cohn, 2026, needs more optimization.
3 909 0.992428356067 Henry Cohn, 2026, needs more optimization.
3 910 0.992437123795 Henry Cohn, 2025.
3 911 0.992442944074 Henry Cohn, 2026.
3 912 0.992454600852 Henry Cohn, 2025.
3 913 0.992469409936 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 0.992505586908 Henry Cohn, 2026, needs more optimization.
3 919 0.992512397512 Henry Cohn, 2026.
3 920 0.992517498611 Henry Cohn, 2026.
3 921 0.992531088356 Henry Cohn, 2026, needs more optimization.
3 922 0.992534994238 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 0.992576722563 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 0.992611564654 Henry Cohn, 2026, needs more optimization.
3 933 0.992624602034 Henry Cohn, 2025.
3 934 0.992625562478 Henry Cohn, 2026, needs more optimization.
3 935 0.992636962822 Henry Cohn, 2026, needs more optimization.
3 936 0.992645528874 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 0.992698785176 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 0.992721619544 Henry Cohn, 2026, needs more optimization.
3 947 0.992726855397 Henry Cohn, 2026.
3 948 0.992731848428 Henry Cohn, 2026, needs more optimization.
3 949 0.992751074856 Henry Cohn, 2026.
3 950 0.992751415901 Henry Cohn, 2026, needs more optimization.
3 951 0.992759834272 Henry Cohn, 2026.
3 952 0.992771438024 Henry Cohn, 2025.
3 953 0.992777286390 Henry Cohn, 2026, needs more optimization.
3 954 0.992782542839 Henry Cohn, 2026, needs more optimization.
3 955 0.992790113965 Henry Cohn, 2026, needs more optimization.
3 956 0.992801093482 Henry Cohn, 2025.
3 957 0.992810004476 Henry Cohn, 2025.
3 958 0.992816897919 Henry Cohn, 2026, needs more optimization.
3 959 0.992823549807 Henry Cohn, 2026.
3 960 0.992829048036 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 0.992867450055 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 0.992900101770 Henry Cohn, 2026, needs more optimization.
3 971 0.992910234827 Henry Cohn, 2025.
3 972 0.992915598654 Henry Cohn, 2025.
3 973 0.992916191307 Henry Cohn, 2026, needs more optimization.
3 974 0.992924646469 Henry Cohn, 2026.
3 975 0.992931434432 Henry Cohn, 2026.
3 976 0.992939135834 Henry Cohn, 2026, needs more optimization.
3 977 0.992953433939 Henry Cohn, 2025.
3 978 0.992956414996 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 0.993045751650 Henry Cohn, 2025.
3 991 0.993048484035 Henry Cohn, 2026, needs more optimization.
3 992 0.993056523152 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 0.993082348997 Henry Cohn, 2026, needs more optimization.
3 997 0.993095076600 Henry Cohn, 2026, needs more optimization.
3 998 0.993095697499 Henry Cohn, 2026, needs more optimization.
3 999 0.993104406489 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 0.993135721387 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 0.993168698943 Henry Cohn, 2026, needs more optimization.
3 1010 0.993175003357 Henry Cohn, 2026, needs more optimization.
3 1011 0.993182202668 Henry Cohn, 2026, needs more optimization.
3 1012 0.993189191930 Henry Cohn, 2026, needs more optimization.
3 1013 0.993196507117 Henry Cohn, 2026, needs more optimization.
3 1014 0.993201606413 Henry Cohn, 2026, needs more optimization.
3 1015 0.993208460986 Henry Cohn, 2026, needs more optimization.
3 1016 0.993214865526 Henry Cohn, 2026, needs more optimization.
3 1017 0.993221389003 Henry Cohn, 2026, needs more optimization.
3 1018 0.993228968640 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 0.993243005702 Henry Cohn, 2026, needs more optimization.
3 1022 0.993250016189 Henry Cohn, 2026, needs more optimization.
3 1023 0.993256159915 Henry Cohn, 2026, needs more optimization.
3 1024 0.993262743306 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 0.784899018852 Henry Cohn, 2025.
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 0.807104890332 Henry Cohn, 2025.
4 106 0.807600771583 Henry Cohn, 2025.
4 107 0.808031793624 Henry Cohn, 2025.
4 108 0.808488610194 Henry Cohn, 2025.
4 109 0.808687291189 Henry Cohn, 2025.
4 110 0.808927278480 Henry Cohn, 2025.
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 0.824638011670 Henry Cohn, 2025.
4 122 0.826371365501 Henry Cohn, 2025.
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 0.833179391366 Henry Cohn, 2025.
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 0.848008139501 Henry Cohn, 2025.
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 0.856498246684 Henry Cohn, 2025.
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 0.859313343133 Henry Cohn, 2025.
4 169 0.860417510162 Henry Cohn, 2025.
4 170 0.861320274459 Henry Cohn, 2026.
4 171 0.861877205800 Henry Cohn, 2025.
4 172 0.862347282110 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 0.867174335033 Henry Cohn, 2025.
4 183 0.867335807322 Henry Cohn, 2025.
4 184 0.867763055785 Henry Cohn, 2025.
4 185 0.868215850425 Henry Cohn, 2026.
4 186 0.868518800651 Henry Cohn, 2025.
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 0.871341712847 Henry Cohn, 2025.
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 0.875066499628 Henry Cohn, 2026.
4 200 0.875686480655 Henry Cohn, 2025.
4 201 0.876289870766 Henry Cohn, 2026.
4 202 0.876662092953 Henry Cohn, 2025.
4 203 0.876807613055 Henry Cohn, 2026.
4 204 0.877193219688 Henry Cohn, 2026.
4 205 0.877534211883 Henry Cohn, 2025.
4 206 0.877831247728 Henry Cohn, 2025.
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 0.879586628106 Henry Cohn, 2025.
4 212 0.879653371881 Henry Cohn, 2026.
4 213 0.879817587919 Henry Cohn, 2026.
4 214 0.879945724274 Henry Cohn, 2025.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880902709084 Henry Cohn, 2026.
4 217 0.881535768813 Henry Cohn, 2025.
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 0.885323871301 Henry Cohn, 2026, needs more optimization.
4 227 0.885541386047 Henry Cohn, 2025.
4 228 0.885824040293 Henry Cohn, 2025.
4 229 0.886054621852 Henry Cohn, 2026, needs more optimization.
4 230 0.886372063295 Henry Cohn, 2025.
4 231 0.886803796459 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 0.887931434008 Henry Cohn, 2025.
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 0.889490760287 Henry Cohn, 2026, needs more optimization.
4 241 0.889886657931 Henry Cohn, 2025.
4 242 0.890234249504 Henry Cohn, 2025.
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 0.891998665833 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 0.893056431141 Henry Cohn, 2026, needs more optimization.
4 252 0.893324841746 Henry Cohn, 2026.
4 253 0.893448665997 Henry Cohn, 2026, needs more optimization.
4 254 0.893921415901 Henry Cohn, 2026.
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 0.894983025797 Henry Cohn, 2026, needs more optimization.
4 259 0.895408555760 Henry Cohn, 2026, needs more optimization.
4 260 0.895633158406 Henry Cohn, 2026.
4 261 0.895904728646 Henry Cohn, 2026, needs more optimization.
4 262 0.896205734599 Henry Cohn, 2026.
4 263 0.896400276225 Henry Cohn, 2026, needs more optimization.
4 264 0.896671845836 Henry Cohn, 2026.
4 265 0.896833096504 Henry Cohn, 2026, needs more optimization.
4 266 0.897010030544 Henry Cohn, 2026, needs more optimization.
4 267 0.897216331693 Henry Cohn, 2026, needs more optimization.
4 268 0.897341443704 Henry Cohn, 2026, needs more optimization.
4 269 0.897584249844 Henry Cohn, 2026, needs more optimization.
4 270 0.897722405122 Henry Cohn, 2026, needs more optimization.
4 271 0.897984717497 Henry Cohn, 2026, needs more optimization.
4 272 0.898196108609 Henry Cohn, 2026, needs more optimization.
4 273 0.898338831510 Henry Cohn, 2026, needs more optimization.
4 274 0.898507453079 Henry Cohn, 2026, needs more optimization.
4 275 0.898703285489 Henry Cohn, 2026, needs more optimization.
4 276 0.898990509891 Henry Cohn, 2026, needs more optimization.
4 277 0.899257716082 Henry Cohn, 2026, needs more optimization.
4 278 0.899399764294 Henry Cohn, 2026, needs more optimization.
4 279 0.899551098551 Henry Cohn, 2026, needs more optimization.
4 280 0.899640975210 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 0.901162008148 Henry Cohn, 2026, needs more optimization.
4 285 0.901208850582 Henry Cohn, 2026, needs more optimization.
4 286 0.901352037990 Henry Cohn, 2026, needs more optimization.
4 287 0.901408241003 Henry Cohn, 2026, needs more optimization.
4 288 0.901415628426 Henry Cohn, 2026, needs more optimization.
4 289 0.902147462122 Henry Cohn, 2026, needs more optimization.
4 290 0.902668032652 Henry Cohn, 2026, needs more optimization.
4 291 0.903108218652 Henry Cohn, 2026, needs more optimization.
4 292 0.903479788245 Henry Cohn, 2026, needs more optimization.
4 293 0.903762089966 Henry Cohn, 2026, needs more optimization.
4 294 0.903947280983 Henry Cohn, 2026, needs more optimization.
4 295 0.904226222560 Henry Cohn, 2026, needs more optimization.
4 296 0.904541783579 Henry Cohn, 2026, needs more optimization.
4 297 0.904746060747 Henry Cohn, 2026, needs more optimization.
4 298 0.904877270133 Henry Cohn, 2026, needs more optimization.
4 299 0.905146611996 Henry Cohn, 2026, needs more optimization.
4 300 0.905313494754 Henry Cohn, 2026, needs more optimization.
4 301 0.905597318680 Henry Cohn, 2026, needs more optimization.
4 302 0.905815767688 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 0.921184373600 Henry Cohn, 2026, needs more optimization.
4 400 0.921353549198 Henry Cohn, 2026, needs more optimization.
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 0.936670541912 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.
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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.
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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.
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4 584 0.939329798612 Henry Cohn, 2026, needs more optimization.
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4 587 0.939550383261 Henry Cohn, 2026, needs more optimization.
4 588 0.939559793000 Henry Cohn, 2026, needs more optimization.
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4 595 0.939917387324 Henry Cohn, 2026, needs more optimization.
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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.
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4 612 0.940999234162 Henry Cohn, 2026, needs more optimization.
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4 625 0.941838431002 Henry Cohn, 2026, needs more optimization.
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4 627 0.941998018942 Henry Cohn, 2026, needs more optimization.
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4 641 0.942876039843 Henry Cohn, 2026, needs more optimization.
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4 644 0.943073892703 Henry Cohn, 2026, needs more optimization.
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4 647 0.943207668875 Henry Cohn, 2026, needs more optimization.
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4 683 0.944832790327 Henry Cohn, 2026, needs more optimization.
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4 688 0.945215918865 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 0.945502815449 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 0.945721201559 Henry Cohn, 2026, needs more optimization.
4 696 0.945812268570 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 0.946788543187 Henry Cohn, 2026, needs more optimization.
4 715 0.946814487460 Henry Cohn, 2026, needs more optimization.
4 716 0.946822220619 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 0.947101547618 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 0.947204824714 Henry Cohn, 2026, needs more optimization.
4 727 0.947252653863 Henry Cohn, 2026, needs more optimization.
4 728 0.947309211212 Henry Cohn, 2026, needs more optimization.
4 729 0.947341100381 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 0.947676706000 Henry Cohn, 2026, needs more optimization.
4 739 0.947707474168 Henry Cohn, 2026, needs more optimization.
4 740 0.947738131287 Henry Cohn, 2026, needs more optimization.
4 741 0.947822685297 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 0.947997727674 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 0.948317587811 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 0.948420326896 Henry Cohn, 2026, needs more optimization.
4 757 0.948469628121 Henry Cohn, 2026, needs more optimization.
4 758 0.948528431153 Henry Cohn, 2026, needs more optimization.
4 759 0.948556622265 Henry Cohn, 2026, needs more optimization.
4 760 0.948640911164 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 0.948840737744 Henry Cohn, 2026, needs more optimization.
4 765 0.948849334885 Henry Cohn, 2026, needs more optimization.
4 766 0.948910026012 Henry Cohn, 2026, needs more optimization.
4 767 0.948941771118 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 0.949098906560 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 0.949228913632 Henry Cohn, 2026, needs more optimization.
4 774 0.949298593935 Henry Cohn, 2026, needs more optimization.
4 775 0.949335160224 Henry Cohn, 2026, needs more optimization.
4 776 0.949366078418 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 0.949499055777 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 0.949545767956 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 0.949821936952 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 0.949937433690 Henry Cohn, 2026, needs more optimization.
4 793 0.949989750186 Henry Cohn, 2026, needs more optimization.
4 794 0.949990996985 Henry Cohn, 2026, needs more optimization.
4 795 0.950018077494 Henry Cohn, 2026, needs more optimization.
4 796 0.950052272705 Henry Cohn, 2026, needs more optimization.
4 797 0.950071960003 Henry Cohn, 2026, needs more optimization.
4 798 0.950090336964 Henry Cohn, 2026, needs more optimization.
4 799 0.950137129360 Henry Cohn, 2026, needs more optimization.
4 800 0.950162327666 Henry Cohn, 2026, needs more optimization.
4 801 0.950164850476 Henry Cohn, 2026, needs more optimization.
4 802 0.950168450827 Henry Cohn, 2026, needs more optimization.
4 803 0.950212243578 Henry Cohn, 2026, needs more optimization.
4 804 0.950237932324 Henry Cohn, 2026, needs more optimization.
4 805 0.950268737989 Henry Cohn, 2026, needs more optimization.
4 806 0.950296520661 Henry Cohn, 2026, needs more optimization.
4 807 0.950314407050 Henry Cohn, 2026, needs more optimization.
4 808 0.950365117534 Henry Cohn, 2026, needs more optimization.
4 809 0.950366408762 Henry Cohn, 2026, needs more optimization.
4 810 0.950415319981 Henry Cohn, 2026, needs more optimization.
4 811 0.950418597636 Henry Cohn, 2026, needs more optimization.
4 812 0.950466101888 Henry Cohn, 2026, needs more optimization.
4 813 0.950486450299 Henry Cohn, 2026, needs more optimization.
4 814 0.950519507929 Henry Cohn, 2026, needs more optimization.
4 815 0.950522924790 Henry Cohn, 2026, needs more optimization.
4 816 0.950548368615 Henry Cohn, 2026, needs more optimization.
4 817 0.950562564196 Henry Cohn, 2026, needs more optimization.
4 818 0.950567855728 Henry Cohn, 2026, needs more optimization.
4 819 0.950571143365 Henry Cohn, 2026, needs more optimization.
4 820 0.950600399066 Henry Cohn, 2026, needs more optimization.
4 821 0.950613132539 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 0.950783672506 Henry Cohn, 2026, needs more optimization.
4 825 0.950784234601 Henry Cohn, 2026, needs more optimization.
4 826 0.950785037965 Henry Cohn, 2026, needs more optimization.
4 827 0.950785992625 Henry Cohn, 2026, needs more optimization.
4 828 0.950786501723 Henry Cohn, 2026, needs more optimization.
4 829 0.950787414175 Henry Cohn, 2026, needs more optimization.
4 830 0.950788870796 Henry Cohn, 2026, needs more optimization.
4 831 0.950790865322 Henry Cohn, 2026, needs more optimization.
4 832 0.950791781680 Henry Cohn, 2026, needs more optimization.
4 833 0.950791870889 Henry Cohn, 2026, needs more optimization.
4 834 0.950793565414 Henry Cohn, 2026, needs more optimization.
4 835 0.950794471947 Henry Cohn, 2026, needs more optimization.
4 836 0.950795413157 Henry Cohn, 2026, needs more optimization.
4 837 0.950795677351 Henry Cohn, 2026, needs more optimization.
4 838 0.950796998582 Henry Cohn, 2026, needs more optimization.
4 840 0.950797547280 Henry Cohn, 2025, needs more optimization.
4 841 0.950955648144 Henry Cohn, 2026, needs more optimization.
4 842 0.951052062313 Henry Cohn, 2026, needs more optimization.
4 843 0.951118475901 Henry Cohn, 2026, needs more optimization.
4 844 0.951235550244 Henry Cohn, 2026, needs more optimization.
4 845 0.951287707295 Henry Cohn, 2026, needs more optimization.
4 846 0.951404214537 Henry Cohn, 2026, needs more optimization.
4 847 0.951467821148 Henry Cohn, 2026, needs more optimization.
4 848 0.951552114074 Henry Cohn, 2026, needs more optimization.
4 849 0.951612720239 Henry Cohn, 2026, needs more optimization.
4 850 0.951689389223 Henry Cohn, 2026, needs more optimization.
4 851 0.951797684087 Henry Cohn, 2026, needs more optimization.
4 852 0.951836726287 Henry Cohn, 2026, needs more optimization.
4 853 0.951908221851 Henry Cohn, 2026, needs more optimization.
4 854 0.951987051546 Henry Cohn, 2026, needs more optimization.
4 855 0.952036941947 Henry Cohn, 2026, needs more optimization.
4 856 0.952135299987 Henry Cohn, 2026, needs more optimization.
4 857 0.952191618329 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 0.952374309723 Henry Cohn, 2026, needs more optimization.
4 861 0.952476139491 Henry Cohn, 2026, needs more optimization.
4 862 0.952489029549 Henry Cohn, 2026, needs more optimization.
4 863 0.952569830310 Henry Cohn, 2026, needs more optimization.
4 864 0.952616760577 Henry Cohn, 2026, needs more optimization.
4 865 0.952690554913 Henry Cohn, 2026, needs more optimization.
4 866 0.952773092049 Henry Cohn, 2026, needs more optimization.
4 867 0.952837166259 Henry Cohn, 2026, needs more optimization.
4 868 0.952844089566 Henry Cohn, 2026, needs more optimization.
4 869 0.952844882392 Henry Cohn, 2026, needs more optimization.
4 870 0.952849002283 Henry Cohn, 2026, needs more optimization.
4 871 0.952872338516 Henry Cohn, 2026, needs more optimization.
4 872 0.952917907875 Henry Cohn, 2026, needs more optimization.
4 873 0.952950755488 Henry Cohn, 2026, needs more optimization.
4 874 0.952962427453 Henry Cohn, 2026, needs more optimization.
4 875 0.953000535577 Henry Cohn, 2026, needs more optimization.
4 876 0.953014226290 Henry Cohn, 2026, needs more optimization.
4 877 0.953069172989 Henry Cohn, 2026, needs more optimization.
4 878 0.953112695671 Henry Cohn, 2026, needs more optimization.
4 879 0.953154681075 Henry Cohn, 2026, needs more optimization.
4 880 0.953172076511 Henry Cohn, 2026, needs more optimization.
4 881 0.953218919758 Henry Cohn, 2026, needs more optimization.
4 882 0.953261994346 Henry Cohn, 2026, needs more optimization.
4 883 0.953292381315 Henry Cohn, 2026, needs more optimization.
4 884 0.953301932273 Henry Cohn, 2026, needs more optimization.
4 885 0.953337203181 Henry Cohn, 2026, needs more optimization.
4 886 0.953394160874 Henry Cohn, 2026, needs more optimization.
4 887 0.953416891638 Henry Cohn, 2026, needs more optimization.
4 888 0.953422239756 Henry Cohn, 2026, needs more optimization.
4 889 0.953473089597 Henry Cohn, 2026, needs more optimization.
4 890 0.953542161707 Henry Cohn, 2026, needs more optimization.
4 891 0.953577463762 Henry Cohn, 2026, needs more optimization.
4 892 0.953594208115 Henry Cohn, 2026, needs more optimization.
4 893 0.953641878032 Henry Cohn, 2026, needs more optimization.
4 894 0.953641880786 Henry Cohn, 2026, needs more optimization.
4 895 0.953696463190 Henry Cohn, 2026, needs more optimization.
4 896 0.953697563559 Henry Cohn, 2026, needs more optimization.
4 897 0.953714094510 Henry Cohn, 2026, needs more optimization.
4 898 0.953776146418 Henry Cohn, 2026, needs more optimization.
4 899 0.953783740464 Henry Cohn, 2026, needs more optimization.
4 900 0.953839740761 Henry Cohn, 2026, needs more optimization.
4 901 0.953855632936 Henry Cohn, 2026, needs more optimization.
4 902 0.953892134802 Henry Cohn, 2026, needs more optimization.
4 903 0.953932291069 Henry Cohn, 2026, needs more optimization.
4 904 0.953972653700 Henry Cohn, 2026, needs more optimization.
4 905 0.954046618433 Henry Cohn, 2026, needs more optimization.
4 906 0.954083682650 Henry Cohn, 2026, needs more optimization.
4 907 0.954116981720 Henry Cohn, 2026, needs more optimization.
4 908 0.954119171799 Henry Cohn, 2026, needs more optimization.
4 909 0.954120178168 Henry Cohn, 2026, needs more optimization.
4 910 0.954139390169 Henry Cohn, 2026, needs more optimization.
4 911 0.954148151810 Henry Cohn, 2026, needs more optimization.
4 912 0.954156238395 Henry Cohn, 2026, needs more optimization.
4 913 0.954158076169 Henry Cohn, 2026, needs more optimization.
4 914 0.954189277276 Henry Cohn, 2026, needs more optimization.
4 915 0.954211932743 Henry Cohn, 2026, needs more optimization.
4 916 0.954241497440 Henry Cohn, 2026, needs more optimization.
4 917 0.954300040812 Henry Cohn, 2026, needs more optimization.
4 918 0.954336131435 Henry Cohn, 2026, needs more optimization.
4 919 0.954387122733 Henry Cohn, 2026, needs more optimization.
4 920 0.954436260169 Henry Cohn, 2026, needs more optimization.
4 921 0.954439554001 Henry Cohn, 2026, needs more optimization.
4 922 0.954485741907 Henry Cohn, 2026, needs more optimization.
4 923 0.954545891532 Henry Cohn, 2026, needs more optimization.
4 924 0.954586511643 Henry Cohn, 2026, needs more optimization.
4 925 0.954611986356 Henry Cohn, 2026, needs more optimization.
4 926 0.954615840237 Henry Cohn, 2026, needs more optimization.
4 927 0.954675205958 Henry Cohn, 2026, needs more optimization.
4 928 0.954733765794 Henry Cohn, 2026, needs more optimization.
4 929 0.954784500901 Henry Cohn, 2026, needs more optimization.
4 930 0.954827119605 Henry Cohn, 2026, needs more optimization.
4 931 0.954892633205 Henry Cohn, 2026, needs more optimization.
4 932 0.954920625772 Henry Cohn, 2026, needs more optimization.
4 933 0.955008682083 Henry Cohn, 2026, needs more optimization.
4 934 0.955010487590 Henry Cohn, 2026, needs more optimization.
4 935 0.955019221900 Henry Cohn, 2026, needs more optimization.
4 936 0.955077651638 Henry Cohn, 2026, needs more optimization.
4 937 0.955098604541 Henry Cohn, 2026, needs more optimization.
4 938 0.955131409543 Henry Cohn, 2026, needs more optimization.
4 939 0.955145153269 Henry Cohn, 2026, needs more optimization.
4 940 0.955164701600 Henry Cohn, 2026, needs more optimization.
4 941 0.955208533343 Henry Cohn, 2026, needs more optimization.
4 942 0.955247926715 Henry Cohn, 2026, needs more optimization.
4 943 0.955275664530 Henry Cohn, 2026, needs more optimization.
4 944 0.955321294402 Henry Cohn, 2026, needs more optimization.
4 945 0.955348985018 Henry Cohn, 2026, needs more optimization.
4 946 0.955389214870 Henry Cohn, 2026, needs more optimization.
4 947 0.955396688631 Henry Cohn, 2026, needs more optimization.
4 948 0.955463995553 Henry Cohn, 2026, needs more optimization.
4 949 0.955495987881 Henry Cohn, 2026, needs more optimization.
4 950 0.955541503868 Henry Cohn, 2026, needs more optimization.
4 951 0.955545110942 Henry Cohn, 2026, needs more optimization.
4 952 0.955547728712 Henry Cohn, 2026, needs more optimization.
4 954 0.955568075817 Henry Cohn, 2026, needs more optimization.
4 955 0.955597841157 Henry Cohn, 2026, needs more optimization.
4 956 0.955645740001 Henry Cohn, 2026, needs more optimization.
4 957 0.955649494495 Henry Cohn, 2026, needs more optimization.
4 958 0.955683940906 Henry Cohn, 2026, needs more optimization.
4 959 0.955725688876 Henry Cohn, 2026, needs more optimization.
4 960 0.955787000120 Henry Cohn, 2026, needs more optimization.
4 961 0.955903058305 Henry Cohn, 2026, needs more optimization.
4 962 0.955915274279 Henry Cohn, 2026, needs more optimization.
4 963 0.955922055690 Henry Cohn, 2026, needs more optimization.
4 964 0.956031053373 Henry Cohn, 2026, needs more optimization.
4 965 0.956049323288 Henry Cohn, 2026, needs more optimization.
4 966 0.956072726092 Henry Cohn, 2026, needs more optimization.
4 967 0.956078910481 Henry Cohn, 2026, needs more optimization.
4 968 0.956088564323 Henry Cohn, 2026, needs more optimization.
4 969 0.956105234503 Henry Cohn, 2026, needs more optimization.
4 970 0.956120519679 Henry Cohn, 2026, needs more optimization.
4 971 0.956127800420 Henry Cohn, 2026, needs more optimization.
4 972 0.956149363741 Henry Cohn, 2026, needs more optimization.
4 973 0.956164229033 Henry Cohn, 2026, needs more optimization.
4 974 0.956173152719 Henry Cohn, 2026, needs more optimization.
4 975 0.956188074138 Henry Cohn, 2026, needs more optimization.
4 976 0.956227055056 Henry Cohn, 2026, needs more optimization.
4 977 0.956298552339 Henry Cohn, 2026, needs more optimization.
4 978 0.956306186233 Henry Cohn, 2026, needs more optimization.
4 979 0.956335659912 Henry Cohn, 2026, needs more optimization.
4 980 0.956379507689 Henry Cohn, 2026, needs more optimization.
4 981 0.956447936290 Henry Cohn, 2026, needs more optimization.
4 982 0.956447951112 Henry Cohn, 2026, needs more optimization.
4 983 0.956519066201 Henry Cohn, 2026, needs more optimization.
4 984 0.956638909119 Henry Cohn, 2026, needs more optimization.
4 985 0.956642063244 Henry Cohn, 2026, needs more optimization.
4 986 0.956657962080 Henry Cohn, 2026, needs more optimization.
4 987 0.956658904829 Henry Cohn, 2026, needs more optimization.
4 988 0.956664711435 Henry Cohn, 2026, needs more optimization.
4 989 0.956718208510 Henry Cohn, 2026, needs more optimization.
4 990 0.956774892016 Henry Cohn, 2026, needs more optimization.
4 991 0.956834011764 Henry Cohn, 2026, needs more optimization.
4 992 0.956878283969 Henry Cohn, 2026, needs more optimization.
4 993 0.956950286327 Henry Cohn, 2026, needs more optimization.
4 994 0.956981150628 Henry Cohn, 2026, needs more optimization.
4 995 0.957034687604 Henry Cohn, 2026, needs more optimization.
4 996 0.957060051341 Henry Cohn, 2026, needs more optimization.
4 997 0.957126476698 Henry Cohn, 2026, needs more optimization.
4 998 0.957148536933 Henry Cohn, 2026, needs more optimization.
4 999 0.957195815316 Henry Cohn, 2026, needs more optimization.
4 1000 0.957241281845 Henry Cohn, 2026, needs more optimization.
4 1001 0.957259283408 Henry Cohn, 2026, needs more optimization.
4 1002 0.957293627063 Henry Cohn, 2026, needs more optimization.
4 1003 0.957338851184 Henry Cohn, 2026, needs more optimization.
4 1004 0.957354812486 Henry Cohn, 2026, needs more optimization.
4 1005 0.957373564300 Henry Cohn, 2026, needs more optimization.
4 1006 0.957379507560 Henry Cohn, 2026, needs more optimization.
4 1007 0.957395777274 Henry Cohn, 2026, needs more optimization.
4 1008 0.957445945067 Henry Cohn, 2026, needs more optimization.
4 1009 0.957468080801 Henry Cohn, 2026, needs more optimization.
4 1011 0.957476083617 Henry Cohn, 2026, needs more optimization.
4 1012 0.957516973546 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 0.957635683926 Henry Cohn, 2026, needs more optimization.
4 1016 0.957663308174 Henry Cohn, 2026, needs more optimization.
4 1017 0.957673525651 Henry Cohn, 2026, needs more optimization.
4 1018 0.957717244077 Henry Cohn, 2026, needs more optimization.
4 1019 0.957740842320 Henry Cohn, 2026, needs more optimization.
4 1020 0.957756564847 Henry Cohn, 2026, needs more optimization.
4 1021 0.957779273338 Henry Cohn, 2026, needs more optimization.
4 1022 0.957786481135 Henry Cohn, 2026, needs more optimization.
4 1023 0.957843444734 Henry Cohn, 2026, needs more optimization.
4 1024 0.957881992874 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 0.673631229212 Henry Cohn, 2026.
5 94 0.674852218199 Henry Cohn, 2026.
5 95 0.676048898306 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 0.688903541719 Henry Cohn, 2025.
5 104 0.689715870633 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 105 0.690713474104 Henry Cohn, 2025.
5 106 0.692005491905 Henry Cohn, 2025.
5 107 0.693863512900 Henry Cohn, 2025.
5 108 0.695352226010 Henry Cohn, 2025.
5 109 0.696434500115 Henry Cohn, 2025.
5 110 0.698102767792 Henry Cohn, 2025.
5 111 0.699314990430 Henry Cohn, 2025.
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 0.703016293967 Henry Cohn, 2025.
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 0.709336098101 Henry Cohn, 2025.
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 0.717125378112 Henry Cohn, 2025.
5 127 0.718593652896 Henry Cohn, 2025.
5 128 0.719621301444 Henry Cohn, 2025.
5 129 0.720947646950 Henry Cohn, 2025.
5 130 0.721711816020 Henry Cohn, 2025.
5 131 0.723208608895 Henry Cohn, 2025.
5 132 0.724187140976 Henry Cohn, 2026, needs more optimization.
5 133 0.725083698449 Henry Cohn, 2026, needs more optimization.
5 134 0.726667479410 Henry Cohn, 2026, needs more optimization.
5 135 0.727819930944 Henry Cohn, 2025.
5 136 0.728641959070 Henry Cohn, 2026.
5 137 0.729817090478 Henry Cohn, 2026, needs more optimization.
5 138 0.730143082796 Henry Cohn, 2025.
5 139 0.731003426111 Henry Cohn, 2026, needs more optimization.
5 140 0.731880138963 Henry Cohn, 2025.
5 141 0.732919531483 Henry Cohn, 2026, needs more optimization.
5 142 0.733688627543 Henry Cohn, 2025.
5 143 0.734506087652 Henry Cohn, 2025.
5 144 0.735189318066 Henry Cohn, 2025.
5 145 0.736519094966 Henry Cohn, 2025.
5 146 0.736648368146 Henry Cohn, 2025.
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 0.739520322612 Henry Cohn, 2026, needs more optimization.
5 152 0.739824519106 Henry Cohn, 2025.
5 153 0.740779971316 Henry Cohn, 2025.
5 154 0.741354012157 Henry Cohn, 2025.
5 155 0.742161234709 Henry Cohn, 2025.
5 156 0.742808811623 Henry Cohn, 2025.
5 157 0.743339290160 Henry Cohn, 2025.
5 158 0.743483872286 Henry Cohn, 2026, needs more optimization.
5 159 0.743825044322 Henry Cohn, 2025.
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 0.752079878060 Henry Cohn, 2025.
5 166 0.752534073395 Henry Cohn, 2025.
5 167 0.753532673949 Henry Cohn, 2025.
5 168 0.754218675211 Henry Cohn, 2025.
5 169 0.755416175364 Henry Cohn, 2025.
5 170 0.755993792807 Henry Cohn, 2025.
5 171 0.756800051039 Henry Cohn, 2025.
5 172 0.757288355849 Henry Cohn, 2025.
5 173 0.758578456997 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 0.762581477591 Henry Cohn, 2026, needs more optimization.
5 178 0.763315108223 Henry Cohn, 2025.
5 179 0.763488321703 Henry Cohn, 2026, needs more optimization.
5 180 0.763782659007 Henry Cohn, 2026, needs more optimization.
5 181 0.764588361139 Henry Cohn, 2026, needs more optimization.
5 182 0.765129428834 Henry Cohn, 2026, needs more optimization.
5 183 0.765582256053 Henry Cohn, 2026, needs more optimization.
5 184 0.766275380478 Henry Cohn, 2026, needs more optimization.
5 185 0.766829614240 Henry Cohn, 2026, needs more optimization.
5 186 0.767264937530 Henry Cohn, 2026, needs more optimization.
5 187 0.767582500943 Henry Cohn, 2026, needs more optimization.
5 188 0.768330423732 Henry Cohn, 2026, needs more optimization.
5 189 0.768905500729 Henry Cohn, 2026, needs more optimization.
5 190 0.769546640524 Henry Cohn, 2026, needs more optimization.
5 191 0.770386212083 Henry Cohn, 2026, needs more optimization.
5 192 0.771106184958 Henry Cohn, 2026, needs more optimization.
5 193 0.771226136269 Henry Cohn, 2026, needs more optimization.
5 194 0.772151567093 Henry Cohn, 2026, needs more optimization.
5 195 0.772914025091 Henry Cohn, 2025.
5 196 0.773686897647 Henry Cohn, 2026, needs more optimization.
5 197 0.774037588454 Henry Cohn, 2026, needs more optimization.
5 198 0.774735751022 Henry Cohn, 2026, needs more optimization.
5 199 0.774965878187 Henry Cohn, 2026, needs more optimization.
5 200 0.775317457485 Henry Cohn, 2026, needs more optimization.
5 201 0.775894526514 Henry Cohn, 2026, needs more optimization.
5 202 0.776519699323 Henry Cohn, 2026, needs more optimization.
5 203 0.777286853917 Henry Cohn, 2026, needs more optimization.
5 204 0.777718595433 Henry Cohn, 2026, needs more optimization.
5 205 0.778247356661 Henry Cohn, 2026, needs more optimization.
5 206 0.778902121381 Henry Cohn, 2026, needs more optimization.
5 207 0.779361491430 Henry Cohn, 2026, needs more optimization.
5 208 0.779871323775 Henry Cohn, 2026, needs more optimization.
5 209 0.780497353055 Henry Cohn, 2026, needs more optimization.
5 210 0.780972884880 Henry Cohn, 2026, needs more optimization.
5 211 0.781577235609 Henry Cohn, 2026, needs more optimization.
5 212 0.782104147835 Henry Cohn, 2026, needs more optimization.
5 213 0.782728089506 Henry Cohn, 2026, needs more optimization.
5 214 0.783324929074 Henry Cohn, 2026, needs more optimization.
5 215 0.784002728427 Henry Cohn, 2026, needs more optimization.
5 216 0.784470709123 Henry Cohn, 2026, needs more optimization.
5 217 0.784896362259 Henry Cohn, 2026, needs more optimization.
5 218 0.785309143586 Henry Cohn, 2026, needs more optimization.
5 219 0.785853798043 Henry Cohn, 2026, needs more optimization.
5 220 0.786439607116 Henry Cohn, 2026, needs more optimization.
5 221 0.787120053839 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.
5 222 0.787731314659 Henry Cohn, 2026, needs more optimization.
5 223 0.788033436847 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.
5 224 0.788594800376 Henry Cohn, 2026, needs more optimization.
5 225 0.788927248197 Henry Cohn, 2026, needs more optimization.
5 226 0.789386581450 Henry Cohn, 2026, needs more optimization.
5 227 0.789663036137 Henry Cohn, 2026, needs more optimization.
5 228 0.790347264741 Henry Cohn, 2026, needs more optimization.
5 229 0.790590516829 Henry Cohn, 2026, needs more optimization.
5 230 0.790972585384 Henry Cohn, 2026, needs more optimization.
5 231 0.791480810351 Henry Cohn, 2026, needs more optimization.
5 232 0.792366038620 Henry Cohn, 2026, needs more optimization.
5 233 0.792634070102 Henry Cohn, 2026, needs more optimization.
5 234 0.792916668663 Henry Cohn, 2026, needs more optimization.
5 235 0.793372157350 Henry Cohn, 2026, needs more optimization.
5 236 0.793997898780 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 0.796357275110 Henry Cohn, 2026, needs more optimization.
5 243 0.796601631484 Henry Cohn, 2026, needs more optimization.
5 244 0.796898445762 Henry Cohn, 2026, needs more optimization.
5 245 0.797264978189 Henry Cohn, 2026, needs more optimization.
5 246 0.797740685154 Henry Cohn, 2026, needs more optimization.
5 247 0.797961068192 Henry Cohn, 2026, needs more optimization.
5 248 0.798549025930 Henry Cohn, 2026, needs more optimization.
5 249 0.798774889917 Henry Cohn, 2026, needs more optimization.
5 250 0.798942711861 Henry Cohn, 2026, needs more optimization.
5 251 0.799360589750 Henry Cohn, 2026, needs more optimization.
5 252 0.799655743307 Henry Cohn, 2026, needs more optimization.
5 253 0.800146780510 Henry Cohn, 2026, needs more optimization.
5 254 0.800361565067 Henry Cohn, 2026, needs more optimization.
5 255 0.800622899209 Henry Cohn, 2026, needs more optimization.
5 256 0.801104406643 Henry Cohn, 2026, needs more optimization.
5 257 0.801507262095 Henry Cohn, 2026, needs more optimization.
5 258 0.801975757066 Henry Cohn, 2026, needs more optimization.
5 259 0.802392535257 Henry Cohn, 2026, needs more optimization.
5 260 0.802825045012 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 0.803880217748 Henry Cohn, 2026, needs more optimization.
5 264 0.804081182594 Henry Cohn, 2026, needs more optimization.
5 265 0.804461873167 Henry Cohn, 2026, needs more optimization.
5 266 0.804570277310 Henry Cohn, 2026, needs more optimization.
5 267 0.804872949246 Henry Cohn, 2026, needs more optimization.
5 268 0.805063737167 Henry Cohn, 2026, needs more optimization.
5 269 0.805323879173 Henry Cohn, 2026, needs more optimization.
5 270 0.805497289899 Henry Cohn, 2026, needs more optimization.
5 271 0.805737892270 Henry Cohn, 2026, needs more optimization.
5 272 0.805999314314 Henry Cohn, 2026, needs more optimization.
5 273 0.806034506816 Henry Cohn, 2026, needs more optimization.
5 274 0.806099575012 Henry Cohn, 2026, needs more optimization.
5 275 0.806247499196 Henry Cohn, 2026, needs more optimization.
5 276 0.806327563861 Henry Cohn, 2026, needs more optimization.
5 277 0.806496995009 Henry Cohn, 2026, needs more optimization.
5 278 0.806697926439 Henry Cohn, 2026, needs more optimization.
5 279 0.806779417294 Henry Cohn, 2026, needs more optimization.
5 280 0.807055737375 Henry Cohn, 2026, needs more optimization.
5 281 0.807116873412 Henry Cohn, 2026, needs more optimization.
5 282 0.807160196460 Henry Cohn, 2026, needs more optimization.
5 283 0.807741790346 Henry Cohn, 2026, needs more optimization.
5 284 0.808229711311 Henry Cohn, 2026, needs more optimization.
5 285 0.808652880685 Henry Cohn, 2026, needs more optimization.
5 286 0.809185175075 Henry Cohn, 2026, needs more optimization.
5 287 0.809590215780 Henry Cohn, 2026, needs more optimization.
5 288 0.810241325830 Henry Cohn, 2026, needs more optimization.
5 289 0.810467358660 Henry Cohn, 2026, needs more optimization.
5 290 0.811081555913 Henry Cohn, 2026, needs more optimization.
5 291 0.811567080954 Henry Cohn, 2026, needs more optimization.
5 292 0.812208837819 Henry Cohn, 2026, needs more optimization.
5 293 0.812702082856 Henry Cohn, 2026, needs more optimization.
5 294 0.813139769562 Henry Cohn, 2026, needs more optimization.
5 295 0.813586354352 Henry Cohn, 2026, needs more optimization.
5 296 0.813997556325 Henry Cohn, 2026, needs more optimization.
5 297 0.814424999584 Henry Cohn, 2026, needs more optimization.
5 298 0.815067997631 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 0.842486928652 Henry Cohn, 2026, needs more optimization.
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 0.859506675580 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 0.864134034140 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 0.865276087560 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 0.869108272730 Henry Cohn, 2026, needs more optimization.
5 580 0.869303939159 Henry Cohn, 2026, needs more optimization.
5 581 0.869444873482 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 0.870421093997 Henry Cohn, 2026, needs more optimization.
5 593 0.870576290268 Henry Cohn, 2026, needs more optimization.
5 594 0.870725741504 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 0.871204563133 Henry Cohn, 2026, needs more optimization.
5 599 0.871263185671 Henry Cohn, 2026, needs more optimization.
5 600 0.871357840641 Henry Cohn, 2026, needs more optimization.
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 0.871760304053 Henry Cohn, 2026, needs more optimization.
5 606 0.871839378886 Henry Cohn, 2026, needs more optimization.
5 607 0.871971878702 Henry Cohn, 2026, needs more optimization.
5 608 0.872051497455 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 0.873038824110 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 0.873776310632 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 0.874259146941 Henry Cohn, 2026, needs more optimization.
5 629 0.874405130686 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 0.874890832233 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 0.875214858697 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 0.877332150868 Henry Cohn, 2026, needs more optimization.
5 660 0.877435126829 Henry Cohn, 2026, needs more optimization.
5 661 0.877449204378 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 0.877924680748 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 0.878368862862 Henry Cohn, 2026, needs more optimization.
5 672 0.878443281857 Henry Cohn, 2026, needs more optimization.
5 673 0.878534099642 Henry Cohn, 2026, needs more optimization.
5 674 0.878648219049 Henry Cohn, 2026, needs more optimization.
5 675 0.878671865592 Henry Cohn, 2026, needs more optimization.
5 676 0.878772517655 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 0.879349432604 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 0.879567542316 Henry Cohn, 2026, needs more optimization.
5 686 0.879607043385 Henry Cohn, 2026, needs more optimization.
5 687 0.879826163825 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 0.880547758545 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 0.881068336545 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 0.881730058192 Henry Cohn, 2026, needs more optimization.
5 711 0.881787957298 Henry Cohn, 2026, needs more optimization.
5 712 0.881857943027 Henry Cohn, 2026, needs more optimization.
5 713 0.881947794183 Henry Cohn, 2026, needs more optimization.
5 714 0.882026898858 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 0.882308606501 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 0.882717123713 Henry Cohn, 2026, needs more optimization.
5 723 0.882809088468 Henry Cohn, 2026, needs more optimization.
5 724 0.882892187293 Henry Cohn, 2026, needs more optimization.
5 725 0.882970832072 Henry Cohn, 2026, needs more optimization.
5 726 0.883100301240 Henry Cohn, 2026, needs more optimization.
5 727 0.883129795275 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 0.883341789181 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 0.883725877896 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 0.884395851907 Henry Cohn, 2026, needs more optimization.
5 743 0.884509413333 Henry Cohn, 2026, needs more optimization.
5 744 0.884613154581 Henry Cohn, 2026, needs more optimization.
5 745 0.884661292296 Henry Cohn, 2026, needs more optimization.
5 746 0.884751144796 Henry Cohn, 2026, needs more optimization.
5 747 0.884824317638 Henry Cohn, 2026, needs more optimization.
5 748 0.884911852468 Henry Cohn, 2026, needs more optimization.
5 749 0.884967176920 Henry Cohn, 2026, needs more optimization.
5 750 0.885020872585 Henry Cohn, 2026, needs more optimization.
5 751 0.885121977133 Henry Cohn, 2026, needs more optimization.
5 752 0.885182869690 Henry Cohn, 2026, needs more optimization.
5 753 0.885220115807 Henry Cohn, 2026, needs more optimization.
5 754 0.885313789673 Henry Cohn, 2026, needs more optimization.
5 755 0.885361583651 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 0.885579574423 Henry Cohn, 2026, needs more optimization.
5 759 0.885619098377 Henry Cohn, 2026, needs more optimization.
5 760 0.885674207704 Henry Cohn, 2026, needs more optimization.
5 761 0.885792354988 Henry Cohn, 2026, needs more optimization.
5 762 0.885852291781 Henry Cohn, 2026, needs more optimization.
5 763 0.885935010585 Henry Cohn, 2026, needs more optimization.
5 764 0.886055073269 Henry Cohn, 2026, needs more optimization.
5 765 0.886147678316 Henry Cohn, 2026, needs more optimization.
5 766 0.886224626533 Henry Cohn, 2026, needs more optimization.
5 767 0.886257305017 Henry Cohn, 2026, needs more optimization.
5 768 0.886276949978 Henry Cohn, 2026, needs more optimization.
5 769 0.886326447651 Henry Cohn, 2026, needs more optimization.
5 770 0.886396284630 Henry Cohn, 2026, needs more optimization.
5 771 0.886478203163 Henry Cohn, 2026, needs more optimization.
5 772 0.886552860977 Henry Cohn, 2026, needs more optimization.
5 773 0.886629364733 Henry Cohn, 2026, needs more optimization.
5 774 0.886729041790 Henry Cohn, 2026, needs more optimization.
5 775 0.886817030311 Henry Cohn, 2026, needs more optimization.
5 776 0.886926791056 Henry Cohn, 2026, needs more optimization.
5 777 0.886938306580 Henry Cohn, 2026, needs more optimization.
5 778 0.887039286400 Henry Cohn, 2026, needs more optimization.
5 779 0.887106887598 Henry Cohn, 2026, needs more optimization.
5 780 0.887255942191 Henry Cohn, 2026, needs more optimization.
5 781 0.887275270502 Henry Cohn, 2026, needs more optimization.
5 782 0.887277942631 Henry Cohn, 2026, needs more optimization.
5 783 0.887327485987 Henry Cohn, 2026, needs more optimization.
5 784 0.887399638692 Henry Cohn, 2026, needs more optimization.
5 785 0.887468768246 Henry Cohn, 2026, needs more optimization.
5 786 0.887523755388 Henry Cohn, 2026, needs more optimization.
5 787 0.887642165907 Henry Cohn, 2026, needs more optimization.
5 788 0.887720894108 Henry Cohn, 2026, needs more optimization.
5 789 0.887793334680 Henry Cohn, 2026, needs more optimization.
5 790 0.887892160168 Henry Cohn, 2026, needs more optimization.
5 791 0.887897966073 Henry Cohn, 2026, needs more optimization.
5 792 0.887989360711 Henry Cohn, 2026, needs more optimization.
5 793 0.888048429444 Henry Cohn, 2026, needs more optimization.
5 794 0.888128674599 Henry Cohn, 2026, needs more optimization.
5 795 0.888172921456 Henry Cohn, 2026, needs more optimization.
5 796 0.888230019352 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 0.888518571109 Henry Cohn, 2026, needs more optimization.
5 801 0.888549483214 Henry Cohn, 2026, needs more optimization.
5 802 0.888647925638 Henry Cohn, 2026, needs more optimization.
5 803 0.888778764195 Henry Cohn, 2026, needs more optimization.
5 804 0.888897682449 Henry Cohn, 2026, needs more optimization.
5 805 0.888913820440 Henry Cohn, 2026, needs more optimization.
5 806 0.888950728339 Henry Cohn, 2026, needs more optimization.
5 807 0.889002753504 Henry Cohn, 2026, needs more optimization.
5 808 0.889098051318 Henry Cohn, 2026, needs more optimization.
5 809 0.889220593589 Henry Cohn, 2026, needs more optimization.
5 810 0.889234419889 Henry Cohn, 2026, needs more optimization.
5 811 0.889369961501 Henry Cohn, 2026, needs more optimization.
5 812 0.889455683318 Henry Cohn, 2026, needs more optimization.
5 813 0.889527722381 Henry Cohn, 2026, needs more optimization.
5 814 0.889657019686 Henry Cohn, 2026, needs more optimization.
5 815 0.889691600578 Henry Cohn, 2026, needs more optimization.
5 816 0.889694338987 Henry Cohn, 2026, needs more optimization.
5 817 0.889711653227 Henry Cohn, 2026, needs more optimization.
5 818 0.889819148023 Henry Cohn, 2026, needs more optimization.
5 819 0.889855766057 Henry Cohn, 2026, needs more optimization.
5 820 0.889878877469 Henry Cohn, 2026, needs more optimization.
5 821 0.889981806798 Henry Cohn, 2026, needs more optimization.
5 822 0.890017549561 Henry Cohn, 2026, needs more optimization.
5 823 0.890104121451 Henry Cohn, 2026, needs more optimization.
5 824 0.890248066616 Henry Cohn, 2026, needs more optimization.
5 825 0.890340043496 Henry Cohn, 2026, needs more optimization.
5 826 0.890340059783 Henry Cohn, 2026, needs more optimization.
5 827 0.890419311351 Henry Cohn, 2026, needs more optimization.
5 828 0.890537753010 Henry Cohn, 2026, needs more optimization.
5 829 0.890543867285 Henry Cohn, 2026, needs more optimization.
5 830 0.890626382802 Henry Cohn, 2026, needs more optimization.
5 831 0.890713052908 Henry Cohn, 2026, needs more optimization.
5 832 0.890713077407 Henry Cohn, 2026, needs more optimization.
5 833 0.890723614037 Henry Cohn, 2026, needs more optimization.
5 834 0.890780278108 Henry Cohn, 2026, needs more optimization.
5 835 0.890867058871 Henry Cohn, 2026, needs more optimization.
5 836 0.891001836358 Henry Cohn, 2026, needs more optimization.
5 837 0.891081749590 Henry Cohn, 2026, needs more optimization.
5 838 0.891157416643 Henry Cohn, 2026, needs more optimization.
5 839 0.891220776808 Henry Cohn, 2026, needs more optimization.
5 840 0.891290256147 Henry Cohn, 2026, needs more optimization.
5 841 0.891365671978 Henry Cohn, 2026, needs more optimization.
5 842 0.891413438679 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 0.891546154925 Henry Cohn, 2026, needs more optimization.
5 846 0.891653729567 Henry Cohn, 2026, needs more optimization.
5 847 0.891720810747 Henry Cohn, 2026, needs more optimization.
5 848 0.891803294249 Henry Cohn, 2026, needs more optimization.
5 849 0.891859481163 Henry Cohn, 2026, needs more optimization.
5 850 0.891897896412 Henry Cohn, 2026, needs more optimization.
5 851 0.891944505485 Henry Cohn, 2026, needs more optimization.
5 852 0.892047280887 Henry Cohn, 2026, needs more optimization.
5 853 0.892101949948 Henry Cohn, 2026, needs more optimization.
5 854 0.892148935669 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 0.892354703888 Henry Cohn, 2026, needs more optimization.
5 858 0.892395435493 Henry Cohn, 2026, needs more optimization.
5 859 0.892503710281 Henry Cohn, 2026, needs more optimization.
5 860 0.892574675572 Henry Cohn, 2026, needs more optimization.
5 861 0.892591538718 Henry Cohn, 2026, needs more optimization.
5 862 0.892625327965 Henry Cohn, 2026, needs more optimization.
5 863 0.892692965051 Henry Cohn, 2026, needs more optimization.
5 864 0.892754849096 Henry Cohn, 2026, needs more optimization.
5 865 0.892870380543 Henry Cohn, 2026, needs more optimization.
5 866 0.892879812468 Henry Cohn, 2026, needs more optimization.
5 867 0.892993852460 Henry Cohn, 2026, needs more optimization.
5 868 0.893077924999 Henry Cohn, 2026, needs more optimization.
5 869 0.893080474119 Henry Cohn, 2026, needs more optimization.
5 870 0.893170138028 Henry Cohn, 2026, needs more optimization.
5 871 0.893249233448 Henry Cohn, 2026, needs more optimization.
5 872 0.893301025663 Henry Cohn, 2026, needs more optimization.
5 873 0.893319229119 Henry Cohn, 2026, needs more optimization.
5 874 0.893377806698 Henry Cohn, 2026, needs more optimization.
5 875 0.893472150758 Henry Cohn, 2026, needs more optimization.
5 876 0.893522011094 Henry Cohn, 2026, needs more optimization.
5 877 0.893612535450 Henry Cohn, 2026, needs more optimization.
5 878 0.893661618050 Henry Cohn, 2026, needs more optimization.
5 879 0.893723100851 Henry Cohn, 2026, needs more optimization.
5 880 0.893796607547 Henry Cohn, 2026, needs more optimization.
5 881 0.893799338944 Henry Cohn, 2026, needs more optimization.
5 882 0.893815342184 Henry Cohn, 2026, needs more optimization.
5 883 0.893944906448 Henry Cohn, 2026, needs more optimization.
5 884 0.894001591891 Henry Cohn, 2026, needs more optimization.
5 885 0.894070272381 Henry Cohn, 2026, needs more optimization.
5 886 0.894123948913 Henry Cohn, 2026, needs more optimization.
5 887 0.894210766752 Henry Cohn, 2026, needs more optimization.
5 888 0.894287884662 Henry Cohn, 2026, needs more optimization.
5 889 0.894298171851 Henry Cohn, 2026, needs more optimization.
5 890 0.894353374476 Henry Cohn, 2026, needs more optimization.
5 891 0.894388349955 Henry Cohn, 2026, needs more optimization.
5 892 0.894525313713 Henry Cohn, 2026, needs more optimization.
5 893 0.894577680072 Henry Cohn, 2026, needs more optimization.
5 894 0.894638659678 Henry Cohn, 2026, needs more optimization.
5 895 0.894640818820 Henry Cohn, 2026, needs more optimization.
5 896 0.894725763426 Henry Cohn, 2026, needs more optimization.
5 897 0.894729430422 Henry Cohn, 2026, needs more optimization.
5 898 0.894815529350 Henry Cohn, 2026, needs more optimization.
5 899 0.894872792436 Henry Cohn, 2026, needs more optimization.
5 900 0.894893321616 Henry Cohn, 2026, needs more optimization.
5 901 0.894966992467 Henry Cohn, 2026, needs more optimization.
5 902 0.895045335244 Henry Cohn, 2026, needs more optimization.
5 903 0.895142798579 Henry Cohn, 2026, needs more optimization.
5 904 0.895209339173 Henry Cohn, 2026, needs more optimization.
5 905 0.895273846277 Henry Cohn, 2026, needs more optimization.
5 906 0.895385295979 Henry Cohn, 2026, needs more optimization.
5 907 0.895387086078 Henry Cohn, 2026, needs more optimization.
5 908 0.895469997493 Henry Cohn, 2026, needs more optimization.
5 909 0.895494358014 Henry Cohn, 2026, needs more optimization.
5 910 0.895554488551 Henry Cohn, 2026, needs more optimization.
5 911 0.895662017054 Henry Cohn, 2026, needs more optimization.
5 912 0.895697151011 Henry Cohn, 2026, needs more optimization.
5 913 0.895773385490 Henry Cohn, 2026, needs more optimization.
5 914 0.895817411528 Henry Cohn, 2026, needs more optimization.
5 915 0.895835930898 Henry Cohn, 2026, needs more optimization.
5 916 0.895926898626 Henry Cohn, 2026, needs more optimization.
5 917 0.895958512608 Henry Cohn, 2026, needs more optimization.
5 918 0.896047065049 Henry Cohn, 2026, needs more optimization.
5 919 0.896056541486 Henry Cohn, 2026, needs more optimization.
5 920 0.896155943347 Henry Cohn, 2026, needs more optimization.
5 921 0.896172509378 Henry Cohn, 2026, needs more optimization.
5 922 0.896266439777 Henry Cohn, 2026, needs more optimization.
5 923 0.896287886483 Henry Cohn, 2026, needs more optimization.
5 924 0.896375773438 Henry Cohn, 2026, needs more optimization.
5 925 0.896392975064 Henry Cohn, 2026, needs more optimization.
5 926 0.896458360832 Henry Cohn, 2026, needs more optimization.
5 927 0.896478747636 Henry Cohn, 2026, needs more optimization.
5 928 0.896559400123 Henry Cohn, 2026, needs more optimization.
5 929 0.896621402869 Henry Cohn, 2026, needs more optimization.
5 930 0.896692811080 Henry Cohn, 2026, needs more optimization.
5 931 0.896764898313 Henry Cohn, 2026, needs more optimization.
5 932 0.896824616291 Henry Cohn, 2026, needs more optimization.
5 933 0.896864926468 Henry Cohn, 2026, needs more optimization.
5 934 0.896922272712 Henry Cohn, 2026, needs more optimization.
5 935 0.896990544561 Henry Cohn, 2026, needs more optimization.
5 936 0.897003889523 Henry Cohn, 2026, needs more optimization.
5 937 0.897072081509 Henry Cohn, 2026, needs more optimization.
5 938 0.897153283648 Henry Cohn, 2026, needs more optimization.
5 939 0.897167680638 Henry Cohn, 2026, needs more optimization.
5 940 0.897210032060 Henry Cohn, 2026, needs more optimization.
5 941 0.897251669147 Henry Cohn, 2026, needs more optimization.
5 942 0.897324527247 Henry Cohn, 2026, needs more optimization.
5 943 0.897426483193 Henry Cohn, 2026, needs more optimization.
5 944 0.897503280626 Henry Cohn, 2026, needs more optimization.
5 945 0.897522795310 Henry Cohn, 2026, needs more optimization.
5 946 0.897574150432 Henry Cohn, 2026, needs more optimization.
5 947 0.897647743656 Henry Cohn, 2026, needs more optimization.
5 948 0.897720425803 Henry Cohn, 2026, needs more optimization.
5 949 0.897796269456 Henry Cohn, 2026, needs more optimization.
5 950 0.897847154951 Henry Cohn, 2026, needs more optimization.
5 951 0.897900865957 Henry Cohn, 2026, needs more optimization.
5 952 0.897949372923 Henry Cohn, 2026, needs more optimization.
5 953 0.897974766168 Henry Cohn, 2026, needs more optimization.
5 954 0.897989970716 Henry Cohn, 2026, needs more optimization.
5 955 0.897993641127 Henry Cohn, 2026, needs more optimization.
5 956 0.898013025834 Henry Cohn, 2026, needs more optimization.
5 957 0.898093123218 Henry Cohn, 2026, needs more optimization.
5 958 0.898195019491 Henry Cohn, 2026, needs more optimization.
5 959 0.898241499165 Henry Cohn, 2026, needs more optimization.
5 960 0.898259297396 Henry Cohn, 2026, needs more optimization.
5 961 0.898350985452 Henry Cohn, 2026, needs more optimization.
5 962 0.898394842288 Henry Cohn, 2026, needs more optimization.
5 963 0.898410557948 Henry Cohn, 2026, needs more optimization.
5 964 0.898493758946 Henry Cohn, 2026, needs more optimization.
5 965 0.898526797930 Henry Cohn, 2026, needs more optimization.
5 966 0.898573023330 Henry Cohn, 2026, needs more optimization.
5 967 0.898582698258 Henry Cohn, 2026, needs more optimization.
5 968 0.898723663322 Henry Cohn, 2026, needs more optimization.
5 969 0.898809144589 Henry Cohn, 2026, needs more optimization.
5 970 0.898829269613 Henry Cohn, 2026, needs more optimization.
5 971 0.898874640864 Henry Cohn, 2026, needs more optimization.
5 972 0.898895667711 Henry Cohn, 2026, needs more optimization.
5 973 0.898933468906 Henry Cohn, 2026, needs more optimization.
5 974 0.899017074128 Henry Cohn, 2026, needs more optimization.
5 975 0.899093980593 Henry Cohn, 2026, needs more optimization.
5 976 0.899120310113 Henry Cohn, 2026, needs more optimization.
5 977 0.899142236103 Henry Cohn, 2026, needs more optimization.
5 978 0.899221282200 Henry Cohn, 2026, needs more optimization.
5 979 0.899224691401 Henry Cohn, 2026, needs more optimization.
5 980 0.899328332110 Henry Cohn, 2026, needs more optimization.
5 981 0.899360737305 Henry Cohn, 2026, needs more optimization.
5 982 0.899422850284 Henry Cohn, 2026, needs more optimization.
5 983 0.899480927491 Henry Cohn, 2026, needs more optimization.
5 984 0.899493849328 Henry Cohn, 2026, needs more optimization.
5 985 0.899617556016 Henry Cohn, 2026, needs more optimization.
5 986 0.899697283207 Henry Cohn, 2026, needs more optimization.
5 987 0.899712797484 Henry Cohn, 2026, needs more optimization.
5 988 0.899770019992 Henry Cohn, 2026, needs more optimization.
5 989 0.899856487483 Henry Cohn, 2026, needs more optimization.
5 990 0.899871367114 Henry Cohn, 2026, needs more optimization.
5 991 0.899894654776 Henry Cohn, 2026, needs more optimization.
5 992 0.899923326375 Henry Cohn, 2026, needs more optimization.
5 993 0.899992749423 Henry Cohn, 2026, needs more optimization.
5 994 0.900048299972 Henry Cohn, 2026, needs more optimization.
5 995 0.900104096617 Henry Cohn, 2026, needs more optimization.
5 996 0.900203356643 Henry Cohn, 2026, needs more optimization.
5 997 0.900241109572 Henry Cohn, 2026, needs more optimization.
5 998 0.900318588116 Henry Cohn, 2026, needs more optimization.
5 999 0.900394008168 Henry Cohn, 2026, needs more optimization.
5 1000 0.900398100792 Henry Cohn, 2026, needs more optimization.
5 1001 0.900454417632 Henry Cohn, 2026, needs more optimization.
5 1002 0.900500776580 Henry Cohn, 2026, needs more optimization.
5 1003 0.900551176128 Henry Cohn, 2026, needs more optimization.
5 1004 0.900558267595 Henry Cohn, 2026, needs more optimization.
5 1005 0.900623181960 Henry Cohn, 2026, needs more optimization.
5 1006 0.900676989707 Henry Cohn, 2026, needs more optimization.
5 1007 0.900684712008 Henry Cohn, 2026, needs more optimization.
5 1008 0.900831216945 Henry Cohn, 2026, needs more optimization.
5 1009 0.900844323757 Henry Cohn, 2026, needs more optimization.
5 1010 0.900906178181 Henry Cohn, 2026, needs more optimization.
5 1011 0.900956376945 Henry Cohn, 2026, needs more optimization.
5 1012 0.900967101604 Henry Cohn, 2026, needs more optimization.
5 1013 0.901008974700 Henry Cohn, 2026, needs more optimization.
5 1014 0.901094864000 Henry Cohn, 2026, needs more optimization.
5 1015 0.901105294288 Henry Cohn, 2026, needs more optimization.
5 1016 0.901109583524 Henry Cohn, 2026, needs more optimization.
5 1017 0.901151869393 Henry Cohn, 2026, needs more optimization.
5 1018 0.901203311911 Henry Cohn, 2026, needs more optimization.
5 1019 0.901292993021 Henry Cohn, 2026, needs more optimization.
5 1020 0.901302755735 Henry Cohn, 2026, needs more optimization.
5 1021 0.901387245381 Henry Cohn, 2026, needs more optimization.
5 1022 0.901434646356 Henry Cohn, 2026, needs more optimization.
5 1023 0.901472132318 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 0.486085706237 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, needs more optimization.
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.
6 106 0.583371498649 Henry Cohn, 2026.
6 107 0.583372432432 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 0.596439214295 Henry Cohn, 2025.
6 117 0.596439359703 Henry Cohn, 2025, needs more optimization.
6 118 0.596439417437 Henry Cohn, 2026.
6 119 0.598424125415 Henry Cohn, 2025.
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 0.607973280229 Henry Cohn, 2026, needs more optimization.
6 126 0.610385711272 Henry Cohn, 2026.
6 127 0.616412773395 Henry Cohn, 2026.
6 128 0.618886710990 Henry Cohn, 2026.
6 129 0.620224367829 Henry Cohn, 2025.
6 130 0.623410242886 Henry Cohn, 2026, needs more optimization.
6 132 0.624698587658 Henry Cohn, 2026, needs more optimization.
6 133 0.626200565619 Henry Cohn, 2026, needs more optimization.
6 134 0.628625328947 Henry Cohn, 2026, needs more optimization.
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 0.634581517382 Henry Cohn, 2026, needs more optimization.
6 139 0.636150042225 Henry Cohn, 2026, needs more optimization.
6 140 0.637374263264 Henry Cohn, 2026, needs more optimization.
6 141 0.639325003085 Henry Cohn, 2026, needs more optimization.
6 142 0.639907720797 Henry Cohn, 2026, needs more optimization.
6 143 0.641418520213 Henry Cohn, 2026, needs more optimization.
6 144 0.642197635997 Henry Cohn, 2026, needs more optimization.
6 145 0.643736553697 Henry Cohn, 2026, needs more optimization.
6 146 0.644835823726 Henry Cohn, 2026, needs more optimization.
6 147 0.645786741328 Henry Cohn, 2026, needs more optimization.
6 148 0.646694161647 Henry Cohn, 2026, needs more optimization.
6 149 0.647934344411 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 0.651009745432 Henry Cohn, 2026, needs more optimization.
6 153 0.651424838401 Henry Cohn, 2026, needs more optimization.
6 154 0.651891077139 Henry Cohn, 2026, needs more optimization.
6 155 0.652677694649 Henry Cohn, 2026, needs more optimization.
6 156 0.653218828402 Henry Cohn, 2026, needs more optimization.
6 157 0.653539053075 Henry Cohn, 2026, needs more optimization.
6 158 0.654174169895 Henry Cohn, 2026, needs more optimization.
6 159 0.654917497394 Henry Cohn, 2026, needs more optimization.
6 160 0.655640275823 Henry Cohn, 2026, needs more optimization.
6 161 0.656172727972 Henry Cohn, 2026, needs more optimization.
6 162 0.656797245916 Henry Cohn, 2026, needs more optimization.
6 163 0.657620192189 Henry Cohn, 2026, needs more optimization.
6 164 0.658348653642 Henry Cohn, 2026, needs more optimization.
6 165 0.659084509520 Henry Cohn, 2026, needs more optimization.
6 166 0.659931336472 Henry Cohn, 2026, needs more optimization.
6 167 0.660355875176 Henry Cohn, 2026, needs more optimization.
6 168 0.660627528646 Henry Cohn, 2026, needs more optimization.
6 169 0.661754053888 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 0.664870950288 Henry Cohn, 2026, needs more optimization.
6 175 0.665443411314 Henry Cohn, 2026, needs more optimization.
6 176 0.666108316168 Henry Cohn, 2026, needs more optimization.
6 177 0.667548831820 Henry Cohn, 2026, needs more optimization.
6 178 0.668541726252 Henry Cohn, 2026, needs more optimization.
6 179 0.670026054447 Henry Cohn, 2026, needs more optimization.
6 180 0.671113494040 Henry Cohn, 2026, needs more optimization.
6 181 0.671959630941 Henry Cohn, 2026, needs more optimization.
6 182 0.672541542400 Henry Cohn, 2026, needs more optimization.
6 183 0.673120391466 Henry Cohn, 2026, needs more optimization.
6 184 0.673479432664 Henry Cohn, 2026, needs more optimization.
6 185 0.674052746169 Henry Cohn, 2026, needs more optimization.
6 186 0.674292180631 Henry Cohn, 2026, needs more optimization.
6 187 0.674648752351 Henry Cohn, 2026, needs more optimization.
6 188 0.675448996075 Henry Cohn, 2026, needs more optimization.
6 189 0.676165824000 Henry Cohn, 2026, needs more optimization.
6 190 0.677079062813 Henry Cohn, 2026, needs more optimization.
6 191 0.678090048687 Henry Cohn, 2026, needs more optimization.
6 192 0.678538993914 Henry Cohn, 2026, needs more optimization.
6 193 0.679065210648 Henry Cohn, 2026, needs more optimization.
6 194 0.679780411125 Henry Cohn, 2026, needs more optimization.
6 195 0.680832050419 Henry Cohn, 2026, needs more optimization.
6 196 0.681042163443 Henry Cohn, 2026, needs more optimization.
6 197 0.681777361862 Henry Cohn, 2026, needs more optimization.
6 198 0.682600728399 Henry Cohn, 2026, needs more optimization.
6 199 0.683180906975 Henry Cohn, 2026, needs more optimization.
6 200 0.683918738918 Henry Cohn, 2026, needs more optimization.
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 0.685824072471 Henry Cohn, 2026, needs more optimization.
6 205 0.686229429138 Henry Cohn, 2026, needs more optimization.
6 206 0.686784247805 Henry Cohn, 2026, needs more optimization.
6 207 0.687792664686 Henry Cohn, 2026, needs more optimization.
6 208 0.688115875441 Henry Cohn, 2026, needs more optimization.
6 209 0.688653947068 Henry Cohn, 2026, needs more optimization.
6 210 0.689119669405 Henry Cohn, 2026, needs more optimization.
6 211 0.689772455312 Henry Cohn, 2026, needs more optimization.
6 212 0.690463198425 Henry Cohn, 2026, needs more optimization.
6 213 0.691196768958 Henry Cohn, 2026, needs more optimization.
6 214 0.691935634490 Henry Cohn, 2026, needs more optimization.
6 215 0.692810411301 Henry Cohn, 2026, needs more optimization.
6 216 0.693151133181 Henry Cohn, 2026, needs more optimization.
6 217 0.694030817995 Henry Cohn, 2026, needs more optimization.
6 218 0.694428133214 Henry Cohn, 2026, needs more optimization.
6 219 0.694881763545 Henry Cohn, 2026, needs more optimization.
6 220 0.695009246996 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 0.696218097426 Henry Cohn, 2026, needs more optimization.
6 224 0.697123573666 Henry Cohn, 2026, needs more optimization.
6 225 0.697415677677 Henry Cohn, 2026, needs more optimization.
6 226 0.697996733888 Henry Cohn, 2026, needs more optimization.
6 227 0.698315779214 Henry Cohn, 2026, needs more optimization.
6 228 0.698897624639 Henry Cohn, 2026, needs more optimization.
6 229 0.699495105657 Henry Cohn, 2026, needs more optimization.
6 230 0.699810621517 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.
6 243 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 0.703811225569 Henry Cohn, 2026, needs more optimization.
6 245 0.703829064960 Henry Cohn, 2026, needs more optimization.
6 247 0.704068291221 Henry Cohn, 2026, needs more optimization.
6 248 0.704239232973 Henry Cohn, 2026, needs more optimization.
6 249 0.704292043779 Henry Cohn, 2026, needs more optimization.
6 250 0.704483687828 Henry Cohn, 2026, needs more optimization.
6 251 0.704633068602 Henry Cohn, 2026, needs more optimization.
6 252 0.704726065719 Henry Cohn, 2026, needs more optimization.
6 253 0.704943057084 Henry Cohn, 2026, needs more optimization.
6 254 0.705090523351 Henry Cohn, 2026, needs more optimization.
6 255 0.705176652829 Henry Cohn, 2026, needs more optimization.
6 256 0.705181763211 Henry Cohn, 2026, needs more optimization.
6 257 0.705432059080 Henry Cohn, 2026, needs more optimization.
6 258 0.706001251636 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 0.709272032981 Henry Cohn, 2026, needs more optimization.
6 264 0.709773900620 Henry Cohn, 2026, needs more optimization.
6 265 0.711047799367 Henry Cohn, 2026, needs more optimization.
6 266 0.712056158723 Henry Cohn, 2026, needs more optimization.
6 267 0.712797549428 Henry Cohn, 2026, needs more optimization.
6 268 0.713114273493 Henry Cohn, 2026, needs more optimization.
6 269 0.713601345738 Henry Cohn, 2026, needs more optimization.
6 270 0.714525044859 Henry Cohn, 2026, needs more optimization.
6 271 0.715193035860 Henry Cohn, 2026, needs more optimization.
6 272 0.716089085390 Henry Cohn, 2026, needs more optimization.
6 273 0.716724836699 Henry Cohn, 2026, needs more optimization.
6 274 0.717514232491 Henry Cohn, 2026, needs more optimization.
6 275 0.718332543147 Henry Cohn, 2026, needs more optimization.
6 276 0.718921350111 Henry Cohn, 2026, needs more optimization.
6 277 0.719526311640 Henry Cohn, 2026, needs more optimization.
6 278 0.720053174881 Henry Cohn, 2026, needs more optimization.
6 279 0.720802822121 Henry Cohn, 2026, needs more optimization.
6 280 0.721717943238 Henry Cohn, 2026, needs more optimization.
6 281 0.722070189457 Henry Cohn, 2026, needs more optimization.
6 282 0.722538082444 Henry Cohn, 2026, needs more optimization.
6 283 0.723449631370 Henry Cohn, 2026, needs more optimization.
6 284 0.723876567321 Henry Cohn, 2026, needs more optimization.
6 285 0.724560497991 Henry Cohn, 2026, needs more optimization.
6 286 0.725089860320 Henry Cohn, 2026, needs more optimization.
6 287 0.725210861714 Henry Cohn, 2026, needs more optimization.
6 288 0.725968021172 Henry Cohn, 2026, needs more optimization.
6 289 0.726301718815 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 0.728865960565 Henry Cohn, 2026, needs more optimization.
6 295 0.729390664112 Henry Cohn, 2026, needs more optimization.
6 296 0.729924070292 Henry Cohn, 2026, needs more optimization.
6 297 0.730347732498 Henry Cohn, 2026, needs more optimization.
6 298 0.730862703924 Henry Cohn, 2026, needs more optimization.
6 299 0.731065269229 Henry Cohn, 2026, needs more optimization.
6 300 0.731538373606 Henry Cohn, 2026, needs more optimization.
6 301 0.732020939485 Henry Cohn, 2026, needs more optimization.
6 302 0.732595312148 Henry Cohn, 2026, needs more optimization.
6 303 0.732976794742 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 0.733857071568 Henry Cohn, 2026, needs more optimization.
6 307 0.734319881442 Henry Cohn, 2026, needs more optimization.
6 308 0.734489715727 Henry Cohn, 2026, needs more optimization.
6 309 0.734839795040 Henry Cohn, 2026, needs more optimization.
6 310 0.734886388184 Henry Cohn, 2026, needs more optimization.
6 311 0.735647373548 Henry Cohn, 2026, needs more optimization.
6 312 0.736466930225 Henry Cohn, 2026, needs more optimization.
6 313 0.736730526827 Henry Cohn, 2026, needs more optimization.
6 314 0.737283817280 Henry Cohn, 2026, needs more optimization.
6 315 0.737795174178 Henry Cohn, 2026, needs more optimization.
6 316 0.738120997618 Henry Cohn, 2026, needs more optimization.
6 317 0.738591889613 Henry Cohn, 2026, needs more optimization.
6 318 0.738920082353 Henry Cohn, 2026, needs more optimization.
6 319 0.739355165987 Henry Cohn, 2026, needs more optimization.
6 320 0.739819633211 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.
6 398 0.763520494846 Henry Cohn, 2026, needs more optimization.
6 399 0.763761786023 Henry Cohn, 2026, needs more optimization.
6 400 0.763829216813 Henry Cohn, 2026, needs more optimization.
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 0.783276031250 Henry Cohn, 2026, needs more optimization.
6 496 0.783452416656 Henry Cohn, 2026, needs more optimization.
6 497 0.783649962319 Henry Cohn, 2026, needs more optimization.
6 498 0.783834402090 Henry Cohn, 2026, needs more optimization.
6 499 0.783840263927 Henry Cohn, 2026, needs more optimization.
6 500 0.784062321707 Henry Cohn, 2026, needs more optimization.
6 501 0.784438857427 Henry Cohn, 2026, needs more optimization.
6 502 0.784671697704 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 0.785861805163 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 0.786285940551 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 0.786774046795 Henry Cohn, 2026, needs more optimization.
6 517 0.786913218630 Henry Cohn, 2026, needs more optimization.
6 518 0.787265128324 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 0.787664113669 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 0.789223575612 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 0.790290111838 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 0.790876624882 Henry Cohn, 2026, needs more optimization.
6 542 0.790903544182 Henry Cohn, 2026, needs more optimization.
6 543 0.791091493591 Henry Cohn, 2026, needs more optimization.
6 544 0.791287066424 Henry Cohn, 2026, needs more optimization.
6 545 0.791480835856 Henry Cohn, 2026, needs more optimization.
6 546 0.791753496700 Henry Cohn, 2026, needs more optimization.
6 547 0.791796789597 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 0.792440693396 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 0.793487790622 Henry Cohn, 2026, needs more optimization.
6 560 0.793734837753 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 0.794209331678 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 0.795151284266 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 0.795571705527 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 0.796074504920 Henry Cohn, 2026, needs more optimization.
6 577 0.796191267467 Henry Cohn, 2026, needs more optimization.
6 578 0.796324950480 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 0.796935198518 Henry Cohn, 2026, needs more optimization.
6 583 0.797063396873 Henry Cohn, 2026, needs more optimization.
6 584 0.797348157487 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 0.797506939525 Henry Cohn, 2026, needs more optimization.
6 588 0.797679508555 Henry Cohn, 2026, needs more optimization.
6 589 0.797817253969 Henry Cohn, 2026, needs more optimization.
6 590 0.797910928249 Henry Cohn, 2026, needs more optimization.
6 591 0.798112573157 Henry Cohn, 2026, needs more optimization.
6 592 0.798367973674 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 0.798783203575 Henry Cohn, 2026, needs more optimization.
6 596 0.798920532360 Henry Cohn, 2026, needs more optimization.
6 597 0.799043119104 Henry Cohn, 2026, needs more optimization.
6 598 0.799233568559 Henry Cohn, 2026, needs more optimization.
6 599 0.799356612818 Henry Cohn, 2026, needs more optimization.
6 600 0.799532892456 Henry Cohn, 2026, needs more optimization.
6 601 0.799659012682 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 0.800057954983 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 0.800469454393 Henry Cohn, 2026, needs more optimization.
6 608 0.800480506369 Henry Cohn, 2026, needs more optimization.
6 609 0.800618933317 Henry Cohn, 2026, needs more optimization.
6 610 0.800759288408 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 0.801159472697 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 0.801644772931 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 0.802418969434 Henry Cohn, 2026, needs more optimization.
6 623 0.802560377832 Henry Cohn, 2026, needs more optimization.
6 624 0.802573805045 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 0.803288391015 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 0.803972924069 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 0.804211991671 Henry Cohn, 2026, needs more optimization.
6 638 0.804378807116 Henry Cohn, 2026, needs more optimization.
6 639 0.804379865537 Henry Cohn, 2026, needs more optimization.
6 640 0.804586122508 Henry Cohn, 2026, needs more optimization.
6 641 0.804604405801 Henry Cohn, 2026, needs more optimization.
6 642 0.804663290819 Henry Cohn, 2026, needs more optimization.
6 643 0.804766598690 Henry Cohn, 2026, needs more optimization.
6 644 0.804939569756 Henry Cohn, 2026, needs more optimization.
6 645 0.805177143288 Henry Cohn, 2026, needs more optimization.
6 646 0.805254018823 Henry Cohn, 2026, needs more optimization.
6 647 0.805428708397 Henry Cohn, 2026, needs more optimization.
6 648 0.805449569725 Henry Cohn, 2026, needs more optimization.
6 649 0.805546180061 Henry Cohn, 2026, needs more optimization.
6 650 0.805651356929 Henry Cohn, 2026, needs more optimization.
6 651 0.805794215540 Henry Cohn, 2026, needs more optimization.
6 652 0.805921443896 Henry Cohn, 2026, needs more optimization.
6 653 0.806067249783 Henry Cohn, 2026, needs more optimization.
6 654 0.806182518616 Henry Cohn, 2026, needs more optimization.
6 655 0.806367634591 Henry Cohn, 2026, needs more optimization.
6 656 0.806396066248 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 0.806749701935 Henry Cohn, 2026, needs more optimization.
6 661 0.806892166992 Henry Cohn, 2026, needs more optimization.
6 662 0.807082160083 Henry Cohn, 2026, needs more optimization.
6 663 0.807251286564 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 0.807578913124 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 0.807890815552 Henry Cohn, 2026, needs more optimization.
6 671 0.808064173527 Henry Cohn, 2026, needs more optimization.
6 672 0.808129076706 Henry Cohn, 2026, needs more optimization.
6 673 0.808284888147 Henry Cohn, 2026, needs more optimization.
6 674 0.808454476202 Henry Cohn, 2026, needs more optimization.
6 675 0.808542942911 Henry Cohn, 2026, needs more optimization.
6 676 0.808752247244 Henry Cohn, 2026, needs more optimization.
6 677 0.808925618162 Henry Cohn, 2026, needs more optimization.
6 678 0.808977553361 Henry Cohn, 2026, needs more optimization.
6 679 0.809095644145 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 0.809508563100 Henry Cohn, 2026, needs more optimization.
6 683 0.809570381100 Henry Cohn, 2026, needs more optimization.
6 684 0.809704030004 Henry Cohn, 2026, needs more optimization.
6 685 0.809808123836 Henry Cohn, 2026, needs more optimization.
6 686 0.809901222873 Henry Cohn, 2026, needs more optimization.
6 687 0.809947533533 Henry Cohn, 2026, needs more optimization.
6 688 0.810112204993 Henry Cohn, 2026, needs more optimization.
6 689 0.810278351949 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 0.810571587759 Henry Cohn, 2026, needs more optimization.
6 693 0.810669400328 Henry Cohn, 2026, needs more optimization.
6 694 0.810820936033 Henry Cohn, 2026, needs more optimization.
6 695 0.810853765537 Henry Cohn, 2026, needs more optimization.
6 696 0.811064007322 Henry Cohn, 2026, needs more optimization.
6 697 0.811156182717 Henry Cohn, 2026, needs more optimization.
6 698 0.811429054132 Henry Cohn, 2026, needs more optimization.
6 699 0.811547676724 Henry Cohn, 2026, needs more optimization.
6 700 0.811670259678 Henry Cohn, 2026, needs more optimization.
6 701 0.811690737392 Henry Cohn, 2026, needs more optimization.
6 702 0.811744595398 Henry Cohn, 2026, needs more optimization.
6 703 0.811870937445 Henry Cohn, 2026, needs more optimization.
6 704 0.811886613167 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 0.812327864400 Henry Cohn, 2026, needs more optimization.
6 708 0.812445949579 Henry Cohn, 2026, needs more optimization.
6 709 0.812551941906 Henry Cohn, 2026, needs more optimization.
6 710 0.812662053245 Henry Cohn, 2026, needs more optimization.
6 711 0.812741483060 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 0.813300029512 Henry Cohn, 2026, needs more optimization.
6 716 0.813305135633 Henry Cohn, 2026, needs more optimization.
6 717 0.813333682183 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 0.813658721378 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 0.813954548264 Henry Cohn, 2026, needs more optimization.
6 724 0.814055286790 Henry Cohn, 2026, needs more optimization.
6 725 0.814197622080 Henry Cohn, 2026, needs more optimization.
6 726 0.814314783134 Henry Cohn, 2026, needs more optimization.
6 727 0.814485855612 Henry Cohn, 2026, needs more optimization.
6 728 0.814494772988 Henry Cohn, 2026, needs more optimization.
6 729 0.814545366725 Henry Cohn, 2026, needs more optimization.
6 730 0.814683699116 Henry Cohn, 2026, needs more optimization.
6 731 0.814841766561 Henry Cohn, 2026, needs more optimization.
6 732 0.814846898863 Henry Cohn, 2026, needs more optimization.
6 733 0.814911279900 Henry Cohn, 2026, needs more optimization.
6 734 0.815064855673 Henry Cohn, 2026, needs more optimization.
6 735 0.815092865255 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 0.815534480356 Henry Cohn, 2026, needs more optimization.
6 739 0.815622415513 Henry Cohn, 2026, needs more optimization.
6 740 0.815757971886 Henry Cohn, 2026, needs more optimization.
6 741 0.815871158202 Henry Cohn, 2026, needs more optimization.
6 742 0.816007259905 Henry Cohn, 2026, needs more optimization.
6 743 0.816027602319 Henry Cohn, 2026, needs more optimization.
6 744 0.816066216933 Henry Cohn, 2026, needs more optimization.
6 745 0.816200845559 Henry Cohn, 2026, needs more optimization.
6 746 0.816297910660 Henry Cohn, 2026, needs more optimization.
6 747 0.816512636442 Henry Cohn, 2026, needs more optimization.
6 748 0.816584160484 Henry Cohn, 2026, needs more optimization.
6 749 0.816586863596 Henry Cohn, 2026, needs more optimization.
6 750 0.816802948303 Henry Cohn, 2026, needs more optimization.
6 751 0.816947224053 Henry Cohn, 2026, needs more optimization.
6 752 0.816969481398 Henry Cohn, 2026, needs more optimization.
6 753 0.817114900823 Henry Cohn, 2026, needs more optimization.
6 754 0.817236210299 Henry Cohn, 2026, needs more optimization.
6 755 0.817239161708 Henry Cohn, 2026, needs more optimization.
6 756 0.817374183819 Henry Cohn, 2026, needs more optimization.
6 757 0.817455793966 Henry Cohn, 2026, needs more optimization.
6 758 0.817487090764 Henry Cohn, 2026, needs more optimization.
6 759 0.817672634375 Henry Cohn, 2026, needs more optimization.
6 760 0.817688102203 Henry Cohn, 2026, needs more optimization.
6 761 0.817731640849 Henry Cohn, 2026, needs more optimization.
6 762 0.817911113615 Henry Cohn, 2026, needs more optimization.
6 763 0.818092791232 Henry Cohn, 2026, needs more optimization.
6 764 0.818166320615 Henry Cohn, 2026, needs more optimization.
6 765 0.818293383622 Henry Cohn, 2026, needs more optimization.
6 766 0.818338308244 Henry Cohn, 2026, needs more optimization.
6 767 0.818383112047 Henry Cohn, 2026, needs more optimization.
6 768 0.818552321061 Henry Cohn, 2026, needs more optimization.
6 769 0.818614910072 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 0.818895995252 Henry Cohn, 2026, needs more optimization.
6 773 0.818930884205 Henry Cohn, 2026, needs more optimization.
6 774 0.819065229540 Henry Cohn, 2026, needs more optimization.
6 775 0.819098459600 Henry Cohn, 2026, needs more optimization.
6 776 0.819215122616 Henry Cohn, 2026, needs more optimization.
6 777 0.819286978371 Henry Cohn, 2026, needs more optimization.
6 778 0.819461187329 Henry Cohn, 2026, needs more optimization.
6 779 0.819542272389 Henry Cohn, 2026, needs more optimization.
6 780 0.819640701051 Henry Cohn, 2026, needs more optimization.
6 781 0.819687944003 Henry Cohn, 2026, needs more optimization.
6 782 0.819716498311 Henry Cohn, 2026, needs more optimization.
6 783 0.819821698846 Henry Cohn, 2026, needs more optimization.
6 784 0.819931674385 Henry Cohn, 2026, needs more optimization.
6 785 0.819971510334 Henry Cohn, 2026, needs more optimization.
6 786 0.820156163296 Henry Cohn, 2026, needs more optimization.
6 787 0.820173498227 Henry Cohn, 2026, needs more optimization.
6 788 0.820326306445 Henry Cohn, 2026, needs more optimization.
6 789 0.820411066060 Henry Cohn, 2026, needs more optimization.
6 790 0.820514412035 Henry Cohn, 2026, needs more optimization.
6 791 0.820568029108 Henry Cohn, 2026, needs more optimization.
6 792 0.820775584103 Henry Cohn, 2026, needs more optimization.
6 793 0.820777185824 Henry Cohn, 2026, needs more optimization.
6 794 0.820977681817 Henry Cohn, 2026, needs more optimization.
6 795 0.820987552116 Henry Cohn, 2026, needs more optimization.
6 796 0.820994458310 Henry Cohn, 2026, needs more optimization.
6 797 0.821048821362 Henry Cohn, 2026, needs more optimization.
6 798 0.821151549995 Henry Cohn, 2026, needs more optimization.
6 799 0.821261148722 Henry Cohn, 2026, needs more optimization.
6 800 0.821415789721 Henry Cohn, 2026, needs more optimization.
6 801 0.821558140064 Henry Cohn, 2026, needs more optimization.
6 802 0.821660771957 Henry Cohn, 2026, needs more optimization.
6 803 0.821705165074 Henry Cohn, 2026, needs more optimization.
6 804 0.821735491454 Henry Cohn, 2026, needs more optimization.
6 805 0.821802323004 Henry Cohn, 2026, needs more optimization.
6 806 0.821881322078 Henry Cohn, 2026, needs more optimization.
6 807 0.821936251612 Henry Cohn, 2026, needs more optimization.
6 808 0.821974342562 Henry Cohn, 2026, needs more optimization.
6 809 0.822125648162 Henry Cohn, 2026, needs more optimization.
6 810 0.822290800769 Henry Cohn, 2026, needs more optimization.
6 811 0.822348702020 Henry Cohn, 2026, needs more optimization.
6 812 0.822487016540 Henry Cohn, 2026, needs more optimization.
6 813 0.822636888845 Henry Cohn, 2026, needs more optimization.
6 814 0.822685148490 Henry Cohn, 2026, needs more optimization.
6 815 0.822760207195 Henry Cohn, 2026, needs more optimization.
6 816 0.822790302020 Henry Cohn, 2026, needs more optimization.
6 817 0.822972027463 Henry Cohn, 2026, needs more optimization.
6 818 0.823013509114 Henry Cohn, 2026, needs more optimization.
6 819 0.823124327877 Henry Cohn, 2026, needs more optimization.
6 820 0.823158866410 Henry Cohn, 2026, needs more optimization.
6 821 0.823312032365 Henry Cohn, 2026, needs more optimization.
6 822 0.823425090375 Henry Cohn, 2026, needs more optimization.
6 823 0.823634787852 Henry Cohn, 2026, needs more optimization.
6 824 0.823638634066 Henry Cohn, 2026, needs more optimization.
6 825 0.823712356380 Henry Cohn, 2026, needs more optimization.
6 826 0.823851673776 Henry Cohn, 2026, needs more optimization.
6 827 0.823988848860 Henry Cohn, 2026, needs more optimization.
6 828 0.823991425689 Henry Cohn, 2026, needs more optimization.
6 829 0.824032851882 Henry Cohn, 2026, needs more optimization.
6 830 0.824123254770 Henry Cohn, 2026, needs more optimization.
6 831 0.824245286006 Henry Cohn, 2026, needs more optimization.
6 832 0.824306972703 Henry Cohn, 2026, needs more optimization.
6 833 0.824353380156 Henry Cohn, 2026, needs more optimization.
6 834 0.824456022336 Henry Cohn, 2026, needs more optimization.
6 835 0.824516925497 Henry Cohn, 2026, needs more optimization.
6 836 0.824526636586 Henry Cohn, 2026, needs more optimization.
6 837 0.824643580141 Henry Cohn, 2026, needs more optimization.
6 838 0.824727652868 Henry Cohn, 2026, needs more optimization.
6 839 0.824871822318 Henry Cohn, 2026, needs more optimization.
6 840 0.824901582819 Henry Cohn, 2026, needs more optimization.
6 841 0.824989509132 Henry Cohn, 2026, needs more optimization.
6 842 0.825097259096 Henry Cohn, 2026, needs more optimization.
6 843 0.825129362461 Henry Cohn, 2026, needs more optimization.
6 844 0.825310935702 Henry Cohn, 2026, needs more optimization.
6 845 0.825390765441 Henry Cohn, 2026, needs more optimization.
6 846 0.825550853768 Henry Cohn, 2026, needs more optimization.
6 847 0.825558859189 Henry Cohn, 2026, needs more optimization.
6 848 0.825579227672 Henry Cohn, 2026, needs more optimization.
6 849 0.825775662596 Henry Cohn, 2026, needs more optimization.
6 850 0.825857259926 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 0.826135640725 Henry Cohn, 2026, needs more optimization.
6 854 0.826225307695 Henry Cohn, 2026, needs more optimization.
6 855 0.826390520625 Henry Cohn, 2026, needs more optimization.
6 856 0.826404628823 Henry Cohn, 2026, needs more optimization.
6 857 0.826505417336 Henry Cohn, 2026, needs more optimization.
6 858 0.826623674433 Henry Cohn, 2026, needs more optimization.
6 859 0.826623674534 Henry Cohn, 2026, needs more optimization.
6 860 0.826624782996 Henry Cohn, 2026, needs more optimization.
6 861 0.826631859155 Henry Cohn, 2026, needs more optimization.
6 862 0.826709211871 Henry Cohn, 2026, needs more optimization.
6 863 0.826871655379 Henry Cohn, 2026, needs more optimization.
6 864 0.827005448058 Henry Cohn, 2026, needs more optimization.
6 865 0.827013668771 Henry Cohn, 2026, needs more optimization.
6 866 0.827183329674 Henry Cohn, 2026, needs more optimization.
6 867 0.827199668001 Henry Cohn, 2026, needs more optimization.
6 868 0.827212284475 Henry Cohn, 2026, needs more optimization.
6 869 0.827342067932 Henry Cohn, 2026, needs more optimization.
6 870 0.827544303231 Henry Cohn, 2026, needs more optimization.
6 871 0.827544316008 Henry Cohn, 2026, needs more optimization.
6 872 0.827545591245 Henry Cohn, 2026, needs more optimization.
6 873 0.827648963549 Henry Cohn, 2026, needs more optimization.
6 874 0.827653765861 Henry Cohn, 2026, needs more optimization.
6 875 0.827657657793 Henry Cohn, 2026, needs more optimization.
6 876 0.827667139037 Henry Cohn, 2026, needs more optimization.
6 877 0.827816512705 Henry Cohn, 2026, needs more optimization.
6 878 0.827859911063 Henry Cohn, 2026, needs more optimization.
6 879 0.827882155399 Henry Cohn, 2026, needs more optimization.
6 880 0.827914350076 Henry Cohn, 2026, needs more optimization.
6 881 0.827974325884 Henry Cohn, 2026, needs more optimization.
6 882 0.827998488146 Henry Cohn, 2026, needs more optimization.
6 883 0.828017236402 Henry Cohn, 2026, needs more optimization.
6 884 0.828082755176 Henry Cohn, 2026, needs more optimization.
6 885 0.828312301010 Henry Cohn, 2026, needs more optimization.
6 886 0.828351533866 Henry Cohn, 2026, needs more optimization.
6 887 0.828416898167 Henry Cohn, 2026, needs more optimization.
6 888 0.828456233610 Henry Cohn, 2026, needs more optimization.
6 889 0.828554491084 Henry Cohn, 2026, needs more optimization.
6 890 0.828586246222 Henry Cohn, 2026, needs more optimization.
6 891 0.828610338687 Henry Cohn, 2026, needs more optimization.
6 892 0.828746783135 Henry Cohn, 2026, needs more optimization.
6 893 0.828777233457 Henry Cohn, 2026, needs more optimization.
6 894 0.828848913509 Henry Cohn, 2026, needs more optimization.
6 895 0.828850214370 Henry Cohn, 2026, needs more optimization.
6 896 0.828933332263 Henry Cohn, 2026, needs more optimization.
6 897 0.828968340290 Henry Cohn, 2026, needs more optimization.
6 898 0.829076964359 Henry Cohn, 2026, needs more optimization.
6 899 0.829083553904 Henry Cohn, 2026, needs more optimization.
6 900 0.829104133796 Henry Cohn, 2026, needs more optimization.
6 901 0.829304099250 Henry Cohn, 2026, needs more optimization.
6 902 0.829320783338 Henry Cohn, 2026, needs more optimization.
6 903 0.829431199111 Henry Cohn, 2026, needs more optimization.
6 904 0.829515684965 Henry Cohn, 2026, needs more optimization.
6 905 0.829604756605 Henry Cohn, 2026, needs more optimization.
6 906 0.829653026664 Henry Cohn, 2026, needs more optimization.
6 908 0.829782225097 Henry Cohn, 2026, needs more optimization.
6 909 0.829895525915 Henry Cohn, 2026, needs more optimization.
6 910 0.829940139325 Henry Cohn, 2026, needs more optimization.
6 911 0.829947323745 Henry Cohn, 2026, needs more optimization.
6 912 0.830008461618 Henry Cohn, 2026, needs more optimization.
6 913 0.830069146605 Henry Cohn, 2026, needs more optimization.
6 914 0.830151242659 Henry Cohn, 2026, needs more optimization.
6 916 0.830450166226 Henry Cohn, 2026, needs more optimization.
6 917 0.830454223396 Henry Cohn, 2026, needs more optimization.
6 918 0.830463209155 Henry Cohn, 2026, needs more optimization.
6 919 0.830487927069 Henry Cohn, 2026, needs more optimization.
6 920 0.830601381814 Henry Cohn, 2026, needs more optimization.
6 921 0.830622524231 Henry Cohn, 2026, needs more optimization.
6 922 0.830625293430 Henry Cohn, 2026, needs more optimization.
6 923 0.830742656325 Henry Cohn, 2026, needs more optimization.
6 924 0.830748785702 Henry Cohn, 2026, needs more optimization.
6 925 0.830773363755 Henry Cohn, 2026, needs more optimization.
6 926 0.830846129373 Henry Cohn, 2026, needs more optimization.
6 927 0.831055903070 Henry Cohn, 2026, needs more optimization.
6 928 0.831081793581 Henry Cohn, 2026, needs more optimization.
6 929 0.831184206661 Henry Cohn, 2026, needs more optimization.
6 930 0.831220289379 Henry Cohn, 2026, needs more optimization.
6 931 0.831282155385 Henry Cohn, 2026, needs more optimization.
6 932 0.831282237733 Henry Cohn, 2026, needs more optimization.
6 933 0.831290782401 Henry Cohn, 2026, needs more optimization.
6 934 0.831293093815 Henry Cohn, 2026, needs more optimization.
6 935 0.831326634223 Henry Cohn, 2026, needs more optimization.
6 936 0.831343225249 Henry Cohn, 2026, needs more optimization.
6 937 0.831404515812 Henry Cohn, 2026, needs more optimization.
6 938 0.831435861298 Henry Cohn, 2026, needs more optimization.
6 939 0.831688963259 Henry Cohn, 2026, needs more optimization.
6 940 0.831694362523 Henry Cohn, 2026, needs more optimization.
6 941 0.831697016339 Henry Cohn, 2026, needs more optimization.
6 942 0.831750546572 Henry Cohn, 2026, needs more optimization.
6 943 0.831774903503 Henry Cohn, 2026, needs more optimization.
6 945 0.831884757104 Henry Cohn, 2026, needs more optimization.
6 946 0.831907516523 Henry Cohn, 2026, needs more optimization.
6 947 0.831955028901 Henry Cohn, 2026, needs more optimization.
6 948 0.832013445188 Henry Cohn, 2026, needs more optimization.
6 949 0.832044640027 Henry Cohn, 2026, needs more optimization.
6 950 0.832054529413 Henry Cohn, 2026, needs more optimization.
6 951 0.832158518556 Henry Cohn, 2026, needs more optimization.
6 952 0.832192896422 Henry Cohn, 2026, needs more optimization.
6 953 0.832204867009 Henry Cohn, 2026, needs more optimization.
6 954 0.832224869527 Henry Cohn, 2026, needs more optimization.
6 955 0.832297768576 Henry Cohn, 2026, needs more optimization.
6 956 0.832309758483 Henry Cohn, 2026, needs more optimization.
6 957 0.832309822503 Henry Cohn, 2026, needs more optimization.
6 958 0.832324617575 Henry Cohn, 2026, needs more optimization.
6 959 0.832421474540 Henry Cohn, 2026, needs more optimization.
6 960 0.832466136662 Henry Cohn, 2026, needs more optimization.
6 961 0.832484117417 Henry Cohn, 2026, needs more optimization.
6 962 0.832513439778 Henry Cohn, 2026, needs more optimization.
6 963 0.832563224586 Henry Cohn, 2026, needs more optimization.
6 964 0.832623632710 Henry Cohn, 2026, needs more optimization.
6 965 0.832696333220 Henry Cohn, 2026, needs more optimization.
6 966 0.832724323178 Henry Cohn, 2026, needs more optimization.
6 967 0.832755662531 Henry Cohn, 2026, needs more optimization.
6 968 0.832820152412 Henry Cohn, 2026, needs more optimization.
6 969 0.832835317589 Henry Cohn, 2026, needs more optimization.
6 970 0.832865938394 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 0.835109209895 Henry Cohn, 2026, needs more optimization.
6 1004 0.836165329693 Henry Cohn, 2026, needs more optimization.
6 1005 0.836786742270 Henry Cohn, 2026, needs more optimization.
6 1006 0.837252368301 Henry Cohn, 2026, needs more optimization.
6 1007 0.837323111064 Henry Cohn, 2026, needs more optimization.
6 1008 0.837375765389 Henry Cohn, 2026, needs more optimization.
6 1009 0.837498856913 Henry Cohn, 2026, needs more optimization.
6 1010 0.837618364916 Henry Cohn, 2026, needs more optimization.
6 1011 0.837637098000 Henry Cohn, 2026, needs more optimization.
6 1012 0.837644626519 Henry Cohn, 2026, needs more optimization.
6 1013 0.837785140793 Henry Cohn, 2026, needs more optimization.
6 1014 0.837795131456 Henry Cohn, 2026, needs more optimization.
6 1015 0.837903804235 Henry Cohn, 2026, needs more optimization.
6 1016 0.837919921018 Henry Cohn, 2026, needs more optimization.
6 1017 0.837931372124 Henry Cohn, 2026, needs more optimization.
6 1018 0.838084883844 Henry Cohn, 2026, needs more optimization.
6 1019 0.838121767222 Henry Cohn, 2026, needs more optimization.
6 1020 0.838321766321 Henry Cohn, 2026, needs more optimization.
6 1021 0.838333047775 Henry Cohn, 2026, needs more optimization.
6 1022 0.838387762373 Henry Cohn, 2026, needs more optimization.
6 1023 0.838501910845 Henry Cohn, 2026, needs more optimization.
6 1024 0.838615228274 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 0.427637413235 Henry Cohn, 2026.
7 69 0.428316243154 Henry Cohn, 2026.
7 70 0.428552368060 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 0.458141126431 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 0.493009413613 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 0.494302166677 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 0.496875584216 Henry Cohn, 2026, needs more optimization.
7 104 0.497402630798 Henry Cohn, 2026, needs more optimization.
7 105 0.497982353835 Henry Cohn, 2026, needs more optimization.
7 106 0.498675447307 Henry Cohn, 2026.
7 107 0.499020848953 Henry Cohn, 2026, needs more optimization.
7 108 0.499537237708 Henry Cohn, 2026, needs more optimization.
7 109 0.499941753582 Henry Cohn, 2026, needs more optimization.
7 110 0.499970532677 Henry Cohn, 2026, needs more optimization.
7 111 0.499999466338 Henry Cohn, 2026, needs more optimization.
7 112 0.499999954889 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.
7 133 0.519150367709 Henry Cohn, 2026, needs more optimization.
7 134 0.519150815992 Henry Cohn, 2026, needs more optimization.
7 135 0.519150974253 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 0.530460442462 Henry Cohn, 2026, needs more optimization.
7 140 0.531592018813 Henry Cohn, 2026, needs more optimization.
7 141 0.531592018960 Henry Cohn, 2026, needs more optimization.
7 142 0.531593676857 Henry Cohn, 2026, needs more optimization.
7 143 0.531593683602 Henry Cohn, 2026, needs more optimization.
7 144 0.531632269397 Henry Cohn, 2026, needs more optimization.
7 145 0.532533319720 Henry Cohn, 2026, needs more optimization.
7 146 0.532826667776 Henry Cohn, 2026, needs more optimization.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.533995828316 Henry Cohn, 2026.
7 149 0.545947606461 Henry Cohn, 2026, needs more optimization.
7 150 0.545969849267 Henry Cohn, 2026, needs more optimization.
7 151 0.545974732293 Henry Cohn, 2026, needs more optimization.
7 152 0.546228007983 Henry Cohn, 2026, needs more optimization.
7 153 0.546232240764 Henry Cohn, 2026, needs more optimization.
7 154 0.546280792445 Henry Cohn, 2026, needs more optimization.
7 155 0.546473189225 Henry Cohn, 2026, needs more optimization.
7 156 0.552236677871 Henry Cohn, 2026, needs more optimization.
7 157 0.557006813536 Henry Cohn, 2026, needs more optimization.
7 158 0.558187412475 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.
7 159 0.559258460237 Henry Cohn, 2026, needs more optimization.
7 161 0.559629605008 Henry Cohn, 2026, needs more optimization.
7 162 0.559666725356 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.
7 165 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 0.563591813282 Henry Cohn, 2026, needs more optimization.
7 171 0.568958802433 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.
7 173 0.569969259979 Henry Cohn, 2026, needs more optimization.
7 174 0.569971767212 Henry Cohn, 2026, needs more optimization.
7 175 0.569971783601 Henry Cohn, 2026, needs more optimization.
7 176 0.570443827677 Henry Cohn, 2026, needs more optimization.
7 177 0.570453557788 Henry Cohn, 2026, needs more optimization.
7 178 0.570455793860 Henry Cohn, 2026, needs more optimization.
7 179 0.570549023628 Henry Cohn, 2026, needs more optimization.
7 180 0.570549077323 Henry Cohn, 2026, needs more optimization.
7 181 0.573146522494 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 0.586921645900 Henry Cohn, 2026, needs more optimization.
7 184 0.589765669975 Henry Cohn, 2026, needs more optimization.
7 200 0.590112298788 Henry Cohn, 2026.
19⁢x3−9⁢x2−3⁢x+1
7 201 0.595103914691 Henry Cohn, 2026, needs more optimization.
7 202 0.598322408533 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.
7 203 0.600591134088 Henry Cohn, 2026, needs more optimization.
7 204 0.601298576882 Henry Cohn, 2026, needs more optimization.
7 205 0.602645309932 Henry Cohn, 2026, needs more optimization.
7 206 0.603233304125 Henry Cohn, 2026, needs more optimization.
7 207 0.603917130995 Henry Cohn, 2026, needs more optimization.
7 208 0.606759030766 Henry Cohn, 2026, needs more optimization.
7 209 0.608558550519 Henry Cohn, 2026, needs more optimization.
7 210 0.610416606052 Henry Cohn, 2026, needs more optimization.
7 211 0.611227871575 Henry Cohn, 2026, needs more optimization.
7 212 0.612383667093 Henry Cohn, 2026, needs more optimization.
7 213 0.612940894935 Henry Cohn, 2026, needs more optimization.
7 214 0.613786883501 Henry Cohn, 2026, needs more optimization.
7 215 0.615184195086 Henry Cohn, 2026, needs more optimization.
7 216 0.615236258830 Henry Cohn, 2026, needs more optimization.
7 217 0.616423937335 Henry Cohn, 2026, needs more optimization.
7 218 0.618010848372 Henry Cohn, 2026, needs more optimization.
7 219 0.618781972402 Henry Cohn, 2026, needs more optimization.
7 220 0.618794444779 Henry Cohn, 2026, needs more optimization.
7 221 0.619647773084 Henry Cohn, 2026, needs more optimization.
7 222 0.619889857761 Henry Cohn, 2026, needs more optimization.
7 223 0.620022335353 Henry Cohn, 2026, needs more optimization.
7 224 0.623028970891 Henry Cohn, 2026, needs more optimization.
7 225 0.623058419724 Henry Cohn, 2026, needs more optimization.
7 226 0.623147224175 Henry Cohn, 2026, needs more optimization.
7 227 0.625175086322 Henry Cohn, 2026, needs more optimization.
7 228 0.625201853199 Henry Cohn, 2026, needs more optimization.
7 229 0.625827024533 Henry Cohn, 2026, needs more optimization.
7 230 0.626068583506 Henry Cohn, 2026, needs more optimization.
7 231 0.626316870318 Henry Cohn, 2026, needs more optimization.
7 232 0.627144040900 Henry Cohn, 2026, needs more optimization.
7 233 0.627575514220 Henry Cohn, 2026, needs more optimization.
7 234 0.627645548935 Henry Cohn, 2026, needs more optimization.
7 235 0.627727348074 Henry Cohn, 2026, needs more optimization.
7 236 0.628416454563 Henry Cohn, 2026, needs more optimization.
7 237 0.629695440719 Henry Cohn, 2026, needs more optimization.
7 238 0.629699588740 Henry Cohn, 2026, needs more optimization.
7 239 0.630353079283 Henry Cohn, 2026, needs more optimization.
7 240 0.630964352274 Henry Cohn, 2026, needs more optimization.
7 241 0.631259460200 Henry Cohn, 2026, needs more optimization.
7 242 0.633346217056 Henry Cohn, 2026, needs more optimization.
7 243 0.633570287797 Henry Cohn, 2026, needs more optimization.
7 244 0.633940936409 Henry Cohn, 2026, needs more optimization.
7 245 0.634467493853 Henry Cohn, 2026, needs more optimization.
7 246 0.634597756512 Henry Cohn, 2026, needs more optimization.
7 247 0.634833639095 Henry Cohn, 2026, needs more optimization.
7 248 0.634861186102 Henry Cohn, 2026, needs more optimization.
7 249 0.636496107317 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.
7 250 0.636607588973 Henry Cohn, 2026, needs more optimization.
7 251 0.636643149497 Henry Cohn, 2026, needs more optimization.
7 252 0.637102760837 Henry Cohn, 2026, needs more optimization.
7 253 0.638304453527 Henry Cohn, 2026, needs more optimization.
7 254 0.638948460950 Henry Cohn, 2026, needs more optimization.
7 255 0.638948468794 Henry Cohn, 2026, needs more optimization.
7 256 0.639091969747 Henry Cohn, 2026, needs more optimization.
7 257 0.639827056068 Henry Cohn, 2026, needs more optimization.
7 258 0.641003368840 Henry Cohn, 2026, needs more optimization.
7 259 0.641106388984 Henry Cohn, 2026, needs more optimization.
7 260 0.641257302670 Henry Cohn, 2026, needs more optimization.
7 261 0.641552528416 Henry Cohn, 2026, needs more optimization.
7 262 0.642506116704 Henry Cohn, 2026, needs more optimization.
7 263 0.644832852898 Henry Cohn, 2026, needs more optimization.
7 264 0.645653977604 Henry Cohn, 2026, needs more optimization.
7 265 0.645812941334 Henry Cohn, 2026, needs more optimization.
7 266 0.646310602531 Henry Cohn, 2026, needs more optimization.
7 267 0.646971737463 Henry Cohn, 2026, needs more optimization.
7 268 0.647235579857 Henry Cohn, 2026, needs more optimization.
7 269 0.647818829898 Henry Cohn, 2026, needs more optimization.
7 270 0.648443151873 Henry Cohn, 2026, needs more optimization.
7 271 0.648624846054 Henry Cohn, 2026, needs more optimization.
7 272 0.649009215199 Henry Cohn, 2026, needs more optimization.
7 273 0.649503276865 Henry Cohn, 2026, needs more optimization.
7 274 0.649787123676 Henry Cohn, 2026, needs more optimization.
7 275 0.650336505289 Henry Cohn, 2026, needs more optimization.
7 276 0.650589940420 Henry Cohn, 2026, needs more optimization.
7 277 0.651301590711 Henry Cohn, 2026, needs more optimization.
7 278 0.651803466926 Henry Cohn, 2026, needs more optimization.
7 279 0.652273519588 Henry Cohn, 2026, needs more optimization.
7 280 0.652760559986 Henry Cohn, 2026, needs more optimization.
7 281 0.653342273433 Henry Cohn, 2026, needs more optimization.
7 282 0.653589225926 Henry Cohn, 2026, needs more optimization.
7 283 0.654062206393 Henry Cohn, 2026, needs more optimization.
7 284 0.654528026414 Henry Cohn, 2026, needs more optimization.
7 285 0.655139831157 Henry Cohn, 2026, needs more optimization.
7 286 0.655479948376 Henry Cohn, 2026, needs more optimization.
7 287 0.655816481308 Henry Cohn, 2026, needs more optimization.
7 288 0.656429142278 Henry Cohn, 2026, needs more optimization.
7 289 0.656865854423 Henry Cohn, 2026, needs more optimization.
7 290 0.657208924846 Henry Cohn, 2026, needs more optimization.
7 291 0.657464792271 Henry Cohn, 2026, needs more optimization.
7 292 0.658031383955 Henry Cohn, 2026, needs more optimization.
7 293 0.658409307350 Henry Cohn, 2026, needs more optimization.
7 294 0.658961462276 Henry Cohn, 2026, needs more optimization.
7 295 0.659128395633 Henry Cohn, 2026, needs more optimization.
7 296 0.659601188631 Henry Cohn, 2026, needs more optimization.
7 297 0.660007999656 Henry Cohn, 2026, needs more optimization.
7 298 0.660383470454 Henry Cohn, 2026, needs more optimization.
7 299 0.660987386856 Henry Cohn, 2026, needs more optimization.
7 300 0.661151369079 Henry Cohn, 2026, needs more optimization.
7 301 0.661608281597 Henry Cohn, 2026, needs more optimization.
7 302 0.661958112583 Henry Cohn, 2026, needs more optimization.
7 303 0.662617298627 Henry Cohn, 2026, needs more optimization.
7 304 0.664311984801 Henry Cohn, 2026, needs more optimization.
7 305 0.664326476970 Henry Cohn, 2026, needs more optimization.
7 306 0.664476113843 Henry Cohn, 2026, needs more optimization.
7 307 0.665082951854 Henry Cohn, 2026, needs more optimization.
7 308 0.665456388324 Henry Cohn, 2026, needs more optimization.
7 309 0.665860403020 Henry Cohn, 2026, needs more optimization.
7 310 0.666282316422 Henry Cohn, 2026, needs more optimization.
7 322 0.666512177546 Henry Cohn, 2026, needs more optimization.
7 324 0.666585783652 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 0.666633537002 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 0.669367871651 Henry Cohn, 2026, needs more optimization.
7 361 0.669635403320 Henry Cohn, 2026, needs more optimization.
7 362 0.670193176232 Henry Cohn, 2026, needs more optimization.
7 363 0.670766643768 Henry Cohn, 2026, needs more optimization.
7 364 0.671303752871 Henry Cohn, 2026, needs more optimization.
7 365 0.671894276281 Henry Cohn, 2026, needs more optimization.
7 366 0.671936598422 Henry Cohn, 2026, needs more optimization.
7 367 0.672596945092 Henry Cohn, 2026, needs more optimization.
7 368 0.673280129116 Henry Cohn, 2026, needs more optimization.
7 369 0.673359058105 Henry Cohn, 2026, needs more optimization.
7 370 0.673509414578 Henry Cohn, 2026, needs more optimization.
7 371 0.673680893414 Henry Cohn, 2026, needs more optimization.
7 372 0.673939422545 Henry Cohn, 2026, needs more optimization.
7 373 0.675207751757 Henry Cohn, 2026, needs more optimization.
7 374 0.675814904197 Henry Cohn, 2026, needs more optimization.
7 375 0.676170413030 Henry Cohn, 2026, needs more optimization.
7 376 0.676765383086 Henry Cohn, 2026, needs more optimization.
7 377 0.676816491168 Henry Cohn, 2026, needs more optimization.
7 378 0.676969744133 Henry Cohn, 2026, needs more optimization.
7 379 0.676982377256 Henry Cohn, 2026, needs more optimization.
7 380 0.677004265910 Henry Cohn, 2026, needs more optimization.
7 381 0.677307411676 Henry Cohn, 2026, needs more optimization.
7 382 0.677322878008 Henry Cohn, 2026, needs more optimization.
7 383 0.677800936475 Henry Cohn, 2026, needs more optimization.
7 384 0.678293424577 Henry Cohn, 2026, needs more optimization.
7 385 0.678940766091 Henry Cohn, 2026, needs more optimization.
7 386 0.678990747473 Henry Cohn, 2026, needs more optimization.
7 387 0.679095983190 Henry Cohn, 2026, needs more optimization.
7 388 0.679591788345 Henry Cohn, 2026, needs more optimization.
7 389 0.679592020959 Henry Cohn, 2026, needs more optimization.
7 390 0.679902613188 Henry Cohn, 2026, needs more optimization.
7 391 0.680052567023 Henry Cohn, 2026, needs more optimization.
7 392 0.680116442318 Henry Cohn, 2026, needs more optimization.
7 393 0.680139937397 Henry Cohn, 2026, needs more optimization.
7 394 0.680148635190 Henry Cohn, 2026, needs more optimization.
7 395 0.680187518427 Henry Cohn, 2026, needs more optimization.
7 396 0.680437417289 Henry Cohn, 2026, needs more optimization.
7 397 0.680492100541 Henry Cohn, 2026, needs more optimization.
7 398 0.680565234116 Henry Cohn, 2026, needs more optimization.
7 399 0.681188598277 Henry Cohn, 2026, needs more optimization.
7 400 0.681398100273 Henry Cohn, 2026, needs more optimization.
7 401 0.681537535025 Henry Cohn, 2026, needs more optimization.
7 402 0.681935915316 Henry Cohn, 2026, needs more optimization.
7 403 0.681946503551 Henry Cohn, 2026, needs more optimization.
7 404 0.681954416991 Henry Cohn, 2026, needs more optimization.
7 405 0.683030299749 Henry Cohn, 2026, needs more optimization.
7 406 0.683135425088 Henry Cohn, 2026, needs more optimization.
7 407 0.683135442617 Henry Cohn, 2026, needs more optimization.
7 408 0.683334673765 Henry Cohn, 2026, needs more optimization.
7 409 0.683548711983 Henry Cohn, 2026, needs more optimization.
7 410 0.683580893938 Henry Cohn, 2026, needs more optimization.
7 411 0.683859204088 Henry Cohn, 2026, needs more optimization.
7 412 0.684006262033 Henry Cohn, 2026, needs more optimization.
7 413 0.684201561956 Henry Cohn, 2026, needs more optimization.
7 414 0.684224219856 Henry Cohn, 2026, needs more optimization.
7 415 0.684394427511 Henry Cohn, 2026, needs more optimization.
7 416 0.684426887069 Henry Cohn, 2026, needs more optimization.
7 417 0.684617752379 Henry Cohn, 2026, needs more optimization.
7 418 0.685272480756 Henry Cohn, 2026, needs more optimization.
7 419 0.686286297700 Henry Cohn, 2026, needs more optimization.
7 420 0.686425214422 Henry Cohn, 2026, needs more optimization.
7 421 0.686725300929 Henry Cohn, 2026, needs more optimization.
7 422 0.686970881965 Henry Cohn, 2026, needs more optimization.
7 423 0.687055700256 Henry Cohn, 2026, needs more optimization.
7 424 0.687913535564 Henry Cohn, 2026, needs more optimization.
7 425 0.688107383355 Henry Cohn, 2026, needs more optimization.
7 426 0.688880727796 Henry Cohn, 2026, needs more optimization.
7 427 0.690250228066 Henry Cohn, 2026, needs more optimization.
7 428 0.690523983966 Henry Cohn, 2026, needs more optimization.
7 429 0.691165230317 Henry Cohn, 2026, needs more optimization.
7 430 0.691252466939 Henry Cohn, 2026, needs more optimization.
7 431 0.691633033877 Henry Cohn, 2026, needs more optimization.
7 432 0.692329854750 Henry Cohn, 2026, needs more optimization.
7 433 0.692798533474 Henry Cohn, 2026, needs more optimization.
7 434 0.693150966421 Henry Cohn, 2026, needs more optimization.
7 435 0.693358678501 Henry Cohn, 2026, needs more optimization.
7 436 0.693614702562 Henry Cohn, 2026, needs more optimization.
7 437 0.693797157032 Henry Cohn, 2026, needs more optimization.
7 438 0.694219010146 Henry Cohn, 2026, needs more optimization.
7 439 0.694724230542 Henry Cohn, 2026, needs more optimization.
7 440 0.694978982119 Henry Cohn, 2026, needs more optimization.
7 441 0.695511693217 Henry Cohn, 2026, needs more optimization.
7 442 0.695872948906 Henry Cohn, 2026, needs more optimization.
7 443 0.696455460703 Henry Cohn, 2026, needs more optimization.
7 444 0.696518909326 Henry Cohn, 2026, needs more optimization.
7 445 0.696711535196 Henry Cohn, 2026, needs more optimization.
7 446 0.697160970288 Henry Cohn, 2026, needs more optimization.
7 447 0.697643952957 Henry Cohn, 2026, needs more optimization.
7 448 0.697726728625 Henry Cohn, 2026, needs more optimization.
7 449 0.698112706110 Henry Cohn, 2026, needs more optimization.
7 450 0.698829935744 Henry Cohn, 2026, needs more optimization.
7 451 0.699265122996 Henry Cohn, 2026, needs more optimization.
7 452 0.699360668139 Henry Cohn, 2026, needs more optimization.
7 453 0.699865220594 Henry Cohn, 2026, needs more optimization.
7 454 0.700511732496 Henry Cohn, 2026, needs more optimization.
7 455 0.700569718457 Henry Cohn, 2026, needs more optimization.
7 456 0.700663338900 Henry Cohn, 2026, needs more optimization.
7 457 0.700929777833 Henry Cohn, 2026, needs more optimization.
7 458 0.701304983208 Henry Cohn, 2026, needs more optimization.
7 459 0.701940757217 Henry Cohn, 2026, needs more optimization.
7 460 0.702003538385 Henry Cohn, 2026, needs more optimization.
7 461 0.702822375016 Henry Cohn, 2026, needs more optimization.
7 462 0.703378901230 Henry Cohn, 2026, needs more optimization.
7 463 0.703477159639 Henry Cohn, 2026, needs more optimization.
7 464 0.703910869195 Henry Cohn, 2026, needs more optimization.
7 465 0.704390331801 Henry Cohn, 2026, needs more optimization.
7 466 0.705196683376 Henry Cohn, 2026, needs more optimization.
7 467 0.705390191157 Henry Cohn, 2026, needs more optimization.
7 468 0.705704971582 Henry Cohn, 2026, needs more optimization.
7 469 0.705794877267 Henry Cohn, 2026, needs more optimization.
7 470 0.705935121511 Henry Cohn, 2026, needs more optimization.
7 471 0.706012749186 Henry Cohn, 2026, needs more optimization.
7 472 0.706080947973 Henry Cohn, 2026, needs more optimization.
7 473 0.706248806625 Henry Cohn, 2026, needs more optimization.
7 474 0.706525230070 Henry Cohn, 2026, needs more optimization.
7 475 0.706543362144 Henry Cohn, 2026, needs more optimization.
7 476 0.706694118369 Henry Cohn, 2026, needs more optimization.
7 477 0.706812999395 Henry Cohn, 2026, needs more optimization.
7 478 0.706900215932 Henry Cohn, 2026, needs more optimization.
7 479 0.706984087703 Henry Cohn, 2026, needs more optimization.
7 480 0.707067784764 Henry Cohn, 2026, needs more optimization.
7 481 0.707582790811 Henry Cohn, 2026, needs more optimization.
7 482 0.707641651205 Henry Cohn, 2026, needs more optimization.
7 483 0.707645310263 Henry Cohn, 2026, needs more optimization.
7 484 0.707646544999 Henry Cohn, 2026, needs more optimization.
7 485 0.707671814523 Henry Cohn, 2026, needs more optimization.
7 486 0.707738140888 Henry Cohn, 2026, needs more optimization.
7 487 0.707769872107 Henry Cohn, 2026, needs more optimization.
7 488 0.707848042285 Henry Cohn, 2026, needs more optimization.
7 489 0.708001038066 Henry Cohn, 2026, needs more optimization.
7 490 0.708056693511 Henry Cohn, 2026, needs more optimization.
7 491 0.708193533540 Henry Cohn, 2026, needs more optimization.
7 492 0.708195924986 Henry Cohn, 2026, needs more optimization.
7 493 0.708441778400 Henry Cohn, 2026, needs more optimization.
7 494 0.708874206773 Henry Cohn, 2026, needs more optimization.
7 495 0.709120112550 Henry Cohn, 2026, needs more optimization.
7 496 0.709123913009 Henry Cohn, 2026, needs more optimization.
7 497 0.709169872387 Henry Cohn, 2026, needs more optimization.
7 498 0.709281450883 Henry Cohn, 2026, needs more optimization.
7 500 0.709942227838 Henry Cohn, 2026, needs more optimization.
7 501 0.709958550536 Henry Cohn, 2026, needs more optimization.
7 502 0.710434927735 Henry Cohn, 2026, needs more optimization.
7 503 0.710507158090 Henry Cohn, 2026, needs more optimization.
7 504 0.710937586275 Henry Cohn, 2026, needs more optimization.
7 505 0.710939094701 Henry Cohn, 2026, needs more optimization.
7 506 0.710990030426 Henry Cohn, 2026, needs more optimization.
7 507 0.711084697345 Henry Cohn, 2026, needs more optimization.
7 508 0.711111956912 Henry Cohn, 2026, needs more optimization.
7 509 0.711207576943 Henry Cohn, 2026, needs more optimization.
7 510 0.711303012734 Henry Cohn, 2026, needs more optimization.
7 511 0.711375452453 Henry Cohn, 2026, needs more optimization.
7 512 0.711472072013 Henry Cohn, 2026, needs more optimization.
7 513 0.712178008104 Henry Cohn, 2026, needs more optimization.
7 514 0.712179336958 Henry Cohn, 2026, needs more optimization.
7 515 0.712183010199 Henry Cohn, 2026, needs more optimization.
7 516 0.712193257160 Henry Cohn, 2026, needs more optimization.
7 517 0.712218084004 Henry Cohn, 2026, needs more optimization.
7 518 0.712354658088 Henry Cohn, 2026, needs more optimization.
7 519 0.712384047830 Henry Cohn, 2026, needs more optimization.
7 520 0.712559584609 Henry Cohn, 2026, needs more optimization.
7 521 0.713134661763 Henry Cohn, 2026, needs more optimization.
7 522 0.713136431860 Henry Cohn, 2026, needs more optimization.
7 523 0.713138374002 Henry Cohn, 2026, needs more optimization.
7 524 0.713140145219 Henry Cohn, 2026, needs more optimization.
7 525 0.713142214840 Henry Cohn, 2026, needs more optimization.
7 526 0.713143918650 Henry Cohn, 2026, needs more optimization.
7 527 0.713153813446 Henry Cohn, 2026, needs more optimization.
7 528 0.713157074167 Henry Cohn, 2026, needs more optimization.
7 529 0.713165334831 Henry Cohn, 2026, needs more optimization.
7 530 0.713335421766 Henry Cohn, 2026, needs more optimization.
7 531 0.713399485222 Henry Cohn, 2026, needs more optimization.
7 532 0.713423606587 Henry Cohn, 2026, needs more optimization.
7 533 0.713457794282 Henry Cohn, 2026, needs more optimization.
7 534 0.713462498724 Henry Cohn, 2026, needs more optimization.
7 535 0.713485459157 Henry Cohn, 2026, needs more optimization.
7 536 0.713505036432 Henry Cohn, 2026, needs more optimization.
7 537 0.713779561405 Henry Cohn, 2026, needs more optimization.
7 539 0.713851132844 Henry Cohn, 2026, needs more optimization.
7 540 0.713886817935 Henry Cohn, 2026, needs more optimization.
7 541 0.713940207988 Henry Cohn, 2026, needs more optimization.
7 542 0.713991766977 Henry Cohn, 2026, needs more optimization.
7 543 0.714030053100 Henry Cohn, 2026, needs more optimization.
7 544 0.714063184897 Henry Cohn, 2026, needs more optimization.
7 545 0.714064335331 Henry Cohn, 2026, needs more optimization.
7 546 0.714064386051 Henry Cohn, 2026, needs more optimization.
7 547 0.714069798030 Henry Cohn, 2026, needs more optimization.
7 548 0.714189309490 Henry Cohn, 2026, needs more optimization.
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 0.720006418963 Henry Cohn, 2026, needs more optimization.
7 635 0.721180767313 Henry Cohn, 2026, needs more optimization.
7 636 0.722121225973 Henry Cohn, 2026, needs more optimization.
7 637 0.722906182893 Henry Cohn, 2026, needs more optimization.
7 638 0.723681431670 Henry Cohn, 2026, needs more optimization.
7 639 0.724497522585 Henry Cohn, 2026, needs more optimization.
7 640 0.724995131488 Henry Cohn, 2026, needs more optimization.
7 641 0.725511821193 Henry Cohn, 2026, needs more optimization.
7 642 0.726061234855 Henry Cohn, 2026, needs more optimization.
7 643 0.726418284989 Henry Cohn, 2026, needs more optimization.
7 644 0.726765651361 Henry Cohn, 2026, needs more optimization.
7 645 0.727071035655 Henry Cohn, 2026, needs more optimization.
7 646 0.727518491865 Henry Cohn, 2026, needs more optimization.
7 647 0.727897042236 Henry Cohn, 2026, needs more optimization.
7 648 0.728312448058 Henry Cohn, 2026, needs more optimization.
7 649 0.728644455803 Henry Cohn, 2026, needs more optimization.
7 650 0.729056709293 Henry Cohn, 2026, needs more optimization.
7 651 0.729302256230 Henry Cohn, 2026, needs more optimization.
7 652 0.729546990509 Henry Cohn, 2026, needs more optimization.
7 653 0.729787258020 Henry Cohn, 2026, needs more optimization.
7 654 0.729983706507 Henry Cohn, 2026, needs more optimization.
7 655 0.730238870689 Henry Cohn, 2026, needs more optimization.
7 656 0.730557910669 Henry Cohn, 2026, needs more optimization.
7 657 0.730812878540 Henry Cohn, 2026, needs more optimization.
7 658 0.731120547274 Henry Cohn, 2026, needs more optimization.
7 659 0.731370061547 Henry Cohn, 2026, needs more optimization.
7 660 0.731489823113 Henry Cohn, 2026, needs more optimization.
7 661 0.731867528899 Henry Cohn, 2026, needs more optimization.
7 662 0.732092886059 Henry Cohn, 2026, needs more optimization.
7 663 0.732308011173 Henry Cohn, 2026, needs more optimization.
7 664 0.732500088873 Henry Cohn, 2026, needs more optimization.
7 665 0.732900332477 Henry Cohn, 2026, needs more optimization.
7 666 0.733218902183 Henry Cohn, 2026, needs more optimization.
7 667 0.733496194730 Henry Cohn, 2026, needs more optimization.
7 668 0.733764424639 Henry Cohn, 2026, needs more optimization.
7 669 0.734022572254 Henry Cohn, 2026, needs more optimization.
7 670 0.734312753420 Henry Cohn, 2026, needs more optimization.
7 671 0.734589696331 Henry Cohn, 2026, needs more optimization.
7 672 0.734851191533 Henry Cohn, 2026, needs more optimization.
7 673 0.735099135796 Henry Cohn, 2026, needs more optimization.
7 674 0.735518770796 Henry Cohn, 2026, needs more optimization.
7 675 0.735694586137 Henry Cohn, 2026, needs more optimization.
7 676 0.735878376809 Henry Cohn, 2026, needs more optimization.
7 677 0.736131908585 Henry Cohn, 2026, needs more optimization.
7 678 0.736351300762 Henry Cohn, 2026, needs more optimization.
7 679 0.736585073719 Henry Cohn, 2026, needs more optimization.
7 680 0.736871911259 Henry Cohn, 2026, needs more optimization.
7 681 0.737100872666 Henry Cohn, 2026, needs more optimization.
7 682 0.737352410463 Henry Cohn, 2026, needs more optimization.
7 683 0.737502759268 Henry Cohn, 2026, needs more optimization.
7 684 0.737635822668 Henry Cohn, 2026, needs more optimization.
7 685 0.737762340155 Henry Cohn, 2026, needs more optimization.
7 686 0.737995073114 Henry Cohn, 2026, needs more optimization.
7 687 0.737997893387 Henry Cohn, 2026, needs more optimization.
7 688 0.738000349684 Henry Cohn, 2026, needs more optimization.
7 689 0.738002494450 Henry Cohn, 2026, needs more optimization.
7 691 0.738395814348 Henry Cohn, 2026, needs more optimization.
7 693 0.738395872719 Henry Cohn, 2026, needs more optimization.
7 694 0.738396909163 Henry Cohn, 2026, needs more optimization.
7 695 0.738397885575 Henry Cohn, 2026, needs more optimization.
7 696 0.738399042205 Henry Cohn, 2026, needs more optimization.
7 697 0.738400403254 Henry Cohn, 2026, needs more optimization.
7 698 0.738535800617 Henry Cohn, 2026, needs more optimization.
7 699 0.738546881650 Henry Cohn, 2026, needs more optimization.
7 700 0.738656092859 Henry Cohn, 2026, needs more optimization.
7 701 0.739121000448 Henry Cohn, 2026, needs more optimization.
7 702 0.739270755413 Henry Cohn, 2026, needs more optimization.
7 703 0.739883168618 Henry Cohn, 2026, needs more optimization.
7 704 0.739917292067 Henry Cohn, 2026, needs more optimization.
7 705 0.739971920910 Henry Cohn, 2026, needs more optimization.
7 706 0.740017597549 Henry Cohn, 2026, needs more optimization.
7 707 0.740051885191 Henry Cohn, 2026, needs more optimization.
7 708 0.740069944211 Henry Cohn, 2026, needs more optimization.
7 709 0.740080287705 Henry Cohn, 2026, needs more optimization.
7 710 0.740199534330 Henry Cohn, 2026, needs more optimization.
7 711 0.740854150818 Henry Cohn, 2026, needs more optimization.
7 712 0.740857259592 Henry Cohn, 2026, needs more optimization.
7 713 0.740859299906 Henry Cohn, 2026, needs more optimization.
7 714 0.740862275623 Henry Cohn, 2026, needs more optimization.
7 733 0.744904412220 Henry Cohn, 2026, needs more optimization.
7 734 0.749198319896 Henry Cohn, 2026, needs more optimization.
7 735 0.749327854245 Henry Cohn, 2026, needs more optimization.
7 736 0.749511713756 Henry Cohn, 2026, needs more optimization.
7 737 0.749715954872 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 0.755754743972 Henry Cohn, 2026, needs more optimization.
7 884 0.766410581290 Henry Cohn, 2026, needs more optimization.
7 885 0.766514005082 Henry Cohn, 2026, needs more optimization.
7 886 0.766519926672 Henry Cohn, 2026, needs more optimization.
7 887 0.766837891985 Henry Cohn, 2026, needs more optimization.
7 888 0.766875310201 Henry Cohn, 2026, needs more optimization.
7 889 0.766877700809 Henry Cohn, 2026, needs more optimization.
7 890 0.766992722955 Henry Cohn, 2026, needs more optimization.
7 891 0.767031315421 Henry Cohn, 2026, needs more optimization.
7 892 0.767224558255 Henry Cohn, 2026, needs more optimization.
7 893 0.767227061223 Henry Cohn, 2026, needs more optimization.
7 894 0.767243886041 Henry Cohn, 2026, needs more optimization.
7 895 0.767383018030 Henry Cohn, 2026, needs more optimization.
7 896 0.767395465557 Henry Cohn, 2026, needs more optimization.
7 897 0.767666628085 Henry Cohn, 2026, needs more optimization.
7 898 0.767726736741 Henry Cohn, 2026, needs more optimization.
7 899 0.767730199894 Henry Cohn, 2026, needs more optimization.
7 900 0.767765545280 Henry Cohn, 2026, needs more optimization.
7 901 0.767971844641 Henry Cohn, 2026, needs more optimization.
7 902 0.767971859698 Henry Cohn, 2026, needs more optimization.
7 903 0.768096538496 Henry Cohn, 2026, needs more optimization.
7 904 0.768130814035 Henry Cohn, 2026, needs more optimization.
7 905 0.768341150818 Henry Cohn, 2026, needs more optimization.
7 906 0.768381390091 Henry Cohn, 2026, needs more optimization.
7 907 0.768510523220 Henry Cohn, 2026, needs more optimization.
7 908 0.768566921948 Henry Cohn, 2026, needs more optimization.
7 909 0.768692235089 Henry Cohn, 2026, needs more optimization.
7 910 0.768722198474 Henry Cohn, 2026, needs more optimization.
7 911 0.768762906838 Henry Cohn, 2026, needs more optimization.
7 912 0.768911594361 Henry Cohn, 2026, needs more optimization.
7 913 0.768916193005 Henry Cohn, 2026, needs more optimization.
7 914 0.768918701003 Henry Cohn, 2026, needs more optimization.
7 915 0.769144575898 Henry Cohn, 2026, needs more optimization.
7 916 0.769173927314 Henry Cohn, 2026, needs more optimization.
7 917 0.769175615882 Henry Cohn, 2026, needs more optimization.
7 918 0.769525453541 Henry Cohn, 2026, needs more optimization.
7 919 0.769529823867 Henry Cohn, 2026, needs more optimization.
7 920 0.769540684996 Henry Cohn, 2026, needs more optimization.
7 921 0.769694735006 Henry Cohn, 2026, needs more optimization.
7 922 0.769873135860 Henry Cohn, 2026, needs more optimization.
7 923 0.769891569125 Henry Cohn, 2026, needs more optimization.
7 924 0.769915940684 Henry Cohn, 2026, needs more optimization.
7 925 0.769956486155 Henry Cohn, 2026, needs more optimization.
7 926 0.769991356407 Henry Cohn, 2026, needs more optimization.
7 927 0.770114337803 Henry Cohn, 2026, needs more optimization.
7 928 0.770220594232 Henry Cohn, 2026, needs more optimization.
7 929 0.770222897915 Henry Cohn, 2026, needs more optimization.
7 930 0.770257009878 Henry Cohn, 2026, needs more optimization.
7 931 0.770531764608 Henry Cohn, 2026, needs more optimization.
7 932 0.770553462975 Henry Cohn, 2026, needs more optimization.
7 933 0.770576236483 Henry Cohn, 2026, needs more optimization.
7 934 0.770621154173 Henry Cohn, 2026, needs more optimization.
7 935 0.770762076102 Henry Cohn, 2026, needs more optimization.
7 937 0.770892299067 Henry Cohn, 2026, needs more optimization.
7 938 0.771123439151 Henry Cohn, 2026, needs more optimization.
7 939 0.771141230010 Henry Cohn, 2026, needs more optimization.
7 940 0.771184403640 Henry Cohn, 2026, needs more optimization.
7 941 0.771212124866 Henry Cohn, 2026, needs more optimization.
7 942 0.771348484389 Henry Cohn, 2026, needs more optimization.
7 943 0.771351398400 Henry Cohn, 2026, needs more optimization.
7 944 0.771495294599 Henry Cohn, 2026, needs more optimization.
7 945 0.771504715924 Henry Cohn, 2026, needs more optimization.
7 946 0.771687808875 Henry Cohn, 2026, needs more optimization.
7 947 0.771718760650 Henry Cohn, 2026, needs more optimization.
7 948 0.771742169135 Henry Cohn, 2026, needs more optimization.
7 949 0.771746485281 Henry Cohn, 2026, needs more optimization.
7 950 0.771851539029 Henry Cohn, 2026, needs more optimization.
7 951 0.772071987413 Henry Cohn, 2026, needs more optimization.
7 952 0.772201370817 Henry Cohn, 2026, needs more optimization.
7 953 0.772212790911 Henry Cohn, 2026, needs more optimization.
7 954 0.772229332252 Henry Cohn, 2026, needs more optimization.
7 955 0.772306641760 Henry Cohn, 2026, needs more optimization.
7 956 0.772581314084 Henry Cohn, 2026, needs more optimization.
7 957 0.772593720459 Henry Cohn, 2026, needs more optimization.
7 958 0.772697543169 Henry Cohn, 2026, needs more optimization.
7 959 0.772720065246 Henry Cohn, 2026, needs more optimization.
7 960 0.772792018679 Henry Cohn, 2026, needs more optimization.
7 961 0.772797702882 Henry Cohn, 2026, needs more optimization.
7 962 0.772898201462 Henry Cohn, 2026, needs more optimization.
7 963 0.773146256158 Henry Cohn, 2026, needs more optimization.
7 964 0.773166106000 Henry Cohn, 2026, needs more optimization.
7 965 0.773193137628 Henry Cohn, 2026, needs more optimization.
7 966 0.773205115681 Henry Cohn, 2026, needs more optimization.
7 967 0.773294075632 Henry Cohn, 2026, needs more optimization.
7 968 0.773512011596 Henry Cohn, 2026, needs more optimization.
7 969 0.773557232619 Henry Cohn, 2026, needs more optimization.
7 970 0.773578590409 Henry Cohn, 2026, needs more optimization.
7 971 0.773689602625 Henry Cohn, 2026, needs more optimization.
7 972 0.773820636652 Henry Cohn, 2026, needs more optimization.
7 973 0.773826757197 Henry Cohn, 2026, needs more optimization.
7 974 0.773901986814 Henry Cohn, 2026, needs more optimization.
7 975 0.774043532047 Henry Cohn, 2026, needs more optimization.
7 976 0.774168274593 Henry Cohn, 2026, needs more optimization.
7 977 0.774190526476 Henry Cohn, 2026, needs more optimization.
7 978 0.774195519921 Henry Cohn, 2026, needs more optimization.
7 979 0.774274940842 Henry Cohn, 2026, needs more optimization.
7 980 0.774285199241 Henry Cohn, 2026, needs more optimization.
7 981 0.774463863927 Henry Cohn, 2026, needs more optimization.
7 982 0.774483421692 Henry Cohn, 2026, needs more optimization.
7 983 0.774566186215 Henry Cohn, 2026, needs more optimization.
7 984 0.774737637201 Henry Cohn, 2026, needs more optimization.
7 985 0.774742011348 Henry Cohn, 2026, needs more optimization.
7 986 0.774767932131 Henry Cohn, 2026, needs more optimization.
7 987 0.774861266165 Henry Cohn, 2026, needs more optimization.
7 988 0.775029006882 Henry Cohn, 2026, needs more optimization.
7 989 0.775039595101 Henry Cohn, 2026, needs more optimization.
7 990 0.775216185470 Henry Cohn, 2026, needs more optimization.
7 991 0.775253138370 Henry Cohn, 2026, needs more optimization.
7 992 0.775411512138 Henry Cohn, 2026, needs more optimization.
7 993 0.775424177725 Henry Cohn, 2026, needs more optimization.
7 994 0.775439291842 Henry Cohn, 2026, needs more optimization.
7 995 0.775620453334 Henry Cohn, 2026, needs more optimization.
7 996 0.775661874345 Henry Cohn, 2026, needs more optimization.
7 997 0.775694001321 Henry Cohn, 2026, needs more optimization.
7 998 0.775747151345 Henry Cohn, 2026, needs more optimization.
7 999 0.775752990341 Henry Cohn, 2026, needs more optimization.
7 1000 0.775792961205 Henry Cohn, 2026, needs more optimization.
7 1001 0.775954376982 Henry Cohn, 2026, needs more optimization.
7 1002 0.775966900953 Henry Cohn, 2026, needs more optimization.
7 1003 0.776157339900 Henry Cohn, 2026, needs more optimization.
7 1004 0.776178431934 Henry Cohn, 2026, needs more optimization.
7 1005 0.776307470947 Henry Cohn, 2026, needs more optimization.
7 1006 0.776371157254 Henry Cohn, 2026, needs more optimization.
7 1007 0.776412946840 Henry Cohn, 2026, needs more optimization.
7 1008 0.776719163430 Henry Cohn, 2026, needs more optimization.
7 1009 0.776726478527 Henry Cohn, 2026, needs more optimization.
7 1010 0.776775608534 Henry Cohn, 2026, needs more optimization.
7 1011 0.776927009768 Henry Cohn, 2026, needs more optimization.
7 1012 0.776933279835 Henry Cohn, 2026, needs more optimization.
7 1013 0.777116201795 Henry Cohn, 2026, needs more optimization.
7 1014 0.777152344416 Henry Cohn, 2026, needs more optimization.
7 1015 0.777185310687 Henry Cohn, 2026, needs more optimization.
7 1016 0.777306246930 Henry Cohn, 2026, needs more optimization.
7 1017 0.777349964032 Henry Cohn, 2026, needs more optimization.
7 1018 0.777365731334 Henry Cohn, 2026, needs more optimization.
7 1019 0.777455347455 Henry Cohn, 2026, needs more optimization.
7 1020 0.777797243697 Henry Cohn, 2026, needs more optimization.
7 1021 0.777816284519 Henry Cohn, 2026, needs more optimization.
7 1022 0.777979852487 Henry Cohn, 2026, needs more optimization.
7 1023 0.777982535057 Henry Cohn, 2026, needs more optimization.
7 1024 0.777996378882 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 0.288883351523 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 0.395049514668 Henry Cohn, 2024.
8 80 0.396547014941 Henry Cohn, 2026, needs more optimization.
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 0.421656007707 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 0.427518817396 Henry Cohn, 2026.
8 98 0.428413697863 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 0.428561564462 Henry Cohn, 2026, needs more optimization.
8 101 0.428570721180 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 0.447554775429 Henry Cohn, 2026, needs more optimization.
8 116 0.448006674268 Henry Cohn, 2026.
8 117 0.451123128034 Henry Cohn, 2026, needs more optimization.
8 118 0.455245746618 Henry Cohn, 2026, needs more optimization.
8 119 0.460488108267 Henry Cohn, 2026.
8 120 0.461570019406 Henry Cohn, 2026.
8 121 0.461664940349 Henry Cohn, 2026, needs more optimization.
8 122 0.461856796790 Henry Cohn, 2026.
8 123 0.462136061318 Henry Cohn, 2026, needs more optimization.
8 124 0.462496220038 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 0.467415573366 Henry Cohn, 2026, needs more optimization.
8 139 0.468649393371 Henry Cohn, 2026, needs more optimization.
8 140 0.470795586308 Henry Cohn, 2026, needs more optimization.
8 141 0.472527457658 Henry Cohn, 2026, needs more optimization.
8 142 0.476420785351 Henry Cohn, 2026, needs more optimization.
8 143 0.476461615916 Henry Cohn, 2026, needs more optimization.
8 144 0.482729488505 Henry Cohn, 2026, needs more optimization.
8 145 0.485575540357 Henry Cohn, 2026, needs more optimization.
8 146 0.488018229488 Henry Cohn, 2026, needs more optimization.
8 147 0.488151685232 Henry Cohn, 2026, needs more optimization.
8 148 0.488560224968 Henry Cohn, 2026, needs more optimization.
8 149 0.489635878980 Henry Cohn, 2026, needs more optimization.
8 150 0.489666834198 Henry Cohn, 2026, needs more optimization.
8 151 0.490671101579 Henry Cohn, 2026, needs more optimization.
8 152 0.491488635646 Henry Cohn, 2026, needs more optimization.
8 153 0.492431688184 Henry Cohn, 2026, needs more optimization.
8 154 0.492641314465 Henry Cohn, 2026, needs more optimization.
8 155 0.493016011167 Henry Cohn, 2026, needs more optimization.
8 156 0.493408644360 Henry Cohn, 2026, needs more optimization.
8 157 0.493603724967 Henry Cohn, 2026, needs more optimization.
8 158 0.493990620867 Henry Cohn, 2026, needs more optimization.
8 159 0.494190440911 Henry Cohn, 2026, needs more optimization.
8 160 0.494794111456 Henry Cohn, 2026, needs more optimization.
8 161 0.496270071073 Henry Cohn, 2026, needs more optimization.
8 162 0.496385597593 Henry Cohn, 2026, needs more optimization.
8 163 0.496832308247 Henry Cohn, 2026, needs more optimization.
8 164 0.496988070032 Henry Cohn, 2026, needs more optimization.
8 165 0.497136113863 Henry Cohn, 2026, needs more optimization.
8 166 0.497169822914 Henry Cohn, 2026, needs more optimization.
8 167 0.497749217680 Henry Cohn, 2026, needs more optimization.
8 168 0.498096440073 Henry Cohn, 2026, needs more optimization.
8 169 0.498239438147 Henry Cohn, 2026, needs more optimization.
8 170 0.498777446846 Henry Cohn, 2026, needs more optimization.
8 171 0.499092383582 Henry Cohn, 2026, needs more optimization.
8 172 0.499176485965 Henry Cohn, 2026, needs more optimization.
8 173 0.499406665255 Henry Cohn, 2026, needs more optimization.
8 174 0.499702518842 Henry Cohn, 2026, needs more optimization.
8 175 0.499825517235 Henry Cohn, 2026, needs more optimization.
8 176 0.499936578083 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 0.544142574568 Henry Cohn, 2026, needs more optimization.
8 243 0.547275572692 Henry Cohn, 2026, needs more optimization.
8 244 0.549376273665 Henry Cohn, 2026, needs more optimization.
8 245 0.551505618372 Henry Cohn, 2026, needs more optimization.
8 246 0.553440752496 Henry Cohn, 2026, needs more optimization.
8 247 0.555289424875 Henry Cohn, 2026, needs more optimization.
8 248 0.557106074688 Henry Cohn, 2026, needs more optimization.
8 249 0.559174278603 Henry Cohn, 2026, needs more optimization.
8 250 0.560485913848 Henry Cohn, 2026, needs more optimization.
8 251 0.561372013354 Henry Cohn, 2026, needs more optimization.
8 252 0.562684715689 Henry Cohn, 2026, needs more optimization.
8 253 0.564106219521 Henry Cohn, 2026, needs more optimization.
8 254 0.564223460999 Henry Cohn, 2026, needs more optimization.
8 255 0.564245309926 Henry Cohn, 2026, needs more optimization.
8 256 0.564576369083 Henry Cohn, 2026, needs more optimization.
8 257 0.564970981777 Henry Cohn, 2026, needs more optimization.
8 258 0.566631748899 Henry Cohn, 2026, needs more optimization.
8 259 0.568548397044 Henry Cohn, 2026, needs more optimization.
8 260 0.568561078949 Henry Cohn, 2026, needs more optimization.
8 261 0.569474412994 Henry Cohn, 2026, needs more optimization.
8 262 0.570035805948 Henry Cohn, 2026, needs more optimization.
8 263 0.571068458675 Henry Cohn, 2026, needs more optimization.
8 264 0.571403321675 Henry Cohn, 2026, needs more optimization.
8 265 0.572176770330 Henry Cohn, 2026, needs more optimization.
8 266 0.572622182303 Henry Cohn, 2026, needs more optimization.
8 267 0.573379129891 Henry Cohn, 2026, needs more optimization.
8 268 0.573583849050 Henry Cohn, 2026, needs more optimization.
8 269 0.573882852278 Henry Cohn, 2026, needs more optimization.
8 270 0.574627466701 Henry Cohn, 2026, needs more optimization.
8 271 0.575479151527 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.
8 272 0.575768414603 Henry Cohn, 2026, needs more optimization.
8 273 0.576502008889 Henry Cohn, 2026, needs more optimization.
8 274 0.577205779640 Henry Cohn, 2026, needs more optimization.
8 275 0.577886477552 Henry Cohn, 2026, needs more optimization.
8 276 0.578735523009 Henry Cohn, 2026, needs more optimization.
8 277 0.579500526129 Henry Cohn, 2026, needs more optimization.
8 278 0.579911482866 Henry Cohn, 2026, needs more optimization.
8 279 0.580717712525 Henry Cohn, 2026, needs more optimization.
8 280 0.580900386683 Henry Cohn, 2026, needs more optimization.
8 281 0.580913654633 Henry Cohn, 2026, needs more optimization.
8 282 0.581467584759 Henry Cohn, 2026, needs more optimization.
8 283 0.581709881625 Henry Cohn, 2026, needs more optimization.
8 284 0.581930477532 Henry Cohn, 2026, needs more optimization.
8 285 0.582143750656 Henry Cohn, 2026, needs more optimization.
8 286 0.582466448740 Henry Cohn, 2026, needs more optimization.
8 287 0.582990469123 Henry Cohn, 2026, needs more optimization.
8 288 0.584442900576 Henry Cohn, 2026, needs more optimization.
8 289 0.585021719912 Henry Cohn, 2026, needs more optimization.
8 290 0.585254785183 Henry Cohn, 2026, needs more optimization.
8 291 0.585586191341 Henry Cohn, 2026, needs more optimization.
8 292 0.585735419151 Henry Cohn, 2026, needs more optimization.
8 293 0.585780598277 Henry Cohn, 2026, needs more optimization.
8 294 0.586503441640 Henry Cohn, 2026, needs more optimization.
8 295 0.587089045145 Henry Cohn, 2026, needs more optimization.
8 296 0.588199049311 Henry Cohn, 2026, needs more optimization.
8 297 0.589640005842 Henry Cohn, 2026, needs more optimization.
8 298 0.590459192786 Henry Cohn, 2026, needs more optimization.
8 299 0.590459205659 Henry Cohn, 2026, needs more optimization.
8 300 0.590474893714 Henry Cohn, 2026, needs more optimization.
8 301 0.590551707956 Henry Cohn, 2026, needs more optimization.
8 302 0.590573463811 Henry Cohn, 2026, needs more optimization.
8 303 0.590579379531 Henry Cohn, 2026, needs more optimization.
8 304 0.590593403621 Henry Cohn, 2026, needs more optimization.
8 305 0.590645033460 Henry Cohn, 2026, needs more optimization.
8 306 0.590695206700 Henry Cohn, 2026, needs more optimization.
8 307 0.590771799143 Henry Cohn, 2026, needs more optimization.
8 308 0.590980704637 Henry Cohn, 2026, needs more optimization.
8 309 0.590981709164 Henry Cohn, 2026, needs more optimization.
8 310 0.591756399651 Henry Cohn, 2026, needs more optimization.
8 311 0.592700007462 Henry Cohn, 2026, needs more optimization.
8 312 0.593718703540 Henry Cohn, 2026, needs more optimization.
8 313 0.594302418055 Henry Cohn, 2026, needs more optimization.
8 314 0.594425707741 Henry Cohn, 2026, needs more optimization.
8 315 0.594751027226 Henry Cohn, 2026, needs more optimization.
8 316 0.594782823200 Henry Cohn, 2026, needs more optimization.
8 317 0.595141536121 Henry Cohn, 2026, needs more optimization.
8 318 0.595165288309 Henry Cohn, 2026, needs more optimization.
8 319 0.595277324220 Henry Cohn, 2026, needs more optimization.
8 320 0.595808673510 Henry Cohn, 2026, needs more optimization.
8 321 0.596362139277 Henry Cohn, 2026, needs more optimization.
8 322 0.597017246162 Henry Cohn, 2026, needs more optimization.
8 323 0.597598206541 Henry Cohn, 2026, needs more optimization.
8 324 0.598046690750 Henry Cohn, 2026, needs more optimization.
8 325 0.598652883288 Henry Cohn, 2026, needs more optimization.
8 326 0.599039455209 Henry Cohn, 2026, needs more optimization.
8 327 0.599952445977 Henry Cohn, 2026, needs more optimization.
8 328 0.600374517472 Henry Cohn, 2026, needs more optimization.
8 329 0.600642452930 Henry Cohn, 2026, needs more optimization.
8 330 0.600681715726 Henry Cohn, 2026, needs more optimization.
8 331 0.600909517333 Henry Cohn, 2026, needs more optimization.
8 332 0.600926305323 Henry Cohn, 2026, needs more optimization.
8 333 0.601597993158 Henry Cohn, 2026, needs more optimization.
8 334 0.601891906640 Henry Cohn, 2026, needs more optimization.
8 335 0.602167933967 Henry Cohn, 2026, needs more optimization.
8 336 0.602603398939 Henry Cohn, 2026, needs more optimization.
8 337 0.602737532713 Henry Cohn, 2026, needs more optimization.
8 338 0.602868030425 Henry Cohn, 2026, needs more optimization.
8 339 0.602951649124 Henry Cohn, 2026, needs more optimization.
8 340 0.603072299073 Henry Cohn, 2026, needs more optimization.
8 341 0.603121533220 Henry Cohn, 2026, needs more optimization.
8 342 0.603131497370 Henry Cohn, 2026, needs more optimization.
8 343 0.604257026933 Henry Cohn, 2026, needs more optimization.
8 344 0.604339345765 Henry Cohn, 2026, needs more optimization.
8 345 0.604450634022 Henry Cohn, 2026, needs more optimization.
8 346 0.604491714554 Henry Cohn, 2026, needs more optimization.
8 347 0.604494387943 Henry Cohn, 2026, needs more optimization.
8 348 0.604500542032 Henry Cohn, 2026, needs more optimization.
8 349 0.604509942958 Henry Cohn, 2026, needs more optimization.
8 350 0.604521896027 Henry Cohn, 2026, needs more optimization.
8 351 0.604529015096 Henry Cohn, 2026, needs more optimization.
8 352 0.604546486016 Henry Cohn, 2026, needs more optimization.
8 353 0.604549711918 Henry Cohn, 2026, needs more optimization.
8 354 0.604555190432 Henry Cohn, 2026, needs more optimization.
8 355 0.604697233316 Henry Cohn, 2026, needs more optimization.
8 356 0.606386794253 Henry Cohn, 2026, needs more optimization.
8 357 0.606595125920 Henry Cohn, 2026, needs more optimization.
8 358 0.606819531358 Henry Cohn, 2026, needs more optimization.
8 359 0.606927788369 Henry Cohn, 2026, needs more optimization.
8 360 0.606987065559 Henry Cohn, 2026, needs more optimization.
8 361 0.611059242914 Henry Cohn, 2026, needs more optimization.
8 362 0.611393083859 Henry Cohn, 2026, needs more optimization.
8 363 0.611429609169 Henry Cohn, 2026, needs more optimization.
8 364 0.611620766188 Henry Cohn, 2026, needs more optimization.
8 365 0.611791278745 Henry Cohn, 2026, needs more optimization.
8 366 0.612135859962 Henry Cohn, 2026, needs more optimization.
8 367 0.612242029276 Henry Cohn, 2026, needs more optimization.
8 368 0.612277422734 Henry Cohn, 2026, needs more optimization.
8 369 0.612340129242 Henry Cohn, 2026, needs more optimization.
8 370 0.614301090499 Henry Cohn, 2026, needs more optimization.
8 371 0.614473015575 Henry Cohn, 2026, needs more optimization.
8 372 0.615218041904 Henry Cohn, 2026, needs more optimization.
8 373 0.616559800899 Henry Cohn, 2026, needs more optimization.
8 374 0.617381759304 Henry Cohn, 2026, needs more optimization.
8 375 0.618186753772 Henry Cohn, 2026, needs more optimization.
8 376 0.618251883550 Henry Cohn, 2026, needs more optimization.
8 377 0.618680026694 Henry Cohn, 2026, needs more optimization.
8 378 0.621628978547 Henry Cohn, 2026, needs more optimization.
8 379 0.622060207307 Henry Cohn, 2026, needs more optimization.
8 380 0.622745298722 Henry Cohn, 2026, needs more optimization.
8 381 0.624164510090 Henry Cohn, 2026, needs more optimization.
8 382 0.624733585656 Henry Cohn, 2026, needs more optimization.
8 383 0.624866328812 Henry Cohn, 2026, needs more optimization.
8 384 0.625027034906 Henry Cohn, 2026, needs more optimization.
8 385 0.625395168343 Henry Cohn, 2026, needs more optimization.
8 386 0.625623089802 Henry Cohn, 2026, needs more optimization.
8 387 0.625892819685 Henry Cohn, 2026, needs more optimization.
8 388 0.626423348395 Henry Cohn, 2026, needs more optimization.
8 389 0.626827475302 Henry Cohn, 2026, needs more optimization.
8 390 0.627055314905 Henry Cohn, 2026, needs more optimization.
8 391 0.627519135259 Henry Cohn, 2026, needs more optimization.
8 392 0.627774644336 Henry Cohn, 2026, needs more optimization.
8 393 0.628165263438 Henry Cohn, 2026, needs more optimization.
8 394 0.628323492948 Henry Cohn, 2026, needs more optimization.
8 395 0.628601366158 Henry Cohn, 2026, needs more optimization.
8 396 0.629023496798 Henry Cohn, 2026, needs more optimization.
8 397 0.629130027988 Henry Cohn, 2026, needs more optimization.
8 398 0.629512026824 Henry Cohn, 2026, needs more optimization.
8 399 0.629831927920 Henry Cohn, 2026, needs more optimization.
8 400 0.630160809692 Henry Cohn, 2026, needs more optimization.
8 401 0.630349868637 Henry Cohn, 2026, needs more optimization.
8 402 0.630561992274 Henry Cohn, 2026, needs more optimization.
8 403 0.630799246488 Henry Cohn, 2026, needs more optimization.
8 404 0.631448084493 Henry Cohn, 2026, needs more optimization.
8 405 0.631956687195 Henry Cohn, 2026, needs more optimization.
8 406 0.632037950564 Henry Cohn, 2026, needs more optimization.
8 407 0.632320981993 Henry Cohn, 2026, needs more optimization.
8 408 0.632580905382 Henry Cohn, 2026, needs more optimization.
8 409 0.632761211570 Henry Cohn, 2026, needs more optimization.
8 410 0.633035049831 Henry Cohn, 2026, needs more optimization.
8 411 0.633310991072 Henry Cohn, 2026, needs more optimization.
8 412 0.633620235148 Henry Cohn, 2026, needs more optimization.
8 413 0.633870234031 Henry Cohn, 2026, needs more optimization.
8 414 0.634125023553 Henry Cohn, 2026, needs more optimization.
8 415 0.634368370377 Henry Cohn, 2026, needs more optimization.
8 416 0.634665133333 Henry Cohn, 2026, needs more optimization.
8 417 0.634761325524 Henry Cohn, 2026, needs more optimization.
8 418 0.634844015978 Henry Cohn, 2026, needs more optimization.
8 419 0.634987597896 Henry Cohn, 2026, needs more optimization.
8 420 0.635015890442 Henry Cohn, 2026, needs more optimization.
8 421 0.635215986221 Henry Cohn, 2026, needs more optimization.
8 422 0.635676581085 Henry Cohn, 2026, needs more optimization.
8 423 0.635761494412 Henry Cohn, 2026, needs more optimization.
8 424 0.635854835883 Henry Cohn, 2026, needs more optimization.
8 425 0.636004533521 Henry Cohn, 2026, needs more optimization.
8 426 0.636155326610 Henry Cohn, 2026, needs more optimization.
8 427 0.636392528965 Henry Cohn, 2026, needs more optimization.
8 428 0.636539059543 Henry Cohn, 2026, needs more optimization.
8 429 0.636750214327 Henry Cohn, 2026, needs more optimization.
8 430 0.636862174936 Henry Cohn, 2026, needs more optimization.
8 431 0.637183758638 Henry Cohn, 2026, needs more optimization.
8 432 0.637257892630 Henry Cohn, 2026, needs more optimization.
8 433 0.637688545273 Henry Cohn, 2026, needs more optimization.
8 434 0.637841684613 Henry Cohn, 2026, needs more optimization.
8 435 0.637910846109 Henry Cohn, 2026, needs more optimization.
8 436 0.638127791787 Henry Cohn, 2026, needs more optimization.
8 437 0.638710536776 Henry Cohn, 2026, needs more optimization.
8 438 0.639275051398 Henry Cohn, 2026, needs more optimization.
8 439 0.639344898664 Henry Cohn, 2026, needs more optimization.
8 440 0.639466118441 Henry Cohn, 2026, needs more optimization.
8 441 0.639739652645 Henry Cohn, 2026, needs more optimization.
8 442 0.639912015344 Henry Cohn, 2026, needs more optimization.
8 443 0.639949823899 Henry Cohn, 2026, needs more optimization.
8 444 0.640183132888 Henry Cohn, 2026, needs more optimization.
8 445 0.640373549345 Henry Cohn, 2026, needs more optimization.
8 446 0.640592744308 Henry Cohn, 2026, needs more optimization.
8 447 0.640907922703 Henry Cohn, 2026, needs more optimization.
8 448 0.641215438461 Henry Cohn, 2026, needs more optimization.
8 449 0.641514175590 Henry Cohn, 2026, needs more optimization.
8 450 0.641542541667 Henry Cohn, 2026, needs more optimization.
8 451 0.641559649836 Henry Cohn, 2026, needs more optimization.
8 452 0.641580586267 Henry Cohn, 2026, needs more optimization.
8 453 0.641659534976 Henry Cohn, 2026, needs more optimization.
8 454 0.641701140814 Henry Cohn, 2026, needs more optimization.
8 455 0.641753053523 Henry Cohn, 2026, needs more optimization.
8 456 0.641850799541 Henry Cohn, 2026, needs more optimization.
8 457 0.641892558727 Henry Cohn, 2026, needs more optimization.
8 458 0.641923529198 Henry Cohn, 2026, needs more optimization.
8 459 0.641961255792 Henry Cohn, 2026, needs more optimization.
8 460 0.642088397694 Henry Cohn, 2026, needs more optimization.
8 461 0.642136530809 Henry Cohn, 2026, needs more optimization.
8 462 0.642171430915 Henry Cohn, 2026, needs more optimization.
8 463 0.642269194886 Henry Cohn, 2026, needs more optimization.
8 464 0.642314054544 Henry Cohn, 2026, needs more optimization.
8 465 0.642353853146 Henry Cohn, 2026, needs more optimization.
8 466 0.642556996089 Henry Cohn, 2026, needs more optimization.
8 467 0.642697856545 Henry Cohn, 2026, needs more optimization.
8 468 0.642937066703 Henry Cohn, 2026, needs more optimization.
8 469 0.643132128423 Henry Cohn, 2026, needs more optimization.
8 470 0.643310936505 Henry Cohn, 2026, needs more optimization.
8 471 0.643446532752 Henry Cohn, 2026, needs more optimization.
8 472 0.643657905097 Henry Cohn, 2026, needs more optimization.
8 473 0.643825833851 Henry Cohn, 2026, needs more optimization.
8 474 0.643841385531 Henry Cohn, 2026, needs more optimization.
8 475 0.644062181911 Henry Cohn, 2026, needs more optimization.
8 476 0.644205648921 Henry Cohn, 2026, needs more optimization.
8 477 0.644355136211 Henry Cohn, 2026, needs more optimization.
8 478 0.644660254347 Henry Cohn, 2026, needs more optimization.
8 479 0.644783776150 Henry Cohn, 2026, needs more optimization.
8 480 0.645245949788 Henry Cohn, 2026, needs more optimization.
8 481 0.645350305623 Henry Cohn, 2026, needs more optimization.
8 482 0.645560490129 Henry Cohn, 2026, needs more optimization.
8 483 0.645634337652 Henry Cohn, 2026, needs more optimization.
8 484 0.646174630323 Henry Cohn, 2026, needs more optimization.
8 485 0.646396967457 Henry Cohn, 2026, needs more optimization.
8 486 0.646820463152 Henry Cohn, 2026, needs more optimization.
8 487 0.647268914019 Henry Cohn, 2026, needs more optimization.
8 488 0.647388389043 Henry Cohn, 2026, needs more optimization.
8 489 0.647419053455 Henry Cohn, 2026, needs more optimization.
8 490 0.647737626597 Henry Cohn, 2026, needs more optimization.
8 491 0.648010756801 Henry Cohn, 2026, needs more optimization.
8 492 0.648397646032 Henry Cohn, 2026, needs more optimization.
8 493 0.648781447780 Henry Cohn, 2026, needs more optimization.
8 494 0.648999670376 Henry Cohn, 2026, needs more optimization.
8 495 0.649035971006 Henry Cohn, 2026, needs more optimization.
8 497 0.649064011275 Henry Cohn, 2026, needs more optimization.
8 498 0.649088203905 Henry Cohn, 2026, needs more optimization.
8 499 0.649390144454 Henry Cohn, 2026, needs more optimization.
8 500 0.649506328292 Henry Cohn, 2026, needs more optimization.
8 501 0.649612779557 Henry Cohn, 2026, needs more optimization.
8 502 0.649832407415 Henry Cohn, 2026, needs more optimization.
8 503 0.650164032697 Henry Cohn, 2026, needs more optimization.
8 504 0.650346153958 Henry Cohn, 2026, needs more optimization.
8 505 0.650419149415 Henry Cohn, 2026, needs more optimization.
8 506 0.651019905120 Henry Cohn, 2026, needs more optimization.
8 507 0.651484985935 Henry Cohn, 2026, needs more optimization.
8 508 0.651597747678 Henry Cohn, 2026, needs more optimization.
8 509 0.651806665409 Henry Cohn, 2026, needs more optimization.
8 510 0.652113104043 Henry Cohn, 2026, needs more optimization.
8 511 0.652190716212 Henry Cohn, 2026, needs more optimization.
8 512 0.652237121948 Henry Cohn, 2026, needs more optimization.
8 513 0.652383673207 Henry Cohn, 2026, needs more optimization.
8 514 0.652383709744 Henry Cohn, 2026, needs more optimization.
8 515 0.652437825738 Henry Cohn, 2026, needs more optimization.
8 516 0.652716646714 Henry Cohn, 2026, needs more optimization.
8 517 0.652824886668 Henry Cohn, 2026, needs more optimization.
8 518 0.653056173267 Henry Cohn, 2026, needs more optimization.
8 519 0.653308938241 Henry Cohn, 2026, needs more optimization.
8 520 0.653663811681 Henry Cohn, 2026, needs more optimization.
8 521 0.653793641370 Henry Cohn, 2026, needs more optimization.
8 522 0.654212638217 Henry Cohn, 2026, needs more optimization.
8 523 0.654212887539 Henry Cohn, 2026, needs more optimization.
8 524 0.654290581287 Henry Cohn, 2026, needs more optimization.
8 525 0.654405874760 Henry Cohn, 2026, needs more optimization.
8 526 0.654565114384 Henry Cohn, 2026, needs more optimization.
8 527 0.654620340769 Henry Cohn, 2026, needs more optimization.
8 528 0.654703412656 Henry Cohn, 2026, needs more optimization.
8 529 0.655038362275 Henry Cohn, 2026, needs more optimization.
8 530 0.655257439792 Henry Cohn, 2026, needs more optimization.
8 531 0.655747692450 Henry Cohn, 2026, needs more optimization.
8 532 0.655809562207 Henry Cohn, 2026, needs more optimization.
8 533 0.656013481069 Henry Cohn, 2026, needs more optimization.
8 534 0.656167941460 Henry Cohn, 2026, needs more optimization.
8 535 0.656464113891 Henry Cohn, 2026, needs more optimization.
8 536 0.656718117907 Henry Cohn, 2026, needs more optimization.
8 537 0.657044347988 Henry Cohn, 2026, needs more optimization.
8 538 0.657361006632 Henry Cohn, 2026, needs more optimization.
8 539 0.657522830877 Henry Cohn, 2026, needs more optimization.
8 540 0.657725999862 Henry Cohn, 2026, needs more optimization.
8 541 0.657814729047 Henry Cohn, 2026, needs more optimization.
8 542 0.658036043835 Henry Cohn, 2026, needs more optimization.
8 543 0.658326571517 Henry Cohn, 2026, needs more optimization.
8 544 0.658651175452 Henry Cohn, 2026, needs more optimization.
8 545 0.658874110751 Henry Cohn, 2026, needs more optimization.
8 546 0.659020937483 Henry Cohn, 2026, needs more optimization.
8 547 0.659354020953 Henry Cohn, 2026, needs more optimization.
8 548 0.659552093940 Henry Cohn, 2026, needs more optimization.
8 549 0.659638224633 Henry Cohn, 2026, needs more optimization.
8 550 0.659640264196 Henry Cohn, 2026, needs more optimization.
8 551 0.659974096843 Henry Cohn, 2026, needs more optimization.
8 552 0.660509387616 Henry Cohn, 2026, needs more optimization.
8 553 0.660639707351 Henry Cohn, 2026, needs more optimization.
8 554 0.660781968131 Henry Cohn, 2026, needs more optimization.
8 555 0.660877658638 Henry Cohn, 2026, needs more optimization.
8 556 0.661121196754 Henry Cohn, 2026, needs more optimization.
8 557 0.661273878866 Henry Cohn, 2026, needs more optimization.
8 558 0.661417156944 Henry Cohn, 2026, needs more optimization.
8 559 0.661750702452 Henry Cohn, 2026, needs more optimization.
8 560 0.661921194717 Henry Cohn, 2026, needs more optimization.
8 561 0.662040038708 Henry Cohn, 2026, needs more optimization.
8 562 0.662315348726 Henry Cohn, 2026, needs more optimization.
8 563 0.662448394727 Henry Cohn, 2026, needs more optimization.
8 564 0.662592964801 Henry Cohn, 2026, needs more optimization.
8 565 0.662701546424 Henry Cohn, 2026, needs more optimization.
8 566 0.662773863265 Henry Cohn, 2026, needs more optimization.
8 567 0.662796604273 Henry Cohn, 2026, needs more optimization.
8 568 0.662923716263 Henry Cohn, 2026, needs more optimization.
8 569 0.663104498008 Henry Cohn, 2026, needs more optimization.
8 570 0.663144985512 Henry Cohn, 2026, needs more optimization.
8 571 0.663323662457 Henry Cohn, 2026, needs more optimization.
8 572 0.663484049202 Henry Cohn, 2026, needs more optimization.
8 573 0.663533097859 Henry Cohn, 2026, needs more optimization.
8 574 0.663813762207 Henry Cohn, 2026, needs more optimization.
8 575 0.663947645436 Henry Cohn, 2026, needs more optimization.
8 576 0.664023362122 Henry Cohn, 2026, needs more optimization.
8 577 0.664101763846 Henry Cohn, 2026, needs more optimization.
8 578 0.664203102306 Henry Cohn, 2026, needs more optimization.
8 579 0.664364357711 Henry Cohn, 2026, needs more optimization.
8 580 0.664420326169 Henry Cohn, 2026, needs more optimization.
8 581 0.664537459829 Henry Cohn, 2026, needs more optimization.
8 582 0.664559675236 Henry Cohn, 2026, needs more optimization.
8 583 0.664770464231 Henry Cohn, 2026, needs more optimization.
8 584 0.664777760881 Henry Cohn, 2026, needs more optimization.
8 585 0.664795710980 Henry Cohn, 2026, needs more optimization.
8 586 0.664876839932 Henry Cohn, 2026, needs more optimization.
8 587 0.664960640714 Henry Cohn, 2026, needs more optimization.
8 588 0.665040453804 Henry Cohn, 2026, needs more optimization.
8 589 0.665217434931 Henry Cohn, 2026, needs more optimization.
8 590 0.665281897726 Henry Cohn, 2026, needs more optimization.
8 591 0.665281953407 Henry Cohn, 2026, needs more optimization.
8 592 0.665282944519 Henry Cohn, 2026, needs more optimization.
8 593 0.665283513151 Henry Cohn, 2026, needs more optimization.
8 594 0.665315380765 Henry Cohn, 2026, needs more optimization.
8 595 0.665347373138 Henry Cohn, 2026, needs more optimization.
8 596 0.665369707758 Henry Cohn, 2026, needs more optimization.
8 598 0.665382930833 Henry Cohn, 2026, needs more optimization.
8 599 0.665382992615 Henry Cohn, 2026, needs more optimization.
8 600 0.665383016877 Henry Cohn, 2026, needs more optimization.
8 601 0.665388885976 Henry Cohn, 2026, needs more optimization.
8 602 0.665472545021 Henry Cohn, 2026, needs more optimization.
8 603 0.665490273479 Henry Cohn, 2026, needs more optimization.
8 604 0.665503101366 Henry Cohn, 2026, needs more optimization.
8 605 0.665523495623 Henry Cohn, 2026, needs more optimization.
8 606 0.665554664692 Henry Cohn, 2026, needs more optimization.
8 607 0.665565105361 Henry Cohn, 2026, needs more optimization.
8 608 0.665587323139 Henry Cohn, 2026, needs more optimization.
8 609 0.665624694137 Henry Cohn, 2026, needs more optimization.
8 610 0.665642492238 Henry Cohn, 2026, needs more optimization.
8 611 0.665657662360 Henry Cohn, 2026, needs more optimization.
8 612 0.665668504305 Henry Cohn, 2026, needs more optimization.
8 613 0.665682905251 Henry Cohn, 2026, needs more optimization.
8 614 0.665691284060 Henry Cohn, 2026, needs more optimization.
8 615 0.665727457341 Henry Cohn, 2026, needs more optimization.
8 616 0.665737430130 Henry Cohn, 2026, needs more optimization.
8 617 0.665738791008 Henry Cohn, 2026, needs more optimization.
8 618 0.665762796872 Henry Cohn, 2026, needs more optimization.
8 619 0.665896361113 Henry Cohn, 2026, needs more optimization.
8 620 0.665965785605 Henry Cohn, 2026, needs more optimization.
8 621 0.666004273024 Henry Cohn, 2026, needs more optimization.
8 622 0.666015509770 Henry Cohn, 2026, needs more optimization.
8 623 0.666034234517 Henry Cohn, 2026, needs more optimization.
8 624 0.666041220366 Henry Cohn, 2026, needs more optimization.
8 628 0.666102650224 Henry Cohn, 2026, needs more optimization.
8 629 0.666127019090 Henry Cohn, 2026, needs more optimization.
8 630 0.666161515473 Henry Cohn, 2026, needs more optimization.
8 631 0.666189539120 Henry Cohn, 2026, needs more optimization.
8 632 0.666211685030 Henry Cohn, 2026, needs more optimization.
8 633 0.666213266409 Henry Cohn, 2026, needs more optimization.
8 634 0.666220362369 Henry Cohn, 2026, needs more optimization.
8 635 0.666223641612 Henry Cohn, 2026, needs more optimization.
8 636 0.666318205400 Henry Cohn, 2026, needs more optimization.
8 637 0.666331910330 Henry Cohn, 2026, needs more optimization.
8 638 0.666346038674 Henry Cohn, 2026, needs more optimization.
8 639 0.666371509494 Henry Cohn, 2026, needs more optimization.
8 640 0.666396420530 Henry Cohn, 2026, needs more optimization.
8 641 0.666514211395 Henry Cohn, 2026, needs more optimization.
8 643 0.666514558761 Henry Cohn, 2026, needs more optimization.
8 644 0.666514581482 Henry Cohn, 2026, needs more optimization.
8 645 0.666514631824 Henry Cohn, 2026, needs more optimization.
8 646 0.666535254174 Henry Cohn, 2026, needs more optimization.
8 647 0.666541664973 Henry Cohn, 2026, needs more optimization.
8 648 0.666545732338 Henry Cohn, 2026, needs more optimization.
8 649 0.666546027931 Henry Cohn, 2026, needs more optimization.
8 650 0.666548379027 Henry Cohn, 2026, needs more optimization.
8 651 0.666579188168 Henry Cohn, 2026, needs more optimization.
8 652 0.666579628660 Henry Cohn, 2026, needs more optimization.
8 653 0.666595210549 Henry Cohn, 2026, needs more optimization.
8 654 0.666595831731 Henry Cohn, 2026, needs more optimization.
8 655 0.666595971599 Henry Cohn, 2026, needs more optimization.
8 656 0.666596213991 Henry Cohn, 2026, needs more optimization.
8 657 0.666596738851 Henry Cohn, 2026, needs more optimization.
8 658 0.666597010579 Henry Cohn, 2026, needs more optimization.
8 659 0.666597356513 Henry Cohn, 2026, needs more optimization.
8 660 0.666754996918 Henry Cohn, 2026, needs more optimization.
8 661 0.667066532254 Henry Cohn, 2026, needs more optimization.
8 662 0.667280273853 Henry Cohn, 2026, needs more optimization.
8 663 0.668192444670 Henry Cohn, 2026, needs more optimization.
8 664 0.668393060810 Henry Cohn, 2026, needs more optimization.
8 665 0.668688053346 Henry Cohn, 2026, needs more optimization.
8 666 0.668701473676 Henry Cohn, 2026, needs more optimization.
8 667 0.668705896089 Henry Cohn, 2026, needs more optimization.
8 668 0.668757800472 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 0.669195380792 Henry Cohn, 2026, needs more optimization.
8 671 0.669719758280 Henry Cohn, 2026, needs more optimization.
8 672 0.669896926815 Henry Cohn, 2026, needs more optimization.
8 673 0.670180125381 Henry Cohn, 2026, needs more optimization.
8 674 0.670508246375 Henry Cohn, 2026, needs more optimization.
8 675 0.670790341886 Henry Cohn, 2026, needs more optimization.
8 676 0.671144987540 Henry Cohn, 2026, needs more optimization.
8 677 0.671565083798 Henry Cohn, 2026, needs more optimization.
8 678 0.672021797186 Henry Cohn, 2026, needs more optimization.
8 679 0.673168489252 Henry Cohn, 2026, needs more optimization.
8 680 0.673424485782 Henry Cohn, 2026, needs more optimization.
8 681 0.673460570469 Henry Cohn, 2026, needs more optimization.
8 682 0.673496903962 Henry Cohn, 2026, needs more optimization.
8 683 0.673501353921 Henry Cohn, 2026, needs more optimization.
8 684 0.673554603849 Henry Cohn, 2026, needs more optimization.
8 685 0.674085320273 Henry Cohn, 2026, needs more optimization.
8 686 0.674233366027 Henry Cohn, 2026, needs more optimization.
8 687 0.674568138336 Henry Cohn, 2026, needs more optimization.
8 688 0.674956454359 Henry Cohn, 2026, needs more optimization.
8 689 0.675189663496 Henry Cohn, 2026, needs more optimization.
8 690 0.675542756719 Henry Cohn, 2026, needs more optimization.
8 691 0.676077095689 Henry Cohn, 2026, needs more optimization.
8 692 0.676455395103 Henry Cohn, 2026, needs more optimization.
8 693 0.676927307831 Henry Cohn, 2026, needs more optimization.
8 694 0.677381826067 Henry Cohn, 2026, needs more optimization.
8 695 0.677470912466 Henry Cohn, 2026, needs more optimization.
8 696 0.677698265355 Henry Cohn, 2026, needs more optimization.
8 697 0.677825836148 Henry Cohn, 2026, needs more optimization.
8 698 0.678237171055 Henry Cohn, 2026, needs more optimization.
8 699 0.678462282975 Henry Cohn, 2026, needs more optimization.
8 700 0.678640712555 Henry Cohn, 2026, needs more optimization.
8 701 0.679091238367 Henry Cohn, 2026, needs more optimization.
8 702 0.679320860756 Henry Cohn, 2026, needs more optimization.
8 703 0.679815479542 Henry Cohn, 2026, needs more optimization.
8 704 0.680166674945 Henry Cohn, 2026, needs more optimization.
8 705 0.680274923118 Henry Cohn, 2026, needs more optimization.
8 706 0.680447574788 Henry Cohn, 2026, needs more optimization.
8 707 0.680548847505 Henry Cohn, 2026, needs more optimization.
8 708 0.680620141056 Henry Cohn, 2026, needs more optimization.
8 709 0.680929914824 Henry Cohn, 2026, needs more optimization.
8 710 0.681426115014 Henry Cohn, 2026, needs more optimization.
8 711 0.681581937205 Henry Cohn, 2026, needs more optimization.
8 712 0.681917859300 Henry Cohn, 2026, needs more optimization.
8 713 0.682080441023 Henry Cohn, 2026, needs more optimization.
8 714 0.682479553575 Henry Cohn, 2026, needs more optimization.
8 715 0.682483976261 Henry Cohn, 2026, needs more optimization.
8 716 0.682957257047 Henry Cohn, 2026, needs more optimization.
8 717 0.683269503571 Henry Cohn, 2026, needs more optimization.
8 718 0.683543769444 Henry Cohn, 2026, needs more optimization.
8 719 0.683556198557 Henry Cohn, 2026, needs more optimization.
8 720 0.683921415483 Henry Cohn, 2026, needs more optimization.
8 721 0.684008562012 Henry Cohn, 2026, needs more optimization.
8 722 0.684099608030 Henry Cohn, 2026, needs more optimization.
8 723 0.684359429520 Henry Cohn, 2026, needs more optimization.
8 724 0.684591168921 Henry Cohn, 2026, needs more optimization.
8 725 0.685005472885 Henry Cohn, 2026, needs more optimization.
8 726 0.685157274940 Henry Cohn, 2026, needs more optimization.
8 727 0.685438903164 Henry Cohn, 2026, needs more optimization.
8 728 0.685513125398 Henry Cohn, 2026, needs more optimization.
8 729 0.685814266886 Henry Cohn, 2026, needs more optimization.
8 730 0.686140959860 Henry Cohn, 2026, needs more optimization.
8 731 0.686258101697 Henry Cohn, 2026, needs more optimization.
8 732 0.686468832145 Henry Cohn, 2026, needs more optimization.
8 733 0.686468852212 Henry Cohn, 2026, needs more optimization.
8 734 0.686809396650 Henry Cohn, 2026, needs more optimization.
8 735 0.686847157235 Henry Cohn, 2026, needs more optimization.
8 736 0.687520920013 Henry Cohn, 2026, needs more optimization.
8 737 0.687582925958 Henry Cohn, 2026, needs more optimization.
8 738 0.687693226885 Henry Cohn, 2026, needs more optimization.
8 739 0.687786619183 Henry Cohn, 2026, needs more optimization.
8 740 0.687949751558 Henry Cohn, 2026, needs more optimization.
8 741 0.688138177899 Henry Cohn, 2026, needs more optimization.
8 742 0.688258315212 Henry Cohn, 2026, needs more optimization.
8 743 0.688518414143 Henry Cohn, 2026, needs more optimization.
8 744 0.688521480914 Henry Cohn, 2026, needs more optimization.
8 745 0.688706435178 Henry Cohn, 2026, needs more optimization.
8 746 0.688909060388 Henry Cohn, 2026, needs more optimization.
8 747 0.688940934759 Henry Cohn, 2026, needs more optimization.
8 748 0.689167736950 Henry Cohn, 2026, needs more optimization.
8 749 0.689303417081 Henry Cohn, 2026, needs more optimization.
8 750 0.689305067255 Henry Cohn, 2026, needs more optimization.
8 751 0.689469121373 Henry Cohn, 2026, needs more optimization.
8 752 0.689842046599 Henry Cohn, 2026, needs more optimization.
8 753 0.689981891810 Henry Cohn, 2026, needs more optimization.
8 754 0.690131651995 Henry Cohn, 2026, needs more optimization.
8 755 0.690133432239 Henry Cohn, 2026, needs more optimization.
8 756 0.690134913953 Henry Cohn, 2026, needs more optimization.
8 757 0.690138140868 Henry Cohn, 2026, needs more optimization.
8 758 0.690141508615 Henry Cohn, 2026, needs more optimization.
8 759 0.690143793367 Henry Cohn, 2026, needs more optimization.
8 760 0.690146333106 Henry Cohn, 2026, needs more optimization.
8 761 0.690148473984 Henry Cohn, 2026, needs more optimization.
8 762 0.690182723561 Henry Cohn, 2026, needs more optimization.
8 763 0.690187317297 Henry Cohn, 2026, needs more optimization.
8 764 0.690929147768 Henry Cohn, 2026, needs more optimization.
8 765 0.691009700105 Henry Cohn, 2026, needs more optimization.
8 766 0.691031140029 Henry Cohn, 2026, needs more optimization.
8 767 0.691161537839 Henry Cohn, 2026, needs more optimization.
8 768 0.691295845011 Henry Cohn, 2026, needs more optimization.
8 769 0.691312937465 Henry Cohn, 2026, needs more optimization.
8 770 0.691522041667 Henry Cohn, 2026, needs more optimization.
8 771 0.691672206662 Henry Cohn, 2026, needs more optimization.
8 772 0.691676466529 Henry Cohn, 2026, needs more optimization.
8 773 0.691679844922 Henry Cohn, 2026, needs more optimization.
8 774 0.691765791113 Henry Cohn, 2026, needs more optimization.
8 775 0.691809501725 Henry Cohn, 2026, needs more optimization.
8 776 0.692240185203 Henry Cohn, 2026, needs more optimization.
8 777 0.692364927975 Henry Cohn, 2026, needs more optimization.
8 778 0.692459041299 Henry Cohn, 2026, needs more optimization.
8 779 0.692462688985 Henry Cohn, 2026, needs more optimization.
8 780 0.692536330519 Henry Cohn, 2026, needs more optimization.
8 781 0.692563271253 Henry Cohn, 2026, needs more optimization.
8 782 0.692606141471 Henry Cohn, 2026, needs more optimization.
8 783 0.692723157762 Henry Cohn, 2026, needs more optimization.
8 784 0.692788153017 Henry Cohn, 2026, needs more optimization.
8 785 0.693264079215 Henry Cohn, 2026, needs more optimization.
8 786 0.693500633390 Henry Cohn, 2026, needs more optimization.
8 787 0.693732713120 Henry Cohn, 2026, needs more optimization.
8 788 0.693774508044 Henry Cohn, 2026, needs more optimization.
8 789 0.694044258808 Henry Cohn, 2026, needs more optimization.
8 790 0.694181682395 Henry Cohn, 2026, needs more optimization.
8 791 0.694191368851 Henry Cohn, 2026, needs more optimization.
8 792 0.694207506491 Henry Cohn, 2026, needs more optimization.
8 793 0.694586819635 Henry Cohn, 2026, needs more optimization.
8 794 0.694595642005 Henry Cohn, 2026, needs more optimization.
8 795 0.694631277850 Henry Cohn, 2026, needs more optimization.
8 796 0.694632466929 Henry Cohn, 2026, needs more optimization.
8 797 0.694638656522 Henry Cohn, 2026, needs more optimization.
8 798 0.694833484058 Henry Cohn, 2026, needs more optimization.
8 799 0.694875816286 Henry Cohn, 2026, needs more optimization.
8 800 0.695084464426 Henry Cohn, 2026, needs more optimization.
8 801 0.695322288456 Henry Cohn, 2026, needs more optimization.
8 802 0.695570216532 Henry Cohn, 2026, needs more optimization.
8 803 0.695624061955 Henry Cohn, 2026, needs more optimization.
8 804 0.695878178894 Henry Cohn, 2026, needs more optimization.
8 805 0.696129440940 Henry Cohn, 2026, needs more optimization.
8 806 0.696206384025 Henry Cohn, 2026, needs more optimization.
8 807 0.696238529010 Henry Cohn, 2026, needs more optimization.
8 808 0.696242371998 Henry Cohn, 2026, needs more optimization.
8 809 0.696296617646 Henry Cohn, 2026, needs more optimization.
8 810 0.696299733672 Henry Cohn, 2026, needs more optimization.
8 811 0.696679557072 Henry Cohn, 2026, needs more optimization.
8 812 0.696686489814 Henry Cohn, 2026, needs more optimization.
8 813 0.696824922055 Henry Cohn, 2026, needs more optimization.
8 814 0.697495692066 Henry Cohn, 2026, needs more optimization.
8 815 0.697498783083 Henry Cohn, 2026, needs more optimization.
8 816 0.697539646501 Henry Cohn, 2026, needs more optimization.
8 817 0.697541497720 Henry Cohn, 2026, needs more optimization.
8 818 0.697562859169 Henry Cohn, 2026, needs more optimization.
8 819 0.697595451397 Henry Cohn, 2026, needs more optimization.
8 820 0.697611597898 Henry Cohn, 2026, needs more optimization.
8 821 0.697679872411 Henry Cohn, 2026, needs more optimization.
8 822 0.697887948151 Henry Cohn, 2026, needs more optimization.
8 823 0.697947522878 Henry Cohn, 2026, needs more optimization.
8 824 0.697982794418 Henry Cohn, 2026, needs more optimization.
8 825 0.697987515393 Henry Cohn, 2026, needs more optimization.
8 826 0.698121830322 Henry Cohn, 2026, needs more optimization.
8 827 0.698602361212 Henry Cohn, 2026, needs more optimization.
8 828 0.698605246750 Henry Cohn, 2026, needs more optimization.
8 829 0.698622956548 Henry Cohn, 2026, needs more optimization.
8 832 0.698865691307 Henry Cohn, 2026, needs more optimization.
8 834 0.698867131099 Henry Cohn, 2026, needs more optimization.
8 835 0.698867382976 Henry Cohn, 2026, needs more optimization.
8 836 0.699615575107 Henry Cohn, 2026, needs more optimization.
8 837 0.699618119382 Henry Cohn, 2026, needs more optimization.
8 838 0.699623452736 Henry Cohn, 2026, needs more optimization.
8 839 0.699633691296 Henry Cohn, 2026, needs more optimization.
8 840 0.699998422316 Henry Cohn, 2026, needs more optimization.
8 841 0.700483453532 Henry Cohn, 2026, needs more optimization.
8 842 0.700484734545 Henry Cohn, 2026, needs more optimization.
8 843 0.700510430102 Henry Cohn, 2026, needs more optimization.
8 844 0.700514247986 Henry Cohn, 2026, needs more optimization.
8 845 0.700538756517 Henry Cohn, 2026, needs more optimization.
8 846 0.700540657293 Henry Cohn, 2026, needs more optimization.
8 847 0.700548846828 Henry Cohn, 2026, needs more optimization.
8 848 0.700588816419 Henry Cohn, 2026, needs more optimization.
8 849 0.701146674152 Henry Cohn, 2026, needs more optimization.
8 850 0.701148606664 Henry Cohn, 2026, needs more optimization.
8 851 0.701150667715 Henry Cohn, 2026, needs more optimization.
8 852 0.701224141264 Henry Cohn, 2026, needs more optimization.
8 853 0.701532976727 Henry Cohn, 2026, needs more optimization.
8 854 0.701535985912 Henry Cohn, 2026, needs more optimization.
8 855 0.702090978794 Henry Cohn, 2026, needs more optimization.
8 856 0.702093128996 Henry Cohn, 2026, needs more optimization.
8 857 0.702094625745 Henry Cohn, 2026, needs more optimization.
8 858 0.702095965441 Henry Cohn, 2026, needs more optimization.
8 859 0.702259376001 Henry Cohn, 2026, needs more optimization.
8 860 0.702278868514 Henry Cohn, 2026, needs more optimization.
8 861 0.702304508527 Henry Cohn, 2026, needs more optimization.
8 862 0.702307472017 Henry Cohn, 2026, needs more optimization.
8 863 0.702393194866 Henry Cohn, 2026, needs more optimization.
8 864 0.702394872626 Henry Cohn, 2026, needs more optimization.
8 865 0.702400307085 Henry Cohn, 2026, needs more optimization.
8 867 0.702411913492 Henry Cohn, 2026, needs more optimization.
8 868 0.702418738685 Henry Cohn, 2026, needs more optimization.
8 869 0.702448520506 Henry Cohn, 2026, needs more optimization.
8 870 0.702486963018 Henry Cohn, 2026, needs more optimization.
8 871 0.702552400748 Henry Cohn, 2026, needs more optimization.
8 872 0.702552479515 Henry Cohn, 2026, needs more optimization.
8 873 0.702552545062 Henry Cohn, 2026, needs more optimization.
8 874 0.703840456850 Henry Cohn, 2026, needs more optimization.
8 875 0.703843517080 Henry Cohn, 2026, needs more optimization.
8 876 0.703844448512 Henry Cohn, 2026, needs more optimization.
8 877 0.704325193132 Henry Cohn, 2026, needs more optimization.
8 878 0.704350835263 Henry Cohn, 2026, needs more optimization.
8 879 0.704353163148 Henry Cohn, 2026, needs more optimization.
8 880 0.704356410661 Henry Cohn, 2026, needs more optimization.
8 881 0.704359428085 Henry Cohn, 2026, needs more optimization.
8 882 0.704373889262 Henry Cohn, 2026, needs more optimization.
8 883 0.704525191103 Henry Cohn, 2026, needs more optimization.
8 884 0.704538065507 Henry Cohn, 2026, needs more optimization.
8 885 0.704543320169 Henry Cohn, 2026, needs more optimization.
8 886 0.704977507272 Henry Cohn, 2026, needs more optimization.
8 887 0.704983620601 Henry Cohn, 2026, needs more optimization.
8 888 0.704984868391 Henry Cohn, 2026, needs more optimization.
8 889 0.705012811044 Henry Cohn, 2026, needs more optimization.
8 890 0.705030471581 Henry Cohn, 2026, needs more optimization.
8 891 0.705397030844 Henry Cohn, 2026, needs more optimization.
8 892 0.705608515588 Henry Cohn, 2026, needs more optimization.
8 893 0.705627410719 Henry Cohn, 2026, needs more optimization.
8 894 0.705634595921 Henry Cohn, 2026, needs more optimization.
8 895 0.705641228254 Henry Cohn, 2026, needs more optimization.
8 896 0.705645000224 Henry Cohn, 2026, needs more optimization.
8 897 0.705651650327 Henry Cohn, 2026, needs more optimization.
8 898 0.705652470783 Henry Cohn, 2026, needs more optimization.
8 899 0.705654044225 Henry Cohn, 2026, needs more optimization.
8 901 0.705686898705 Henry Cohn, 2026, needs more optimization.
8 902 0.705686898941 Henry Cohn, 2026, needs more optimization.
8 903 0.705693316477 Henry Cohn, 2026, needs more optimization.
8 904 0.705977820887 Henry Cohn, 2026, needs more optimization.
8 905 0.705978913422 Henry Cohn, 2026, needs more optimization.
8 907 0.706408307193 Henry Cohn, 2026, needs more optimization.
8 908 0.706412317530 Henry Cohn, 2026, needs more optimization.
8 909 0.706424329572 Henry Cohn, 2026, needs more optimization.
8 910 0.706424329817 Henry Cohn, 2026, needs more optimization.
8 911 0.706436132526 Henry Cohn, 2026, needs more optimization.
8 912 0.706445736411 Henry Cohn, 2026, needs more optimization.
8 913 0.706464144736 Henry Cohn, 2026, needs more optimization.
8 914 0.706512970854 Henry Cohn, 2026, needs more optimization.
8 915 0.706845882851 Henry Cohn, 2026, needs more optimization.
8 916 0.706864929886 Henry Cohn, 2026, needs more optimization.
8 917 0.706877547883 Henry Cohn, 2026, needs more optimization.
8 918 0.707071232091 Henry Cohn, 2026, needs more optimization.
8 919 0.707073332947 Henry Cohn, 2026, needs more optimization.
8 920 0.707075172704 Henry Cohn, 2026, needs more optimization.
8 922 0.707527391511 Henry Cohn, 2026, needs more optimization.
8 923 0.707533625860 Henry Cohn, 2026, needs more optimization.
8 924 0.707533635342 Henry Cohn, 2026, needs more optimization.
8 925 0.707538995242 Henry Cohn, 2026, needs more optimization.
8 926 0.707649342678 Henry Cohn, 2026, needs more optimization.
8 927 0.707929507941 Henry Cohn, 2026, needs more optimization.
8 928 0.707934377146 Henry Cohn, 2026, needs more optimization.
8 929 0.707948045509 Henry Cohn, 2026, needs more optimization.
8 930 0.707948046288 Henry Cohn, 2026, needs more optimization.
8 931 0.707965662850 Henry Cohn, 2026, needs more optimization.
8 932 0.708013144570 Henry Cohn, 2026, needs more optimization.
8 933 0.708016313674 Henry Cohn, 2026, needs more optimization.
8 934 0.708314529485 Henry Cohn, 2026, needs more optimization.
8 935 0.708314531918 Henry Cohn, 2026, needs more optimization.
8 936 0.708316211353 Henry Cohn, 2026, needs more optimization.
8 937 0.708319018252 Henry Cohn, 2026, needs more optimization.
8 938 0.708330368996 Henry Cohn, 2026, needs more optimization.
8 939 0.708871757850 Henry Cohn, 2026, needs more optimization.
8 940 0.708897444923 Henry Cohn, 2026, needs more optimization.
8 942 0.708899602206 Henry Cohn, 2026, needs more optimization.
8 943 0.708955657423 Henry Cohn, 2026, needs more optimization.
8 944 0.708974570211 Henry Cohn, 2026, needs more optimization.
8 945 0.709118433666 Henry Cohn, 2026, needs more optimization.
8 947 0.709122297045 Henry Cohn, 2026, needs more optimization.
8 949 0.709507675013 Henry Cohn, 2026, needs more optimization.
8 950 0.709511000030 Henry Cohn, 2026, needs more optimization.
8 951 0.709517954818 Henry Cohn, 2026, needs more optimization.
8 952 0.709517957264 Henry Cohn, 2026, needs more optimization.
8 953 0.709517959994 Henry Cohn, 2026, needs more optimization.
8 954 0.709525737619 Henry Cohn, 2026, needs more optimization.
8 955 0.709888715986 Henry Cohn, 2026, needs more optimization.
8 956 0.709913405789 Henry Cohn, 2026, needs more optimization.
8 957 0.709970316508 Henry Cohn, 2026, needs more optimization.
8 958 0.709982399164 Henry Cohn, 2026, needs more optimization.
8 960 0.710162458605 Henry Cohn, 2026, needs more optimization.
8 961 0.710168906964 Henry Cohn, 2026, needs more optimization.
8 962 0.710641912825 Henry Cohn, 2026, needs more optimization.
8 963 0.710661046192 Henry Cohn, 2026, needs more optimization.
8 965 0.710735257978 Henry Cohn, 2026, needs more optimization.
8 966 0.710765325663 Henry Cohn, 2026, needs more optimization.
8 968 0.710765327390 Henry Cohn, 2026, needs more optimization.
8 969 0.710785278902 Henry Cohn, 2026, needs more optimization.
8 970 0.710866941082 Henry Cohn, 2026, needs more optimization.
8 971 0.711360968043 Henry Cohn, 2026, needs more optimization.
8 973 0.711416252383 Henry Cohn, 2026, needs more optimization.
8 974 0.711463372336 Henry Cohn, 2026, needs more optimization.
8 976 0.711467517760 Henry Cohn, 2026, needs more optimization.
8 977 0.711473047960 Henry Cohn, 2026, needs more optimization.
8 978 0.711486110469 Henry Cohn, 2026, needs more optimization.
8 979 0.711879409034 Henry Cohn, 2026, needs more optimization.
8 980 0.711892058456 Henry Cohn, 2026, needs more optimization.
8 981 0.711918738203 Henry Cohn, 2026, needs more optimization.
8 982 0.711949501868 Henry Cohn, 2026, needs more optimization.
8 983 0.711976959183 Henry Cohn, 2026, needs more optimization.
8 984 0.711989665174 Henry Cohn, 2026, needs more optimization.
8 985 0.712243042729 Henry Cohn, 2026, needs more optimization.
8 986 0.712299619233 Henry Cohn, 2026, needs more optimization.
8 987 0.712309173471 Henry Cohn, 2026, needs more optimization.
8 988 0.712322292821 Henry Cohn, 2026, needs more optimization.
8 989 0.712568048372 Henry Cohn, 2026, needs more optimization.
8 990 0.712951188423 Henry Cohn, 2026, needs more optimization.
8 992 0.712951325934 Henry Cohn, 2026, needs more optimization.
8 993 0.712965976177 Henry Cohn, 2026, needs more optimization.
8 994 0.712966853104 Henry Cohn, 2026, needs more optimization.
8 995 0.712974812848 Henry Cohn, 2026, needs more optimization.
8 996 0.712974813018 Henry Cohn, 2026, needs more optimization.
8 997 0.713035247883 Henry Cohn, 2026, needs more optimization.
8 998 0.713058736548 Henry Cohn, 2026, needs more optimization.
8 999 0.713105449505 Henry Cohn, 2026, needs more optimization.
8 1000 0.713107285511 Henry Cohn, 2026, needs more optimization.
8 1001 0.713169011057 Henry Cohn, 2026, needs more optimization.
8 1002 0.713221589703 Henry Cohn, 2026, needs more optimization.
8 1003 0.713257684296 Henry Cohn, 2026, needs more optimization.
8 1004 0.713285336148 Henry Cohn, 2026, needs more optimization.
8 1005 0.713365699215 Henry Cohn, 2026, needs more optimization.
8 1006 0.713369249980 Henry Cohn, 2026, needs more optimization.
8 1007 0.713469256707 Henry Cohn, 2026, needs more optimization.
8 1008 0.713539771891 Henry Cohn, 2026, needs more optimization.
8 1010 0.713587861880 Henry Cohn, 2026, needs more optimization.
8 1011 0.713632979185 Henry Cohn, 2026, needs more optimization.
8 1012 0.713686685327 Henry Cohn, 2026, needs more optimization.
8 1013 0.713692241978 Henry Cohn, 2026, needs more optimization.
8 1014 0.713718095478 Henry Cohn, 2026, needs more optimization.
8 1015 0.713718100540 Henry Cohn, 2026, needs more optimization.
8 1016 0.713740728261 Henry Cohn, 2026, needs more optimization.
8 1017 0.713776229962 Henry Cohn, 2026, needs more optimization.
8 1018 0.713820912225 Henry Cohn, 2026, needs more optimization.
8 1019 0.713830137154 Henry Cohn, 2026, needs more optimization.
8 1020 0.713832805928 Henry Cohn, 2026, needs more optimization.
8 1021 0.713875816940 Henry Cohn, 2026, needs more optimization.
8 1022 0.713883690543 Henry Cohn, 2026, needs more optimization.
8 1023 0.713883691070 Henry Cohn, 2026, needs more optimization.
8 1024 0.713975644255 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 0.299405580557 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 0.329470710923 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 0.397621609602 Henry Cohn, 2026, needs more optimization.
9 108 0.399008208476 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.
9 109 0.401811528436 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 0.406324045396 Henry Cohn, 2026, needs more optimization.
9 112 0.408810852555 Henry Cohn, 2026, needs more optimization.
9 113 0.410378156097 Henry Cohn, 2026, needs more optimization.
9 114 0.411216453306 Henry Cohn, 2026, needs more optimization.
9 115 0.412584039974 Henry Cohn, 2026, needs more optimization.
9 116 0.413818623867 Henry Cohn, 2026, needs more optimization.
9 117 0.414584290588 Henry Cohn, 2026, needs more optimization.
9 118 0.415632758194 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 0.416545172579 Henry Cohn, 2026, needs more optimization.
9 121 0.417014521621 Henry Cohn, 2026, needs more optimization.
9 122 0.418282170106 Henry Cohn, 2026.
9 123 0.419108120200 Henry Cohn, 2026, needs more optimization.
9 124 0.419764234534 Henry Cohn, 2026, needs more optimization.
9 125 0.421595397673 Henry Cohn, 2026, needs more optimization.
9 126 0.422021310558 Henry Cohn, 2026, needs more optimization.
9 127 0.422098110407 Henry Cohn, 2026, needs more optimization.
9 128 0.422283903009 Henry Cohn, 2026, needs more optimization.
9 129 0.422438034546 Henry Cohn, 2026, needs more optimization.
9 130 0.422439717778 Henry Cohn, 2026, needs more optimization.
9 131 0.422500643187 Henry Cohn, 2026, needs more optimization.
9 132 0.426502904784 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.
9 133 0.427221001251 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.
9 134 0.428560132634 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.
9 146 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 0.441617210744 Henry Cohn, 2026, needs more optimization.
9 148 0.444822266109 Henry Cohn, 2026, needs more optimization.
9 149 0.447378139290 Henry Cohn, 2026, needs more optimization.
9 150 0.449526152712 Henry Cohn, 2026, needs more optimization.
9 151 0.449962147950 Henry Cohn, 2026, needs more optimization.
9 152 0.453419362403 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
9 170 0.454589422184 Henry Cohn, 2026, needs more optimization.
9 171 0.455786210539 Henry Cohn, 2026, needs more optimization.
9 172 0.456116159666 Henry Cohn, 2026, needs more optimization.
9 173 0.461165940115 Henry Cohn, 2026, needs more optimization.
9 174 0.461353018855 Henry Cohn, 2026, needs more optimization.
9 175 0.461482645903 Henry Cohn, 2026, needs more optimization.
9 176 0.462225204765 Henry Cohn, 2026, needs more optimization.
9 177 0.462263997670 Henry Cohn, 2026, needs more optimization.
9 178 0.462315323810 Henry Cohn, 2026, needs more optimization.
9 179 0.462362678215 Henry Cohn, 2026, needs more optimization.
9 180 0.462409395031 Henry Cohn, 2026, needs more optimization.
9 181 0.462512779496 Henry Cohn, 2026, needs more optimization.
9 182 0.463538450715 Henry Cohn, 2026, needs more optimization.
9 183 0.465284184728 Henry Cohn, 2026, needs more optimization.
9 184 0.467331176924 Henry Cohn, 2026, needs more optimization.
9 185 0.468797045077 Henry Cohn, 2026, needs more optimization.
9 186 0.470176161214 Henry Cohn, 2026, needs more optimization.
9 187 0.472930313106 Henry Cohn, 2026, needs more optimization.
9 209 0.475156558223 Henry Cohn, 2026.
103⁢x2−30⁢x−9
9 210 0.475244235817 Henry Cohn, 2026, needs more optimization.
9 211 0.478989231786 Henry Cohn, 2026, needs more optimization.
9 212 0.481610902773 Henry Cohn, 2026, needs more optimization.
9 213 0.483377225138 Henry Cohn, 2026, needs more optimization.
9 214 0.484889684040 Henry Cohn, 2026, needs more optimization.
9 215 0.485428831737 Henry Cohn, 2026, needs more optimization.
9 216 0.486052933237 Henry Cohn, 2026, needs more optimization.
9 217 0.486674703586 Henry Cohn, 2026, needs more optimization.
9 218 0.492826829238 Henry Cohn, 2026, needs more optimization.
9 219 0.492977616575 Henry Cohn, 2026, needs more optimization.
9 220 0.495588232675 Henry Cohn, 2026, needs more optimization.
9 221 0.496152389191 Henry Cohn, 2026, needs more optimization.
9 222 0.496710200471 Henry Cohn, 2026, needs more optimization.
9 223 0.496884245686 Henry Cohn, 2026, needs more optimization.
9 224 0.496974196547 Henry Cohn, 2026, needs more optimization.
9 225 0.497114638962 Henry Cohn, 2026, needs more optimization.
9 226 0.497549725720 Henry Cohn, 2026, needs more optimization.
9 227 0.497570998534 Henry Cohn, 2026, needs more optimization.
9 228 0.498123522163 Henry Cohn, 2026, needs more optimization.
9 229 0.498320363380 Henry Cohn, 2026, needs more optimization.
9 230 0.498505148470 Henry Cohn, 2026, needs more optimization.
9 231 0.498610479594 Henry Cohn, 2026, needs more optimization.
9 232 0.498618396787 Henry Cohn, 2026, needs more optimization.
9 233 0.498819454293 Henry Cohn, 2026, needs more optimization.
9 234 0.499053762340 Henry Cohn, 2026, needs more optimization.
9 235 0.499181919891 Henry Cohn, 2026, needs more optimization.
9 236 0.499212051259 Henry Cohn, 2026, needs more optimization.
9 237 0.499219521614 Henry Cohn, 2026, needs more optimization.
9 238 0.499306974479 Henry Cohn, 2026, needs more optimization.
9 239 0.499405317420 Henry Cohn, 2026, needs more optimization.
9 240 0.499519334408 Henry Cohn, 2026, needs more optimization.
9 241 0.499586789596 Henry Cohn, 2026, needs more optimization.
9 242 0.499599224047 Henry Cohn, 2026, needs more optimization.
9 243 0.499615824827 Henry Cohn, 2026, needs more optimization.
9 244 0.499653415200 Henry Cohn, 2026, needs more optimization.
9 245 0.499738409601 Henry Cohn, 2026, needs more optimization.
9 246 0.499876424332 Henry Cohn, 2026, needs more optimization.
9 247 0.499892836507 Henry Cohn, 2026, needs more optimization.
9 248 0.499960584819 Henry Cohn, 2026, needs more optimization.
9 249 0.499967165386 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 0.517066107150 Henry Cohn, 2026, needs more optimization.
9 308 0.518936372116 Henry Cohn, 2026, needs more optimization.
9 309 0.520865103162 Henry Cohn, 2026, needs more optimization.
9 310 0.521840859935 Henry Cohn, 2026, needs more optimization.
9 311 0.521855859435 Henry Cohn, 2026, needs more optimization.
9 312 0.521858880989 Henry Cohn, 2026, needs more optimization.
9 313 0.522207904639 Henry Cohn, 2026, needs more optimization.
9 330 0.523809523810 Henry Cohn and Ilmari Vahteristo (independently), 2026.
21⁢x−11
9 331 0.528494852229 Henry Cohn, 2026, needs more optimization.
9 332 0.530017216619 Henry Cohn, 2026, needs more optimization.
9 333 0.533329881708 Henry Cohn, 2026, needs more optimization.
9 334 0.534897265607 Henry Cohn, 2026, needs more optimization.
9 335 0.536097304446 Henry Cohn, 2026, needs more optimization.
9 336 0.536226180199 Henry Cohn, 2026, needs more optimization.
9 337 0.536447977275 Henry Cohn, 2026, needs more optimization.
9 338 0.536454854231 Henry Cohn, 2026, needs more optimization.
9 339 0.537026749820 Henry Cohn, 2026, needs more optimization.
9 340 0.538014429278 Henry Cohn, 2026, needs more optimization.
9 341 0.538074023132 Henry Cohn, 2026, needs more optimization.
9 342 0.539501585294 Henry Cohn, 2026, needs more optimization.
9 343 0.540106711782 Henry Cohn, 2026, needs more optimization.
9 344 0.540260652552 Henry Cohn, 2026, needs more optimization.
9 345 0.540690007088 Henry Cohn, 2026, needs more optimization.
9 346 0.541068924685 Henry Cohn, 2026, needs more optimization.
9 347 0.541594841096 Henry Cohn, 2026, needs more optimization.
9 348 0.542563521143 Henry Cohn, 2026, needs more optimization.
9 349 0.543252958440 Henry Cohn, 2026, needs more optimization.
9 350 0.543353640863 Henry Cohn, 2026, needs more optimization.
9 351 0.543647901571 Henry Cohn, 2026, needs more optimization.
9 352 0.543843597030 Henry Cohn, 2026, needs more optimization.
9 353 0.543939188209 Henry Cohn, 2026, needs more optimization.
9 354 0.544008333182 Henry Cohn, 2026, needs more optimization.
9 355 0.544071433816 Henry Cohn, 2026, needs more optimization.
9 356 0.544188254479 Henry Cohn, 2026, needs more optimization.
9 357 0.544725724663 Henry Cohn, 2026, needs more optimization.
9 358 0.544861187989 Henry Cohn, 2026, needs more optimization.
9 359 0.546090529379 Henry Cohn, 2026, needs more optimization.
9 360 0.546547064101 Henry Cohn, 2026, needs more optimization.
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 0.555132374859 Henry Cohn, 2026, needs more optimization.
9 484 0.556746835972 Henry Cohn, 2026, needs more optimization.
9 485 0.562170857286 Henry Cohn, 2026, needs more optimization.
9 486 0.565403997454 Henry Cohn, 2026, needs more optimization.
9 487 0.568230007617 Henry Cohn, 2026, needs more optimization.
9 488 0.569262257297 Henry Cohn, 2026, needs more optimization.
9 489 0.570794328174 Henry Cohn, 2026, needs more optimization.
9 490 0.572437695095 Henry Cohn, 2026, needs more optimization.
9 491 0.574097446346 Henry Cohn, 2026, needs more optimization.
9 492 0.574937867899 Henry Cohn, 2026, needs more optimization.
9 493 0.576339351869 Henry Cohn, 2026, needs more optimization.
9 494 0.577946431841 Henry Cohn, 2026, needs more optimization.
9 495 0.578774315519 Henry Cohn, 2026, needs more optimization.
9 496 0.580085950148 Henry Cohn, 2026, needs more optimization.
9 497 0.580582087188 Henry Cohn, 2026, needs more optimization.
9 498 0.581690892475 Henry Cohn, 2026, needs more optimization.
9 499 0.582992594710 Henry Cohn, 2026, needs more optimization.
9 500 0.583874914842 Henry Cohn, 2026, needs more optimization.
9 501 0.584662879416 Henry Cohn, 2026, needs more optimization.
9 502 0.585622134269 Henry Cohn, 2026, needs more optimization.
9 503 0.586205783107 Henry Cohn, 2026, needs more optimization.
9 504 0.586683948385 Henry Cohn, 2026, needs more optimization.
9 505 0.587113139995 Henry Cohn, 2026, needs more optimization.
9 506 0.588097985161 Henry Cohn, 2026, needs more optimization.
9 507 0.588240910586 Henry Cohn, 2026, needs more optimization.
9 508 0.589108515697 Henry Cohn, 2026, needs more optimization.
9 509 0.589589882708 Henry Cohn, 2026, needs more optimization.
9 510 0.589601101541 Henry Cohn, 2026, needs more optimization.
9 511 0.589607209965 Henry Cohn, 2026, needs more optimization.
9 512 0.589607217324 Henry Cohn, 2026, needs more optimization.
9 513 0.589824074371 Henry Cohn, 2026, needs more optimization.
9 514 0.589828100608 Henry Cohn, 2026, needs more optimization.
9 515 0.589828419438 Henry Cohn, 2026, needs more optimization.
9 516 0.589828665915 Henry Cohn, 2026, needs more optimization.
9 517 0.589841280074 Henry Cohn, 2026, needs more optimization.
9 518 0.589857411900 Henry Cohn, 2026, needs more optimization.
9 519 0.589891839586 Henry Cohn, 2026, needs more optimization.
9 520 0.589891852450 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 0.589915181798 Henry Cohn, 2026, needs more optimization.
9 523 0.589917746375 Henry Cohn, 2026, needs more optimization.
9 524 0.589921797567 Henry Cohn, 2026, needs more optimization.
9 525 0.590372970800 Henry Cohn, 2026, needs more optimization.
9 526 0.591453133837 Henry Cohn, 2026, needs more optimization.
9 527 0.593623061723 Henry Cohn, 2026, needs more optimization.
9 528 0.594388557829 Henry Cohn, 2026, needs more optimization.
9 529 0.595190508487 Henry Cohn, 2026, needs more optimization.
9 530 0.595873841971 Henry Cohn, 2026, needs more optimization.
9 531 0.596450139381 Henry Cohn, 2026, needs more optimization.
9 532 0.596863673747 Henry Cohn, 2026, needs more optimization.
9 533 0.596978869604 Henry Cohn, 2026, needs more optimization.
9 534 0.597612226838 Henry Cohn, 2026, needs more optimization.
9 535 0.597927321951 Henry Cohn, 2026, needs more optimization.
9 536 0.598648244312 Henry Cohn, 2026, needs more optimization.
9 537 0.598815951107 Henry Cohn, 2026, needs more optimization.
9 538 0.599017768356 Henry Cohn, 2026, needs more optimization.
9 539 0.599452642948 Henry Cohn, 2026, needs more optimization.
9 540 0.599777818951 Henry Cohn, 2026, needs more optimization.
9 541 0.599873219660 Henry Cohn, 2026, needs more optimization.
9 542 0.599969256640 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 0.605101157612 Henry Cohn, 2026, needs more optimization.
9 614 0.606329030606 Henry Cohn, 2026, needs more optimization.
9 615 0.606837244710 Henry Cohn, 2026, needs more optimization.
9 616 0.607976024630 Henry Cohn, 2026, needs more optimization.
9 617 0.608256021171 Henry Cohn, 2026, needs more optimization.
9 618 0.608623615066 Henry Cohn, 2026, needs more optimization.
9 619 0.608631062713 Henry Cohn, 2026, needs more optimization.
9 620 0.613571750415 Henry Cohn, 2026, needs more optimization.
9 621 0.613636962673 Henry Cohn, 2026, needs more optimization.
9 622 0.613636968173 Henry Cohn, 2026, needs more optimization.
9 623 0.613650676421 Henry Cohn, 2026, needs more optimization.
9 624 0.613714739798 Henry Cohn, 2026, needs more optimization.
9 625 0.613723924290 Henry Cohn, 2026, needs more optimization.
9 626 0.613838634113 Henry Cohn, 2026, needs more optimization.
9 627 0.614370887907 Henry Cohn, 2026, needs more optimization.
9 628 0.614807532182 Henry Cohn, 2026, needs more optimization.
9 629 0.615202579967 Henry Cohn, 2026, needs more optimization.
9 630 0.615626366896 Henry Cohn, 2026, needs more optimization.
9 631 0.615999755497 Henry Cohn, 2026, needs more optimization.
9 632 0.617581462382 Henry Cohn, 2026, needs more optimization.
9 633 0.617747674381 Henry Cohn, 2026, needs more optimization.
9 634 0.618033151660 Henry Cohn, 2026, needs more optimization.
9 636 0.618033155793 Henry Cohn, 2026, needs more optimization.
9 637 0.618033261320 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 0.618033650000 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 0.624151904431 Henry Cohn, 2026, needs more optimization.
9 724 0.642725304312 Henry Cohn, 2026, needs more optimization.
9 725 0.642932628460 Henry Cohn, 2026, needs more optimization.
9 726 0.643189464860 Henry Cohn, 2026, needs more optimization.
9 727 0.643243824821 Henry Cohn, 2026, needs more optimization.
9 728 0.643360394250 Henry Cohn, 2026, needs more optimization.
9 729 0.643388370394 Henry Cohn, 2026, needs more optimization.
9 730 0.643675450625 Henry Cohn, 2026, needs more optimization.
9 731 0.643695758529 Henry Cohn, 2026, needs more optimization.
9 732 0.643708760460 Henry Cohn, 2026, needs more optimization.
9 733 0.643823337228 Henry Cohn, 2026, needs more optimization.
9 734 0.644265753125 Henry Cohn, 2026, needs more optimization.
9 735 0.644265753264 Henry Cohn, 2026, needs more optimization.
9 736 0.644488318497 Henry Cohn, 2026, needs more optimization.
9 737 0.644562624370 Henry Cohn, 2026, needs more optimization.
9 738 0.644565349987 Henry Cohn, 2026, needs more optimization.
9 739 0.644825126644 Henry Cohn, 2026, needs more optimization.
9 740 0.645083541796 Henry Cohn, 2026, needs more optimization.
9 741 0.645103429943 Henry Cohn, 2026, needs more optimization.
9 742 0.645165758745 Henry Cohn, 2026, needs more optimization.
9 743 0.645215067641 Henry Cohn, 2026, needs more optimization.
9 744 0.645318882889 Henry Cohn, 2026, needs more optimization.
9 745 0.645582919414 Henry Cohn, 2026, needs more optimization.
9 746 0.645588677264 Henry Cohn, 2026, needs more optimization.
9 747 0.645600129867 Henry Cohn, 2026, needs more optimization.
9 748 0.645601311321 Henry Cohn, 2026, needs more optimization.
9 749 0.645604199108 Henry Cohn, 2026, needs more optimization.
9 750 0.645604199109 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 0.646106993122 Henry Cohn, 2026, needs more optimization.
9 752 0.646431873111 Henry Cohn, 2026, needs more optimization.
9 753 0.646618647314 Henry Cohn, 2026, needs more optimization.
9 754 0.646635884111 Henry Cohn, 2026, needs more optimization.
9 755 0.646640079958 Henry Cohn, 2026, needs more optimization.
9 756 0.646799147147 Henry Cohn, 2026, needs more optimization.
9 757 0.646999951676 Henry Cohn, 2026, needs more optimization.
9 758 0.647164343495 Henry Cohn, 2026, needs more optimization.
9 759 0.647398672233 Henry Cohn, 2026, needs more optimization.
9 760 0.647400750218 Henry Cohn, 2026, needs more optimization.
9 761 0.647436980897 Henry Cohn, 2026, needs more optimization.
9 762 0.647488386758 Henry Cohn, 2026, needs more optimization.
9 763 0.647866445591 Henry Cohn, 2026, needs more optimization.
9 764 0.647888137754 Henry Cohn, 2026, needs more optimization.
9 765 0.647993992705 Henry Cohn, 2026, needs more optimization.
9 766 0.648007753573 Henry Cohn, 2026, needs more optimization.
9 767 0.648197289219 Henry Cohn, 2026, needs more optimization.
9 768 0.648272147796 Henry Cohn, 2026, needs more optimization.
9 769 0.648384862671 Henry Cohn, 2026, needs more optimization.
9 770 0.648407239778 Henry Cohn, 2026, needs more optimization.
9 771 0.648948273121 Henry Cohn, 2026, needs more optimization.
9 772 0.648964700353 Henry Cohn, 2026, needs more optimization.
9 773 0.648972858955 Henry Cohn, 2026, needs more optimization.
9 774 0.649039228960 Henry Cohn, 2026, needs more optimization.
9 775 0.649284128404 Henry Cohn, 2026, needs more optimization.
9 776 0.649284128539 Henry Cohn, 2026, needs more optimization.
9 777 0.649362213354 Henry Cohn, 2026, needs more optimization.
9 778 0.649378577427 Henry Cohn, 2026, needs more optimization.
9 779 0.649793571300 Henry Cohn, 2026, needs more optimization.
9 780 0.649813987304 Henry Cohn, 2026, needs more optimization.
9 781 0.649819945439 Henry Cohn, 2026, needs more optimization.
9 782 0.649830456454 Henry Cohn, 2026, needs more optimization.
9 783 0.649834805935 Henry Cohn, 2026, needs more optimization.
9 784 0.649839191767 Henry Cohn, 2026, needs more optimization.
9 785 0.649841688307 Henry Cohn, 2026, needs more optimization.
9 786 0.649845948892 Henry Cohn, 2026, needs more optimization.
9 787 0.650702018727 Henry Cohn, 2026, needs more optimization.
9 788 0.650736817895 Henry Cohn, 2026, needs more optimization.
9 789 0.650808733289 Henry Cohn, 2026, needs more optimization.
9 790 0.651037002860 Henry Cohn, 2026, needs more optimization.
9 791 0.651283206612 Henry Cohn, 2026, needs more optimization.
9 792 0.651292285611 Henry Cohn, 2026, needs more optimization.
9 793 0.651372351528 Henry Cohn, 2026, needs more optimization.
9 794 0.651513175002 Henry Cohn, 2026, needs more optimization.
9 795 0.651641866734 Henry Cohn, 2026, needs more optimization.
9 796 0.651649477527 Henry Cohn, 2026, needs more optimization.
9 797 0.651677173331 Henry Cohn, 2026, needs more optimization.
9 798 0.651869209435 Henry Cohn, 2026, needs more optimization.
9 799 0.652144196585 Henry Cohn, 2026, needs more optimization.
9 800 0.652157252611 Henry Cohn, 2026, needs more optimization.
9 801 0.652207844794 Henry Cohn, 2026, needs more optimization.
9 802 0.652265554442 Henry Cohn, 2026, needs more optimization.
9 803 0.652509836440 Henry Cohn, 2026, needs more optimization.
9 804 0.652542796175 Henry Cohn, 2026, needs more optimization.
9 805 0.652546983675 Henry Cohn, 2026, needs more optimization.
9 806 0.652695654756 Henry Cohn, 2026, needs more optimization.
9 807 0.652901858662 Henry Cohn, 2026, needs more optimization.
9 808 0.652947436086 Henry Cohn, 2026, needs more optimization.
9 809 0.653146959679 Henry Cohn, 2026, needs more optimization.
9 810 0.653158518053 Henry Cohn, 2026, needs more optimization.
9 811 0.653211110943 Henry Cohn, 2026, needs more optimization.
9 812 0.653355952374 Henry Cohn, 2026, needs more optimization.
9 813 0.653413955507 Henry Cohn, 2026, needs more optimization.
9 814 0.653672288440 Henry Cohn, 2026, needs more optimization.
9 815 0.653761878803 Henry Cohn, 2026, needs more optimization.
9 816 0.653810785701 Henry Cohn, 2026, needs more optimization.
9 817 0.653838978987 Henry Cohn, 2026, needs more optimization.
9 818 0.653915237531 Henry Cohn, 2026, needs more optimization.
9 819 0.654120491300 Henry Cohn, 2026, needs more optimization.
9 820 0.654123903478 Henry Cohn, 2026, needs more optimization.
9 821 0.654206084947 Henry Cohn, 2026, needs more optimization.
9 822 0.654232255809 Henry Cohn, 2026, needs more optimization.
9 823 0.654369426535 Henry Cohn, 2026, needs more optimization.
9 824 0.654461644022 Henry Cohn, 2026, needs more optimization.
9 825 0.654608455726 Henry Cohn, 2026, needs more optimization.
9 826 0.654794561838 Henry Cohn, 2026, needs more optimization.
9 827 0.654989036181 Henry Cohn, 2026, needs more optimization.
9 828 0.654996014227 Henry Cohn, 2026, needs more optimization.
9 829 0.655127544715 Henry Cohn, 2026, needs more optimization.
9 830 0.655138002450 Henry Cohn, 2026, needs more optimization.
9 831 0.655443721881 Henry Cohn, 2026, needs more optimization.
9 832 0.655451420059 Henry Cohn, 2026, needs more optimization.
9 833 0.655642533549 Henry Cohn, 2026, needs more optimization.
9 834 0.655671174278 Henry Cohn, 2026, needs more optimization.
9 835 0.655715538345 Henry Cohn, 2026, needs more optimization.
9 836 0.655717929260 Henry Cohn, 2026, needs more optimization.
9 837 0.655721265731 Henry Cohn, 2026, needs more optimization.
9 838 0.655721477243 Henry Cohn, 2026, needs more optimization.
9 839 0.656333013248 Henry Cohn, 2026, needs more optimization.
9 840 0.656390039876 Henry Cohn, 2026, needs more optimization.
9 841 0.656799040903 Henry Cohn, 2026, needs more optimization.
9 842 0.656800565364 Henry Cohn, 2026, needs more optimization.
9 843 0.657079528218 Henry Cohn, 2026, needs more optimization.
9 844 0.657091431218 Henry Cohn, 2026, needs more optimization.
9 845 0.657133331539 Henry Cohn, 2026, needs more optimization.
9 846 0.657386713928 Henry Cohn, 2026, needs more optimization.
9 847 0.657408319910 Henry Cohn, 2026, needs more optimization.
9 848 0.657410505618 Henry Cohn, 2026, needs more optimization.
9 849 0.657441574398 Henry Cohn, 2026, needs more optimization.
9 850 0.657514846733 Henry Cohn, 2026, needs more optimization.
9 851 0.657742159320 Henry Cohn, 2026, needs more optimization.
9 852 0.657785151949 Henry Cohn, 2026, needs more optimization.
9 853 0.657797450799 Henry Cohn, 2026, needs more optimization.
9 854 0.657808352792 Henry Cohn, 2026, needs more optimization.
9 855 0.657991257782 Henry Cohn, 2026, needs more optimization.
9 856 0.658315202064 Henry Cohn, 2026, needs more optimization.
9 857 0.658358018067 Henry Cohn, 2026, needs more optimization.
9 858 0.658552645178 Henry Cohn, 2026, needs more optimization.
9 859 0.658604451269 Henry Cohn, 2026, needs more optimization.
9 860 0.658764325424 Henry Cohn, 2026, needs more optimization.
9 861 0.658819498413 Henry Cohn, 2026, needs more optimization.
9 862 0.659014055992 Henry Cohn, 2026, needs more optimization.
9 863 0.659014056565 Henry Cohn, 2026, needs more optimization.
9 864 0.659014056861 Henry Cohn, 2026, needs more optimization.
9 865 0.659020325859 Henry Cohn, 2026, needs more optimization.
9 866 0.659020326227 Henry Cohn, 2026, needs more optimization.
9 867 0.659048166010 Henry Cohn, 2026, needs more optimization.
9 868 0.659054387435 Henry Cohn, 2026, needs more optimization.
9 869 0.659054792139 Henry Cohn, 2026, needs more optimization.
9 870 0.659683249196 Henry Cohn, 2026, needs more optimization.
9 871 0.659693298125 Henry Cohn, 2026, needs more optimization.
9 872 0.659700876272 Henry Cohn, 2026, needs more optimization.
9 873 0.660090615863 Henry Cohn, 2026, needs more optimization.
9 874 0.660090616409 Henry Cohn, 2026, needs more optimization.
9 875 0.660123025173 Henry Cohn, 2026, needs more optimization.
9 876 0.660147960367 Henry Cohn, 2026, needs more optimization.
9 877 0.660147964070 Henry Cohn, 2026, needs more optimization.
9 878 0.660168999434 Henry Cohn, 2026, needs more optimization.
9 879 0.660177360158 Henry Cohn, 2026, needs more optimization.
9 880 0.660177360310 Henry Cohn, 2026, needs more optimization.
9 881 0.660735243225 Henry Cohn, 2026, needs more optimization.
9 882 0.660738732988 Henry Cohn, 2026, needs more optimization.
9 883 0.660746563581 Henry Cohn, 2026, needs more optimization.
9 884 0.660758468104 Henry Cohn, 2026, needs more optimization.
9 885 0.660758657192 Henry Cohn, 2026, needs more optimization.
9 886 0.660758915709 Henry Cohn, 2026, needs more optimization.
9 887 0.661274595072 Henry Cohn, 2026, needs more optimization.
9 888 0.661637262962 Henry Cohn, 2026, needs more optimization.
9 889 0.661684576568 Henry Cohn, 2026, needs more optimization.
9 890 0.661732435705 Henry Cohn, 2026, needs more optimization.
9 891 0.661734179218 Henry Cohn, 2026, needs more optimization.
9 892 0.661922959184 Henry Cohn, 2026, needs more optimization.
9 893 0.661979605524 Henry Cohn, 2026, needs more optimization.
9 894 0.662026656223 Henry Cohn, 2026, needs more optimization.
9 895 0.662240077708 Henry Cohn, 2026, needs more optimization.
9 896 0.662264021393 Henry Cohn, 2026, needs more optimization.
9 897 0.662299979401 Henry Cohn, 2026, needs more optimization.
9 898 0.662515558187 Henry Cohn, 2026, needs more optimization.
9 899 0.662530855613 Henry Cohn, 2026, needs more optimization.
9 900 0.662626959034 Henry Cohn, 2026, needs more optimization.
9 901 0.662633947210 Henry Cohn, 2026, needs more optimization.
9 902 0.662791569537 Henry Cohn, 2026, needs more optimization.
9 903 0.663119316825 Henry Cohn, 2026, needs more optimization.
9 904 0.663123174673 Henry Cohn, 2026, needs more optimization.
9 905 0.663176824201 Henry Cohn, 2026, needs more optimization.
9 906 0.663315619150 Henry Cohn, 2026, needs more optimization.
9 907 0.663368266217 Henry Cohn, 2026, needs more optimization.
9 908 0.663382931988 Henry Cohn, 2026, needs more optimization.
9 909 0.663566591995 Henry Cohn, 2026, needs more optimization.
9 910 0.663615304726 Henry Cohn, 2026, needs more optimization.
9 911 0.663715919696 Henry Cohn, 2026, needs more optimization.
9 912 0.663847044299 Henry Cohn, 2026, needs more optimization.
9 913 0.663869012057 Henry Cohn, 2026, needs more optimization.
9 914 0.663888256414 Henry Cohn, 2026, needs more optimization.
9 915 0.663934042801 Henry Cohn, 2026, needs more optimization.
9 916 0.664195904862 Henry Cohn, 2026, needs more optimization.
9 917 0.664208603378 Henry Cohn, 2026, needs more optimization.
9 918 0.664309802571 Henry Cohn, 2026, needs more optimization.
9 919 0.664669378555 Henry Cohn, 2026, needs more optimization.
9 920 0.664695623199 Henry Cohn, 2026, needs more optimization.
9 921 0.664718999202 Henry Cohn, 2026, needs more optimization.
9 922 0.664741264832 Henry Cohn, 2026, needs more optimization.
9 923 0.665022930108 Henry Cohn, 2026, needs more optimization.
9 924 0.665075723649 Henry Cohn, 2026, needs more optimization.
9 925 0.665319792101 Henry Cohn, 2026, needs more optimization.
9 926 0.665342211507 Henry Cohn, 2026, needs more optimization.
9 927 0.665367977494 Henry Cohn, 2026, needs more optimization.
9 928 0.665641249249 Henry Cohn, 2026, needs more optimization.
9 929 0.665647031955 Henry Cohn, 2026, needs more optimization.
9 930 0.665719703729 Henry Cohn, 2026, needs more optimization.
9 931 0.665770715524 Henry Cohn, 2026, needs more optimization.
9 932 0.665814521465 Henry Cohn, 2026, needs more optimization.
9 933 0.665836348613 Henry Cohn, 2026, needs more optimization.
9 934 0.666173191035 Henry Cohn, 2026, needs more optimization.
9 935 0.666179272684 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 0.150182198338 Henry Cohn, 2025.
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 0.269696017725 Henry Cohn, 2026, needs more optimization.
10 70 0.271728068029 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 0.289698982860 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 0.301759908598 Henry Cohn, 2026, needs more optimization.
10 82 0.304396879638 Henry Cohn, 2026, needs more optimization.
10 83 0.307851642008 Henry Cohn, 2026, needs more optimization.
10 84 0.310848806540 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 0.324778519496 Henry Cohn, 2026, needs more optimization.
10 90 0.325389381674 Henry Cohn, 2026, needs more optimization.
10 91 0.326254849551 Henry Cohn, 2026, needs more optimization.
10 92 0.327937279523 Henry Cohn, 2026, needs more optimization.
10 93 0.328576505748 Henry Cohn, 2026, needs more optimization.
10 94 0.329294456265 Henry Cohn, 2026, needs more optimization.
10 95 0.329854824816 Henry Cohn, 2026, needs more optimization.
10 96 0.330233069839 Henry Cohn, 2026, needs more optimization.
10 98 0.330436975080 Henry Cohn, 2026, needs more optimization.
10 99 0.330654923978 Henry Cohn, 2026.
10 100 0.330962913172 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 0.333136086650 Henry Cohn, 2026, needs more optimization.
10 104 0.333227863020 Henry Cohn, 2026, needs more optimization.
10 105 0.333257174187 Henry Cohn, 2026, needs more optimization.
10 106 0.333289229235 Henry Cohn, 2026, needs more optimization.
10 107 0.333306657651 Henry Cohn, 2026, needs more optimization.
10 108 0.333307673892 Henry Cohn, 2026, needs more optimization.
10 109 0.335268813852 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 0.342174882434 Henry Cohn, 2026, needs more optimization.
10 112 0.344829852887 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 0.353518633041 Henry Cohn, 2026, needs more optimization.
10 117 0.358340499611 Henry Cohn, 2026, needs more optimization.
10 118 0.361656836454 Henry Cohn, 2026, needs more optimization.
10 119 0.363761710067 Henry Cohn, 2026, needs more optimization.
10 120 0.364674968141 Henry Cohn, 2026, needs more optimization.
10 121 0.365191096657 Henry Cohn, 2026.
10 122 0.365459215843 Henry Cohn, 2026, needs more optimization.
10 124 0.365550021054 Henry Cohn, 2026, needs more optimization.
10 125 0.365550181476 Henry Cohn, 2026, needs more optimization.
10 126 0.365557275483 Henry Cohn, 2026, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367843362410 Henry Cohn, 2026, needs more optimization.
10 129 0.370352757621 Henry Cohn, 2026, needs more optimization.
10 130 0.371246951366 Henry Cohn, 2026, needs more optimization.
10 131 0.371343446600 Henry Cohn, 2026, needs more optimization.
10 132 0.371409893582 Henry Cohn, 2026, needs more optimization.
10 133 0.385286495596 Henry Cohn, 2026, needs more optimization.
10 134 0.389768459429 Henry Cohn, 2026, needs more optimization.
10 135 0.392340761166 Henry Cohn, 2026, needs more optimization.
10 136 0.392922374482 Henry Cohn, 2026, needs more optimization.
10 137 0.396210893031 Henry Cohn, 2026, needs more optimization.
10 138 0.398651390909 Henry Cohn, 2026, needs more optimization.
10 139 0.400187109545 Henry Cohn, 2026, needs more optimization.
10 140 0.401787413762 Henry Cohn, 2026, needs more optimization.
10 141 0.403139490783 Henry Cohn, 2026, needs more optimization.
10 142 0.404397831058 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 0.413096978622 Henry Cohn, 2026, needs more optimization.
10 158 0.414013597729 Henry Cohn, 2026, needs more optimization.
10 159 0.414529606083 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 0.419208075238 Henry Cohn, 2026, needs more optimization.
10 164 0.420594116234 Henry Cohn, 2026, needs more optimization.
10 165 0.421679220306 Henry Cohn, 2026, needs more optimization.
10 166 0.422486763429 Henry Cohn, 2026, needs more optimization.
10 167 0.423423740045 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 0.425992943038 Henry Cohn, 2026, needs more optimization.
10 171 0.427021657819 Henry Cohn, 2026, needs more optimization.
10 172 0.428123699246 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 0.438692154259 Henry Cohn, 2026, needs more optimization.
10 196 0.441226110602 Henry Cohn, 2026, needs more optimization.
10 197 0.443912268851 Henry Cohn, 2026, needs more optimization.
10 198 0.445538482333 Henry Cohn, 2026, needs more optimization.
10 199 0.447137178527 Henry Cohn, 2026, needs more optimization.
10 200 0.448192344036 Henry Cohn, 2026, needs more optimization.
10 201 0.449230572516 Henry Cohn, 2026, needs more optimization.
10 202 0.450490527639 Henry Cohn, 2026, needs more optimization.
10 203 0.451663310532 Henry Cohn, 2026, needs more optimization.
10 204 0.452579690892 Henry Cohn, 2026, needs more optimization.
10 205 0.453663103731 Henry Cohn, 2026, needs more optimization.
10 206 0.454659098938 Henry Cohn, 2026, needs more optimization.
10 207 0.454704022153 Henry Cohn, 2026, needs more optimization.
10 208 0.454722022747 Henry Cohn, 2026, needs more optimization.
10 209 0.454748193085 Henry Cohn, 2026, needs more optimization.
10 210 0.454935539914 Henry Cohn, 2026, needs more optimization.
10 211 0.455019456103 Henry Cohn, 2026, needs more optimization.
10 212 0.455033844658 Henry Cohn, 2026, needs more optimization.
10 213 0.455043485352 Henry Cohn, 2026, needs more optimization.
10 214 0.455131172809 Henry Cohn, 2026, needs more optimization.
10 215 0.455229767762 Henry Cohn, 2026, needs more optimization.
10 216 0.455244551520 Henry Cohn, 2026, needs more optimization.
10 217 0.455266058464 Henry Cohn, 2026, needs more optimization.
10 218 0.455275116436 Henry Cohn, 2026, needs more optimization.
10 219 0.455289240962 Henry Cohn, 2026, needs more optimization.
10 238 0.455341801262 Henry Cohn, 2026.
18⁢x2−6⁢x−1
10 239 0.455411328598 Henry Cohn, 2026, needs more optimization.
10 240 0.455775275865 Henry Cohn, 2026, needs more optimization.
10 241 0.455995382070 Henry Cohn, 2026, needs more optimization.
10 242 0.456237787380 Henry Cohn, 2026, needs more optimization.
10 243 0.456328851766 Henry Cohn, 2026, needs more optimization.
10 244 0.456387607657 Henry Cohn, 2026, needs more optimization.
10 245 0.457723144491 Henry Cohn, 2026, needs more optimization.
10 246 0.460280163851 Henry Cohn, 2026, needs more optimization.
10 247 0.462322466762 Henry Cohn, 2026, needs more optimization.
10 248 0.464411407911 Henry Cohn, 2026, needs more optimization.
10 249 0.464411407914 Henry Cohn, 2026, needs more optimization.
10 250 0.464774458748 Henry Cohn, 2026, needs more optimization.
10 251 0.465520576285 Henry Cohn, 2026, needs more optimization.
10 252 0.465580135944 Henry Cohn, 2026, needs more optimization.
10 253 0.466538415958 Henry Cohn, 2026, needs more optimization.
10 254 0.468234705403 Henry Cohn, 2026, needs more optimization.
10 255 0.469533083225 Henry Cohn, 2026, needs more optimization.
10 256 0.470700602113 Henry Cohn, 2026, needs more optimization.
10 257 0.471498515461 Henry Cohn, 2026, needs more optimization.
10 258 0.473610010013 Henry Cohn, 2026, needs more optimization.
10 259 0.474557931355 Henry Cohn, 2026, needs more optimization.
10 260 0.475056551404 Henry Cohn, 2026, needs more optimization.
10 261 0.475790285868 Henry Cohn, 2026, needs more optimization.
10 262 0.476352902313 Henry Cohn, 2026, needs more optimization.
10 263 0.476827037008 Henry Cohn, 2026, needs more optimization.
10 264 0.477845976559 Henry Cohn, 2026, needs more optimization.
10 265 0.477963378444 Henry Cohn, 2026, needs more optimization.
10 266 0.477963380348 Henry Cohn, 2026, needs more optimization.
10 267 0.478094977194 Henry Cohn, 2026, needs more optimization.
10 268 0.478242875773 Henry Cohn, 2026, needs more optimization.
10 269 0.478322027740 Henry Cohn, 2026, needs more optimization.
10 270 0.478501704997 Henry Cohn, 2026, needs more optimization.
10 271 0.478515135703 Henry Cohn, 2026, needs more optimization.
10 272 0.478935083900 Henry Cohn, 2026, needs more optimization.
10 273 0.479450532344 Henry Cohn, 2026, needs more optimization.
10 274 0.479893553805 Henry Cohn, 2026, needs more optimization.
10 275 0.480479028158 Henry Cohn, 2026, needs more optimization.
10 276 0.481100840128 Henry Cohn, 2026, needs more optimization.
10 277 0.481577506467 Henry Cohn, 2026, needs more optimization.
10 278 0.483359058357 Henry Cohn, 2026, needs more optimization.
10 279 0.483627750779 Henry Cohn, 2026, needs more optimization.
10 280 0.483943535167 Henry Cohn, 2026, needs more optimization.
10 281 0.484141082545 Henry Cohn, 2026, needs more optimization.
10 282 0.484191234027 Henry Cohn, 2026, needs more optimization.
10 283 0.484338614318 Henry Cohn, 2026, needs more optimization.
10 284 0.484622824405 Henry Cohn, 2026, needs more optimization.
10 285 0.484782567988 Henry Cohn, 2026, needs more optimization.
10 286 0.484964128657 Henry Cohn, 2026, needs more optimization.
10 287 0.485113195215 Henry Cohn, 2026, needs more optimization.
10 288 0.485324752474 Henry Cohn, 2026, needs more optimization.
10 289 0.485438047180 Henry Cohn, 2026, needs more optimization.
10 290 0.485757933955 Henry Cohn, 2026, needs more optimization.
10 291 0.485950652109 Henry Cohn, 2026, needs more optimization.
10 292 0.486343766668 Henry Cohn, 2026, needs more optimization.
10 293 0.486574047741 Henry Cohn, 2026, needs more optimization.
10 294 0.486933277052 Henry Cohn, 2026, needs more optimization.
10 295 0.487337686201 Henry Cohn, 2026, needs more optimization.
10 296 0.487618197304 Henry Cohn, 2026, needs more optimization.
10 297 0.487857323191 Henry Cohn, 2026, needs more optimization.
10 298 0.488251561101 Henry Cohn, 2026, needs more optimization.
10 299 0.488634531787 Henry Cohn, 2026, needs more optimization.
10 300 0.489089812353 Henry Cohn, 2026, needs more optimization.
10 301 0.489361691257 Henry Cohn, 2026, needs more optimization.
10 302 0.489529004684 Henry Cohn, 2026, needs more optimization.
10 303 0.489675071479 Henry Cohn, 2026, needs more optimization.
10 304 0.490048912745 Henry Cohn, 2026, needs more optimization.
10 305 0.490279988012 Henry Cohn, 2026, needs more optimization.
10 306 0.490878337467 Henry Cohn, 2026, needs more optimization.
10 307 0.490912429871 Henry Cohn, 2026, needs more optimization.
10 308 0.490993019129 Henry Cohn, 2026, needs more optimization.
10 309 0.491001237559 Henry Cohn, 2026, needs more optimization.
10 310 0.491001967633 Henry Cohn, 2026, needs more optimization.
10 311 0.491049251531 Henry Cohn, 2026, needs more optimization.
10 312 0.491085274650 Henry Cohn, 2026, needs more optimization.
10 313 0.491241178751 Henry Cohn, 2026, needs more optimization.
10 314 0.491265242708 Henry Cohn, 2026, needs more optimization.
10 315 0.491767481382 Henry Cohn, 2026, needs more optimization.
10 316 0.491780188927 Henry Cohn, 2026, needs more optimization.
10 317 0.491856202770 Henry Cohn, 2026, needs more optimization.
10 318 0.492051282409 Henry Cohn, 2026, needs more optimization.
10 319 0.492145587568 Henry Cohn, 2026, needs more optimization.
10 320 0.492447766690 Henry Cohn, 2026, needs more optimization.
10 321 0.492985203808 Henry Cohn, 2026, needs more optimization.
10 322 0.493363484780 Henry Cohn, 2026, needs more optimization.
10 323 0.493429429877 Henry Cohn, 2026, needs more optimization.
10 324 0.493664692814 Henry Cohn, 2026, needs more optimization.
10 325 0.494182447112 Henry Cohn, 2026, needs more optimization.
10 326 0.494272792142 Henry Cohn, 2026, needs more optimization.
10 327 0.494565897188 Henry Cohn, 2026, needs more optimization.
10 328 0.494922370046 Henry Cohn, 2026, needs more optimization.
10 329 0.495034748532 Henry Cohn, 2026, needs more optimization.
10 330 0.495091634860 Henry Cohn, 2026, needs more optimization.
10 331 0.495304218554 Henry Cohn, 2026, needs more optimization.
10 332 0.495450691806 Henry Cohn, 2026, needs more optimization.
10 333 0.495576708877 Henry Cohn, 2026, needs more optimization.
10 334 0.496295353545 Henry Cohn, 2026, needs more optimization.
10 335 0.496384503594 Henry Cohn, 2026, needs more optimization.
10 336 0.496560355361 Henry Cohn, 2026, needs more optimization.
10 337 0.496781285330 Henry Cohn, 2026, needs more optimization.
10 338 0.496922952634 Henry Cohn, 2026, needs more optimization.
10 339 0.497020558719 Henry Cohn, 2026, needs more optimization.
10 340 0.497160903412 Henry Cohn, 2026, needs more optimization.
10 341 0.497229502650 Henry Cohn, 2026, needs more optimization.
10 342 0.497277061262 Henry Cohn, 2026, needs more optimization.
10 343 0.497374307877 Henry Cohn, 2026, needs more optimization.
10 344 0.497446592394 Henry Cohn, 2026, needs more optimization.
10 345 0.497542613700 Henry Cohn, 2026, needs more optimization.
10 346 0.498127944250 Henry Cohn, 2026, needs more optimization.
10 347 0.498234182741 Henry Cohn, 2026, needs more optimization.
10 348 0.498338728979 Henry Cohn, 2026, needs more optimization.
10 349 0.498386477765 Henry Cohn, 2026, needs more optimization.
10 350 0.498472032314 Henry Cohn, 2026, needs more optimization.
10 351 0.498489213054 Henry Cohn, 2026, needs more optimization.
10 352 0.498499708420 Henry Cohn, 2026, needs more optimization.
10 353 0.498600654325 Henry Cohn, 2026, needs more optimization.
10 354 0.498641448971 Henry Cohn, 2026, needs more optimization.
10 355 0.498777045920 Henry Cohn, 2026, needs more optimization.
10 356 0.498814648218 Henry Cohn, 2026, needs more optimization.
10 357 0.498857115319 Henry Cohn, 2026, needs more optimization.
10 358 0.498899137009 Henry Cohn, 2026, needs more optimization.
10 360 0.498913129912 Henry Cohn, 2026, needs more optimization.
10 361 0.498936782844 Henry Cohn, 2026, needs more optimization.
10 362 0.498965844590 Henry Cohn, 2026, needs more optimization.
10 363 0.499014412896 Henry Cohn, 2026, needs more optimization.
10 365 0.499015942153 Henry Cohn, 2026, needs more optimization.
10 366 0.499035934354 Henry Cohn, 2026, needs more optimization.
10 368 0.499296356577 Henry Cohn, 2026, needs more optimization.
10 369 0.499303118621 Henry Cohn, 2026, needs more optimization.
10 370 0.499361469713 Henry Cohn, 2026, needs more optimization.
10 371 0.499437807407 Henry Cohn, 2026, needs more optimization.
10 372 0.499582689840 Henry Cohn, 2026, needs more optimization.
10 373 0.499587634288 Henry Cohn, 2026, needs more optimization.
10 374 0.499649812365 Henry Cohn, 2026, needs more optimization.
10 375 0.499681179864 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 0.526719442067 Henry Cohn, 2026, needs more optimization.
10 512 0.529990921462 Henry Cohn, 2026, needs more optimization.
10 513 0.532753334418 Henry Cohn, 2026, needs more optimization.
10 514 0.533848572299 Henry Cohn, 2026, needs more optimization.
10 515 0.535029681686 Henry Cohn, 2026, needs more optimization.
10 516 0.536941533486 Henry Cohn, 2026, needs more optimization.
10 517 0.538181793604 Henry Cohn, 2026, needs more optimization.
10 518 0.538856264145 Henry Cohn, 2026, needs more optimization.
10 519 0.540297605946 Henry Cohn, 2026, needs more optimization.
10 520 0.541065852820 Henry Cohn, 2026, needs more optimization.
10 521 0.542222009406 Henry Cohn, 2026, needs more optimization.
10 522 0.543006318044 Henry Cohn, 2026, needs more optimization.
10 523 0.543643555979 Henry Cohn, 2026, needs more optimization.
10 524 0.544354883235 Henry Cohn, 2026, needs more optimization.
10 525 0.545220796170 Henry Cohn, 2026, needs more optimization.
10 526 0.545983753178 Henry Cohn, 2026, needs more optimization.
10 527 0.546334510079 Henry Cohn, 2026, needs more optimization.
10 528 0.547371273690 Henry Cohn, 2026, needs more optimization.
10 529 0.548027818625 Henry Cohn, 2026, needs more optimization.
10 530 0.548756152944 Henry Cohn, 2026, needs more optimization.
10 531 0.549360802597 Henry Cohn, 2026, needs more optimization.
10 532 0.549651516648 Henry Cohn, 2026, needs more optimization.
10 533 0.550237805316 Henry Cohn, 2026, needs more optimization.
10 534 0.550814625717 Henry Cohn, 2026, needs more optimization.
10 535 0.551329881798 Henry Cohn, 2026, needs more optimization.
10 536 0.552031051437 Henry Cohn, 2026, needs more optimization.
10 537 0.552516778398 Henry Cohn, 2026, needs more optimization.
10 538 0.553355893237 Henry Cohn, 2026, needs more optimization.
10 539 0.553509996523 Henry Cohn, 2026, needs more optimization.
10 540 0.554028501780 Henry Cohn, 2026, needs more optimization.
10 541 0.554469860309 Henry Cohn, 2026, needs more optimization.
10 542 0.554888104864 Henry Cohn, 2026, needs more optimization.
10 543 0.555234305982 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 0.567867562526 Henry Cohn, 2026, needs more optimization.
10 773 0.569706228267 Henry Cohn, 2026, needs more optimization.
10 774 0.570774619580 Henry Cohn, 2026, needs more optimization.
10 775 0.571625908989 Henry Cohn, 2026, needs more optimization.
10 776 0.571927482222 Henry Cohn, 2026, needs more optimization.
10 778 0.572434165978 Henry Cohn, 2026, needs more optimization.
10 779 0.572929704407 Henry Cohn, 2026, needs more optimization.
10 781 0.573173421052 Henry Cohn, 2026, needs more optimization.
10 782 0.573442177562 Henry Cohn, 2026, needs more optimization.
10 783 0.573472812190 Henry Cohn, 2026, needs more optimization.
10 784 0.573685687610 Henry Cohn, 2026, needs more optimization.
10 785 0.573707483860 Henry Cohn, 2026, needs more optimization.
10 786 0.576360838880 Henry Cohn, 2026, needs more optimization.
10 787 0.576684855967 Henry Cohn, 2026, needs more optimization.
10 788 0.577146196298 Henry Cohn, 2026, needs more optimization.
10 789 0.577207527108 Henry Cohn, 2026, needs more optimization.
10 790 0.577902008344 Henry Cohn, 2026, needs more optimization.
10 791 0.578171380439 Henry Cohn, 2026, needs more optimization.
10 792 0.578631319216 Henry Cohn, 2026, needs more optimization.
10 793 0.578963980283 Henry Cohn, 2026, needs more optimization.
10 794 0.579631137963 Henry Cohn, 2026, needs more optimization.
10 795 0.579877765005 Henry Cohn, 2026, needs more optimization.
10 796 0.580146176027 Henry Cohn, 2026, needs more optimization.
10 797 0.580547066921 Henry Cohn, 2026, needs more optimization.
10 798 0.580626406704 Henry Cohn, 2026, needs more optimization.
10 799 0.581828845541 Henry Cohn, 2026, needs more optimization.
10 800 0.581960347585 Henry Cohn, 2026, needs more optimization.
10 801 0.582166584644 Henry Cohn, 2026, needs more optimization.
10 802 0.583093113075 Henry Cohn, 2026, needs more optimization.
10 803 0.583396935133 Henry Cohn, 2026, needs more optimization.
10 804 0.583572325881 Henry Cohn, 2026, needs more optimization.
10 805 0.584237704361 Henry Cohn, 2026, needs more optimization.
10 806 0.584348771151 Henry Cohn, 2026, needs more optimization.
10 807 0.584451554488 Henry Cohn, 2026, needs more optimization.
10 808 0.584487049871 Henry Cohn, 2026, needs more optimization.
10 809 0.584772356035 Henry Cohn, 2026, needs more optimization.
10 810 0.585268970944 Henry Cohn, 2026, needs more optimization.
10 811 0.585335870387 Henry Cohn, 2026, needs more optimization.
10 812 0.585410363256 Henry Cohn, 2026, needs more optimization.
10 813 0.585471903301 Henry Cohn, 2026, needs more optimization.
10 814 0.585589715948 Henry Cohn, 2026, needs more optimization.
10 815 0.585654597827 Henry Cohn, 2026, needs more optimization.
10 816 0.585776072457 Henry Cohn, 2026, needs more optimization.
10 817 0.585989585334 Henry Cohn, 2026, needs more optimization.
10 818 0.586247961351 Henry Cohn, 2026, needs more optimization.
10 819 0.586495041492 Henry Cohn, 2026, needs more optimization.
10 820 0.586581662506 Henry Cohn, 2026, needs more optimization.
10 821 0.586809854450 Henry Cohn, 2026, needs more optimization.
10 822 0.587087361894 Henry Cohn, 2026, needs more optimization.
10 823 0.587270460191 Henry Cohn, 2026, needs more optimization.
10 824 0.587282148729 Henry Cohn, 2026, needs more optimization.
10 825 0.587339844814 Henry Cohn, 2026, needs more optimization.
10 826 0.587483191767 Henry Cohn, 2026, needs more optimization.
10 827 0.587581703428 Henry Cohn, 2026, needs more optimization.
10 828 0.588502124436 Henry Cohn, 2026, needs more optimization.
10 829 0.588822925961 Henry Cohn, 2026, needs more optimization.
10 830 0.589009048465 Henry Cohn, 2026, needs more optimization.
10 831 0.589308412184 Henry Cohn, 2026, needs more optimization.
10 832 0.589562820471 Henry Cohn, 2026, needs more optimization.
10 833 0.589775111693 Henry Cohn, 2026, needs more optimization.
10 834 0.589780660708 Henry Cohn, 2026, needs more optimization.
10 835 0.589951805154 Henry Cohn, 2026, needs more optimization.
10 836 0.590037429369 Henry Cohn, 2026, needs more optimization.
10 837 0.590078097582 Henry Cohn, 2026, needs more optimization.
10 838 0.590300758729 Henry Cohn, 2026, needs more optimization.
10 839 0.590446848311 Henry Cohn, 2026, needs more optimization.
10 840 0.590677755565 Henry Cohn, 2026, needs more optimization.
10 841 0.590873525027 Henry Cohn, 2026, needs more optimization.
10 842 0.590894722555 Henry Cohn, 2026, needs more optimization.
10 843 0.590907977276 Henry Cohn, 2026, needs more optimization.
10 844 0.590916540903 Henry Cohn, 2026, needs more optimization.
10 845 0.591186655716 Henry Cohn, 2026, needs more optimization.
10 846 0.591519229173 Henry Cohn, 2026, needs more optimization.
10 847 0.591536563472 Henry Cohn, 2026, needs more optimization.
10 848 0.591664778820 Henry Cohn, 2026, needs more optimization.
10 849 0.591685756728 Henry Cohn, 2026, needs more optimization.
10 850 0.591751267362 Henry Cohn, 2026, needs more optimization.
10 851 0.591800798131 Henry Cohn, 2026, needs more optimization.
10 852 0.591800798335 Henry Cohn, 2026, needs more optimization.
10 853 0.591877919159 Henry Cohn, 2026, needs more optimization.
10 854 0.591884795875 Henry Cohn, 2026, needs more optimization.
10 855 0.591884796038 Henry Cohn, 2026, needs more optimization.
10 856 0.591905243354 Henry Cohn, 2026, needs more optimization.
10 857 0.591926853489 Henry Cohn, 2026, needs more optimization.
10 858 0.592021968631 Henry Cohn, 2026, needs more optimization.
10 859 0.592069452070 Henry Cohn, 2026, needs more optimization.
10 860 0.592310393106 Henry Cohn, 2026, needs more optimization.
10 861 0.592413974731 Henry Cohn, 2026, needs more optimization.
10 862 0.592438316816 Henry Cohn, 2026, needs more optimization.
10 863 0.592557836790 Henry Cohn, 2026, needs more optimization.
10 864 0.592572200105 Henry Cohn, 2026, needs more optimization.
10 865 0.592593046003 Henry Cohn, 2026, needs more optimization.
10 866 0.592602546110 Henry Cohn, 2026, needs more optimization.
10 867 0.592607487267 Henry Cohn, 2026, needs more optimization.
10 868 0.592618384305 Henry Cohn, 2026, needs more optimization.
10 869 0.592693480071 Henry Cohn, 2026, needs more optimization.
10 870 0.592697865880 Henry Cohn, 2026, needs more optimization.
10 871 0.592704558476 Henry Cohn, 2026, needs more optimization.
10 872 0.592712176977 Henry Cohn, 2026, needs more optimization.
10 873 0.592712896462 Henry Cohn, 2026, needs more optimization.
10 874 0.592960031966 Henry Cohn, 2026, needs more optimization.
10 875 0.592987581880 Henry Cohn, 2026, needs more optimization.
10 876 0.593000983637 Henry Cohn, 2026, needs more optimization.
10 877 0.593069646367 Henry Cohn, 2026, needs more optimization.
10 878 0.593073139956 Henry Cohn, 2026, needs more optimization.
10 879 0.593087483251 Henry Cohn, 2026, needs more optimization.
10 880 0.593087483497 Henry Cohn, 2026, needs more optimization.
10 881 0.593096847323 Henry Cohn, 2026, needs more optimization.
10 882 0.593096847716 Henry Cohn, 2026, needs more optimization.
10 883 0.593105835568 Henry Cohn, 2026, needs more optimization.
10 884 0.593143397865 Henry Cohn, 2026, needs more optimization.
10 885 0.593298733878 Henry Cohn, 2026, needs more optimization.
10 886 0.593536643598 Henry Cohn, 2026, needs more optimization.
10 887 0.593664767285 Henry Cohn, 2026, needs more optimization.
10 888 0.593736166885 Henry Cohn, 2026, needs more optimization.
10 889 0.593782311322 Henry Cohn, 2026, needs more optimization.
10 890 0.593784342925 Henry Cohn, 2026, needs more optimization.
10 891 0.593812855118 Henry Cohn, 2026, needs more optimization.
10 892 0.593873344424 Henry Cohn, 2026, needs more optimization.
10 893 0.593877521524 Henry Cohn, 2026, needs more optimization.
10 894 0.593900646130 Henry Cohn, 2026, needs more optimization.
10 895 0.593974373252 Henry Cohn, 2026, needs more optimization.
10 896 0.594004440178 Henry Cohn, 2026, needs more optimization.
10 897 0.594071687728 Henry Cohn, 2026, needs more optimization.
10 898 0.594071687774 Henry Cohn, 2026, needs more optimization.
10 903 0.594072194329 Henry Cohn, 2026, needs more optimization.
10 904 0.594074180469 Henry Cohn, 2026, needs more optimization.
10 905 0.594075544930 Henry Cohn, 2026, needs more optimization.
10 907 0.594076758710 Henry Cohn, 2026, needs more optimization.
10 908 0.594078325086 Henry Cohn, 2026, needs more optimization.
10 909 0.594096201289 Henry Cohn, 2026, needs more optimization.
10 910 0.594106354936 Henry Cohn, 2026, needs more optimization.
10 911 0.594167886455 Henry Cohn, 2026, needs more optimization.
10 912 0.594172593800 Henry Cohn, 2026, needs more optimization.
10 913 0.594183629062 Henry Cohn, 2026, needs more optimization.
10 914 0.594199659313 Henry Cohn, 2026, needs more optimization.
10 915 0.594258104953 Henry Cohn, 2026, needs more optimization.
10 916 0.594261333360 Henry Cohn, 2026, needs more optimization.
10 917 0.594275885829 Henry Cohn, 2026, needs more optimization.
10 919 0.594361757663 Henry Cohn, 2026, needs more optimization.
10 920 0.594384474852 Henry Cohn, 2026, needs more optimization.
10 921 0.594394435685 Henry Cohn, 2026, needs more optimization.
10 922 0.594410940659 Henry Cohn, 2026, needs more optimization.
10 923 0.594482823882 Henry Cohn, 2026, needs more optimization.
10 925 0.594546456035 Henry Cohn, 2026, needs more optimization.
10 927 0.594643074494 Henry Cohn, 2026, needs more optimization.
10 928 0.594671585750 Henry Cohn, 2026, needs more optimization.
10 929 0.594793259675 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 0.232764852407 Henry Cohn, 2024.
295⁢x2−30⁢x−9
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 0.253227719831 Henry Cohn, 2026, needs more optimization.
11 73 0.253338654684 Henry Cohn, 2026, needs more optimization.
11 74 0.254512603343 Henry Cohn, 2026, needs more optimization.
11 75 0.255729522058 Henry Cohn, 2026, needs more optimization.
11 76 0.255801424652 Henry Cohn, 2026, needs more optimization.
11 77 0.259892832741 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 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 0.263230805623 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 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 0.265027768340 Henry Cohn, 2026, needs more optimization.
11 85 0.266213158428 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 0.280562763187 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 93 0.281614170724 Henry Cohn, 2026, needs more optimization.
11 94 0.282805919347 Henry Cohn, 2026, needs more optimization.
11 95 0.283424585215 Henry Cohn, 2026, needs more optimization.
11 96 0.284712124032 Henry Cohn, 2026, needs more optimization.
11 97 0.285756941400 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 0.288711819016 Henry Cohn, 2026, needs more optimization.
11 100 0.299860274487 Henry Cohn, 2026, needs more optimization.
11 101 0.302859566827 Henry Cohn, 2026, needs more optimization.
11 102 0.304440333187 Henry Cohn, 2026, needs more optimization.
11 104 0.305242207297 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.
11 105 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 0.307220308762 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.
11 107 0.310786210597 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 0.321716622227 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 0.322397019959 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.
11 113 0.322495674810 Henry Cohn, 2026, needs more optimization.
11 114 0.322821812490 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.
11 115 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 0.330506263206 Henry Cohn, 2026, needs more optimization.
11 126 0.331465446794 Henry Cohn, 2026, needs more optimization.
11 127 0.332272120333 Henry Cohn, 2026, needs more optimization.
11 128 0.332276380864 Henry Cohn, 2026, needs more optimization.
11 129 0.332384034942 Henry Cohn, 2026, needs more optimization.
11 130 0.332408349524 Henry Cohn, 2026, needs more optimization.
11 131 0.332683425859 Henry Cohn, 2026, needs more optimization.
11 132 0.333242889281 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 0.360563699341 Henry Cohn, 2026, needs more optimization.
11 158 0.363818046932 Henry Cohn, 2026, needs more optimization.
11 159 0.368509314453 Henry Cohn, 2026, needs more optimization.
11 160 0.371731306253 Henry Cohn, 2026, needs more optimization.
11 161 0.373108489356 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 0.384622490872 Henry Cohn, 2026, needs more optimization.
11 168 0.385234042238 Henry Cohn, 2026, needs more optimization.
11 169 0.386585972528 Henry Cohn, 2026, needs more optimization.
11 170 0.389153494397 Henry Cohn, 2026, needs more optimization.
11 171 0.391487790976 Henry Cohn, 2026, needs more optimization.
11 172 0.391570969170 Henry Cohn, 2026, needs more optimization.
11 173 0.391589155283 Henry Cohn, 2026, needs more optimization.
11 174 0.391890564349 Henry Cohn, 2026, needs more optimization.
11 175 0.392596956590 Henry Cohn, 2026, needs more optimization.
11 176 0.393349025911 Henry Cohn, 2026, needs more optimization.
11 177 0.393905198575 Henry Cohn, 2026, needs more optimization.
11 178 0.394098656943 Henry Cohn, 2026, needs more optimization.
11 179 0.394883587561 Henry Cohn, 2026, needs more optimization.
11 180 0.395423150652 Henry Cohn, 2026, needs more optimization.
11 181 0.396164943845 Henry Cohn, 2026, needs more optimization.
11 182 0.396845342536 Henry Cohn, 2026, needs more optimization.
11 183 0.397265518901 Henry Cohn, 2026, needs more optimization.
11 184 0.397621707273 Henry Cohn, 2026, needs more optimization.
11 185 0.398484946859 Henry Cohn, 2026, needs more optimization.
11 186 0.399288615482 Henry Cohn, 2026, needs more optimization.
11 187 0.399800831642 Henry Cohn, 2026, needs more optimization.
11 188 0.400248784533 Henry Cohn, 2026, needs more optimization.
11 189 0.400791831010 Henry Cohn, 2026, needs more optimization.
11 190 0.401713205483 Henry Cohn, 2026, needs more optimization.
11 191 0.402667178860 Henry Cohn, 2026, needs more optimization.
11 192 0.403023615951 Henry Cohn, 2026, needs more optimization.
11 193 0.403497806477 Henry Cohn, 2026, needs more optimization.
11 194 0.403785808453 Henry Cohn, 2026, needs more optimization.
11 195 0.404516715739 Henry Cohn, 2026, needs more optimization.
11 196 0.406958111406 Henry Cohn, 2026, needs more optimization.
11 197 0.408055659893 Henry Cohn, 2026, needs more optimization.
11 198 0.409009683292 Henry Cohn, 2026, needs more optimization.
11 199 0.410354056248 Henry Cohn, 2026, needs more optimization.
11 200 0.410532358494 Henry Cohn, 2026, needs more optimization.
11 201 0.411042502860 Henry Cohn, 2026, needs more optimization.
11 202 0.411548296421 Henry Cohn, 2026, needs more optimization.
11 203 0.412155119286 Henry Cohn, 2026, needs more optimization.
11 204 0.412885570122 Henry Cohn, 2026, needs more optimization.
11 205 0.413253387631 Henry Cohn, 2026, needs more optimization.
11 206 0.413862091307 Henry Cohn, 2026, needs more optimization.
11 207 0.413868532449 Henry Cohn, 2026, needs more optimization.
11 208 0.414301119908 Henry Cohn, 2026, needs more optimization.
11 209 0.414793060434 Henry Cohn, 2026, needs more optimization.
11 210 0.415130240025 Henry Cohn, 2026, needs more optimization.
11 211 0.415408610376 Henry Cohn, 2026, needs more optimization.
11 212 0.416172001509 Henry Cohn, 2026, needs more optimization.
11 213 0.416530386359 Henry Cohn, 2026, needs more optimization.
11 214 0.417327484553 Henry Cohn, 2026, needs more optimization.
11 215 0.417860254107 Henry Cohn, 2026, needs more optimization.
11 216 0.418437270766 Henry Cohn, 2026, needs more optimization.
11 217 0.418727098232 Henry Cohn, 2026, needs more optimization.
11 218 0.419764082283 Henry Cohn, 2026, needs more optimization.
11 219 0.420129747717 Henry Cohn, 2026, needs more optimization.
11 220 0.420561603751 Henry Cohn, 2026, needs more optimization.
11 221 0.421071723131 Henry Cohn, 2026, needs more optimization.
11 222 0.421867114246 Henry Cohn, 2026, needs more optimization.
11 223 0.422296666507 Henry Cohn, 2026, needs more optimization.
11 224 0.422904305788 Henry Cohn, 2026, needs more optimization.
11 225 0.423233494968 Henry Cohn, 2026, needs more optimization.
11 226 0.423612201924 Henry Cohn, 2026, needs more optimization.
11 227 0.423768826876 Henry Cohn, 2026, needs more optimization.
11 228 0.424182257026 Henry Cohn, 2026, needs more optimization.
11 229 0.424446762062 Henry Cohn, 2026, needs more optimization.
11 230 0.425093293056 Henry Cohn, 2026, needs more optimization.
11 231 0.425415012720 Henry Cohn, 2026, needs more optimization.
11 232 0.425743164729 Henry Cohn, 2026, needs more optimization.
11 233 0.425937966062 Henry Cohn, 2026, needs more optimization.
11 234 0.426271581387 Henry Cohn, 2026, needs more optimization.
11 235 0.426732360481 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 0.427622573805 Henry Cohn, 2026, needs more optimization.
11 239 0.427804341692 Henry Cohn, 2026, needs more optimization.
11 240 0.427995147379 Henry Cohn, 2026, needs more optimization.
11 241 0.428363440321 Henry Cohn, 2026, needs more optimization.
11 242 0.428508464469 Henry Cohn, 2026, needs more optimization.
11 243 0.429038939106 Henry Cohn, 2026, needs more optimization.
11 244 0.429658115918 Henry Cohn, 2026, needs more optimization.
11 245 0.430431411282 Henry Cohn, 2026, needs more optimization.
11 246 0.430675783815 Henry Cohn, 2026, needs more optimization.
11 247 0.430837043993 Henry Cohn, 2026, needs more optimization.
11 248 0.431482180625 Henry Cohn, 2026, needs more optimization.
11 249 0.432401171396 Henry Cohn, 2026, needs more optimization.
11 250 0.433209536925 Henry Cohn, 2026, needs more optimization.
11 251 0.433550663658 Henry Cohn, 2026, needs more optimization.
11 252 0.433994313454 Henry Cohn, 2026, needs more optimization.
11 253 0.435473263389 Henry Cohn, 2026, needs more optimization.
11 254 0.435935134191 Henry Cohn, 2026, needs more optimization.
11 255 0.436507992312 Henry Cohn, 2026, needs more optimization.
11 256 0.437928868146 Henry Cohn, 2026, needs more optimization.
11 257 0.438164894983 Henry Cohn, 2026, needs more optimization.
11 258 0.438191398234 Henry Cohn, 2026, needs more optimization.
11 259 0.438225135375 Henry Cohn, 2026, needs more optimization.
11 260 0.438225233105 Henry Cohn, 2026, needs more optimization.
11 261 0.438231500382 Henry Cohn, 2026, needs more optimization.
11 262 0.438280508709 Henry Cohn, 2026, needs more optimization.
11 263 0.438289247370 Henry Cohn, 2026, needs more optimization.
11 264 0.438289292525 Henry Cohn, 2026, needs more optimization.
11 265 0.438371646039 Henry Cohn, 2026, needs more optimization.
11 266 0.438429796854 Henry Cohn, 2026, needs more optimization.
11 267 0.438487444787 Henry Cohn, 2026, needs more optimization.
11 268 0.438506652378 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.
11 269 0.438623203694 Henry Cohn, 2026, needs more optimization.
11 270 0.439123307460 Henry Cohn, 2026, needs more optimization.
11 271 0.439360394875 Henry Cohn, 2026, needs more optimization.
11 272 0.439856802546 Henry Cohn, 2026, needs more optimization.
11 273 0.440070907347 Henry Cohn, 2026, needs more optimization.
11 274 0.440163130963 Henry Cohn, 2026, needs more optimization.
11 275 0.440520936547 Henry Cohn, 2026, needs more optimization.
11 276 0.440749032163 Henry Cohn, 2026, needs more optimization.
11 277 0.441105966892 Henry Cohn, 2026, needs more optimization.
11 278 0.441356083028 Henry Cohn, 2026, needs more optimization.
11 279 0.441568331293 Henry Cohn, 2026, needs more optimization.
11 280 0.441930474511 Henry Cohn, 2026, needs more optimization.
11 281 0.442407551175 Henry Cohn, 2026, needs more optimization.
11 282 0.442680141262 Henry Cohn, 2026, needs more optimization.
11 283 0.442753152319 Henry Cohn, 2026, needs more optimization.
11 284 0.443024923520 Henry Cohn, 2026, needs more optimization.
11 285 0.443573525121 Henry Cohn, 2026, needs more optimization.
11 286 0.444109061833 Henry Cohn, 2026, needs more optimization.
11 287 0.444195197277 Henry Cohn, 2026, needs more optimization.
11 288 0.444766563968 Henry Cohn, 2026, needs more optimization.
11 289 0.445146520054 Henry Cohn, 2026, needs more optimization.
11 290 0.445398313080 Henry Cohn, 2026, needs more optimization.
11 291 0.445954351976 Henry Cohn, 2026, needs more optimization.
11 292 0.445969206393 Henry Cohn, 2026, needs more optimization.
11 293 0.446839406971 Henry Cohn, 2026, needs more optimization.
11 294 0.447698316754 Henry Cohn, 2026, needs more optimization.
11 295 0.449281584761 Henry Cohn, 2026, needs more optimization.
11 296 0.450186169017 Henry Cohn, 2026, needs more optimization.
11 297 0.451022543822 Henry Cohn, 2026, needs more optimization.
11 298 0.453332449358 Henry Cohn, 2026, needs more optimization.
11 299 0.454253058965 Henry Cohn, 2026, needs more optimization.
11 300 0.455147997221 Henry Cohn, 2026, needs more optimization.
11 301 0.455684282415 Henry Cohn, 2026, needs more optimization.
11 302 0.456179733454 Henry Cohn, 2026, needs more optimization.
11 303 0.457623018096 Henry Cohn, 2026, needs more optimization.
11 304 0.458913936154 Henry Cohn, 2026, needs more optimization.
11 305 0.459751174217 Henry Cohn, 2026, needs more optimization.
11 306 0.460533113491 Henry Cohn, 2026, needs more optimization.
11 307 0.461226019833 Henry Cohn, 2026, needs more optimization.
11 308 0.462086918793 Henry Cohn, 2026, needs more optimization.
11 309 0.462668037908 Henry Cohn, 2026, needs more optimization.
11 310 0.463364790449 Henry Cohn, 2026, needs more optimization.
11 311 0.463576042772 Henry Cohn, 2026, needs more optimization.
11 312 0.464074697332 Henry Cohn, 2026, needs more optimization.
11 313 0.464242803981 Henry Cohn, 2026, needs more optimization.
11 314 0.464725623414 Henry Cohn, 2026, needs more optimization.
11 315 0.464914813048 Henry Cohn, 2026, needs more optimization.
11 316 0.465137447506 Henry Cohn, 2026, needs more optimization.
11 317 0.465601362410 Henry Cohn, 2026, needs more optimization.
11 318 0.465940255100 Henry Cohn, 2026, needs more optimization.
11 319 0.466200017843 Henry Cohn, 2026, needs more optimization.
11 320 0.466353447013 Henry Cohn, 2026, needs more optimization.
11 321 0.466879411434 Henry Cohn, 2026, needs more optimization.
11 322 0.466995491928 Henry Cohn, 2026, needs more optimization.
11 323 0.467741964155 Henry Cohn, 2026, needs more optimization.
11 324 0.468128298217 Henry Cohn, 2026, needs more optimization.
11 325 0.468674985459 Henry Cohn, 2026, needs more optimization.
11 326 0.468906870042 Henry Cohn, 2026, needs more optimization.
11 327 0.469211800343 Henry Cohn, 2026, needs more optimization.
11 328 0.469740353778 Henry Cohn, 2026, needs more optimization.
11 329 0.470023400593 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 0.474462046557 Henry Cohn, 2026, needs more optimization.
11 346 0.474891615211 Henry Cohn, 2026, needs more optimization.
11 347 0.475249844861 Henry Cohn, 2026, needs more optimization.
11 348 0.475929647934 Henry Cohn, 2026, needs more optimization.
11 349 0.476440198574 Henry Cohn, 2026, needs more optimization.
11 350 0.476740483666 Henry Cohn, 2026, needs more optimization.
11 351 0.477072081160 Henry Cohn, 2026, needs more optimization.
11 352 0.477384778314 Henry Cohn, 2026, needs more optimization.
11 353 0.477684408429 Henry Cohn, 2026, needs more optimization.
11 354 0.478293617237 Henry Cohn, 2026, needs more optimization.
11 355 0.478650407925 Henry Cohn, 2026, needs more optimization.
11 356 0.478967874972 Henry Cohn, 2026, needs more optimization.
11 357 0.479094693317 Henry Cohn, 2026, needs more optimization.
11 358 0.479224399617 Henry Cohn, 2026, needs more optimization.
11 359 0.479321032828 Henry Cohn, 2026, needs more optimization.
11 360 0.479401587538 Henry Cohn, 2026, needs more optimization.
11 361 0.479516025576 Henry Cohn, 2026, needs more optimization.
11 362 0.479516036499 Henry Cohn, 2026, needs more optimization.
11 363 0.479736965925 Henry Cohn, 2026, needs more optimization.
11 364 0.479784060147 Henry Cohn, 2026, needs more optimization.
11 365 0.479910760991 Henry Cohn, 2026, needs more optimization.
11 366 0.480018741054 Henry Cohn, 2026, needs more optimization.
11 367 0.480030508465 Henry Cohn, 2026, needs more optimization.
11 368 0.480119708329 Henry Cohn, 2026, needs more optimization.
11 369 0.480187664052 Henry Cohn, 2026, needs more optimization.
11 370 0.480229093551 Henry Cohn, 2026, needs more optimization.
11 371 0.480370513727 Henry Cohn, 2026, needs more optimization.
11 372 0.480455384389 Henry Cohn, 2026, needs more optimization.
11 373 0.480471299131 Henry Cohn, 2026, needs more optimization.
11 374 0.480692531085 Henry Cohn, 2026, needs more optimization.
11 375 0.481007518675 Henry Cohn, 2026, needs more optimization.
11 376 0.481619243394 Henry Cohn, 2026, needs more optimization.
11 377 0.481694713243 Henry Cohn, 2026, needs more optimization.
11 378 0.481801556999 Henry Cohn, 2026, needs more optimization.
11 379 0.482282440125 Henry Cohn, 2026, needs more optimization.
11 380 0.482811509490 Henry Cohn, 2026, needs more optimization.
11 381 0.482949276597 Henry Cohn, 2026, needs more optimization.
11 382 0.483195712522 Henry Cohn, 2026, needs more optimization.
11 383 0.483515612369 Henry Cohn, 2026, needs more optimization.
11 384 0.483882242741 Henry Cohn, 2026, needs more optimization.
11 385 0.483980429649 Henry Cohn, 2026, needs more optimization.
11 386 0.484133722870 Henry Cohn, 2026, needs more optimization.
11 387 0.484246424998 Henry Cohn, 2026, needs more optimization.
11 388 0.484868006493 Henry Cohn, 2026, needs more optimization.
11 389 0.485105788567 Henry Cohn, 2026, needs more optimization.
11 390 0.485127281116 Henry Cohn, 2026, needs more optimization.
11 391 0.485162991518 Henry Cohn, 2026, needs more optimization.
11 392 0.485164988386 Henry Cohn, 2026, needs more optimization.
11 393 0.485174277784 Henry Cohn, 2026, needs more optimization.
11 394 0.485204585978 Henry Cohn, 2026, needs more optimization.
11 395 0.485236343496 Henry Cohn, 2026, needs more optimization.
11 396 0.485257784747 Henry Cohn, 2026, needs more optimization.
11 397 0.485686743462 Henry Cohn, 2026, needs more optimization.
11 398 0.485690421832 Henry Cohn, 2026, needs more optimization.
11 399 0.485738610783 Henry Cohn, 2026, needs more optimization.
11 400 0.486016917778 Henry Cohn, 2026, needs more optimization.
11 402 0.486177654226 Henry Cohn, 2026, needs more optimization.
11 403 0.486177675592 Henry Cohn, 2026, needs more optimization.
11 404 0.486177698338 Henry Cohn, 2026, needs more optimization.
11 406 0.486246131472 Henry Cohn, 2026, needs more optimization.
11 407 0.486252771527 Henry Cohn, 2026, needs more optimization.
11 408 0.486462185324 Henry Cohn, 2026, needs more optimization.
11 409 0.486586164517 Henry Cohn, 2026, needs more optimization.
11 410 0.486724662702 Henry Cohn, 2026, needs more optimization.
11 411 0.487360749795 Henry Cohn, 2026, needs more optimization.
11 412 0.488086407248 Henry Cohn, 2026, needs more optimization.
11 413 0.488462985491 Henry Cohn, 2026, needs more optimization.
11 414 0.488913380687 Henry Cohn, 2026, needs more optimization.
11 415 0.488944270311 Henry Cohn, 2026, needs more optimization.
11 416 0.489075003587 Henry Cohn, 2026, needs more optimization.
11 417 0.489155439073 Henry Cohn, 2026, needs more optimization.
11 418 0.489312156692 Henry Cohn, 2026, needs more optimization.
11 419 0.489369392973 Henry Cohn, 2026, needs more optimization.
11 420 0.489559938355 Henry Cohn, 2026, needs more optimization.
11 421 0.489639835714 Henry Cohn, 2026, needs more optimization.
11 422 0.489832763516 Henry Cohn, 2026, needs more optimization.
11 423 0.489884554631 Henry Cohn, 2026, needs more optimization.
11 424 0.490016207704 Henry Cohn, 2026, needs more optimization.
11 425 0.490494110540 Henry Cohn, 2026, needs more optimization.
11 426 0.490699958218 Henry Cohn, 2026, needs more optimization.
11 427 0.490926820685 Henry Cohn, 2026, needs more optimization.
11 428 0.491095227209 Henry Cohn, 2026, needs more optimization.
11 429 0.491321709385 Henry Cohn, 2026, needs more optimization.
11 430 0.491604688895 Henry Cohn, 2026, needs more optimization.
11 431 0.491831753998 Henry Cohn, 2026, needs more optimization.
11 432 0.491950184866 Henry Cohn, 2026, needs more optimization.
11 433 0.492117438315 Henry Cohn, 2026, needs more optimization.
11 434 0.492298092366 Henry Cohn, 2026, needs more optimization.
11 435 0.492585153557 Henry Cohn, 2026, needs more optimization.
11 436 0.492660650312 Henry Cohn, 2026, needs more optimization.
11 437 0.492793330968 Henry Cohn, 2026, needs more optimization.
11 438 0.492819265434 Henry Cohn, 2026, needs more optimization.
11 439 0.492852630721 Henry Cohn, 2026, needs more optimization.
11 440 0.493016605491 Henry Cohn, 2026, needs more optimization.
11 441 0.493029198661 Henry Cohn, 2026, needs more optimization.
11 442 0.493056284471 Henry Cohn, 2026, needs more optimization.
11 443 0.493061328994 Henry Cohn, 2026, needs more optimization.
11 444 0.493244041179 Henry Cohn, 2026, needs more optimization.
11 445 0.493310039897 Henry Cohn, 2026, needs more optimization.
11 446 0.493364642381 Henry Cohn, 2026, needs more optimization.
11 447 0.493369832999 Henry Cohn, 2026, needs more optimization.
11 448 0.493394337339 Henry Cohn, 2026, needs more optimization.
11 449 0.495082658698 Henry Cohn, 2026, needs more optimization.
11 450 0.495240179443 Henry Cohn, 2026, needs more optimization.
11 451 0.495431909155 Henry Cohn, 2026, needs more optimization.
11 452 0.495551558448 Henry Cohn, 2026, needs more optimization.
11 453 0.495627230781 Henry Cohn, 2026, needs more optimization.
11 454 0.495846362804 Henry Cohn, 2026, needs more optimization.
11 455 0.495942693263 Henry Cohn, 2026, needs more optimization.
11 456 0.495946383535 Henry Cohn, 2026, needs more optimization.
11 457 0.496015911014 Henry Cohn, 2026, needs more optimization.
11 458 0.496167808961 Henry Cohn, 2026, needs more optimization.
11 459 0.496373153188 Henry Cohn, 2026, needs more optimization.
11 460 0.496662695949 Henry Cohn, 2026, needs more optimization.
11 461 0.496852802842 Henry Cohn, 2026, needs more optimization.
11 462 0.496909691881 Henry Cohn, 2026, needs more optimization.
11 463 0.496985431713 Henry Cohn, 2026, needs more optimization.
11 464 0.497274254111 Henry Cohn, 2026, needs more optimization.
11 465 0.497364482628 Henry Cohn, 2026, needs more optimization.
11 466 0.497368251827 Henry Cohn, 2026, needs more optimization.
11 467 0.497494683489 Henry Cohn, 2026, needs more optimization.
11 468 0.497586554857 Henry Cohn, 2026, needs more optimization.
11 469 0.497740351783 Henry Cohn, 2026, needs more optimization.
11 470 0.497806185268 Henry Cohn, 2026, needs more optimization.
11 471 0.497936467983 Henry Cohn, 2026, needs more optimization.
11 472 0.498023637525 Henry Cohn, 2026, needs more optimization.
11 473 0.498448397158 Henry Cohn, 2026, needs more optimization.
11 474 0.498461886542 Henry Cohn, 2026, needs more optimization.
11 475 0.498762686385 Henry Cohn, 2026, needs more optimization.
11 476 0.498829141037 Henry Cohn, 2026, needs more optimization.
11 477 0.498917096568 Henry Cohn, 2026, needs more optimization.
11 479 0.499631594757 Henry Cohn, 2026, needs more optimization.
11 482 0.499631596302 Henry Cohn, 2026, needs more optimization.
11 484 0.499632155477 Henry Cohn, 2026, needs more optimization.
11 486 0.499636048100 Henry Cohn, 2026, needs more optimization.
11 487 0.499636048693 Henry Cohn, 2026, needs more optimization.
11 489 0.499637204404 Henry Cohn, 2026, needs more optimization.
11 490 0.499637221557 Henry Cohn, 2026, needs more optimization.
11 492 0.499637259182 Henry Cohn, 2026, needs more optimization.
11 493 0.499637582240 Henry Cohn, 2026, needs more optimization.
11 494 0.499637582325 Henry Cohn, 2026, needs more optimization.
11 495 0.499639434323 Henry Cohn, 2026, needs more optimization.
11 496 0.499639576114 Henry Cohn, 2026, needs more optimization.
11 497 0.499639758875 Henry Cohn, 2026, needs more optimization.
11 498 0.499640759842 Henry Cohn, 2026, needs more optimization.
11 500 0.499644117903 Henry Cohn, 2026, needs more optimization.
11 501 0.499644751214 Henry Cohn, 2026, needs more optimization.
11 503 0.499644754038 Henry Cohn, 2026, needs more optimization.
11 505 0.499646036003 Henry Cohn, 2026, needs more optimization.
11 506 0.499646699952 Henry Cohn, 2026, needs more optimization.
11 507 0.499646703168 Henry Cohn, 2026, needs more optimization.
11 510 0.499646719150 Henry Cohn, 2026, needs more optimization.
11 511 0.499646719312 Henry Cohn, 2026, needs more optimization.
11 512 0.499647853996 Henry Cohn, 2026, needs more optimization.
11 514 0.499648646107 Henry Cohn, 2026, needs more optimization.
11 515 0.499649649958 Henry Cohn, 2026, needs more optimization.
11 516 0.499649722240 Henry Cohn, 2026, needs more optimization.
11 517 0.499650817560 Henry Cohn, 2026, needs more optimization.
11 518 0.499650818527 Henry Cohn, 2026, needs more optimization.
11 522 0.499652120096 Henry Cohn, 2026, needs more optimization.
11 523 0.499652986482 Henry Cohn, 2026, needs more optimization.
11 524 0.499652990802 Henry Cohn, 2026, needs more optimization.
11 525 0.499653233140 Henry Cohn, 2026, needs more optimization.
11 526 0.499653245296 Henry Cohn, 2026, needs more optimization.
11 527 0.499653247070 Henry Cohn, 2026, needs more optimization.
11 529 0.499654062179 Henry Cohn, 2026, needs more optimization.
11 530 0.499654930851 Henry Cohn, 2026, needs more optimization.
11 531 0.499654939608 Henry Cohn, 2026, needs more optimization.
11 532 0.499654940547 Henry Cohn, 2026, needs more optimization.
11 535 0.499655844348 Henry Cohn, 2026, needs more optimization.
11 536 0.499655945615 Henry Cohn, 2026, needs more optimization.
11 537 0.499659221464 Henry Cohn, 2026, needs more optimization.
11 539 0.499659229274 Henry Cohn, 2026, needs more optimization.
11 540 0.499659245120 Henry Cohn, 2026, needs more optimization.
11 541 0.499659248195 Henry Cohn, 2026, needs more optimization.
11 542 0.499659273264 Henry Cohn, 2026, needs more optimization.
11 543 0.499659357047 Henry Cohn, 2026, needs more optimization.
11 545 0.499661175314 Henry Cohn, 2026, needs more optimization.
11 547 0.499661201772 Henry Cohn, 2026, needs more optimization.
11 549 0.499661206206 Henry Cohn, 2026, needs more optimization.
11 550 0.499661213378 Henry Cohn, 2026, needs more optimization.
11 552 0.499661222076 Henry Cohn, 2026, needs more optimization.
11 553 0.499661222849 Henry Cohn, 2026, needs more optimization.
11 554 0.499661291929 Henry Cohn, 2026, needs more optimization.
11 555 0.499661512774 Henry Cohn, 2026, needs more optimization.
11 556 0.499661720605 Henry Cohn, 2026, needs more optimization.
11 557 0.499661770933 Henry Cohn, 2026, needs more optimization.
11 558 0.499661904039 Henry Cohn, 2026, needs more optimization.
11 559 0.499662009201 Henry Cohn, 2026, needs more optimization.
11 560 0.499663085540 Henry Cohn, 2026, needs more optimization.
11 564 0.499663102206 Henry Cohn, 2026, needs more optimization.
11 569 0.499663356840 Henry Cohn, 2026, needs more optimization.
11 570 0.499663813526 Henry Cohn, 2026, needs more optimization.
11 571 0.499663818376 Henry Cohn, 2026, needs more optimization.
11 572 0.499663836489 Henry Cohn, 2026, needs more optimization.
11 573 0.499663848095 Henry Cohn, 2026, needs more optimization.
11 574 0.499663853184 Henry Cohn, 2026, needs more optimization.
11 575 0.499663881080 Henry Cohn, 2026, needs more optimization.
11 576 0.499663898591 Henry Cohn, 2026, needs more optimization.
11 578 0.499664011976 Henry Cohn, 2026, needs more optimization.
11 580 0.499664025309 Henry Cohn, 2026, needs more optimization.
11 581 0.499664041999 Henry Cohn, 2026, needs more optimization.
11 582 0.499664042000 Henry Cohn, 2026, needs more optimization.
11 584 0.499664042001 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 0.499666753517 Henry Cohn, 2026, needs more optimization.
11 590 0.499666964843 Henry Cohn, 2026, needs more optimization.
11 591 0.499667317518 Henry Cohn, 2026, needs more optimization.
11 592 0.499674259235 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 0.507422680323 Henry Cohn, 2026, needs more optimization.
11 606 0.511353633675 Henry Cohn, 2026, needs more optimization.
11 607 0.511441608225 Henry Cohn, 2026, needs more optimization.
11 608 0.511774315669 Henry Cohn, 2026, needs more optimization.
11 609 0.512069805900 Henry Cohn, 2026, needs more optimization.
11 610 0.512129521260 Henry Cohn, 2026, needs more optimization.
11 611 0.512226509078 Henry Cohn, 2026, needs more optimization.
11 612 0.512258664283 Henry Cohn, 2026, needs more optimization.
11 613 0.512276155893 Henry Cohn, 2026, needs more optimization.
11 614 0.512277289282 Henry Cohn, 2026, needs more optimization.
11 615 0.512610575107 Henry Cohn, 2026, needs more optimization.
11 616 0.512849041133 Henry Cohn, 2026, needs more optimization.
11 617 0.513097008597 Henry Cohn, 2026, needs more optimization.
11 618 0.513418946196 Henry Cohn, 2026, needs more optimization.
11 619 0.513964381423 Henry Cohn, 2026, needs more optimization.
11 620 0.514048396748 Henry Cohn, 2026, needs more optimization.
11 621 0.514690401800 Henry Cohn, 2026, needs more optimization.
11 622 0.515112121049 Henry Cohn, 2026, needs more optimization.
11 623 0.515495872916 Henry Cohn, 2026, needs more optimization.
11 624 0.515659048818 Henry Cohn, 2026, needs more optimization.
11 625 0.516092794270 Henry Cohn, 2026, needs more optimization.
11 626 0.516389442923 Henry Cohn, 2026, needs more optimization.
11 627 0.516471286234 Henry Cohn, 2026, needs more optimization.
11 628 0.516936421711 Henry Cohn, 2026, needs more optimization.
11 629 0.517548599912 Henry Cohn, 2026, needs more optimization.
11 630 0.518205454408 Henry Cohn, 2026, needs more optimization.
11 631 0.518851194446 Henry Cohn, 2026, needs more optimization.
11 632 0.519513340650 Henry Cohn, 2026, needs more optimization.
11 633 0.520293226379 Henry Cohn, 2026, needs more optimization.
11 634 0.520687238620 Henry Cohn, 2026, needs more optimization.
11 636 0.521934008234 Henry Cohn, 2026, needs more optimization.
11 637 0.523149077122 Henry Cohn, 2026, needs more optimization.
11 638 0.525054398746 Henry Cohn, 2026, needs more optimization.
11 639 0.525664132830 Henry Cohn, 2026, needs more optimization.
11 640 0.527361293268 Henry Cohn, 2026, needs more optimization.
11 641 0.528424590890 Henry Cohn, 2026, needs more optimization.
11 642 0.528428044406 Henry Cohn, 2026, needs more optimization.
11 643 0.528455398681 Henry Cohn, 2026, needs more optimization.
11 644 0.528466076098 Henry Cohn, 2026, needs more optimization.
11 645 0.528493657054 Henry Cohn, 2026, needs more optimization.
11 646 0.528504798284 Henry Cohn, 2026, needs more optimization.
11 647 0.528505897919 Henry Cohn, 2026, needs more optimization.
11 648 0.528528104523 Henry Cohn, 2026, needs more optimization.
11 649 0.528530451741 Henry Cohn, 2026, needs more optimization.
11 650 0.528548478537 Henry Cohn, 2026, needs more optimization.
11 651 0.528556001326 Henry Cohn, 2026, needs more optimization.
11 652 0.528606185789 Henry Cohn, 2026, needs more optimization.
11 653 0.528628368538 Henry Cohn, 2026, needs more optimization.
11 654 0.528990626563 Henry Cohn, 2026, needs more optimization.
11 655 0.529274391871 Henry Cohn, 2026, needs more optimization.
11 656 0.529805231894 Henry Cohn, 2026, needs more optimization.
11 657 0.530475858263 Henry Cohn, 2026, needs more optimization.
11 658 0.531055853769 Henry Cohn, 2026, needs more optimization.
11 659 0.531497820308 Henry Cohn, 2026, needs more optimization.
11 660 0.532000122202 Henry Cohn, 2026, needs more optimization.
11 661 0.533064754658 Henry Cohn, 2026, needs more optimization.
11 662 0.533581560932 Henry Cohn, 2026, needs more optimization.
11 663 0.533948988278 Henry Cohn, 2026, needs more optimization.
11 664 0.534282756329 Henry Cohn, 2026, needs more optimization.
11 665 0.534818171041 Henry Cohn, 2026, needs more optimization.
11 666 0.535094904295 Henry Cohn, 2026, needs more optimization.
11 667 0.535575453205 Henry Cohn, 2026, needs more optimization.
11 668 0.535893892725 Henry Cohn, 2026, needs more optimization.
11 669 0.536148819450 Henry Cohn, 2026, needs more optimization.
11 670 0.536294031040 Henry Cohn, 2026, needs more optimization.
11 671 0.536561687113 Henry Cohn, 2026, needs more optimization.
11 672 0.536620314853 Henry Cohn, 2026, needs more optimization.
11 673 0.536620318376 Henry Cohn, 2026, needs more optimization.
11 674 0.536641319779 Henry Cohn, 2026, needs more optimization.
11 675 0.536824675897 Henry Cohn, 2026, needs more optimization.
11 676 0.537184974062 Henry Cohn, 2026, needs more optimization.
11 677 0.537547101067 Henry Cohn, 2026, needs more optimization.
11 678 0.537637911734 Henry Cohn, 2026, needs more optimization.
11 679 0.538297865734 Henry Cohn, 2026, needs more optimization.
11 680 0.538632001041 Henry Cohn, 2026, needs more optimization.
11 681 0.538869810795 Henry Cohn, 2026, needs more optimization.
11 682 0.539227006281 Henry Cohn, 2026, needs more optimization.
11 683 0.539561346779 Henry Cohn, 2026, needs more optimization.
11 684 0.539725093239 Henry Cohn, 2026, needs more optimization.
11 685 0.540129574883 Henry Cohn, 2026, needs more optimization.
11 686 0.540476157027 Henry Cohn, 2026, needs more optimization.
11 687 0.540817822673 Henry Cohn, 2026, needs more optimization.
11 688 0.541275095269 Henry Cohn, 2026, needs more optimization.
11 689 0.541731645445 Henry Cohn, 2026, needs more optimization.
11 690 0.541766319253 Henry Cohn, 2026, needs more optimization.
11 691 0.541797291869 Henry Cohn, 2026, needs more optimization.
11 692 0.541802268018 Henry Cohn, 2026, needs more optimization.
11 693 0.543059190798 Henry Cohn, 2026, needs more optimization.
11 694 0.543186366976 Henry Cohn, 2026, needs more optimization.
11 695 0.543571960259 Henry Cohn, 2026, needs more optimization.
11 696 0.543979739055 Henry Cohn, 2026, needs more optimization.
11 697 0.544290251083 Henry Cohn, 2026, needs more optimization.
11 698 0.544572831401 Henry Cohn, 2026, needs more optimization.
11 699 0.544785744853 Henry Cohn, 2026, needs more optimization.
11 700 0.545144432045 Henry Cohn, 2026, needs more optimization.
11 701 0.545379426925 Henry Cohn, 2026, needs more optimization.
11 702 0.545683388097 Henry Cohn, 2026, needs more optimization.
11 703 0.545944007549 Henry Cohn, 2026, needs more optimization.
11 704 0.546192407959 Henry Cohn, 2026, needs more optimization.
11 705 0.546496987654 Henry Cohn, 2026, needs more optimization.
11 706 0.546648274628 Henry Cohn, 2026, needs more optimization.
11 707 0.546897528128 Henry Cohn, 2026, needs more optimization.
11 708 0.547107514780 Henry Cohn, 2026, needs more optimization.
11 709 0.547362317924 Henry Cohn, 2026, needs more optimization.
11 710 0.547641865708 Henry Cohn, 2026, needs more optimization.
11 711 0.547942747812 Henry Cohn, 2026, needs more optimization.
11 712 0.548108520102 Henry Cohn, 2026, needs more optimization.
11 713 0.548398729538 Henry Cohn, 2026, needs more optimization.
11 714 0.548398731579 Henry Cohn, 2026, needs more optimization.
11 715 0.548588833853 Henry Cohn, 2026, needs more optimization.
11 716 0.549038091996 Henry Cohn, 2026, needs more optimization.
11 717 0.549088056291 Henry Cohn, 2026, needs more optimization.
11 718 0.549427589972 Henry Cohn, 2026, needs more optimization.
11 719 0.549966630673 Henry Cohn, 2026, needs more optimization.
11 720 0.550004072147 Henry Cohn, 2026, needs more optimization.
11 721 0.550439923603 Henry Cohn, 2026, needs more optimization.
11 722 0.550439927754 Henry Cohn, 2026, needs more optimization.
11 723 0.550598132886 Henry Cohn, 2026, needs more optimization.
11 724 0.550762175668 Henry Cohn, 2026, needs more optimization.
11 725 0.550818256699 Henry Cohn, 2026, needs more optimization.
11 726 0.551363219532 Henry Cohn, 2026, needs more optimization.
11 729 0.551440521846 Henry Cohn, 2026, needs more optimization.
11 730 0.551460497419 Henry Cohn, 2026, needs more optimization.
11 731 0.551610978499 Henry Cohn, 2026, needs more optimization.
11 732 0.551659067695 Henry Cohn, 2026, needs more optimization.
11 733 0.551672840822 Henry Cohn, 2026, needs more optimization.
11 734 0.551746650747 Henry Cohn, 2026, needs more optimization.
11 735 0.551851413215 Henry Cohn, 2026, needs more optimization.
11 736 0.551885241258 Henry Cohn, 2026, needs more optimization.
11 737 0.551933152853 Henry Cohn, 2026, needs more optimization.
11 738 0.551962307441 Henry Cohn, 2026, needs more optimization.
11 739 0.551983989234 Henry Cohn, 2026, needs more optimization.
11 740 0.552001197273 Henry Cohn, 2026, needs more optimization.
11 741 0.554283892636 Henry Cohn, 2026, needs more optimization.
11 742 0.554469549409 Henry Cohn, 2026, needs more optimization.
11 743 0.555090839514 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 0.560839400540 Henry Cohn, 2026, needs more optimization.
11 984 0.562686342311 Henry Cohn, 2026, needs more optimization.
11 985 0.563557873342 Henry Cohn, 2026, needs more optimization.
11 986 0.564056074734 Henry Cohn, 2026, needs more optimization.
11 987 0.564340209017 Henry Cohn, 2026, needs more optimization.
11 988 0.564556926840 Henry Cohn, 2026, needs more optimization.
11 989 0.564692931668 Henry Cohn, 2026, needs more optimization.
11 990 0.564796051331 Henry Cohn, 2026, needs more optimization.
11 991 0.564866785799 Henry Cohn, 2026, needs more optimization.
11 992 0.564920710756 Henry Cohn, 2026, needs more optimization.
11 993 0.566248023325 Henry Cohn, 2026, needs more optimization.
11 994 0.566803546857 Henry Cohn, 2026, needs more optimization.
11 995 0.567175316221 Henry Cohn, 2026, needs more optimization.
11 996 0.567454707068 Henry Cohn, 2026, needs more optimization.
11 997 0.568094700311 Henry Cohn, 2026, needs more optimization.
11 998 0.568470014491 Henry Cohn, 2026, needs more optimization.
11 999 0.568872196549 Henry Cohn, 2026, needs more optimization.
11 1000 0.569150069576 Henry Cohn, 2026, needs more optimization.
11 1001 0.569388273331 Henry Cohn, 2026, needs more optimization.
11 1002 0.569646651841 Henry Cohn, 2026, needs more optimization.
11 1003 0.569907511692 Henry Cohn, 2026, needs more optimization.
11 1004 0.570121084624 Henry Cohn, 2026, needs more optimization.
11 1005 0.570296080258 Henry Cohn, 2026, needs more optimization.
11 1006 0.570506882371 Henry Cohn, 2026, needs more optimization.
11 1007 0.570653790251 Henry Cohn, 2026, needs more optimization.
11 1008 0.570797150900 Henry Cohn, 2026, needs more optimization.
11 1009 0.570933553906 Henry Cohn, 2026, needs more optimization.
11 1010 0.571070309758 Henry Cohn, 2026, needs more optimization.
11 1011 0.571322924696 Henry Cohn, 2026, needs more optimization.
11 1012 0.571451807933 Henry Cohn, 2026, needs more optimization.
11 1013 0.571633422265 Henry Cohn, 2026, needs more optimization.
11 1014 0.571828410737 Henry Cohn, 2026, needs more optimization.
11 1015 0.571947779159 Henry Cohn, 2026, needs more optimization.
11 1016 0.572079322577 Henry Cohn, 2026, needs more optimization.
11 1017 0.572197897460 Henry Cohn, 2026, needs more optimization.
11 1018 0.572364254400 Henry Cohn, 2026, needs more optimization.
11 1019 0.572506570769 Henry Cohn, 2026, needs more optimization.
11 1020 0.572606200132 Henry Cohn, 2026, needs more optimization.
11 1021 0.572681551875 Henry Cohn, 2026, needs more optimization.
11 1022 0.572803253899 Henry Cohn, 2026, needs more optimization.
11 1023 0.572918745320 Henry Cohn, 2026, needs more optimization.
11 1024 0.573050360964 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 0.215062486432 Henry Cohn, 2026.
12 67 0.215314925312 Henry Cohn, 2026.
12 68 0.220678061412 Henry Cohn, 2026.
12 69 0.225477905474 Henry Cohn, 2026.
12 70 0.228644479119 Henry Cohn, 2026, needs more optimization.
12 71 0.230598825166 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 72 0.231870365502 Henry Cohn, 2026.
12 73 0.232384966235 Henry Cohn, 2026, needs more optimization.
12 74 0.233328388920 Henry Cohn, 2026, needs more optimization.
12 75 0.236110825161 Henry Cohn, 2026, needs more optimization.
12 76 0.236987305886 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 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 0.264705823533 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 0.266014388831 Henry Cohn, 2026, needs more optimization.
12 98 0.266356235424 Henry Cohn, 2026, needs more optimization.
12 99 0.266728709267 Henry Cohn, 2026, needs more optimization.
12 100 0.266946573214 Henry Cohn, 2026, needs more optimization.
12 101 0.267154059053 Henry Cohn, 2026, needs more optimization.
12 102 0.267190937318 Henry Cohn, 2026, needs more optimization.
12 103 0.268931208608 Henry Cohn, 2026, needs more optimization.
12 104 0.271253246845 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 0.273390682412 Henry Cohn, 2026, needs more optimization.
12 108 0.276801917363 Henry Cohn, 2026, needs more optimization.
12 109 0.277510575464 Henry Cohn, 2026, needs more optimization.
12 110 0.277891199680 Henry Cohn, 2026, needs more optimization.
12 111 0.278766142607 Henry Cohn, 2026, needs more optimization.
12 112 0.279481318150 Henry Cohn, 2026, needs more optimization.
12 113 0.281954415798 Henry Cohn, 2026, needs more optimization.
12 114 0.291009068926 Henry Cohn, 2026, needs more optimization.
12 115 0.291590842641 Henry Cohn, 2026, needs more optimization.
12 116 0.292145953295 Henry Cohn, 2026, needs more optimization.
12 117 0.292985326594 Henry Cohn, 2026, needs more optimization.
12 118 0.293569909437 Henry Cohn, 2026, needs more optimization.
12 119 0.294623076031 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.
12 121 0.294708984704 Henry Cohn, 2026, needs more optimization.
12 122 0.304153756559 Henry Cohn, 2026, needs more optimization.
12 123 0.304340404139 Henry Cohn, 2026, needs more optimization.
12 124 0.304347195517 Henry Cohn, 2026, needs more optimization.
12 125 0.304349745573 Henry Cohn, 2026, needs more optimization.
12 126 0.304786532401 Henry Cohn, 2026, needs more optimization.
12 127 0.306791570832 Henry Cohn, 2026, needs more optimization.
12 128 0.307567227644 Henry Cohn, 2026, needs more optimization.
12 129 0.307811316623 Henry Cohn, 2026, needs more optimization.
12 130 0.308017981500 Henry Cohn, 2026, needs more optimization.
12 131 0.308546713307 Henry Cohn, 2026, needs more optimization.
12 132 0.309452892700 Henry Cohn, 2026, needs more optimization.
12 133 0.310041371934 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 0.315160907363 Henry Cohn, 2026, needs more optimization.
12 138 0.317525718136 Henry Cohn, 2026, needs more optimization.
12 139 0.319376149051 Henry Cohn, 2026, needs more optimization.
12 140 0.320926386190 Henry Cohn, 2026, needs more optimization.
12 141 0.321313207730 Henry Cohn, 2026, needs more optimization.
12 142 0.321768958767 Henry Cohn, 2026, needs more optimization.
12 143 0.322176303911 Henry Cohn, 2026, needs more optimization.
12 144 0.322647659074 Henry Cohn, 2026, needs more optimization.
12 145 0.323129537790 Henry Cohn, 2026, needs more optimization.
12 146 0.323523473487 Henry Cohn, 2026, needs more optimization.
12 147 0.323959754222 Henry Cohn, 2026, needs more optimization.
12 148 0.324534576283 Henry Cohn, 2026, needs more optimization.
12 149 0.325112276121 Henry Cohn, 2026, needs more optimization.
12 150 0.325628798998 Henry Cohn, 2026, needs more optimization.
12 151 0.325844889882 Henry Cohn, 2026, needs more optimization.
12 152 0.327224221638 Henry Cohn, 2026, needs more optimization.
12 153 0.327922597097 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.
12 154 0.328448036280 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.
12 155 0.328834128808 Henry Cohn, 2026, needs more optimization.
12 156 0.329129231574 Henry Cohn, 2026, needs more optimization.
12 157 0.329314693846 Henry Cohn, 2026, needs more optimization.
12 158 0.329553463302 Henry Cohn, 2026, needs more optimization.
12 159 0.329828830593 Henry Cohn, 2026, needs more optimization.
12 160 0.329934338437 Henry Cohn, 2026, needs more optimization.
12 161 0.329980747077 Henry Cohn, 2026, needs more optimization.
12 162 0.330013677656 Henry Cohn, 2026, needs more optimization.
12 163 0.330873227833 Henry Cohn, 2026, needs more optimization.
12 164 0.331426554467 Henry Cohn, 2026, needs more optimization.
12 165 0.332034987320 Henry Cohn, 2026, needs more optimization.
12 166 0.332620767991 Henry Cohn, 2026, needs more optimization.
12 167 0.332752990531 Henry Cohn, 2026, needs more optimization.
12 168 0.332822455836 Henry Cohn, 2026, needs more optimization.
12 169 0.332924539784 Henry Cohn, 2026, needs more optimization.
12 170 0.332988410856 Henry Cohn, 2026, needs more optimization.
12 171 0.333035218123 Henry Cohn, 2026, needs more optimization.
12 172 0.333035861250 Henry Cohn, 2026, needs more optimization.
12 173 0.333103331901 Henry Cohn, 2026, needs more optimization.
12 174 0.333140968873 Henry Cohn, 2026, needs more optimization.
12 175 0.333163020979 Henry Cohn, 2026, needs more optimization.
12 176 0.333186712241 Henry Cohn, 2026, needs more optimization.
12 177 0.333209829866 Henry Cohn, 2026, needs more optimization.
12 178 0.333243176959 Henry Cohn, 2026, needs more optimization.
12 179 0.333356167918 Henry Cohn, 2026, needs more optimization.
12 180 0.335323133575 Henry Cohn, 2026, needs more optimization.
12 181 0.344155158135 Henry Cohn, 2026, needs more optimization.
12 182 0.345799522605 Henry Cohn, 2026, needs more optimization.
12 183 0.349184102236 Henry Cohn, 2026, needs more optimization.
12 184 0.350909934590 Henry Cohn, 2026, needs more optimization.
12 185 0.351463204620 Henry Cohn, 2026, needs more optimization.
12 186 0.352042910641 Henry Cohn, 2026, needs more optimization.
12 187 0.352418453566 Henry Cohn, 2026, needs more optimization.
12 188 0.354779100628 Henry Cohn, 2026, needs more optimization.
12 189 0.355520638152 Henry Cohn, 2026, needs more optimization.
12 190 0.356435645356 Henry Cohn, 2026, needs more optimization.
12 191 0.356866891360 Henry Cohn, 2026, needs more optimization.
12 192 0.358549522946 Henry Cohn, 2026, needs more optimization.
12 193 0.359232116847 Henry Cohn, 2026, needs more optimization.
12 194 0.360830896529 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.
12 195 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 0.362356273400 Henry Cohn, 2026, needs more optimization.
12 197 0.363769212867 Henry Cohn, 2026, needs more optimization.
12 198 0.364895330578 Henry Cohn, 2026, needs more optimization.
12 199 0.365935565259 Henry Cohn, 2026, needs more optimization.
12 200 0.366556826789 Henry Cohn, 2026, needs more optimization.
12 201 0.367805760253 Henry Cohn, 2026, needs more optimization.
12 202 0.368674998850 Henry Cohn, 2026, needs more optimization.
12 203 0.369915760717 Henry Cohn, 2026, needs more optimization.
12 204 0.370833820860 Henry Cohn, 2026, needs more optimization.
12 205 0.371804813454 Henry Cohn, 2026, needs more optimization.
12 206 0.373053073020 Henry Cohn, 2026, needs more optimization.
12 207 0.374084142144 Henry Cohn, 2026, needs more optimization.
12 208 0.374454067934 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 0.378110335519 Henry Cohn, 2026, needs more optimization.
12 212 0.379154617692 Henry Cohn, 2026, needs more optimization.
12 213 0.379292620128 Henry Cohn, 2026, needs more optimization.
12 214 0.379292621115 Henry Cohn, 2026, needs more optimization.
12 215 0.380612401789 Henry Cohn, 2026, needs more optimization.
12 216 0.381264430019 Henry Cohn, 2026, needs more optimization.
12 217 0.382097666564 Henry Cohn, 2026, needs more optimization.
12 218 0.382744044550 Henry Cohn, 2026, needs more optimization.
12 219 0.383599181126 Henry Cohn, 2026, needs more optimization.
12 220 0.384126660481 Henry Cohn, 2026, needs more optimization.
12 221 0.385628755148 Henry Cohn, 2026, needs more optimization.
12 222 0.386765758075 Henry Cohn, 2026, needs more optimization.
12 223 0.387550450130 Henry Cohn, 2026, needs more optimization.
12 224 0.387797095703 Henry Cohn, 2026, needs more optimization.
12 225 0.388330854706 Henry Cohn, 2026, needs more optimization.
12 226 0.388818882559 Henry Cohn, 2026, needs more optimization.
12 227 0.389318209554 Henry Cohn, 2026, needs more optimization.
12 228 0.389387195092 Henry Cohn, 2026, needs more optimization.
12 229 0.389855222050 Henry Cohn, 2026, needs more optimization.
12 230 0.390274779493 Henry Cohn, 2026, needs more optimization.
12 231 0.390932194945 Henry Cohn, 2026, needs more optimization.
12 232 0.390992017425 Henry Cohn, 2026, needs more optimization.
12 233 0.391299707537 Henry Cohn, 2026, needs more optimization.
12 234 0.391487773025 Henry Cohn, 2026, needs more optimization.
12 235 0.391530952732 Henry Cohn, 2026, needs more optimization.
12 236 0.391972644670 Henry Cohn, 2026, needs more optimization.
12 237 0.392023166048 Henry Cohn, 2026, needs more optimization.
12 238 0.392110517782 Henry Cohn, 2026, needs more optimization.
12 239 0.392520831025 Henry Cohn, 2026, needs more optimization.
12 240 0.392766606107 Henry Cohn, 2026, needs more optimization.
12 241 0.392902020894 Henry Cohn, 2026, needs more optimization.
12 242 0.395052125909 Henry Cohn, 2026, needs more optimization.
12 243 0.396635277061 Henry Cohn, 2026, needs more optimization.
12 244 0.398246760634 Henry Cohn, 2026, needs more optimization.
12 245 0.399510526615 Henry Cohn, 2026, needs more optimization.
12 246 0.399950364157 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 0.401567838119 Henry Cohn, 2026, needs more optimization.
12 292 0.405519668732 Henry Cohn, 2026, needs more optimization.
12 293 0.408678585969 Henry Cohn, 2026, needs more optimization.
12 294 0.410769352784 Henry Cohn, 2026, needs more optimization.
12 295 0.412724195540 Henry Cohn, 2026, needs more optimization.
12 296 0.414026006999 Henry Cohn, 2026, needs more optimization.
12 297 0.414825981512 Henry Cohn, 2026, needs more optimization.
12 298 0.416913509728 Henry Cohn, 2026, needs more optimization.
12 299 0.418419299355 Henry Cohn, 2026, needs more optimization.
12 300 0.419752857452 Henry Cohn, 2026, needs more optimization.
12 301 0.420814269895 Henry Cohn, 2026, needs more optimization.
12 302 0.422041365169 Henry Cohn, 2026, needs more optimization.
12 303 0.423129581400 Henry Cohn, 2026, needs more optimization.
12 304 0.424110669895 Henry Cohn, 2026, needs more optimization.
12 305 0.425043233453 Henry Cohn, 2026, needs more optimization.
12 306 0.426458652683 Henry Cohn, 2026, needs more optimization.
12 307 0.427428248282 Henry Cohn, 2026, needs more optimization.
12 308 0.427691841219 Henry Cohn, 2026, needs more optimization.
12 309 0.428215421599 Henry Cohn, 2026, needs more optimization.
12 310 0.429238868487 Henry Cohn, 2026, needs more optimization.
12 311 0.430190179890 Henry Cohn, 2026, needs more optimization.
12 312 0.430423679666 Henry Cohn, 2026, needs more optimization.
12 313 0.430424854741 Henry Cohn, 2026, needs more optimization.
12 314 0.430424855070 Henry Cohn, 2026, needs more optimization.
12 315 0.430428919143 Henry Cohn, 2026, needs more optimization.
12 316 0.430435528031 Henry Cohn, 2026, needs more optimization.
12 317 0.430446785388 Henry Cohn, 2026, needs more optimization.
12 318 0.430458671529 Henry Cohn, 2026, needs more optimization.
12 319 0.430461648789 Henry Cohn, 2026, needs more optimization.
12 320 0.430466327247 Henry Cohn, 2026, needs more optimization.
12 321 0.430469346708 Henry Cohn, 2026, needs more optimization.
12 323 0.430470036906 Henry Cohn, 2026, needs more optimization.
12 324 0.430474980079 Henry Cohn, 2026, needs more optimization.
12 325 0.430475900129 Henry Cohn, 2026, needs more optimization.
12 326 0.430504142813 Henry Cohn, 2026, needs more optimization.
12 327 0.430508162047 Henry Cohn, 2026, needs more optimization.
12 328 0.430520315884 Henry Cohn, 2026, needs more optimization.
12 329 0.430522138067 Henry Cohn, 2026, needs more optimization.
12 330 0.430541128901 Henry Cohn, 2026, needs more optimization.
12 331 0.430558505162 Henry Cohn, 2026, needs more optimization.
12 332 0.430564668816 Henry Cohn, 2026, needs more optimization.
12 333 0.430566890351 Henry Cohn, 2026, needs more optimization.
12 334 0.430580417609 Henry Cohn, 2026, needs more optimization.
12 335 0.430591781842 Henry Cohn, 2026, needs more optimization.
12 336 0.430607219589 Henry Cohn, 2026, needs more optimization.
12 337 0.430623451278 Henry Cohn, 2026, needs more optimization.
12 338 0.430626623391 Henry Cohn, 2026, needs more optimization.
12 339 0.430626656973 Henry Cohn, 2026, needs more optimization.
12 341 0.430635433735 Henry Cohn, 2026, needs more optimization.
12 342 0.430635708348 Henry Cohn, 2026, needs more optimization.
12 343 0.430636195390 Henry Cohn, 2026, needs more optimization.
12 344 0.430647375476 Henry Cohn, 2026, needs more optimization.
12 345 0.430655396949 Henry Cohn, 2026, needs more optimization.
12 346 0.430665912184 Henry Cohn, 2026, needs more optimization.
12 347 0.430681585965 Henry Cohn, 2026, needs more optimization.
12 348 0.430703413852 Henry Cohn, 2026, needs more optimization.
12 349 0.430719999463 Henry Cohn, 2026, needs more optimization.
12 350 0.430724040341 Henry Cohn, 2026, needs more optimization.
12 351 0.430735562870 Henry Cohn, 2026, needs more optimization.
12 352 0.430899277027 Henry Cohn, 2026, needs more optimization.
12 353 0.431009959157 Henry Cohn, 2026, needs more optimization.
12 354 0.431036284748 Henry Cohn, 2026, needs more optimization.
12 355 0.434332433137 Henry Cohn, 2026, needs more optimization.
12 356 0.436670337231 Henry Cohn, 2026, needs more optimization.
12 357 0.438092793645 Henry Cohn, 2026, needs more optimization.
12 358 0.439022681944 Henry Cohn, 2026, needs more optimization.
12 359 0.439739059023 Henry Cohn, 2026, needs more optimization.
12 360 0.440145323194 Henry Cohn, 2026, needs more optimization.
12 361 0.440160900330 Henry Cohn, 2026, needs more optimization.
12 362 0.440448706224 Henry Cohn, 2026, needs more optimization.
12 363 0.441166979053 Henry Cohn, 2026, needs more optimization.
12 364 0.441348969379 Henry Cohn, 2026, needs more optimization.
12 365 0.441694914748 Henry Cohn, 2026, needs more optimization.
12 366 0.441868293225 Henry Cohn, 2026, needs more optimization.
12 367 0.441870758094 Henry Cohn, 2026, needs more optimization.
12 368 0.441871304778 Henry Cohn, 2026, needs more optimization.
12 369 0.441871993717 Henry Cohn, 2026, needs more optimization.
12 370 0.442117228633 Henry Cohn, 2026, needs more optimization.
12 371 0.442372824017 Henry Cohn, 2026, needs more optimization.
12 372 0.442460738744 Henry Cohn, 2026, needs more optimization.
12 373 0.442765530082 Henry Cohn, 2026, needs more optimization.
12 374 0.443322272672 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 0.447928276888 Henry Cohn, 2026, needs more optimization.
12 411 0.448616515610 Henry Cohn, 2026, needs more optimization.
12 412 0.449179895971 Henry Cohn, 2026, needs more optimization.
12 414 0.450179134205 Henry Cohn, 2026, needs more optimization.
12 415 0.450350405150 Henry Cohn, 2026, needs more optimization.
12 416 0.450351308524 Henry Cohn, 2026, needs more optimization.
12 417 0.450654411865 Henry Cohn, 2026, needs more optimization.
12 418 0.450931836226 Henry Cohn, 2026, needs more optimization.
12 419 0.451171579808 Henry Cohn, 2026, needs more optimization.
12 420 0.451473576935 Henry Cohn, 2026, needs more optimization.
12 421 0.451750830116 Henry Cohn, 2026, needs more optimization.
12 422 0.452049435177 Henry Cohn, 2026, needs more optimization.
12 423 0.452515169482 Henry Cohn, 2026, needs more optimization.
12 424 0.456879003699 Henry Cohn, 2026, needs more optimization.
12 425 0.457289032528 Henry Cohn, 2026, needs more optimization.
12 426 0.458835298695 Henry Cohn, 2026, needs more optimization.
12 427 0.461050715332 Henry Cohn, 2026, needs more optimization.
12 428 0.461075551149 Henry Cohn, 2026, needs more optimization.
12 429 0.462344923065 Henry Cohn, 2026, needs more optimization.
12 430 0.462801203208 Henry Cohn, 2026, needs more optimization.
12 431 0.462835976370 Henry Cohn, 2026, needs more optimization.
12 432 0.463014661551 Henry Cohn, 2026, needs more optimization.
12 433 0.463801208270 Henry Cohn, 2026, needs more optimization.
12 434 0.463955816651 Henry Cohn, 2026, needs more optimization.
12 435 0.464569349050 Henry Cohn, 2026, needs more optimization.
12 436 0.464677666307 Henry Cohn, 2026, needs more optimization.
12 437 0.465606948712 Henry Cohn, 2026, needs more optimization.
12 438 0.466370292285 Henry Cohn, 2026, needs more optimization.
12 439 0.466427220947 Henry Cohn, 2026, needs more optimization.
12 440 0.466433321705 Henry Cohn, 2026, needs more optimization.
12 441 0.466527862077 Henry Cohn, 2026, needs more optimization.
12 442 0.466674290271 Henry Cohn, 2026, needs more optimization.
12 443 0.466779827663 Henry Cohn, 2026, needs more optimization.
12 444 0.466840408052 Henry Cohn, 2026, needs more optimization.
12 445 0.467495040303 Henry Cohn, 2026, needs more optimization.
12 446 0.467557674320 Henry Cohn, 2026, needs more optimization.
12 447 0.467799418611 Henry Cohn, 2026, needs more optimization.
12 448 0.467972804310 Henry Cohn, 2026, needs more optimization.
12 449 0.468566615474 Henry Cohn, 2026, needs more optimization.
12 450 0.468604705756 Henry Cohn, 2026, needs more optimization.
12 451 0.468755812140 Henry Cohn, 2026, needs more optimization.
12 452 0.468788428308 Henry Cohn, 2026, needs more optimization.
12 453 0.468848709325 Henry Cohn, 2026, needs more optimization.
12 454 0.469166793802 Henry Cohn, 2026, needs more optimization.
12 455 0.469252608124 Henry Cohn, 2026, needs more optimization.
12 456 0.469290868760 Henry Cohn, 2026, needs more optimization.
12 457 0.469584023065 Henry Cohn, 2026, needs more optimization.
12 458 0.470001695888 Henry Cohn, 2026, needs more optimization.
12 459 0.470111229903 Henry Cohn, 2026, needs more optimization.
12 460 0.470301517443 Henry Cohn, 2026, needs more optimization.
12 461 0.470413793828 Henry Cohn, 2026, needs more optimization.
12 462 0.470456492462 Henry Cohn, 2026, needs more optimization.
12 463 0.470770543008 Henry Cohn, 2026, needs more optimization.
12 464 0.471176756605 Henry Cohn, 2026, needs more optimization.
12 465 0.471261451840 Henry Cohn, 2026, needs more optimization.
12 466 0.471625334838 Henry Cohn, 2026, needs more optimization.
12 467 0.472122531464 Henry Cohn, 2026, needs more optimization.
12 468 0.472316859266 Henry Cohn, 2026, needs more optimization.
12 469 0.472495974327 Henry Cohn, 2026, needs more optimization.
12 470 0.472560841381 Henry Cohn, 2026, needs more optimization.
12 471 0.472636244898 Henry Cohn, 2026, needs more optimization.
12 473 0.472822833330 Henry Cohn, 2026, needs more optimization.
12 474 0.472903177071 Henry Cohn, 2026, needs more optimization.
12 475 0.473001922341 Henry Cohn, 2026, needs more optimization.
12 476 0.473074710399 Henry Cohn, 2026, needs more optimization.
12 477 0.473231403709 Henry Cohn, 2026, needs more optimization.
12 478 0.473519080442 Henry Cohn, 2026, needs more optimization.
12 479 0.473625731780 Henry Cohn, 2026, needs more optimization.
12 480 0.473961836002 Henry Cohn, 2026, needs more optimization.
12 481 0.473969103301 Henry Cohn, 2026, needs more optimization.
12 482 0.474332838000 Henry Cohn, 2026, needs more optimization.
12 483 0.474346638115 Henry Cohn, 2026, needs more optimization.
12 484 0.474673391314 Henry Cohn, 2026, needs more optimization.
12 485 0.474735216896 Henry Cohn, 2026, needs more optimization.
12 486 0.474848233800 Henry Cohn, 2026, needs more optimization.
12 487 0.474998384582 Henry Cohn, 2026, needs more optimization.
12 488 0.475244758746 Henry Cohn, 2026, needs more optimization.
12 489 0.475990849707 Henry Cohn, 2026, needs more optimization.
12 490 0.476020401487 Henry Cohn, 2026, needs more optimization.
12 491 0.476123174713 Henry Cohn, 2026, needs more optimization.
12 492 0.476252476467 Henry Cohn, 2026, needs more optimization.
12 493 0.476398264255 Henry Cohn, 2026, needs more optimization.
12 494 0.476563797328 Henry Cohn, 2026, needs more optimization.
12 495 0.476725986765 Henry Cohn, 2026, needs more optimization.
12 496 0.476757360045 Henry Cohn, 2026, needs more optimization.
12 497 0.476945463258 Henry Cohn, 2026, needs more optimization.
12 498 0.476954122055 Henry Cohn, 2026, needs more optimization.
12 499 0.477023813798 Henry Cohn, 2026, needs more optimization.
12 500 0.477525813034 Henry Cohn, 2026, needs more optimization.
12 501 0.477562195539 Henry Cohn, 2026, needs more optimization.
12 502 0.477703640707 Henry Cohn, 2026, needs more optimization.
12 503 0.477814120676 Henry Cohn, 2026, needs more optimization.
12 504 0.478181985148 Henry Cohn, 2026, needs more optimization.
12 505 0.478477898588 Henry Cohn, 2026, needs more optimization.
12 506 0.478498210874 Henry Cohn, 2026, needs more optimization.
12 507 0.478788765387 Henry Cohn, 2026, needs more optimization.
12 508 0.478893763066 Henry Cohn, 2026, needs more optimization.
12 509 0.479094309244 Henry Cohn, 2026, needs more optimization.
12 510 0.479107320642 Henry Cohn, 2026, needs more optimization.
12 511 0.479143775906 Henry Cohn, 2026, needs more optimization.
12 512 0.479551593329 Henry Cohn, 2026, needs more optimization.
12 513 0.479717304652 Henry Cohn, 2026, needs more optimization.
12 514 0.479801301031 Henry Cohn, 2026, needs more optimization.
12 515 0.479905955778 Henry Cohn, 2026, needs more optimization.
12 516 0.479950698641 Henry Cohn, 2026, needs more optimization.
12 517 0.480071724993 Henry Cohn, 2026, needs more optimization.
12 518 0.480174023351 Henry Cohn, 2026, needs more optimization.
12 519 0.480441293001 Henry Cohn, 2026, needs more optimization.
12 520 0.480549144964 Henry Cohn, 2026, needs more optimization.
12 521 0.481158431862 Henry Cohn, 2026, needs more optimization.
12 522 0.481231732517 Henry Cohn, 2026, needs more optimization.
12 523 0.481374350049 Henry Cohn, 2026, needs more optimization.
12 524 0.481417605284 Henry Cohn, 2026, needs more optimization.
12 525 0.481619900859 Henry Cohn, 2026, needs more optimization.
12 526 0.481782504871 Henry Cohn, 2026, needs more optimization.
12 527 0.481872660071 Henry Cohn, 2026, needs more optimization.
12 528 0.482002189500 Henry Cohn, 2026, needs more optimization.
12 529 0.482184068781 Henry Cohn, 2026, needs more optimization.
12 530 0.482381706411 Henry Cohn, 2026, needs more optimization.
12 531 0.482432701618 Henry Cohn, 2026, needs more optimization.
12 532 0.482584833851 Henry Cohn, 2026, needs more optimization.
12 533 0.482719063232 Henry Cohn, 2026, needs more optimization.
12 534 0.482759020919 Henry Cohn, 2026, needs more optimization.
12 535 0.482915513486 Henry Cohn, 2026, needs more optimization.
12 536 0.483042233690 Henry Cohn, 2026, needs more optimization.
12 537 0.483103010194 Henry Cohn, 2026, needs more optimization.
12 538 0.483235206348 Henry Cohn, 2026, needs more optimization.
12 539 0.483387213651 Henry Cohn, 2026, needs more optimization.
12 540 0.483463722592 Henry Cohn, 2026, needs more optimization.
12 541 0.483507006851 Henry Cohn, 2026, needs more optimization.
12 542 0.483671625715 Henry Cohn, 2026, needs more optimization.
12 543 0.483815982735 Henry Cohn, 2026, needs more optimization.
12 544 0.483906508437 Henry Cohn, 2026, needs more optimization.
12 545 0.483970592058 Henry Cohn, 2026, needs more optimization.
12 546 0.484078046272 Henry Cohn, 2026, needs more optimization.
12 547 0.484361633955 Henry Cohn, 2026, needs more optimization.
12 548 0.484610768886 Henry Cohn, 2026, needs more optimization.
12 549 0.484872229296 Henry Cohn, 2026, needs more optimization.
12 550 0.485006397882 Henry Cohn, 2026, needs more optimization.
12 551 0.485187109712 Henry Cohn, 2026, needs more optimization.
12 552 0.485319252249 Henry Cohn, 2026, needs more optimization.
12 553 0.485388206814 Henry Cohn, 2026, needs more optimization.
12 554 0.485607226853 Henry Cohn, 2026, needs more optimization.
12 555 0.485678315885 Henry Cohn, 2026, needs more optimization.
12 556 0.485716696319 Henry Cohn, 2026, needs more optimization.
12 557 0.485839369013 Henry Cohn, 2026, needs more optimization.
12 558 0.485949314145 Henry Cohn, 2026, needs more optimization.
12 559 0.486101374840 Henry Cohn, 2026, needs more optimization.
12 560 0.486199004623 Henry Cohn, 2026, needs more optimization.
12 561 0.486298758873 Henry Cohn, 2026, needs more optimization.
12 562 0.486336859962 Henry Cohn, 2026, needs more optimization.
12 563 0.486530693801 Henry Cohn, 2026, needs more optimization.
12 564 0.486599481622 Henry Cohn, 2026, needs more optimization.
12 565 0.486671650800 Henry Cohn, 2026, needs more optimization.
12 566 0.486757874605 Henry Cohn, 2026, needs more optimization.
12 567 0.486803889479 Henry Cohn, 2026, needs more optimization.
12 568 0.487007159754 Henry Cohn, 2026, needs more optimization.
12 569 0.487104134302 Henry Cohn, 2026, needs more optimization.
12 570 0.487266951429 Henry Cohn, 2026, needs more optimization.
12 571 0.487401694559 Henry Cohn, 2026, needs more optimization.
12 572 0.487514557588 Henry Cohn, 2026, needs more optimization.
12 573 0.487573403942 Henry Cohn, 2026, needs more optimization.
12 574 0.487656941257 Henry Cohn, 2026, needs more optimization.
12 575 0.487727688573 Henry Cohn, 2026, needs more optimization.
12 576 0.487767952652 Henry Cohn, 2026, needs more optimization.
12 577 0.487984361168 Henry Cohn, 2026, needs more optimization.
12 578 0.488187826386 Henry Cohn, 2026, needs more optimization.
12 579 0.488288452550 Henry Cohn, 2026, needs more optimization.
12 580 0.488316103973 Henry Cohn, 2026, needs more optimization.
12 581 0.488361982947 Henry Cohn, 2026, needs more optimization.
12 582 0.488361989258 Henry Cohn, 2026, needs more optimization.
12 583 0.488431038093 Henry Cohn, 2026, needs more optimization.
12 584 0.488484097431 Henry Cohn, 2026, needs more optimization.
12 585 0.488638295179 Henry Cohn, 2026, needs more optimization.
12 586 0.488706708186 Henry Cohn, 2026, needs more optimization.
12 587 0.488763120692 Henry Cohn, 2026, needs more optimization.
12 588 0.488904623780 Henry Cohn, 2026, needs more optimization.
12 589 0.488978838357 Henry Cohn, 2026, needs more optimization.
12 590 0.489110103781 Henry Cohn, 2026, needs more optimization.
12 591 0.489166797044 Henry Cohn, 2026, needs more optimization.
12 592 0.489225191322 Henry Cohn, 2026, needs more optimization.
12 593 0.489339404230 Henry Cohn, 2026, needs more optimization.
12 594 0.489393671454 Henry Cohn, 2026, needs more optimization.
12 595 0.489556917621 Henry Cohn, 2026, needs more optimization.
12 596 0.489564922639 Henry Cohn, 2026, needs more optimization.
12 597 0.489579022722 Henry Cohn, 2026, needs more optimization.
12 598 0.489697647164 Henry Cohn, 2026, needs more optimization.
12 599 0.489785271029 Henry Cohn, 2026, needs more optimization.
12 600 0.489787889108 Henry Cohn, 2026, needs more optimization.
12 601 0.489909350875 Henry Cohn, 2026, needs more optimization.
12 602 0.489974885869 Henry Cohn, 2026, needs more optimization.
12 603 0.490120379893 Henry Cohn, 2026, needs more optimization.
12 604 0.490211954426 Henry Cohn, 2026, needs more optimization.
12 605 0.490299874875 Henry Cohn, 2026, needs more optimization.
12 606 0.490362484689 Henry Cohn, 2026, needs more optimization.
12 607 0.490505571944 Henry Cohn, 2026, needs more optimization.
12 608 0.490535338278 Henry Cohn, 2026, needs more optimization.
12 609 0.490554444130 Henry Cohn, 2026, needs more optimization.
12 610 0.490614724739 Henry Cohn, 2026, needs more optimization.
12 611 0.490716010423 Henry Cohn, 2026, needs more optimization.
12 612 0.490731021942 Henry Cohn, 2026, needs more optimization.
12 613 0.490916837525 Henry Cohn, 2026, needs more optimization.
12 614 0.490967715948 Henry Cohn, 2026, needs more optimization.
12 615 0.491033480518 Henry Cohn, 2026, needs more optimization.
12 616 0.491222645534 Henry Cohn, 2026, needs more optimization.
12 617 0.491352604000 Henry Cohn, 2026, needs more optimization.
12 618 0.491425742635 Henry Cohn, 2026, needs more optimization.
12 619 0.491454533254 Henry Cohn, 2026, needs more optimization.
12 620 0.491599869516 Henry Cohn, 2026, needs more optimization.
12 621 0.491664313465 Henry Cohn, 2026, needs more optimization.
12 622 0.491730384363 Henry Cohn, 2026, needs more optimization.
12 623 0.491771758094 Henry Cohn, 2026, needs more optimization.
12 624 0.491831288583 Henry Cohn, 2026, needs more optimization.
12 625 0.491867580667 Henry Cohn, 2026, needs more optimization.
12 626 0.491937536008 Henry Cohn, 2026, needs more optimization.
12 627 0.491972197444 Henry Cohn, 2026, needs more optimization.
12 628 0.492051389781 Henry Cohn, 2026, needs more optimization.
12 629 0.492080510522 Henry Cohn, 2026, needs more optimization.
12 630 0.492107281493 Henry Cohn, 2026, needs more optimization.
12 631 0.492185614250 Henry Cohn, 2026, needs more optimization.
12 632 0.492308247033 Henry Cohn, 2026, needs more optimization.
12 633 0.492365339820 Henry Cohn, 2026, needs more optimization.
12 634 0.492365344384 Henry Cohn, 2026, needs more optimization.
12 635 0.492365363662 Henry Cohn, 2026, needs more optimization.
12 636 0.492365369550 Henry Cohn, 2026, needs more optimization.
12 637 0.492386827855 Henry Cohn, 2026, needs more optimization.
12 638 0.492386830200 Henry Cohn, 2026, needs more optimization.
12 639 0.492458232642 Henry Cohn, 2026, needs more optimization.
12 640 0.492514661100 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 0.492563453854 Henry Cohn, 2026, needs more optimization.
12 644 0.492666781332 Henry Cohn, 2026, needs more optimization.
12 645 0.492751804303 Henry Cohn, 2026, needs more optimization.
12 646 0.492772029024 Henry Cohn, 2026, needs more optimization.
12 647 0.492878249679 Henry Cohn, 2026, needs more optimization.
12 648 0.493253409950 Henry Cohn, 2026, needs more optimization.
12 649 0.493337407655 Henry Cohn, 2026, needs more optimization.
12 650 0.493359911631 Henry Cohn, 2026, needs more optimization.
12 651 0.493419165233 Henry Cohn, 2026, needs more optimization.
12 652 0.493440771936 Henry Cohn, 2026, needs more optimization.
12 653 0.493478644893 Henry Cohn, 2026, needs more optimization.
12 654 0.493492419891 Henry Cohn, 2026, needs more optimization.
12 655 0.493606249066 Henry Cohn, 2026, needs more optimization.
12 656 0.493649385566 Henry Cohn, 2026, needs more optimization.
12 657 0.493652352452 Henry Cohn, 2026, needs more optimization.
12 658 0.493782130567 Henry Cohn, 2026, needs more optimization.
12 659 0.493825131862 Henry Cohn, 2026, needs more optimization.
12 660 0.493845313898 Henry Cohn, 2026, needs more optimization.
12 661 0.493900537686 Henry Cohn, 2026, needs more optimization.
12 662 0.493950518574 Henry Cohn, 2026, needs more optimization.
12 663 0.493994851907 Henry Cohn, 2026, needs more optimization.
12 664 0.494103066004 Henry Cohn, 2026, needs more optimization.
12 665 0.494257996076 Henry Cohn, 2026, needs more optimization.
12 666 0.494292469076 Henry Cohn, 2026, needs more optimization.
12 667 0.494337510524 Henry Cohn, 2026, needs more optimization.
12 668 0.494351911751 Henry Cohn, 2026, needs more optimization.
12 669 0.494409994134 Henry Cohn, 2026, needs more optimization.
12 670 0.494560510629 Henry Cohn, 2026, needs more optimization.
12 671 0.494581420921 Henry Cohn, 2026, needs more optimization.
12 672 0.494679639663 Henry Cohn, 2026, needs more optimization.
12 673 0.494683069315 Henry Cohn, 2026, needs more optimization.
12 674 0.494685528156 Henry Cohn, 2026, needs more optimization.
12 675 0.494709350573 Henry Cohn, 2026, needs more optimization.
12 676 0.494730757181 Henry Cohn, 2026, needs more optimization.
12 677 0.494740307264 Henry Cohn, 2026, needs more optimization.
12 678 0.494758445802 Henry Cohn, 2026, needs more optimization.
12 679 0.494839711687 Henry Cohn, 2026, needs more optimization.
12 680 0.494876035153 Henry Cohn, 2026, needs more optimization.
12 681 0.494916185941 Henry Cohn, 2026, needs more optimization.
12 682 0.495022868983 Henry Cohn, 2026, needs more optimization.
12 683 0.495096847434 Henry Cohn, 2026, needs more optimization.
12 684 0.495128515282 Henry Cohn, 2026, needs more optimization.
12 685 0.495139776394 Henry Cohn, 2026, needs more optimization.
12 686 0.495156349133 Henry Cohn, 2026, needs more optimization.
12 687 0.495174917162 Henry Cohn, 2026, needs more optimization.
12 688 0.495253521202 Henry Cohn, 2026, needs more optimization.
12 689 0.495335942129 Henry Cohn, 2026, needs more optimization.
12 690 0.495398296156 Henry Cohn, 2026, needs more optimization.
12 691 0.495448172648 Henry Cohn, 2026, needs more optimization.
12 692 0.495478756984 Henry Cohn, 2026, needs more optimization.
12 693 0.495559379295 Henry Cohn, 2026, needs more optimization.
12 694 0.495563358652 Henry Cohn, 2026, needs more optimization.
12 695 0.495588905737 Henry Cohn, 2026, needs more optimization.
12 696 0.495609687530 Henry Cohn, 2026, needs more optimization.
12 697 0.495681292696 Henry Cohn, 2026, needs more optimization.
12 698 0.495693689807 Henry Cohn, 2026, needs more optimization.
12 699 0.495773900509 Henry Cohn, 2026, needs more optimization.
12 700 0.495797280614 Henry Cohn, 2026, needs more optimization.
12 701 0.495805740406 Henry Cohn, 2026, needs more optimization.
12 702 0.495892733555 Henry Cohn, 2026, needs more optimization.
12 703 0.495899746058 Henry Cohn, 2026, needs more optimization.
12 704 0.495940090636 Henry Cohn, 2026, needs more optimization.
12 705 0.495977519582 Henry Cohn, 2026, needs more optimization.
12 706 0.496052812130 Henry Cohn, 2026, needs more optimization.
12 707 0.496069552389 Henry Cohn, 2026, needs more optimization.
12 708 0.496127947239 Henry Cohn, 2026, needs more optimization.
12 709 0.496179159073 Henry Cohn, 2026, needs more optimization.
12 710 0.496193750863 Henry Cohn, 2026, needs more optimization.
12 711 0.496222591306 Henry Cohn, 2026, needs more optimization.
12 712 0.496241634619 Henry Cohn, 2026, needs more optimization.
12 713 0.496341432241 Henry Cohn, 2026, needs more optimization.
12 714 0.496345675698 Henry Cohn, 2026, needs more optimization.
12 715 0.496348540737 Henry Cohn, 2026, needs more optimization.
12 716 0.496352244584 Henry Cohn, 2026, needs more optimization.
12 717 0.496368309917 Henry Cohn, 2026, needs more optimization.
12 718 0.496412453037 Henry Cohn, 2026, needs more optimization.
12 719 0.496417610115 Henry Cohn, 2026, needs more optimization.
12 720 0.496455033009 Henry Cohn, 2026, needs more optimization.
12 721 0.496480561421 Henry Cohn, 2026, needs more optimization.
12 722 0.496480564926 Henry Cohn, 2026, needs more optimization.
12 723 0.496480568264 Henry Cohn, 2026, needs more optimization.
12 724 0.496480569872 Henry Cohn, 2026, needs more optimization.
12 725 0.496480570533 Henry Cohn, 2026, needs more optimization.
12 726 0.496522683549 Henry Cohn, 2026, needs more optimization.
12 727 0.496532597345 Henry Cohn, 2026, needs more optimization.
12 728 0.496532802833 Henry Cohn, 2026, needs more optimization.
12 729 0.496550956465 Henry Cohn, 2026, needs more optimization.
12 730 0.496554475580 Henry Cohn, 2026, needs more optimization.
12 731 0.496559211300 Henry Cohn, 2026, needs more optimization.
12 732 0.496560350857 Henry Cohn, 2026, needs more optimization.
12 733 0.496560350952 Henry Cohn, 2026, needs more optimization.
12 734 0.496562605972 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 0.496830962408 Henry Cohn, 2026, needs more optimization.
12 736 0.496837727454 Henry Cohn, 2026, needs more optimization.
12 737 0.496840830471 Henry Cohn, 2026, needs more optimization.
12 738 0.496858168754 Henry Cohn, 2026, needs more optimization.
12 739 0.496864099895 Henry Cohn, 2026, needs more optimization.
12 740 0.496869819104 Henry Cohn, 2026, needs more optimization.
12 741 0.496872219977 Henry Cohn, 2026, needs more optimization.
12 742 0.496876465225 Henry Cohn, 2026, needs more optimization.
12 743 0.496883790270 Henry Cohn, 2026, needs more optimization.
12 744 0.496887887448 Henry Cohn, 2026, needs more optimization.
12 745 0.496904373102 Henry Cohn, 2026, needs more optimization.
12 746 0.496961435133 Henry Cohn, 2026, needs more optimization.
12 747 0.496992530070 Henry Cohn, 2026, needs more optimization.
12 748 0.497019770568 Henry Cohn, 2026, needs more optimization.
12 749 0.497026964864 Henry Cohn, 2026, needs more optimization.
12 750 0.497029158301 Henry Cohn, 2026, needs more optimization.
12 751 0.497040124891 Henry Cohn, 2026, needs more optimization.
12 752 0.497045883279 Henry Cohn, 2026, needs more optimization.
12 753 0.497053317105 Henry Cohn, 2026, needs more optimization.
12 754 0.497060617898 Henry Cohn, 2026, needs more optimization.
12 755 0.497063068321 Henry Cohn, 2026, needs more optimization.
12 756 0.497129237634 Henry Cohn, 2026, needs more optimization.
12 757 0.498343304093 Henry Cohn, 2026, needs more optimization.
12 758 0.499494592666 Henry Cohn, 2026, needs more optimization.
12 759 0.499997153386 Henry Cohn, 2026, needs more optimization.
12 760 0.499997160549 Henry Cohn, 2026, needs more optimization.
12 763 0.499997926078 Henry Cohn, 2026, needs more optimization.
12 765 0.499997926079 Henry Cohn, 2026, needs more optimization.
12 766 0.499997926080 Henry Cohn, 2026, needs more optimization.
12 770 0.499997926849 Henry Cohn, 2026, needs more optimization.
12 773 0.499997927148 Henry Cohn, 2026, needs more optimization.
12 791 0.499997927157 Henry Cohn, 2026, needs more optimization.
12 792 0.499998534540 Henry Cohn, 2026, needs more optimization.
12 796 0.499998542244 Henry Cohn, 2026, needs more optimization.
12 797 0.499998569210 Henry Cohn, 2026, needs more optimization.
12 803 0.499998586988 Henry Cohn, 2026, needs more optimization.
12 804 0.499998691404 Henry Cohn, 2026, needs more optimization.
12 806 0.499998693143 Henry Cohn, 2026, needs more optimization.
12 809 0.499998694968 Henry Cohn, 2026, needs more optimization.
12 818 0.499998767862 Henry Cohn, 2026, needs more optimization.
12 820 0.499998782388 Henry Cohn, 2026, needs more optimization.
12 822 0.499998783457 Henry Cohn, 2026, needs more optimization.
12 829 0.499999450280 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 0.504401014937 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 0.506104912128 Henry Cohn, 2026, needs more optimization.
12 846 0.507168184069 Henry Cohn, 2026, needs more optimization.
12 847 0.508083745994 Henry Cohn, 2026, needs more optimization.
12 848 0.517694811502 Henry Cohn, 2026, needs more optimization.
12 849 0.518027252236 Henry Cohn, 2026, needs more optimization.
12 850 0.518723810476 Henry Cohn, 2026, needs more optimization.
12 851 0.518977001339 Henry Cohn, 2026, needs more optimization.
12 852 0.519387861267 Henry Cohn, 2026, needs more optimization.
12 853 0.519708919597 Henry Cohn, 2026, needs more optimization.
12 854 0.520108173228 Henry Cohn, 2026, needs more optimization.
12 855 0.520370653103 Henry Cohn, 2026, needs more optimization.
12 856 0.520801300798 Henry Cohn, 2026, needs more optimization.
12 857 0.521086217854 Henry Cohn, 2026, needs more optimization.
12 858 0.521427788830 Henry Cohn, 2026, needs more optimization.
12 859 0.521998301056 Henry Cohn, 2026, needs more optimization.
12 860 0.522325975351 Henry Cohn, 2026, needs more optimization.
12 861 0.522629741145 Henry Cohn, 2026, needs more optimization.
12 862 0.522869691796 Henry Cohn, 2026, needs more optimization.
12 863 0.523071901596 Henry Cohn, 2026, needs more optimization.
12 864 0.523313142267 Henry Cohn, 2026, needs more optimization.
12 865 0.523722423767 Henry Cohn, 2026, needs more optimization.
12 866 0.524022537918 Henry Cohn, 2026, needs more optimization.
12 867 0.524207720930 Henry Cohn, 2026, needs more optimization.
12 868 0.524355934992 Henry Cohn, 2026, needs more optimization.
12 869 0.524661983383 Henry Cohn, 2026, needs more optimization.
12 870 0.524857072665 Henry Cohn, 2026, needs more optimization.
12 871 0.525060947757 Henry Cohn, 2026, needs more optimization.
12 872 0.525534913023 Henry Cohn, 2026, needs more optimization.
12 873 0.525802032421 Henry Cohn, 2026, needs more optimization.
12 874 0.526150025117 Henry Cohn, 2026, needs more optimization.
12 875 0.526355232388 Henry Cohn, 2026, needs more optimization.
12 876 0.526612686262 Henry Cohn, 2026, needs more optimization.
12 877 0.526861989880 Henry Cohn, 2026, needs more optimization.
12 878 0.527168207993 Henry Cohn, 2026, needs more optimization.
12 879 0.527396045860 Henry Cohn, 2026, needs more optimization.
12 880 0.527637362162 Henry Cohn, 2026, needs more optimization.
12 881 0.527876143140 Henry Cohn, 2026, needs more optimization.
12 882 0.528200870839 Henry Cohn, 2026, needs more optimization.
12 883 0.528436346281 Henry Cohn, 2026, needs more optimization.
12 884 0.528797322536 Henry Cohn, 2026, needs more optimization.
12 885 0.528992660478 Henry Cohn, 2026, needs more optimization.
12 886 0.529170956384 Henry Cohn, 2026, needs more optimization.
12 887 0.529467064630 Henry Cohn, 2026, needs more optimization.
12 888 0.529696549918 Henry Cohn, 2026, needs more optimization.
12 889 0.530276660920 Henry Cohn, 2026, needs more optimization.
12 890 0.530479458949 Henry Cohn, 2026, needs more optimization.
12 891 0.530622423594 Henry Cohn, 2026, needs more optimization.
12 892 0.530899771449 Henry Cohn, 2026, needs more optimization.
12 893 0.531092956969 Henry Cohn, 2026, needs more optimization.
12 894 0.531325929163 Henry Cohn, 2026, needs more optimization.
12 895 0.531658293651 Henry Cohn, 2026, needs more optimization.
12 896 0.531883637058 Henry Cohn, 2026, needs more optimization.
12 897 0.532177321572 Henry Cohn, 2026, needs more optimization.
12 898 0.532328112997 Henry Cohn, 2026, needs more optimization.
12 899 0.532519445710 Henry Cohn, 2026, needs more optimization.
12 900 0.532669002128 Henry Cohn, 2026, needs more optimization.
12 901 0.532817972796 Henry Cohn, 2026, needs more optimization.
12 902 0.533045998227 Henry Cohn, 2026, needs more optimization.
12 903 0.533221367197 Henry Cohn, 2026, needs more optimization.
12 904 0.533483801585 Henry Cohn, 2026, needs more optimization.
12 905 0.533700678422 Henry Cohn, 2026, needs more optimization.
12 906 0.533935101788 Henry Cohn, 2026, needs more optimization.
12 907 0.534093317588 Henry Cohn, 2026, needs more optimization.
12 908 0.534341317445 Henry Cohn, 2026, needs more optimization.
12 909 0.534471443333 Henry Cohn, 2026, needs more optimization.
12 910 0.534640507898 Henry Cohn, 2026, needs more optimization.
12 911 0.534850443031 Henry Cohn, 2026, needs more optimization.
12 912 0.535058103217 Henry Cohn, 2026, needs more optimization.
12 913 0.535262187746 Henry Cohn, 2026, needs more optimization.
12 914 0.535544034233 Henry Cohn, 2026, needs more optimization.
12 915 0.535854710492 Henry Cohn, 2026, needs more optimization.
12 916 0.536063621712 Henry Cohn, 2026, needs more optimization.
12 917 0.536214047048 Henry Cohn, 2026, needs more optimization.
12 918 0.536580405897 Henry Cohn, 2026, needs more optimization.
12 919 0.536804696999 Henry Cohn, 2026, needs more optimization.
12 920 0.537038371827 Henry Cohn, 2026, needs more optimization.
12 921 0.537178589805 Henry Cohn, 2026, needs more optimization.
12 922 0.537358404700 Henry Cohn, 2026, needs more optimization.
12 923 0.537562546550 Henry Cohn, 2026, needs more optimization.
12 924 0.537768096367 Henry Cohn, 2026, needs more optimization.
12 925 0.537841909869 Henry Cohn, 2026, needs more optimization.
12 926 0.538108880846 Henry Cohn, 2026, needs more optimization.
12 927 0.538214344580 Henry Cohn, 2026, needs more optimization.
12 928 0.538379510144 Henry Cohn, 2026, needs more optimization.
12 929 0.538560438650 Henry Cohn, 2026, needs more optimization.
12 930 0.538716134367 Henry Cohn, 2026, needs more optimization.
12 931 0.538977071231 Henry Cohn, 2026, needs more optimization.
12 932 0.539150223207 Henry Cohn, 2026, needs more optimization.
12 933 0.539333573413 Henry Cohn, 2026, needs more optimization.
12 934 0.539485998590 Henry Cohn, 2026, needs more optimization.
12 935 0.539700231518 Henry Cohn, 2026, needs more optimization.
12 936 0.539864440750 Henry Cohn, 2026, needs more optimization.
12 937 0.540087452582 Henry Cohn, 2026, needs more optimization.
12 938 0.540277377520 Henry Cohn, 2026, needs more optimization.
12 939 0.540499456167 Henry Cohn, 2026, needs more optimization.
12 940 0.540683777447 Henry Cohn, 2026, needs more optimization.
12 941 0.540906436234 Henry Cohn, 2026, needs more optimization.
12 942 0.541010207056 Henry Cohn, 2026, needs more optimization.
12 943 0.541136155844 Henry Cohn, 2026, needs more optimization.
12 944 0.541310076311 Henry Cohn, 2026, needs more optimization.
12 945 0.541521172389 Henry Cohn, 2026, needs more optimization.
12 946 0.541671280261 Henry Cohn, 2026, needs more optimization.
12 947 0.541989169734 Henry Cohn, 2026, needs more optimization.
12 948 0.542101155110 Henry Cohn, 2026, needs more optimization.
12 949 0.542244944374 Henry Cohn, 2026, needs more optimization.
12 950 0.542387022129 Henry Cohn, 2026, needs more optimization.
12 951 0.542539960485 Henry Cohn, 2026, needs more optimization.
12 952 0.542754781720 Henry Cohn, 2026, needs more optimization.
12 953 0.543036918062 Henry Cohn, 2026, needs more optimization.
12 954 0.543187404675 Henry Cohn, 2026, needs more optimization.
12 955 0.543409908571 Henry Cohn, 2026, needs more optimization.
12 956 0.543475802187 Henry Cohn, 2026, needs more optimization.
12 957 0.543660847988 Henry Cohn, 2026, needs more optimization.
12 958 0.543804057462 Henry Cohn, 2026, needs more optimization.
12 959 0.543967421060 Henry Cohn, 2026, needs more optimization.
12 960 0.544111315646 Henry Cohn, 2026, needs more optimization.
12 961 0.544235747508 Henry Cohn, 2026, needs more optimization.
12 962 0.544438121179 Henry Cohn, 2026, needs more optimization.
12 963 0.544541029003 Henry Cohn, 2026, needs more optimization.
12 964 0.544711779113 Henry Cohn, 2026, needs more optimization.
12 965 0.544842318793 Henry Cohn, 2026, needs more optimization.
12 966 0.544926709997 Henry Cohn, 2026, needs more optimization.
12 967 0.545105699926 Henry Cohn, 2026, needs more optimization.
12 968 0.545258959961 Henry Cohn, 2026, needs more optimization.
12 969 0.545465944321 Henry Cohn, 2026, needs more optimization.
12 970 0.545514344234 Henry Cohn, 2026, needs more optimization.
12 971 0.545637491023 Henry Cohn, 2026, needs more optimization.
12 972 0.545746797989 Henry Cohn, 2026, needs more optimization.
12 973 0.545940340333 Henry Cohn, 2026, needs more optimization.
12 974 0.546140088980 Henry Cohn, 2026, needs more optimization.
12 975 0.546278317837 Henry Cohn, 2026, needs more optimization.
12 976 0.546406415595 Henry Cohn, 2026, needs more optimization.
12 977 0.546561957048 Henry Cohn, 2026, needs more optimization.
12 978 0.546679145299 Henry Cohn, 2026, needs more optimization.
12 979 0.546797306202 Henry Cohn, 2026, needs more optimization.
12 980 0.546881677520 Henry Cohn, 2026, needs more optimization.
12 981 0.547056376935 Henry Cohn, 2026, needs more optimization.
12 982 0.547128102188 Henry Cohn, 2026, needs more optimization.
12 983 0.547271068965 Henry Cohn, 2026, needs more optimization.
12 984 0.547424315684 Henry Cohn, 2026, needs more optimization.
12 985 0.547589029236 Henry Cohn, 2026, needs more optimization.
12 986 0.547720710010 Henry Cohn, 2026, needs more optimization.
12 987 0.547805661831 Henry Cohn, 2026, needs more optimization.
12 988 0.547925225576 Henry Cohn, 2026, needs more optimization.
12 989 0.548057067492 Henry Cohn, 2026, needs more optimization.
12 990 0.548092766908 Henry Cohn, 2026, needs more optimization.
12 991 0.548250628336 Henry Cohn, 2026, needs more optimization.
12 992 0.548354896839 Henry Cohn, 2026, needs more optimization.
12 993 0.548488250106 Henry Cohn, 2026, needs more optimization.
12 994 0.548668901437 Henry Cohn, 2026, needs more optimization.
12 995 0.548766594601 Henry Cohn, 2026, needs more optimization.
12 996 0.548983876292 Henry Cohn, 2026, needs more optimization.
12 997 0.549088714551 Henry Cohn, 2026, needs more optimization.
12 998 0.549248065974 Henry Cohn, 2026, needs more optimization.
12 999 0.549410826094 Henry Cohn, 2026, needs more optimization.
12 1000 0.549628447908 Henry Cohn, 2026, needs more optimization.
12 1001 0.549724952380 Henry Cohn, 2026, needs more optimization.
12 1002 0.549956536963 Henry Cohn, 2026, needs more optimization.
12 1003 0.550043382930 Henry Cohn, 2026, needs more optimization.
12 1004 0.550212621994 Henry Cohn, 2026, needs more optimization.
12 1005 0.550292591159 Henry Cohn, 2026, needs more optimization.
12 1006 0.550400534290 Henry Cohn, 2026, needs more optimization.
12 1007 0.550491690327 Henry Cohn, 2026, needs more optimization.
12 1008 0.550645384584 Henry Cohn, 2026, needs more optimization.
12 1009 0.550769314782 Henry Cohn, 2026, needs more optimization.
12 1010 0.550959554210 Henry Cohn, 2026, needs more optimization.
12 1011 0.551078288506 Henry Cohn, 2026, needs more optimization.
12 1012 0.551140861273 Henry Cohn, 2026, needs more optimization.
12 1013 0.551321724990 Henry Cohn, 2026, needs more optimization.
12 1014 0.551400734147 Henry Cohn, 2026, needs more optimization.
12 1015 0.551484808154 Henry Cohn, 2026, needs more optimization.
12 1016 0.551691138757 Henry Cohn, 2026, needs more optimization.
12 1017 0.551783495972 Henry Cohn, 2026, needs more optimization.
12 1018 0.551883370442 Henry Cohn, 2026, needs more optimization.
12 1019 0.552088547813 Henry Cohn, 2026, needs more optimization.
12 1020 0.552208759054 Henry Cohn, 2026, needs more optimization.
12 1021 0.552341894026 Henry Cohn, 2026, needs more optimization.
12 1022 0.552443197978 Henry Cohn, 2026, needs more optimization.
12 1023 0.552565631807 Henry Cohn, 2026, needs more optimization.
12 1024 0.552791951280 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 0.147908234060 Henry Cohn, 2024.
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 59 0.180540658957 Henry Cohn, 2024.
13 60 0.184387527775 Henry Cohn, 2026.
13 61 0.189130618757 Henry Cohn, 2026.
13 62 0.189939244395 Henry Cohn, 2026.
13 63 0.193274783328 Henry Cohn, 2026.
13 64 0.194849252724 Henry Cohn, 2026.
13 65 0.198937958705 Henry Cohn, 2026.
13 66 0.201499955088 Henry Cohn, 2026.
13 67 0.204059765290 Henry Cohn, 2026.
13 68 0.207236674050 Henry Cohn, 2026.
13 69 0.207586830581 Henry Cohn, 2026, needs more optimization.
13 70 0.210761730652 Henry Cohn, 2026, needs more optimization.
13 71 0.212574330623 Henry Cohn, 2025.
13 72 0.214183844238 Henry Cohn, 2025.
13 73 0.216144695979 Henry Cohn, 2026, needs more optimization.
13 74 0.217555077772 Henry Cohn, 2026, needs more optimization.
13 75 0.219796325248 Henry Cohn, 2026, needs more optimization.
13 76 0.222090008822 Henry Cohn, 2026, needs more optimization.
13 77 0.224126205707 Henry Cohn, 2026, needs more optimization.
13 78 0.226253188923 Henry Cohn, 2026, needs more optimization.
13 79 0.228139500103 Henry Cohn, 2026, needs more optimization.
13 80 0.230720126963 Henry Cohn, 2026, needs more optimization.
13 81 0.232720216127 Henry Cohn, 2024, needs more optimization.
13 82 0.234406900251 Henry Cohn, 2026, needs more optimization.
13 83 0.236560164014 Henry Cohn, 2026, needs more optimization.
13 84 0.238093292122 Henry Cohn, 2026, needs more optimization.
13 85 0.239148109868 Henry Cohn, 2026, needs more optimization.
13 86 0.240112147390 Henry Cohn, 2026, needs more optimization.
13 88 0.240727955896 Henry Cohn, 2026, needs more optimization.
13 89 0.240921783853 Henry Cohn, 2026, needs more optimization.
13 90 0.241064336792 Henry Cohn, 2026, needs more optimization.
13 91 0.242907765867 Henry Cohn, 2026, needs more optimization.
13 92 0.244035582683 Henry Cohn, 2026, needs more optimization.
13 93 0.244060811263 Henry Cohn, 2026, needs more optimization.
13 94 0.244143161935 Henry Cohn, 2026, needs more optimization.
13 95 0.244218966023 Henry Cohn, 2026, needs more optimization.
13 96 0.244332030973 Henry Cohn, 2026, needs more optimization.
13 97 0.244403639639 Henry Cohn, 2026, needs more optimization.
13 98 0.244475717847 Henry Cohn, 2026, needs more optimization.
13 99 0.245960286072 Henry Cohn, 2026, needs more optimization.
13 100 0.246850479486 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 0.257876424884 Henry Cohn, 2026, needs more optimization.
13 108 0.258199839838 Henry Cohn, 2026, needs more optimization.
13 109 0.258970157326 Henry Cohn, 2026, needs more optimization.
13 110 0.259443423972 Henry Cohn, 2026, needs more optimization.
13 111 0.259780906598 Henry Cohn, 2026, needs more optimization.
13 112 0.261425518546 Henry Cohn, 2026, needs more optimization.
13 113 0.263324743751 Henry Cohn, 2026, needs more optimization.
13 114 0.263499560835 Henry Cohn, 2026, needs more optimization.
13 115 0.264241092166 Henry Cohn, 2026, needs more optimization.
13 116 0.266807071352 Henry Cohn, 2026, needs more optimization.
13 117 0.270006866946 Henry Cohn, 2026, needs more optimization.
13 118 0.271227692762 Henry Cohn, 2026, needs more optimization.
13 119 0.271262787956 Henry Cohn, 2026, needs more optimization.
13 120 0.271263742530 Henry Cohn, 2026, needs more optimization.
13 121 0.272530440185 Henry Cohn, 2026, needs more optimization.
13 122 0.273634133394 Henry Cohn, 2026, needs more optimization.
13 123 0.274832946315 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 0.277661676441 Henry Cohn, 2026, needs more optimization.
13 127 0.279707056804 Henry Cohn, 2026, needs more optimization.
13 128 0.281299667372 Henry Cohn, 2026, needs more optimization.
13 129 0.282635821143 Henry Cohn, 2026, needs more optimization.
13 130 0.284588341922 Henry Cohn, 2026, needs more optimization.
13 131 0.286350335601 Henry Cohn, 2026, needs more optimization.
13 132 0.287411319135 Henry Cohn, 2026, needs more optimization.
13 133 0.287752207800 Henry Cohn, 2026, needs more optimization.
13 134 0.288493448552 Henry Cohn, 2026, needs more optimization.
13 135 0.289071822702 Henry Cohn, 2026, needs more optimization.
13 136 0.291030440732 Henry Cohn, 2026, needs more optimization.
13 137 0.292414187026 Henry Cohn, 2026, needs more optimization.
13 138 0.294565632057 Henry Cohn, 2026, needs more optimization.
13 139 0.296093686138 Henry Cohn, 2026, needs more optimization.
13 140 0.296826554354 Henry Cohn, 2026, needs more optimization.
13 141 0.297416698816 Henry Cohn, 2026, needs more optimization.
13 142 0.297506513766 Henry Cohn, 2026, needs more optimization.
13 143 0.297664510854 Henry Cohn, 2026, needs more optimization.
13 144 0.299245120098 Henry Cohn, 2026, needs more optimization.
13 145 0.300763460201 Henry Cohn, 2026, needs more optimization.
13 146 0.300800624144 Henry Cohn, 2026, needs more optimization.
13 147 0.300831639827 Henry Cohn, 2026, needs more optimization.
13 148 0.300834705383 Henry Cohn, 2026, needs more optimization.
13 149 0.300898137213 Henry Cohn, 2026, needs more optimization.
13 150 0.300977858049 Henry Cohn, 2026, needs more optimization.
13 151 0.301155400477 Henry Cohn, 2026, needs more optimization.
13 152 0.302252570133 Henry Cohn, 2026, needs more optimization.
13 153 0.302857479333 Henry Cohn, 2026, needs more optimization.
13 154 0.305090112621 Henry Cohn, 2026, needs more optimization.
13 155 0.306480789288 Henry Cohn, 2026, needs more optimization.
13 156 0.307224073716 Henry Cohn, 2026, needs more optimization.
13 157 0.308898557616 Henry Cohn, 2026, needs more optimization.
13 158 0.309814270975 Henry Cohn, 2026, needs more optimization.
13 159 0.311409127223 Henry Cohn, 2026, needs more optimization.
13 160 0.311847196740 Henry Cohn, 2026, needs more optimization.
13 161 0.312208239084 Henry Cohn, 2026, needs more optimization.
13 162 0.312465819553 Henry Cohn, 2026, needs more optimization.
13 163 0.313081875958 Henry Cohn, 2026, needs more optimization.
13 164 0.314608209930 Henry Cohn, 2026, needs more optimization.
13 165 0.315540354127 Henry Cohn, 2026, needs more optimization.
13 166 0.316297136484 Henry Cohn, 2026, needs more optimization.
13 167 0.317126769601 Henry Cohn, 2026, needs more optimization.
13 168 0.317685191539 Henry Cohn, 2026, needs more optimization.
13 169 0.318109508605 Henry Cohn, 2026, needs more optimization.
13 170 0.319092702313 Henry Cohn, 2026, needs more optimization.
13 171 0.319597787380 Henry Cohn, 2026, needs more optimization.
13 172 0.319860385659 Henry Cohn, 2026, needs more optimization.
13 173 0.319926163418 Henry Cohn, 2026, needs more optimization.
13 174 0.320268819244 Henry Cohn, 2026, needs more optimization.
13 175 0.320809964183 Henry Cohn, 2026, needs more optimization.
13 176 0.320858023970 Henry Cohn, 2026, needs more optimization.
13 177 0.321422143489 Henry Cohn, 2026, needs more optimization.
13 178 0.321940666491 Henry Cohn, 2026, needs more optimization.
13 179 0.322682816284 Henry Cohn, 2026, needs more optimization.
13 180 0.323177697711 Henry Cohn, 2026, needs more optimization.
13 181 0.323555451509 Henry Cohn, 2026, needs more optimization.
13 182 0.324060683423 Henry Cohn, 2026, needs more optimization.
13 183 0.324673894358 Henry Cohn, 2026, needs more optimization.
13 184 0.324842823203 Henry Cohn, 2026, needs more optimization.
13 185 0.325422936165 Henry Cohn, 2026, needs more optimization.
13 186 0.326220945626 Henry Cohn, 2026, needs more optimization.
13 187 0.326420263713 Henry Cohn, 2026, needs more optimization.
13 188 0.326749806395 Henry Cohn, 2026, needs more optimization.
13 189 0.326982479141 Henry Cohn, 2026, needs more optimization.
13 190 0.327311156024 Henry Cohn, 2026, needs more optimization.
13 191 0.327712888099 Henry Cohn, 2026, needs more optimization.
13 192 0.328076766427 Henry Cohn, 2026, needs more optimization.
13 193 0.328096737225 Henry Cohn, 2026, needs more optimization.
13 194 0.328300601009 Henry Cohn, 2026, needs more optimization.
13 195 0.328491225633 Henry Cohn, 2026, needs more optimization.
13 196 0.328735892867 Henry Cohn, 2026, needs more optimization.
13 197 0.328873725222 Henry Cohn, 2026, needs more optimization.
13 198 0.328997840395 Henry Cohn, 2026, needs more optimization.
13 199 0.329142755030 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 0.329690749783 Henry Cohn, 2026, needs more optimization.
13 203 0.332319785680 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 0.350454981739 Henry Cohn, 2026, needs more optimization.
13 210 0.351579072152 Henry Cohn, 2026, needs more optimization.
13 211 0.352249768604 Henry Cohn, 2026, needs more optimization.
13 212 0.352778178506 Henry Cohn, 2026, needs more optimization.
13 213 0.353908968586 Henry Cohn, 2026, needs more optimization.
13 214 0.354466062746 Henry Cohn, 2026, needs more optimization.
13 215 0.355369398106 Henry Cohn, 2026, needs more optimization.
13 216 0.355724884701 Henry Cohn, 2026, needs more optimization.
13 217 0.356435440078 Henry Cohn, 2026, needs more optimization.
13 218 0.357592618572 Henry Cohn, 2026, needs more optimization.
13 219 0.358097921079 Henry Cohn, 2026, needs more optimization.
13 220 0.358852636053 Henry Cohn, 2026, needs more optimization.
13 221 0.359893496845 Henry Cohn, 2026, needs more optimization.
13 222 0.360492360520 Henry Cohn, 2026, needs more optimization.
13 223 0.361604733708 Henry Cohn, 2026, needs more optimization.
13 224 0.362377899749 Henry Cohn, 2026, needs more optimization.
13 225 0.363360940064 Henry Cohn, 2026, needs more optimization.
13 226 0.364025150140 Henry Cohn, 2026, needs more optimization.
13 227 0.364774604723 Henry Cohn, 2026, needs more optimization.
13 228 0.365434943660 Henry Cohn, 2026, needs more optimization.
13 229 0.366367041287 Henry Cohn, 2026, needs more optimization.
13 230 0.366888670744 Henry Cohn, 2026, needs more optimization.
13 231 0.367686450660 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 0.371962426867 Henry Cohn, 2026, needs more optimization.
13 248 0.373096758526 Henry Cohn, 2026, needs more optimization.
13 249 0.373120782514 Henry Cohn, 2026, needs more optimization.
13 250 0.374755610167 Henry Cohn, 2026, needs more optimization.
13 251 0.375548004516 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 0.380277700703 Henry Cohn, 2026, needs more optimization.
13 293 0.380292762255 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.
13 294 0.382527252901 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.
13 295 0.383359035137 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.
13 296 0.383950542495 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.
13 306 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 0.389015639892 Henry Cohn, 2026, needs more optimization.
13 315 0.391821251072 Henry Cohn, 2026, needs more optimization.
13 316 0.393363489387 Henry Cohn, 2026, needs more optimization.
13 317 0.393965510405 Henry Cohn, 2026, needs more optimization.
13 318 0.395166322614 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 0.396151717794 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 0.396820139584 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 0.397924181775 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 0.398267614996 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 0.405646182494 Henry Cohn, 2026, needs more optimization.
13 341 0.407423163632 Henry Cohn, 2026, needs more optimization.
13 342 0.407615248683 Henry Cohn, 2026, needs more optimization.
13 343 0.407670567273 Henry Cohn, 2026, needs more optimization.
13 344 0.408195385426 Henry Cohn, 2026, needs more optimization.
13 345 0.408406686764 Henry Cohn, 2026, needs more optimization.
13 346 0.408743603002 Henry Cohn, 2026, needs more optimization.
13 347 0.409553964126 Henry Cohn, 2026, needs more optimization.
13 348 0.410347763276 Henry Cohn, 2026, needs more optimization.
13 349 0.410734760241 Henry Cohn, 2026, needs more optimization.
13 350 0.410951561390 Henry Cohn, 2026, needs more optimization.
13 351 0.411013378219 Henry Cohn, 2026, needs more optimization.
13 352 0.411782645082 Henry Cohn, 2026, needs more optimization.
13 353 0.412569232321 Henry Cohn, 2026, needs more optimization.
13 354 0.413367493752 Henry Cohn, 2026, needs more optimization.
13 355 0.414005915587 Henry Cohn, 2026, needs more optimization.
13 356 0.414626271339 Henry Cohn, 2026, needs more optimization.
13 357 0.415109793583 Henry Cohn, 2026, needs more optimization.
13 358 0.415660746151 Henry Cohn, 2026, needs more optimization.
13 359 0.416145224833 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 0.419650686961 Henry Cohn, 2026, needs more optimization.
13 385 0.420779354814 Henry Cohn, 2026, needs more optimization.
13 386 0.421212816064 Henry Cohn, 2026, needs more optimization.
13 387 0.421627415138 Henry Cohn, 2026, needs more optimization.
13 388 0.422337006704 Henry Cohn, 2026, needs more optimization.
13 389 0.423844132653 Henry Cohn, 2026, needs more optimization.
13 390 0.424234065873 Henry Cohn, 2026, needs more optimization.
13 391 0.424708750709 Henry Cohn, 2026, needs more optimization.
13 392 0.425210980512 Henry Cohn, 2026, needs more optimization.
13 393 0.425974047888 Henry Cohn, 2026, needs more optimization.
13 394 0.426559591508 Henry Cohn, 2026, needs more optimization.
13 395 0.427211140829 Henry Cohn, 2026, needs more optimization.
13 396 0.427844806179 Henry Cohn, 2026, needs more optimization.
13 397 0.427912220550 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 0.429497489265 Henry Cohn, 2026, needs more optimization.
13 501 0.429604828931 Henry Cohn, 2026, needs more optimization.
13 502 0.429675657984 Henry Cohn, 2026, needs more optimization.
13 503 0.429681978125 Henry Cohn, 2026, needs more optimization.
13 504 0.429704831933 Henry Cohn, 2026, needs more optimization.
13 505 0.436915845106 Henry Cohn, 2026, needs more optimization.
13 506 0.439536735008 Henry Cohn, 2026, needs more optimization.
13 507 0.441387911536 Henry Cohn, 2026, needs more optimization.
13 508 0.441576592717 Henry Cohn, 2026, needs more optimization.
13 509 0.441591301842 Henry Cohn, 2026, needs more optimization.
13 510 0.441608953300 Henry Cohn, 2026, needs more optimization.
13 511 0.441624786000 Henry Cohn, 2026, needs more optimization.
13 513 0.441652133822 Henry Cohn, 2026, needs more optimization.
13 514 0.441661234440 Henry Cohn, 2026, needs more optimization.
13 515 0.441667175035 Henry Cohn, 2026, needs more optimization.
13 516 0.441672484457 Henry Cohn, 2026, needs more optimization.
13 517 0.441853280140 Henry Cohn, 2026, needs more optimization.
13 518 0.441883017344 Henry Cohn, 2026, needs more optimization.
13 519 0.442278843298 Henry Cohn, 2026, needs more optimization.
13 520 0.442292513742 Henry Cohn, 2026, needs more optimization.
13 521 0.446609059323 Henry Cohn, 2026, needs more optimization.
13 522 0.446683337910 Henry Cohn, 2026, needs more optimization.
13 523 0.446700945759 Henry Cohn, 2026, needs more optimization.
13 524 0.446714235282 Henry Cohn, 2026, needs more optimization.
13 525 0.446714235435 Henry Cohn, 2026, needs more optimization.
13 528 0.446732031693 Henry Cohn, 2026, needs more optimization.
13 529 0.446732503553 Henry Cohn, 2026, needs more optimization.
13 530 0.446742501623 Henry Cohn, 2026, needs more optimization.
13 536 0.447375039389 Henry Cohn, 2026, needs more optimization.
13 537 0.447389887407 Henry Cohn, 2026, needs more optimization.
13 538 0.447402199286 Henry Cohn, 2026, needs more optimization.
13 539 0.447737302571 Henry Cohn, 2026, needs more optimization.
13 540 0.447758374439 Henry Cohn, 2026, needs more optimization.
13 541 0.448190517220 Henry Cohn, 2026, needs more optimization.
13 542 0.448642330104 Henry Cohn, 2026, needs more optimization.
13 543 0.448659073858 Henry Cohn, 2026, needs more optimization.
13 544 0.448701613028 Henry Cohn, 2026, needs more optimization.
13 546 0.448709737596 Henry Cohn, 2026, needs more optimization.
13 547 0.448738722143 Henry Cohn, 2026, needs more optimization.
13 548 0.449054681379 Henry Cohn, 2026, needs more optimization.
13 549 0.449063626681 Henry Cohn, 2026, needs more optimization.
13 550 0.449074711591 Henry Cohn, 2026, needs more optimization.
13 551 0.449406182916 Henry Cohn, 2026, needs more optimization.
13 552 0.449406198806 Henry Cohn, 2026, needs more optimization.
13 553 0.449418691157 Henry Cohn, 2026, needs more optimization.
13 554 0.449428947235 Henry Cohn, 2026, needs more optimization.
13 555 0.449428962187 Henry Cohn, 2026, needs more optimization.
13 556 0.449428962336 Henry Cohn, 2026, needs more optimization.
13 557 0.449452051084 Henry Cohn, 2026, needs more optimization.
13 561 0.450074917508 Henry Cohn, 2026, needs more optimization.
13 562 0.450079412230 Henry Cohn, 2026, needs more optimization.
13 563 0.450665309000 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 0.458825178501 Henry Cohn, 2026, needs more optimization.
13 580 0.458838666869 Henry Cohn, 2026, needs more optimization.
13 581 0.458841608983 Henry Cohn, 2026, needs more optimization.
13 582 0.458841791409 Henry Cohn, 2026, needs more optimization.
13 583 0.458853108560 Henry Cohn, 2026, needs more optimization.
13 584 0.458860373279 Henry Cohn, 2026, needs more optimization.
13 585 0.458888891004 Henry Cohn, 2026, needs more optimization.
13 586 0.458912910414 Henry Cohn, 2026, needs more optimization.
13 587 0.459815448977 Henry Cohn, 2026, needs more optimization.
13 588 0.459825463586 Henry Cohn, 2026, needs more optimization.
13 589 0.459830899219 Henry Cohn, 2026, needs more optimization.
13 590 0.459849731385 Henry Cohn, 2026, needs more optimization.
13 591 0.459851949458 Henry Cohn, 2026, needs more optimization.
13 592 0.459906593672 Henry Cohn, 2026, needs more optimization.
13 593 0.461566095149 Henry Cohn, 2026, needs more optimization.
13 594 0.461596788092 Henry Cohn, 2026, needs more optimization.
13 595 0.462296178990 Henry Cohn, 2026, needs more optimization.
13 596 0.462998175460 Henry Cohn, 2026, needs more optimization.
13 597 0.463694606325 Henry Cohn, 2026, needs more optimization.
13 598 0.464213654281 Henry Cohn, 2026, needs more optimization.
13 599 0.464702354529 Henry Cohn, 2026, needs more optimization.
13 600 0.465428637470 Henry Cohn, 2026, needs more optimization.
13 601 0.465921439572 Henry Cohn, 2026, needs more optimization.
13 602 0.466226330720 Henry Cohn, 2026, needs more optimization.
13 603 0.466261507343 Henry Cohn, 2026, needs more optimization.
13 604 0.466281908108 Henry Cohn, 2026, needs more optimization.
13 605 0.466374806589 Henry Cohn, 2026, needs more optimization.
13 606 0.466440635383 Henry Cohn, 2026, needs more optimization.
13 607 0.466448721479 Henry Cohn, 2026, needs more optimization.
13 608 0.466518351729 Henry Cohn, 2026, needs more optimization.
13 609 0.466536198659 Henry Cohn, 2026, needs more optimization.
13 610 0.466542167180 Henry Cohn, 2026, needs more optimization.
13 611 0.466551379984 Henry Cohn, 2026, needs more optimization.
13 612 0.466561941535 Henry Cohn, 2026, needs more optimization.
13 613 0.466632651850 Henry Cohn, 2026, needs more optimization.
13 614 0.466637210507 Henry Cohn, 2026, needs more optimization.
13 615 0.466842516588 Henry Cohn, 2026, needs more optimization.
13 616 0.466910719925 Henry Cohn, 2026, needs more optimization.
13 617 0.466912825881 Henry Cohn, 2026, needs more optimization.
13 618 0.467042358968 Henry Cohn, 2026, needs more optimization.
13 619 0.467064855399 Henry Cohn, 2026, needs more optimization.
13 620 0.467142065481 Henry Cohn, 2026, needs more optimization.
13 621 0.467178895935 Henry Cohn, 2026, needs more optimization.
13 622 0.467209837810 Henry Cohn, 2026, needs more optimization.
13 623 0.467284761217 Henry Cohn, 2026, needs more optimization.
13 624 0.467302160560 Henry Cohn, 2026, needs more optimization.
13 625 0.467324460949 Henry Cohn, 2026, needs more optimization.
13 626 0.467367414065 Henry Cohn, 2026, needs more optimization.
13 627 0.467464936813 Henry Cohn, 2026, needs more optimization.
13 628 0.467541880183 Henry Cohn, 2026, needs more optimization.
13 629 0.467680840533 Henry Cohn, 2026, needs more optimization.
13 630 0.467693510331 Henry Cohn, 2026, needs more optimization.
13 631 0.469224245324 Henry Cohn, 2026, needs more optimization.
13 632 0.469485305599 Henry Cohn, 2026, needs more optimization.
13 633 0.470314712699 Henry Cohn, 2026, needs more optimization.
13 634 0.470985811279 Henry Cohn, 2026, needs more optimization.
13 635 0.471595944680 Henry Cohn, 2026, needs more optimization.
13 636 0.472070076801 Henry Cohn, 2026, needs more optimization.
13 637 0.472525643399 Henry Cohn, 2026, needs more optimization.
13 638 0.473155746228 Henry Cohn, 2026, needs more optimization.
13 639 0.473603444501 Henry Cohn, 2026, needs more optimization.
13 640 0.474114156130 Henry Cohn, 2026, needs more optimization.
13 641 0.474365385658 Henry Cohn, 2026, needs more optimization.
13 642 0.474909163146 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 0.476810631759 Henry Cohn, 2026, needs more optimization.
13 648 0.477170653689 Henry Cohn, 2026, needs more optimization.
13 649 0.477413231440 Henry Cohn, 2026, needs more optimization.
13 650 0.477679280302 Henry Cohn, 2026, needs more optimization.
13 651 0.477832074342 Henry Cohn, 2026, needs more optimization.
13 652 0.477953073630 Henry Cohn, 2026, needs more optimization.
13 653 0.478129266405 Henry Cohn, 2026, needs more optimization.
13 654 0.478246084389 Henry Cohn, 2026, needs more optimization.
13 655 0.478404018580 Henry Cohn, 2026, needs more optimization.
13 656 0.478534832747 Henry Cohn, 2026, needs more optimization.
13 657 0.478697293434 Henry Cohn, 2026, needs more optimization.
13 658 0.478812533942 Henry Cohn, 2026, needs more optimization.
13 659 0.478976727640 Henry Cohn, 2026, needs more optimization.
13 660 0.479189991799 Henry Cohn, 2026, needs more optimization.
13 661 0.479297903196 Henry Cohn, 2026, needs more optimization.
13 662 0.479440690477 Henry Cohn, 2026, needs more optimization.
13 663 0.479590618911 Henry Cohn, 2026, needs more optimization.
13 664 0.479699060197 Henry Cohn, 2026, needs more optimization.
13 665 0.479832617739 Henry Cohn, 2026, needs more optimization.
13 666 0.479907964874 Henry Cohn, 2026, needs more optimization.
13 667 0.480040464227 Henry Cohn, 2026, needs more optimization.
13 668 0.480167454714 Henry Cohn, 2026, needs more optimization.
13 669 0.480333876468 Henry Cohn, 2026, needs more optimization.
13 670 0.480512249374 Henry Cohn, 2026, needs more optimization.
13 671 0.480661629935 Henry Cohn, 2026, needs more optimization.
13 672 0.480731423868 Henry Cohn, 2026, needs more optimization.
13 673 0.480866449005 Henry Cohn, 2026, needs more optimization.
13 674 0.480969043258 Henry Cohn, 2026, needs more optimization.
13 675 0.481094051655 Henry Cohn, 2026, needs more optimization.
13 676 0.481207400644 Henry Cohn, 2026, needs more optimization.
13 677 0.481320417241 Henry Cohn, 2026, needs more optimization.
13 678 0.481382522361 Henry Cohn, 2026, needs more optimization.
13 679 0.482034523058 Henry Cohn, 2026, needs more optimization.
13 680 0.482129541047 Henry Cohn, 2026, needs more optimization.
13 681 0.482157180327 Henry Cohn, 2026, needs more optimization.
13 682 0.482321965975 Henry Cohn, 2026, needs more optimization.
13 683 0.482459473100 Henry Cohn, 2026, needs more optimization.
13 684 0.482465908238 Henry Cohn, 2026, needs more optimization.
13 686 0.482472119113 Henry Cohn, 2026, needs more optimization.
13 687 0.482477682148 Henry Cohn, 2026, needs more optimization.
13 688 0.482477682181 Henry Cohn, 2026, needs more optimization.
13 689 0.482504661676 Henry Cohn, 2026, needs more optimization.
13 690 0.482511367158 Henry Cohn, 2026, needs more optimization.
13 691 0.482512081492 Henry Cohn, 2026, needs more optimization.
13 692 0.482937898440 Henry Cohn, 2026, needs more optimization.
13 693 0.483015926759 Henry Cohn, 2026, needs more optimization.
13 694 0.483135871315 Henry Cohn, 2026, needs more optimization.
13 695 0.483300311341 Henry Cohn, 2026, needs more optimization.
13 696 0.483417974343 Henry Cohn, 2026, needs more optimization.
13 697 0.483527622392 Henry Cohn, 2026, needs more optimization.
13 698 0.483792882414 Henry Cohn, 2026, needs more optimization.
13 699 0.483916988677 Henry Cohn, 2026, needs more optimization.
13 700 0.483984205222 Henry Cohn, 2026, needs more optimization.
13 701 0.484213051236 Henry Cohn, 2026, needs more optimization.
13 702 0.484245851974 Henry Cohn, 2026, needs more optimization.
13 703 0.484294032211 Henry Cohn, 2026, needs more optimization.
13 704 0.484307885267 Henry Cohn, 2026, needs more optimization.
13 705 0.484317615946 Henry Cohn, 2026, needs more optimization.
13 706 0.484364814133 Henry Cohn, 2026, needs more optimization.
13 707 0.484475821466 Henry Cohn, 2026, needs more optimization.
13 708 0.484570986910 Henry Cohn, 2026, needs more optimization.
13 709 0.484672280511 Henry Cohn, 2026, needs more optimization.
13 710 0.484732956922 Henry Cohn, 2026, needs more optimization.
13 711 0.484745019472 Henry Cohn, 2026, needs more optimization.
13 712 0.484745022183 Henry Cohn, 2026, needs more optimization.
13 713 0.484745024074 Henry Cohn, 2026, needs more optimization.
13 714 0.484774728633 Henry Cohn, 2026, needs more optimization.
13 715 0.484781819623 Henry Cohn, 2026, needs more optimization.
13 716 0.484840860411 Henry Cohn, 2026, needs more optimization.
13 717 0.484860827531 Henry Cohn, 2026, needs more optimization.
13 718 0.484864293656 Henry Cohn, 2026, needs more optimization.
13 719 0.484903219950 Henry Cohn, 2026, needs more optimization.
13 720 0.484907377245 Henry Cohn, 2026, needs more optimization.
13 721 0.484917036070 Henry Cohn, 2026, needs more optimization.
13 722 0.484930101040 Henry Cohn, 2026, needs more optimization.
13 723 0.484937061112 Henry Cohn, 2026, needs more optimization.
13 724 0.484946085509 Henry Cohn, 2026, needs more optimization.
13 725 0.484956519275 Henry Cohn, 2026, needs more optimization.
13 726 0.485557227458 Henry Cohn, 2026, needs more optimization.
13 727 0.485572558395 Henry Cohn, 2026, needs more optimization.
13 728 0.485647724037 Henry Cohn, 2026, needs more optimization.
13 729 0.485733074007 Henry Cohn, 2026, needs more optimization.
13 730 0.485806183298 Henry Cohn, 2026, needs more optimization.
13 731 0.485824018455 Henry Cohn, 2026, needs more optimization.
13 732 0.485880530214 Henry Cohn, 2026, needs more optimization.
13 733 0.485955640470 Henry Cohn, 2026, needs more optimization.
13 734 0.486018176151 Henry Cohn, 2026, needs more optimization.
13 735 0.486129097745 Henry Cohn, 2026, needs more optimization.
13 736 0.486177844983 Henry Cohn, 2026, needs more optimization.
13 737 0.486246825057 Henry Cohn, 2026, needs more optimization.
13 738 0.486275777522 Henry Cohn, 2026, needs more optimization.
13 739 0.486376911437 Henry Cohn, 2026, needs more optimization.
13 740 0.486376911803 Henry Cohn, 2026, needs more optimization.
13 741 0.486432714505 Henry Cohn, 2026, needs more optimization.
13 742 0.486468576479 Henry Cohn, 2026, needs more optimization.
13 743 0.486520791000 Henry Cohn, 2026, needs more optimization.
13 744 0.486625143550 Henry Cohn, 2026, needs more optimization.
13 745 0.486685919232 Henry Cohn, 2026, needs more optimization.
13 746 0.486722097164 Henry Cohn, 2026, needs more optimization.
13 747 0.486737199584 Henry Cohn, 2026, needs more optimization.
13 748 0.486747739443 Henry Cohn, 2026, needs more optimization.
13 749 0.486802346261 Henry Cohn, 2026, needs more optimization.
13 750 0.486859018818 Henry Cohn, 2026, needs more optimization.
13 751 0.486947160280 Henry Cohn, 2026, needs more optimization.
13 752 0.487034368905 Henry Cohn, 2026, needs more optimization.
13 753 0.487152707815 Henry Cohn, 2026, needs more optimization.
13 754 0.487160606784 Henry Cohn, 2026, needs more optimization.
13 755 0.487174148290 Henry Cohn, 2026, needs more optimization.
13 756 0.487249457560 Henry Cohn, 2026, needs more optimization.
13 757 0.487302401048 Henry Cohn, 2026, needs more optimization.
13 758 0.487407698804 Henry Cohn, 2026, needs more optimization.
13 759 0.487441063908 Henry Cohn, 2026, needs more optimization.
13 760 0.487497749087 Henry Cohn, 2026, needs more optimization.
13 761 0.487614624126 Henry Cohn, 2026, needs more optimization.
13 762 0.487638789812 Henry Cohn, 2026, needs more optimization.
13 763 0.487683602920 Henry Cohn, 2026, needs more optimization.
13 764 0.487742816560 Henry Cohn, 2026, needs more optimization.
13 765 0.487751573646 Henry Cohn, 2026, needs more optimization.
13 766 0.487801916198 Henry Cohn, 2026, needs more optimization.
13 767 0.487895790515 Henry Cohn, 2026, needs more optimization.
13 768 0.487932734778 Henry Cohn, 2026, needs more optimization.
13 769 0.487993463779 Henry Cohn, 2026, needs more optimization.
13 770 0.487993463788 Henry Cohn, 2026, needs more optimization.
13 771 0.487993465374 Henry Cohn, 2026, needs more optimization.
13 772 0.488057023493 Henry Cohn, 2026, needs more optimization.
13 773 0.488093325552 Henry Cohn, 2026, needs more optimization.
13 774 0.488127074405 Henry Cohn, 2026, needs more optimization.
13 775 0.488215110476 Henry Cohn, 2026, needs more optimization.
13 776 0.488223531265 Henry Cohn, 2026, needs more optimization.
13 777 0.488292434094 Henry Cohn, 2026, needs more optimization.
13 778 0.488348852820 Henry Cohn, 2026, needs more optimization.
13 779 0.488388362749 Henry Cohn, 2026, needs more optimization.
13 780 0.488505690807 Henry Cohn, 2026, needs more optimization.
13 782 0.488540865231 Henry Cohn, 2026, needs more optimization.
13 783 0.488581055118 Henry Cohn, 2026, needs more optimization.
13 784 0.488675122500 Henry Cohn, 2026, needs more optimization.
13 785 0.488682880056 Henry Cohn, 2026, needs more optimization.
13 786 0.488756552929 Henry Cohn, 2026, needs more optimization.
13 787 0.488770496122 Henry Cohn, 2026, needs more optimization.
13 788 0.488859685410 Henry Cohn, 2026, needs more optimization.
13 789 0.488923815046 Henry Cohn, 2026, needs more optimization.
13 790 0.489039769478 Henry Cohn, 2026, needs more optimization.
13 791 0.489111207989 Henry Cohn, 2026, needs more optimization.
13 792 0.489144361962 Henry Cohn, 2026, needs more optimization.
13 793 0.489146491724 Henry Cohn, 2026, needs more optimization.
13 794 0.489146506036 Henry Cohn, 2026, needs more optimization.
13 795 0.489146523213 Henry Cohn, 2026, needs more optimization.
13 797 0.489146534191 Henry Cohn, 2026, needs more optimization.
13 798 0.489146547738 Henry Cohn, 2026, needs more optimization.
13 799 0.489150191378 Henry Cohn, 2026, needs more optimization.
13 800 0.489189841105 Henry Cohn, 2026, needs more optimization.
13 801 0.489198078620 Henry Cohn, 2026, needs more optimization.
13 802 0.489198080502 Henry Cohn, 2026, needs more optimization.
13 804 0.489236345973 Henry Cohn, 2026, needs more optimization.
13 805 0.489264956131 Henry Cohn, 2026, needs more optimization.
13 806 0.489279968382 Henry Cohn, 2026, needs more optimization.
13 807 0.489306132353 Henry Cohn, 2026, needs more optimization.
13 808 0.489306154064 Henry Cohn, 2026, needs more optimization.
13 809 0.489310953988 Henry Cohn, 2026, needs more optimization.
13 810 0.489310954181 Henry Cohn, 2026, needs more optimization.
13 811 0.489320338105 Henry Cohn, 2026, needs more optimization.
13 812 0.489320338168 Henry Cohn, 2026, needs more optimization.
13 813 0.489337166178 Henry Cohn, 2026, needs more optimization.
13 814 0.489337168574 Henry Cohn, 2026, needs more optimization.
13 815 0.489340546772 Henry Cohn, 2026, needs more optimization.
13 816 0.489352701814 Henry Cohn, 2026, needs more optimization.
13 817 0.489359640930 Henry Cohn, 2026, needs more optimization.
13 818 0.489360444706 Henry Cohn, 2026, needs more optimization.
13 819 0.490559651574 Henry Cohn, 2026, needs more optimization.
13 820 0.490727261822 Henry Cohn, 2026, needs more optimization.
13 821 0.490775313743 Henry Cohn, 2026, needs more optimization.
13 822 0.490833210561 Henry Cohn, 2026, needs more optimization.
13 823 0.490833217378 Henry Cohn, 2026, needs more optimization.
13 824 0.490869554021 Henry Cohn, 2026, needs more optimization.
13 825 0.490910836296 Henry Cohn, 2026, needs more optimization.
13 826 0.490952796411 Henry Cohn, 2026, needs more optimization.
13 827 0.490956534890 Henry Cohn, 2026, needs more optimization.
13 828 0.491041458823 Henry Cohn, 2026, needs more optimization.
13 829 0.491199353769 Henry Cohn, 2026, needs more optimization.
13 830 0.491245507245 Henry Cohn, 2026, needs more optimization.
13 831 0.491285943590 Henry Cohn, 2026, needs more optimization.
13 832 0.491355949301 Henry Cohn, 2026, needs more optimization.
13 833 0.491439093404 Henry Cohn, 2026, needs more optimization.
13 834 0.491461488761 Henry Cohn, 2026, needs more optimization.
13 835 0.491461519558 Henry Cohn, 2026, needs more optimization.
13 836 0.491521764770 Henry Cohn, 2026, needs more optimization.
13 837 0.491523449752 Henry Cohn, 2026, needs more optimization.
13 838 0.491623509115 Henry Cohn, 2026, needs more optimization.
13 839 0.491672462816 Henry Cohn, 2026, needs more optimization.
13 840 0.491694246086 Henry Cohn, 2026, needs more optimization.
13 841 0.491736051116 Henry Cohn, 2026, needs more optimization.
13 842 0.491756802645 Henry Cohn, 2026, needs more optimization.
13 843 0.491949050994 Henry Cohn, 2026, needs more optimization.
13 844 0.492045348475 Henry Cohn, 2026, needs more optimization.
13 845 0.492080440973 Henry Cohn, 2026, needs more optimization.
13 846 0.492109752532 Henry Cohn, 2026, needs more optimization.
13 847 0.492196067189 Henry Cohn, 2026, needs more optimization.
13 848 0.492298187438 Henry Cohn, 2026, needs more optimization.
13 849 0.492438856752 Henry Cohn, 2026, needs more optimization.
13 850 0.492646045254 Henry Cohn, 2026, needs more optimization.
13 851 0.492751163165 Henry Cohn, 2026, needs more optimization.
13 852 0.492825800726 Henry Cohn, 2026, needs more optimization.
13 856 0.492826538872 Henry Cohn, 2026, needs more optimization.
13 857 0.493226178829 Henry Cohn, 2026, needs more optimization.
13 858 0.493255270247 Henry Cohn, 2026, needs more optimization.
13 859 0.493273704908 Henry Cohn, 2026, needs more optimization.
13 860 0.493321568870 Henry Cohn, 2026, needs more optimization.
13 861 0.493372949674 Henry Cohn, 2026, needs more optimization.
13 862 0.493736220115 Henry Cohn, 2026, needs more optimization.
13 863 0.493825963776 Henry Cohn, 2026, needs more optimization.
13 864 0.493849511513 Henry Cohn, 2026, needs more optimization.
13 865 0.494237241693 Henry Cohn, 2026, needs more optimization.
13 866 0.494237244526 Henry Cohn, 2026, needs more optimization.
13 867 0.494262254027 Henry Cohn, 2026, needs more optimization.
13 868 0.494345933401 Henry Cohn, 2026, needs more optimization.
13 869 0.494723657217 Henry Cohn, 2026, needs more optimization.
13 870 0.494797886987 Henry Cohn, 2026, needs more optimization.
13 871 0.494903720589 Henry Cohn, 2026, needs more optimization.
13 872 0.495169245891 Henry Cohn, 2026, needs more optimization.
13 874 0.495256145697 Henry Cohn, 2026, needs more optimization.
13 875 0.495501417732 Henry Cohn, 2026, needs more optimization.
13 876 0.495504613703 Henry Cohn, 2026, needs more optimization.
13 877 0.495573980983 Henry Cohn, 2026, needs more optimization.
13 878 0.495578139343 Henry Cohn, 2026, needs more optimization.
13 879 0.495596388548 Henry Cohn, 2026, needs more optimization.
13 880 0.495636052096 Henry Cohn, 2026, needs more optimization.
13 881 0.495636251285 Henry Cohn, 2026, needs more optimization.
13 882 0.495636251287 Henry Cohn, 2026, needs more optimization.
13 883 0.497206698479 Henry Cohn, 2026, needs more optimization.
13 884 0.497267108991 Henry Cohn, 2026, needs more optimization.
13 885 0.497311301198 Henry Cohn, 2026, needs more optimization.
13 886 0.497423354138 Henry Cohn, 2026, needs more optimization.
13 887 0.497888428382 Henry Cohn, 2026, needs more optimization.
13 888 0.497924458314 Henry Cohn, 2026, needs more optimization.
13 889 0.497967922801 Henry Cohn, 2026, needs more optimization.
13 890 0.498482867982 Henry Cohn, 2026, needs more optimization.
13 891 0.498648422823 Henry Cohn, 2026, needs more optimization.
13 892 0.498803038299 Henry Cohn, 2026, needs more optimization.
13 893 0.499177561614 Henry Cohn, 2026, needs more optimization.
13 894 0.499395389629 Henry Cohn, 2026, needs more optimization.
13 895 0.499576129800 Henry Cohn, 2026, needs more optimization.
13 896 0.499705346351 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 0.191437503966 Henry Cohn, 2026, needs more optimization.
14 79 0.193295826526 Henry Cohn, 2026, needs more optimization.
14 80 0.195567887108 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 0.198449039643 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 0.219093745555 Henry Cohn, 2026, needs more optimization.
14 100 0.223682381813 Henry Cohn, 2026, needs more optimization.
14 101 0.225613148985 Henry Cohn, 2026, needs more optimization.
14 102 0.227325776888 Henry Cohn, 2026, needs more optimization.
14 103 0.228478286962 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.
14 112 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 0.240633273834 Henry Cohn, 2026, needs more optimization.
14 117 0.242107966247 Henry Cohn, 2026, needs more optimization.
14 118 0.243575589615 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 0.247981010333 Henry Cohn, 2026, needs more optimization.
14 123 0.249951572500 Henry Cohn, 2026, needs more optimization.
14 124 0.251242938878 Henry Cohn, 2026, needs more optimization.
14 125 0.252284925630 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 0.255999519127 Henry Cohn, 2026, needs more optimization.
14 131 0.258094827642 Henry Cohn, 2026, needs more optimization.
14 132 0.259498069700 Henry Cohn, 2026, needs more optimization.
14 133 0.261808031005 Henry Cohn, 2026, needs more optimization.
14 134 0.263524188501 Henry Cohn, 2026, needs more optimization.
14 135 0.265066394989 Henry Cohn, 2026, needs more optimization.
14 136 0.266894239553 Henry Cohn, 2026, needs more optimization.
14 137 0.268271970629 Henry Cohn, 2026, needs more optimization.
14 138 0.269360778102 Henry Cohn, 2026, needs more optimization.
14 139 0.269360778112 Henry Cohn, 2026, needs more optimization.
14 140 0.269363487446 Henry Cohn, 2026, needs more optimization.
14 141 0.269364653587 Henry Cohn, 2026, needs more optimization.
14 142 0.269374502318 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 0.269509625258 Henry Cohn, 2026, needs more optimization.
14 151 0.269752143836 Henry Cohn, 2026, needs more optimization.
14 152 0.269752143884 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 0.276372454661 Henry Cohn, 2026, needs more optimization.
14 158 0.276419043706 Henry Cohn, 2026, needs more optimization.
14 159 0.276645024948 Henry Cohn, 2026, needs more optimization.
14 160 0.276965031145 Henry Cohn, 2026, needs more optimization.
14 161 0.277324903367 Henry Cohn, 2026, needs more optimization.
14 162 0.277834331200 Henry Cohn, 2026, needs more optimization.
14 163 0.278239418479 Henry Cohn, 2026, needs more optimization.
14 164 0.278745364900 Henry Cohn, 2026, needs more optimization.
14 165 0.279342784941 Henry Cohn, 2026, needs more optimization.
14 166 0.280063078921 Henry Cohn, 2026, needs more optimization.
14 167 0.281212620023 Henry Cohn, 2026, needs more optimization.
14 168 0.285641948320 Henry Cohn, 2026, needs more optimization.
14 169 0.287714199955 Henry Cohn, 2026, needs more optimization.
14 170 0.288137077143 Henry Cohn, 2026, needs more optimization.
14 171 0.289702336931 Henry Cohn, 2026, needs more optimization.
14 172 0.290667732730 Henry Cohn, 2026, needs more optimization.
14 173 0.290952094444 Henry Cohn, 2026, needs more optimization.
14 174 0.292005285293 Henry Cohn, 2026, needs more optimization.
14 175 0.293051048978 Henry Cohn, 2026, needs more optimization.
14 176 0.293649344228 Henry Cohn, 2026, needs more optimization.
14 177 0.294408007268 Henry Cohn, 2026, needs more optimization.
14 178 0.295390516115 Henry Cohn, 2026, needs more optimization.
14 179 0.295920510792 Henry Cohn, 2026, needs more optimization.
14 180 0.296637418164 Henry Cohn, 2026, needs more optimization.
14 181 0.297697533488 Henry Cohn, 2026, needs more optimization.
14 182 0.297711417464 Henry Cohn, 2026, needs more optimization.
14 183 0.297832426062 Henry Cohn, 2026, needs more optimization.
14 184 0.298059359924 Henry Cohn, 2026, needs more optimization.
14 185 0.298565943101 Henry Cohn, 2026, needs more optimization.
14 186 0.299230671675 Henry Cohn, 2026, needs more optimization.
14 187 0.299620542942 Henry Cohn, 2026, needs more optimization.
14 188 0.300677796504 Henry Cohn, 2026, needs more optimization.
14 189 0.301661051776 Henry Cohn, 2026, needs more optimization.
14 190 0.301802276386 Henry Cohn, 2026, needs more optimization.
14 191 0.302343384163 Henry Cohn, 2026, needs more optimization.
14 192 0.303610833853 Henry Cohn, 2026, needs more optimization.
14 193 0.304411268923 Henry Cohn, 2026, needs more optimization.
14 194 0.305386004765 Henry Cohn, 2026, needs more optimization.
14 195 0.306373421454 Henry Cohn, 2026, needs more optimization.
14 196 0.307741272633 Henry Cohn, 2026, needs more optimization.
14 197 0.308798061437 Henry Cohn, 2026, needs more optimization.
14 198 0.309625125505 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 0.312453273428 Henry Cohn, 2026, needs more optimization.
14 202 0.313545756677 Henry Cohn, 2026, needs more optimization.
14 203 0.313776954541 Henry Cohn, 2026, needs more optimization.
14 204 0.313844484655 Henry Cohn, 2026, needs more optimization.
14 205 0.314016868165 Henry Cohn, 2026, needs more optimization.
14 206 0.314259532905 Henry Cohn, 2026, needs more optimization.
14 207 0.314609988339 Henry Cohn, 2026, needs more optimization.
14 208 0.315014350472 Henry Cohn, 2026, needs more optimization.
14 209 0.315343208191 Henry Cohn, 2026, needs more optimization.
14 210 0.315611107785 Henry Cohn, 2026, needs more optimization.
14 211 0.315963184461 Henry Cohn, 2026, needs more optimization.
14 212 0.316357184068 Henry Cohn, 2026, needs more optimization.
14 213 0.317118880630 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 0.318903206758 Henry Cohn, 2026, needs more optimization.
14 217 0.319499210791 Henry Cohn, 2026, needs more optimization.
14 218 0.320059442900 Henry Cohn, 2026, needs more optimization.
14 219 0.320688249607 Henry Cohn, 2026, needs more optimization.
14 220 0.321046761171 Henry Cohn, 2026, needs more optimization.
14 221 0.321539817567 Henry Cohn, 2026, needs more optimization.
14 222 0.321925427547 Henry Cohn, 2026, needs more optimization.
14 223 0.322282342892 Henry Cohn, 2026, needs more optimization.
14 224 0.322800155581 Henry Cohn, 2026, needs more optimization.
14 225 0.323217541574 Henry Cohn, 2026, needs more optimization.
14 226 0.324023941371 Henry Cohn, 2026, needs more optimization.
14 227 0.324628662392 Henry Cohn, 2026, needs more optimization.
14 228 0.325279292895 Henry Cohn, 2026, needs more optimization.
14 229 0.325854185657 Henry Cohn, 2026, needs more optimization.
14 230 0.326369546046 Henry Cohn, 2026, needs more optimization.
14 231 0.326895593598 Henry Cohn, 2026, needs more optimization.
14 232 0.327532648826 Henry Cohn, 2026, needs more optimization.
14 233 0.328696134765 Henry Cohn, 2026, needs more optimization.
14 234 0.329429684622 Henry Cohn, 2026, needs more optimization.
14 235 0.330547734813 Henry Cohn, 2026, needs more optimization.
14 236 0.331742173879 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
14 253 0.339417208755 Henry Cohn, 2026, needs more optimization.
14 254 0.339706467202 Henry Cohn, 2026, needs more optimization.
14 255 0.339728298549 Henry Cohn, 2026, needs more optimization.
14 256 0.339768345810 Henry Cohn, 2026, needs more optimization.
14 257 0.339787713711 Henry Cohn, 2026, needs more optimization.
14 258 0.339890083447 Henry Cohn, 2026, needs more optimization.
14 259 0.339988229573 Henry Cohn, 2026, needs more optimization.
14 260 0.347325597157 Henry Cohn, 2026, needs more optimization.
14 261 0.347352018865 Henry Cohn, 2026, needs more optimization.
14 262 0.347547728852 Henry Cohn, 2026, needs more optimization.
14 263 0.347743035918 Henry Cohn, 2026, needs more optimization.
14 264 0.348086610872 Henry Cohn, 2026, needs more optimization.
14 265 0.348210882064 Henry Cohn, 2026, needs more optimization.
14 266 0.348655096737 Henry Cohn, 2026, needs more optimization.
14 267 0.349031772848 Henry Cohn, 2026, needs more optimization.
14 268 0.349144807074 Henry Cohn, 2026, needs more optimization.
14 269 0.349221936204 Henry Cohn, 2026, needs more optimization.
14 270 0.349508784133 Henry Cohn, 2026, needs more optimization.
14 271 0.350077979599 Henry Cohn, 2026, needs more optimization.
14 272 0.350637009908 Henry Cohn, 2026, needs more optimization.
14 273 0.351123161000 Henry Cohn, 2026, needs more optimization.
14 274 0.351405979330 Henry Cohn, 2026, needs more optimization.
14 275 0.351663116737 Henry Cohn, 2026, needs more optimization.
14 276 0.352000803053 Henry Cohn, 2026, needs more optimization.
14 277 0.352287428076 Henry Cohn, 2026, needs more optimization.
14 278 0.352325281759 Henry Cohn, 2026, needs more optimization.
14 279 0.352631359610 Henry Cohn, 2026, needs more optimization.
14 280 0.352754627837 Henry Cohn, 2026, needs more optimization.
14 281 0.353074887517 Henry Cohn, 2026, needs more optimization.
14 282 0.353288499450 Henry Cohn, 2026, needs more optimization.
14 283 0.353565626557 Henry Cohn, 2026, needs more optimization.
14 284 0.353885793545 Henry Cohn, 2026, needs more optimization.
14 285 0.353933650593 Henry Cohn, 2026, needs more optimization.
14 286 0.354095506008 Henry Cohn, 2026, needs more optimization.
14 287 0.354181943851 Henry Cohn, 2026, needs more optimization.
14 288 0.354482881558 Henry Cohn, 2026, needs more optimization.
14 289 0.354533792302 Henry Cohn, 2026, needs more optimization.
14 290 0.354550309483 Henry Cohn, 2026, needs more optimization.
14 291 0.354604066572 Henry Cohn, 2026, needs more optimization.
14 292 0.354616987899 Henry Cohn, 2026, needs more optimization.
14 293 0.354693136376 Henry Cohn, 2026, needs more optimization.
14 294 0.354726871236 Henry Cohn, 2026, needs more optimization.
14 295 0.354851563871 Henry Cohn, 2026, needs more optimization.
14 296 0.354990841344 Henry Cohn, 2026, needs more optimization.
14 299 0.355067845419 Henry Cohn, 2026, needs more optimization.
14 301 0.355067852698 Henry Cohn, 2026, needs more optimization.
14 303 0.355067862218 Henry Cohn, 2026, needs more optimization.
14 313 0.355067862796 Henry Cohn, 2026, needs more optimization.
14 333 0.355068102202 Henry Cohn, 2026, needs more optimization.
14 335 0.355071028991 Henry Cohn, 2026, needs more optimization.
14 336 0.355119724789 Henry Cohn, 2026, needs more optimization.
14 337 0.355143691318 Henry Cohn, 2026, needs more optimization.
14 338 0.355176524992 Henry Cohn, 2026, needs more optimization.
14 339 0.355796639994 Henry Cohn, 2026, needs more optimization.
14 340 0.357434544513 Henry Cohn, 2026, needs more optimization.
14 341 0.358556735991 Henry Cohn, 2026, needs more optimization.
14 342 0.358560813489 Henry Cohn, 2026, needs more optimization.
14 343 0.358638751459 Henry Cohn, 2026, needs more optimization.
14 344 0.360083228013 Henry Cohn, 2026, needs more optimization.
14 345 0.360778578385 Henry Cohn, 2026, needs more optimization.
14 346 0.362869694167 Henry Cohn, 2026, needs more optimization.
14 347 0.365240791825 Henry Cohn, 2026, needs more optimization.
14 348 0.365661512821 Henry Cohn, 2026, needs more optimization.
14 349 0.366618556058 Henry Cohn, 2026, needs more optimization.
14 350 0.366922515607 Henry Cohn, 2026, needs more optimization.
14 351 0.367276813411 Henry Cohn, 2026, needs more optimization.
14 352 0.367366500423 Henry Cohn, 2026, needs more optimization.
14 353 0.368137126326 Henry Cohn, 2026, needs more optimization.
14 354 0.369522149931 Henry Cohn, 2026, needs more optimization.
14 355 0.370427132278 Henry Cohn, 2026, needs more optimization.
14 356 0.371165918388 Henry Cohn, 2026, needs more optimization.
14 357 0.372032801751 Henry Cohn, 2026, needs more optimization.
14 358 0.374088820841 Henry Cohn, 2026, needs more optimization.
14 359 0.374788167306 Henry Cohn, 2026, needs more optimization.
14 360 0.375252036707 Henry Cohn, 2026, needs more optimization.
14 361 0.377519025558 Henry Cohn, 2026, needs more optimization.
14 362 0.377537233046 Henry Cohn, 2026, needs more optimization.
14 363 0.377541625400 Henry Cohn, 2026, needs more optimization.
14 364 0.377561145244 Henry Cohn, 2026, needs more optimization.
14 365 0.377567951197 Henry Cohn, 2026, needs more optimization.
14 366 0.377601775512 Henry Cohn, 2026, needs more optimization.
14 367 0.377609394543 Henry Cohn, 2026, needs more optimization.
14 368 0.377623216390 Henry Cohn, 2026, needs more optimization.
14 369 0.377752156589 Henry Cohn, 2026, needs more optimization.
14 370 0.377908195831 Henry Cohn, 2026, needs more optimization.
14 371 0.378146951854 Henry Cohn, 2026, needs more optimization.
14 372 0.379332007897 Henry Cohn, 2026, needs more optimization.
14 373 0.379341805416 Henry Cohn, 2026, needs more optimization.
14 374 0.379351704125 Henry Cohn, 2026, needs more optimization.
14 375 0.379351932915 Henry Cohn, 2026, needs more optimization.
14 376 0.379403292184 Henry Cohn, 2026, needs more optimization.
14 377 0.381669364567 Henry Cohn, 2026, needs more optimization.
14 378 0.381669607842 Henry Cohn, 2026, needs more optimization.
14 379 0.381669659212 Henry Cohn, 2026, needs more optimization.
14 380 0.381683338851 Henry Cohn, 2026, needs more optimization.
14 381 0.381692169110 Henry Cohn, 2026, needs more optimization.
14 382 0.381694647801 Henry Cohn, 2026, needs more optimization.
14 383 0.381701701308 Henry Cohn, 2026, needs more optimization.
14 384 0.381704190403 Henry Cohn, 2026, needs more optimization.
14 385 0.381785013465 Henry Cohn, 2026, needs more optimization.
14 386 0.381813619711 Henry Cohn, 2026, needs more optimization.
14 387 0.381948902367 Henry Cohn, 2026, needs more optimization.
14 388 0.383679372994 Henry Cohn, 2026, needs more optimization.
14 389 0.384349061682 Henry Cohn, 2026, needs more optimization.
14 390 0.384736376123 Henry Cohn, 2026, needs more optimization.
14 391 0.385071397380 Henry Cohn, 2026, needs more optimization.
14 392 0.385185346220 Henry Cohn, 2026, needs more optimization.
14 393 0.385310389481 Henry Cohn, 2026, needs more optimization.
14 394 0.385395445344 Henry Cohn, 2026, needs more optimization.
14 395 0.385411174373 Henry Cohn, 2026, needs more optimization.
14 396 0.385437791166 Henry Cohn, 2026, needs more optimization.
14 397 0.385502071971 Henry Cohn, 2026, needs more optimization.
14 398 0.385522770331 Henry Cohn, 2026, needs more optimization.
14 399 0.386661659810 Henry Cohn, 2026, needs more optimization.
14 400 0.387682182264 Henry Cohn, 2026, needs more optimization.
14 401 0.387696590611 Henry Cohn, 2026, needs more optimization.
14 402 0.387803148364 Henry Cohn, 2026, needs more optimization.
14 403 0.388921857239 Henry Cohn, 2026, needs more optimization.
14 404 0.389141455847 Henry Cohn, 2026, needs more optimization.
14 405 0.389259461813 Henry Cohn, 2026, needs more optimization.
14 406 0.389269344653 Henry Cohn, 2026, needs more optimization.
14 407 0.389287842689 Henry Cohn, 2026, needs more optimization.
14 408 0.389345499810 Henry Cohn, 2026, needs more optimization.
14 409 0.389393115841 Henry Cohn, 2026, needs more optimization.
14 410 0.390045456274 Henry Cohn, 2026, needs more optimization.
14 411 0.390072916609 Henry Cohn, 2026, needs more optimization.
14 412 0.390110096100 Henry Cohn, 2026, needs more optimization.
14 413 0.390128512226 Henry Cohn, 2026, needs more optimization.
14 414 0.390158965247 Henry Cohn, 2026, needs more optimization.
14 415 0.390309034039 Henry Cohn, 2026, needs more optimization.
14 416 0.391234380264 Henry Cohn, 2026, needs more optimization.
14 417 0.391347870717 Henry Cohn, 2026, needs more optimization.
14 435 0.391891891892 Henry Cohn, 2026.
74⁢x−29
14 436 0.394834515706 Henry Cohn, 2026, needs more optimization.
14 437 0.395907747663 Henry Cohn, 2026, needs more optimization.
14 438 0.396551648476 Henry Cohn, 2026, needs more optimization.
14 439 0.396990281380 Henry Cohn, 2026, needs more optimization.
14 440 0.397346809347 Henry Cohn, 2026, needs more optimization.
14 441 0.397630185622 Henry Cohn, 2026, needs more optimization.
14 442 0.398093258442 Henry Cohn, 2026, needs more optimization.
14 443 0.398792061611 Henry Cohn, 2026, needs more optimization.
14 444 0.399267216513 Henry Cohn, 2026, needs more optimization.
14 445 0.399602601157 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 0.402765422771 Henry Cohn, 2026, needs more optimization.
14 498 0.402855678021 Henry Cohn, 2026, needs more optimization.
14 499 0.404932859447 Henry Cohn, 2026, needs more optimization.
14 500 0.405756684158 Henry Cohn, 2026, needs more optimization.
14 501 0.406004827759 Henry Cohn, 2026, needs more optimization.
14 502 0.407342331712 Henry Cohn, 2026, needs more optimization.
14 503 0.407837236746 Henry Cohn, 2026, needs more optimization.
14 504 0.409470566782 Henry Cohn, 2026, needs more optimization.
14 505 0.410165995306 Henry Cohn, 2026, needs more optimization.
14 506 0.411354772589 Henry Cohn, 2026, needs more optimization.
14 507 0.411609547640 Henry Cohn, 2026, needs more optimization.
14 508 0.411632127764 Henry Cohn, 2026, needs more optimization.
14 510 0.411770578778 Henry Cohn, 2026, needs more optimization.
14 511 0.411778142792 Henry Cohn, 2026, needs more optimization.
14 512 0.411811586803 Henry Cohn, 2026, needs more optimization.
14 513 0.411936692293 Henry Cohn, 2026, needs more optimization.
14 514 0.411952344360 Henry Cohn, 2026, needs more optimization.
14 515 0.415493718136 Henry Cohn, 2026, needs more optimization.
14 516 0.415546564263 Henry Cohn, 2026, needs more optimization.
14 517 0.416202025106 Henry Cohn, 2026, needs more optimization.
14 555 0.423076923077 Henry Cohn, 2026.
26⁢x−11
14 557 0.423235878892 Henry Cohn, 2026, needs more optimization.
14 558 0.423240411323 Henry Cohn, 2026, needs more optimization.
14 559 0.427444757423 Henry Cohn, 2026, needs more optimization.
14 560 0.427997358117 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 0.429745873879 Henry Cohn, 2026, needs more optimization.
14 602 0.430055334271 Henry Cohn, 2026, needs more optimization.
14 603 0.430223263935 Henry Cohn, 2026, needs more optimization.
14 604 0.430588037803 Henry Cohn, 2026, needs more optimization.
14 605 0.430986674846 Henry Cohn, 2026, needs more optimization.
14 606 0.431127288714 Henry Cohn, 2026, needs more optimization.
14 607 0.431172957392 Henry Cohn, 2026, needs more optimization.
14 608 0.431348065961 Henry Cohn, 2026, needs more optimization.
14 609 0.431490159536 Henry Cohn, 2026, needs more optimization.
14 610 0.431598639558 Henry Cohn, 2026, needs more optimization.
14 611 0.431620273256 Henry Cohn, 2026, needs more optimization.
14 612 0.432123266369 Henry Cohn, 2026, needs more optimization.
14 613 0.432212494110 Henry Cohn, 2026, needs more optimization.
14 614 0.432258187520 Henry Cohn, 2026, needs more optimization.
14 615 0.432786777362 Henry Cohn, 2026, needs more optimization.
14 616 0.432822022526 Henry Cohn, 2026, needs more optimization.
14 617 0.432841723151 Henry Cohn, 2026, needs more optimization.
14 618 0.432862241901 Henry Cohn, 2026, needs more optimization.
14 619 0.432910209888 Henry Cohn, 2026, needs more optimization.
14 620 0.432940198162 Henry Cohn, 2026, needs more optimization.
14 621 0.432962684394 Henry Cohn, 2026, needs more optimization.
14 622 0.432994739250 Henry Cohn, 2026, needs more optimization.
14 623 0.433029956559 Henry Cohn, 2026, needs more optimization.
14 624 0.433078146497 Henry Cohn, 2026, needs more optimization.
14 625 0.433118662500 Henry Cohn, 2026, needs more optimization.
14 626 0.433169427481 Henry Cohn, 2026, needs more optimization.
14 627 0.433214976075 Henry Cohn, 2026, needs more optimization.
14 628 0.433478324941 Henry Cohn, 2026, needs more optimization.
14 629 0.433496564150 Henry Cohn, 2026, needs more optimization.
14 630 0.433541608268 Henry Cohn, 2026, needs more optimization.
14 631 0.433597664915 Henry Cohn, 2026, needs more optimization.
14 632 0.433642725522 Henry Cohn, 2026, needs more optimization.
14 633 0.433684283715 Henry Cohn, 2026, needs more optimization.
14 634 0.433708470488 Henry Cohn, 2026, needs more optimization.
14 635 0.433775881335 Henry Cohn, 2026, needs more optimization.
14 636 0.433803043249 Henry Cohn, 2026, needs more optimization.
14 637 0.433854913835 Henry Cohn, 2026, needs more optimization.
14 638 0.433909206482 Henry Cohn, 2026, needs more optimization.
14 639 0.433916384040 Henry Cohn, 2026, needs more optimization.
14 640 0.434142046046 Henry Cohn, 2026, needs more optimization.
14 641 0.434172547122 Henry Cohn, 2026, needs more optimization.
14 642 0.434173050991 Henry Cohn, 2026, needs more optimization.
14 643 0.434177901948 Henry Cohn, 2026, needs more optimization.
14 644 0.434220723927 Henry Cohn, 2026, needs more optimization.
14 645 0.434407150906 Henry Cohn, 2026, needs more optimization.
14 646 0.434963861405 Henry Cohn, 2026, needs more optimization.
14 647 0.435571756321 Henry Cohn, 2026, needs more optimization.
14 648 0.436678320411 Henry Cohn, 2026, needs more optimization.
14 649 0.437228203537 Henry Cohn, 2026, needs more optimization.
14 650 0.437721279565 Henry Cohn, 2026, needs more optimization.
14 651 0.438001403194 Henry Cohn, 2026, needs more optimization.
14 652 0.438071503272 Henry Cohn, 2026, needs more optimization.
14 653 0.438803703953 Henry Cohn, 2026, needs more optimization.
14 654 0.439315975672 Henry Cohn, 2026, needs more optimization.
14 655 0.439491361204 Henry Cohn, 2026, needs more optimization.
14 656 0.440443951257 Henry Cohn, 2026, needs more optimization.
14 657 0.440815362818 Henry Cohn, 2026, needs more optimization.
14 658 0.440999595099 Henry Cohn, 2026, needs more optimization.
14 659 0.441384409594 Henry Cohn, 2026, needs more optimization.
14 660 0.442019740263 Henry Cohn, 2026, needs more optimization.
14 661 0.442060257280 Henry Cohn, 2026, needs more optimization.
14 662 0.442188180255 Henry Cohn, 2026, needs more optimization.
14 663 0.442324394979 Henry Cohn, 2026, needs more optimization.
14 664 0.442786172453 Henry Cohn, 2026, needs more optimization.
14 665 0.443560998653 Henry Cohn, 2026, needs more optimization.
14 666 0.444037893683 Henry Cohn, 2026, needs more optimization.
14 667 0.444485968793 Henry Cohn, 2026, needs more optimization.
14 668 0.444539760488 Henry Cohn, 2026, needs more optimization.
14 669 0.444873493202 Henry Cohn, 2026, needs more optimization.
14 670 0.445483598020 Henry Cohn, 2026, needs more optimization.
14 671 0.445799774327 Henry Cohn, 2026, needs more optimization.
14 672 0.446322403699 Henry Cohn, 2026, needs more optimization.
14 673 0.446522626195 Henry Cohn, 2026, needs more optimization.
14 674 0.446522635183 Henry Cohn, 2026, needs more optimization.
14 675 0.446839025570 Henry Cohn, 2026, needs more optimization.
14 676 0.446925201687 Henry Cohn, 2026, needs more optimization.
14 677 0.447047474216 Henry Cohn, 2026, needs more optimization.
14 678 0.447170829847 Henry Cohn, 2026, needs more optimization.
14 679 0.447444530988 Henry Cohn, 2026, needs more optimization.
14 680 0.447709240527 Henry Cohn, 2026, needs more optimization.
14 681 0.447780840577 Henry Cohn, 2026, needs more optimization.
14 682 0.448154633401 Henry Cohn, 2026, needs more optimization.
14 683 0.448501456045 Henry Cohn, 2026, needs more optimization.
14 684 0.448755909091 Henry Cohn, 2026, needs more optimization.
14 685 0.448791337948 Henry Cohn, 2026, needs more optimization.
14 686 0.448907181105 Henry Cohn, 2026, needs more optimization.
14 687 0.449010734322 Henry Cohn, 2026, needs more optimization.
14 688 0.449175314291 Henry Cohn, 2026, needs more optimization.
14 689 0.449430503288 Henry Cohn, 2026, needs more optimization.
14 690 0.449640180922 Henry Cohn, 2026, needs more optimization.
14 691 0.449764867399 Henry Cohn, 2026, needs more optimization.
14 692 0.449849198681 Henry Cohn, 2026, needs more optimization.
14 693 0.450095183814 Henry Cohn, 2026, needs more optimization.
14 694 0.450315766689 Henry Cohn, 2026, needs more optimization.
14 695 0.450711873772 Henry Cohn, 2026, needs more optimization.
14 696 0.450799302190 Henry Cohn, 2026, needs more optimization.
14 697 0.450799348285 Henry Cohn, 2026, needs more optimization.
14 698 0.450945236201 Henry Cohn, 2026, needs more optimization.
14 699 0.453796084544 Henry Cohn, 2026, needs more optimization.
14 700 0.453816272988 Henry Cohn, 2026, needs more optimization.
14 703 0.453826918782 Henry Cohn, 2026, needs more optimization.
14 704 0.453848062206 Henry Cohn, 2026, needs more optimization.
14 705 0.453896333207 Henry Cohn, 2026, needs more optimization.
14 706 0.453990307527 Henry Cohn, 2026, needs more optimization.
14 707 0.453990307720 Henry Cohn, 2026, needs more optimization.
14 708 0.453990310161 Henry Cohn, 2026, needs more optimization.
14 719 0.454158870616 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 0.455053121102 Henry Cohn, 2026, needs more optimization.
14 905 0.455088331951 Henry Cohn, 2026, needs more optimization.
14 906 0.455095807062 Henry Cohn, 2026, needs more optimization.
14 907 0.455107633265 Henry Cohn, 2026, needs more optimization.
14 908 0.455119179365 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 0.455173828490 Henry Cohn, 2026, needs more optimization.
14 912 0.455184963099 Henry Cohn, 2026, needs more optimization.
14 913 0.455196163736 Henry Cohn, 2026, needs more optimization.
14 914 0.455207946351 Henry Cohn, 2026, needs more optimization.
14 915 0.455222457141 Henry Cohn, 2026, needs more optimization.
14 916 0.455247174489 Henry Cohn, 2026, needs more optimization.
14 917 0.455258203394 Henry Cohn, 2026, needs more optimization.
14 918 0.455283172844 Henry Cohn, 2026, needs more optimization.
14 919 0.455313890159 Henry Cohn, 2026, needs more optimization.
14 920 0.455324353295 Henry Cohn, 2026, needs more optimization.
14 921 0.455337422378 Henry Cohn, 2026, needs more optimization.
14 922 0.455343293379 Henry Cohn, 2026, needs more optimization.
14 924 0.455349171804 Henry Cohn, 2026, needs more optimization.
14 925 0.455351537723 Henry Cohn, 2026, needs more optimization.
14 926 0.455358896413 Henry Cohn, 2026, needs more optimization.
14 927 0.455366453145 Henry Cohn, 2026, needs more optimization.
14 928 0.455369387330 Henry Cohn, 2026, needs more optimization.
14 929 0.455374081578 Henry Cohn, 2026, needs more optimization.
14 930 0.455378882411 Henry Cohn, 2026, needs more optimization.
14 931 0.455380847317 Henry Cohn, 2026, needs more optimization.
14 932 0.455388143438 Henry Cohn, 2026, needs more optimization.
14 933 0.455393806318 Henry Cohn, 2026, needs more optimization.
14 934 0.455395236754 Henry Cohn, 2026, needs more optimization.
14 935 0.455397379524 Henry Cohn, 2026, needs more optimization.
14 936 0.455402841336 Henry Cohn, 2026, needs more optimization.
14 937 0.455408675534 Henry Cohn, 2026, needs more optimization.
14 938 0.455413257812 Henry Cohn, 2026, needs more optimization.
14 939 0.455419313207 Henry Cohn, 2026, needs more optimization.
14 940 0.455425118727 Henry Cohn, 2026, needs more optimization.
14 941 0.455429276027 Henry Cohn, 2026, needs more optimization.
14 942 0.455435411346 Henry Cohn, 2026, needs more optimization.
14 943 0.455440550119 Henry Cohn, 2026, needs more optimization.
14 944 0.455446818148 Henry Cohn, 2026, needs more optimization.
14 945 0.455450900106 Henry Cohn, 2026, needs more optimization.
14 946 0.455457025616 Henry Cohn, 2026, needs more optimization.
14 947 0.455459871696 Henry Cohn, 2026, needs more optimization.
14 948 0.455469386987 Henry Cohn, 2026, needs more optimization.
14 949 0.455473216803 Henry Cohn, 2026, needs more optimization.
14 950 0.455477645768 Henry Cohn, 2026, needs more optimization.
14 951 0.455486008927 Henry Cohn, 2026, needs more optimization.
14 952 0.455493218185 Henry Cohn, 2026, needs more optimization.
14 953 0.455498726210 Henry Cohn, 2026, needs more optimization.
14 954 0.455509117681 Henry Cohn, 2026, needs more optimization.
14 955 0.455512657812 Henry Cohn, 2026, needs more optimization.
14 956 0.455534335290 Henry Cohn, 2026, needs more optimization.
14 957 0.455540241388 Henry Cohn, 2026, needs more optimization.
14 958 0.455546639329 Henry Cohn, 2026, needs more optimization.
14 959 0.455553967478 Henry Cohn, 2026, needs more optimization.
14 960 0.455557205263 Henry Cohn, 2026, needs more optimization.
14 961 0.455563237992 Henry Cohn, 2026, needs more optimization.
14 962 0.455568083544 Henry Cohn, 2026, needs more optimization.
14 963 0.455577354830 Henry Cohn, 2026, needs more optimization.
14 964 0.455585771683 Henry Cohn, 2026, needs more optimization.
14 965 0.455592710913 Henry Cohn, 2026, needs more optimization.
14 966 0.455598891046 Henry Cohn, 2026, needs more optimization.
14 967 0.455603819071 Henry Cohn, 2026, needs more optimization.
14 968 0.455610032057 Henry Cohn, 2026, needs more optimization.
14 969 0.455612698212 Henry Cohn, 2026, needs more optimization.
14 970 0.455616300651 Henry Cohn, 2026, needs more optimization.
14 971 0.455626379572 Henry Cohn, 2026, needs more optimization.
14 972 0.455632026554 Henry Cohn, 2026, needs more optimization.
14 973 0.455636034266 Henry Cohn, 2026, needs more optimization.
14 974 0.455640320563 Henry Cohn, 2026, needs more optimization.
14 975 0.455647040535 Henry Cohn, 2026, needs more optimization.
14 976 0.455654548525 Henry Cohn, 2026, needs more optimization.
14 978 0.456271734767 Henry Cohn, 2026, needs more optimization.
14 979 0.456271910309 Henry Cohn, 2026, needs more optimization.
14 980 0.456271998011 Henry Cohn, 2026, needs more optimization.
14 982 0.456273066617 Henry Cohn, 2026, needs more optimization.
14 983 0.456275089931 Henry Cohn, 2026, needs more optimization.
14 984 0.456278684601 Henry Cohn, 2026, needs more optimization.
14 985 0.456278762516 Henry Cohn, 2026, needs more optimization.
14 987 0.456280694637 Henry Cohn, 2026, needs more optimization.
14 988 0.456283122555 Henry Cohn, 2026, needs more optimization.
14 989 0.456283590297 Henry Cohn, 2026, needs more optimization.
14 990 0.456285696314 Henry Cohn, 2026, needs more optimization.
14 992 0.456288057544 Henry Cohn, 2026, needs more optimization.
14 993 0.456288221134 Henry Cohn, 2026, needs more optimization.
14 994 0.456288960825 Henry Cohn, 2026, needs more optimization.
14 995 0.456292724918 Henry Cohn, 2026, needs more optimization.
14 996 0.456294233096 Henry Cohn, 2026, needs more optimization.
14 997 0.456297054684 Henry Cohn, 2026, needs more optimization.
14 999 0.456297573907 Henry Cohn, 2026, needs more optimization.
14 1002 0.456302494642 Henry Cohn, 2026, needs more optimization.
14 1003 0.456302855580 Henry Cohn, 2026, needs more optimization.
14 1006 0.456305274992 Henry Cohn, 2026, needs more optimization.
14 1007 0.456305455323 Henry Cohn, 2026, needs more optimization.
14 1008 0.456305711107 Henry Cohn, 2026, needs more optimization.
14 1009 0.456306353666 Henry Cohn, 2026, needs more optimization.
14 1010 0.456309641777 Henry Cohn, 2026, needs more optimization.
14 1012 0.456314753150 Henry Cohn, 2026, needs more optimization.
14 1014 0.456315578914 Henry Cohn, 2026, needs more optimization.
14 1015 0.456315596338 Henry Cohn, 2026, needs more optimization.
14 1016 0.457549958837 Henry Cohn, 2026, needs more optimization.
14 1017 0.457552363580 Henry Cohn, 2026, needs more optimization.
14 1018 0.457554380023 Henry Cohn, 2026, needs more optimization.
14 1019 0.457559618085 Henry Cohn, 2026, needs more optimization.
14 1020 0.457566395849 Henry Cohn, 2026, needs more optimization.
14 1021 0.457575307652 Henry Cohn, 2026, needs more optimization.
14 1022 0.457582426375 Henry Cohn, 2026, needs more optimization.
14 1023 0.457587190989 Henry Cohn, 2026, needs more optimization.
14 1024 0.457591788084 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 78 0.168276892978 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 0.189741624080 Henry Cohn, 2026, needs more optimization.
15 101 0.197672143260 Henry Cohn, 2026, needs more optimization.
15 102 0.197758492075 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.
15 108 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 0.216448794533 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 0.226886293202 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 0.237559868370 Henry Cohn, 2026, needs more optimization.
15 146 0.238431353088 Henry Cohn, 2026, needs more optimization.
15 147 0.238762613574 Henry Cohn, 2026, needs more optimization.
15 149 0.239294215248 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.
15 150 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 0.253987633656 Henry Cohn, 2026, needs more optimization.
15 159 0.254474463985 Henry Cohn, 2026, needs more optimization.
15 160 0.254877410325 Henry Cohn, 2026, needs more optimization.
15 161 0.255435867940 Henry Cohn, 2026, needs more optimization.
15 162 0.255998886670 Henry Cohn, 2026, needs more optimization.
15 163 0.257091602564 Henry Cohn, 2026, needs more optimization.
15 164 0.257359308774 Henry Cohn, 2026, needs more optimization.
15 165 0.257391616061 Henry Cohn, 2026, needs more optimization.
15 166 0.257476235366 Henry Cohn, 2026, needs more optimization.
15 167 0.257676625353 Henry Cohn, 2026, needs more optimization.
15 168 0.257853480079 Henry Cohn, 2026, needs more optimization.
15 169 0.258056564231 Henry Cohn, 2026, needs more optimization.
15 170 0.258179090726 Henry Cohn, 2026, needs more optimization.
15 171 0.258368882647 Henry Cohn, 2026, needs more optimization.
15 172 0.258498891522 Henry Cohn, 2026, needs more optimization.
15 173 0.258642110145 Henry Cohn, 2026, needs more optimization.
15 174 0.258728233010 Henry Cohn, 2026, needs more optimization.
15 175 0.258888200861 Henry Cohn, 2026, needs more optimization.
15 176 0.259187685500 Henry Cohn, 2026, needs more optimization.
15 177 0.259564204898 Henry Cohn, 2026, needs more optimization.
15 178 0.259844553114 Henry Cohn, 2026, needs more optimization.
15 179 0.259992969259 Henry Cohn, 2026, needs more optimization.
15 180 0.259994095378 Henry Cohn, 2026, needs more optimization.
15 181 0.260004524383 Henry Cohn, 2026, needs more optimization.
15 182 0.260020831122 Henry Cohn, 2026, needs more optimization.
15 183 0.260128334592 Henry Cohn, 2026, needs more optimization.
15 184 0.260236772707 Henry Cohn, 2026, needs more optimization.
15 185 0.260320202558 Henry Cohn, 2026, needs more optimization.
15 186 0.260378067213 Henry Cohn, 2026, needs more optimization.
15 187 0.260799388302 Henry Cohn, 2026, needs more optimization.
15 188 0.261261056002 Henry Cohn, 2026, needs more optimization.
15 189 0.261743147993 Henry Cohn, 2026, needs more optimization.
15 190 0.262063610061 Henry Cohn, 2026, needs more optimization.
15 191 0.262528959805 Henry Cohn, 2026, needs more optimization.
15 192 0.262841929764 Henry Cohn, 2026, needs more optimization.
15 193 0.263167012138 Henry Cohn, 2026, needs more optimization.
15 194 0.263452726905 Henry Cohn, 2026, needs more optimization.
15 195 0.263685389054 Henry Cohn, 2026, needs more optimization.
15 196 0.263860156305 Henry Cohn, 2026, needs more optimization.
15 197 0.264010214197 Henry Cohn, 2026, needs more optimization.
15 198 0.264192597778 Henry Cohn, 2026, needs more optimization.
15 199 0.264362164942 Henry Cohn, 2026, needs more optimization.
15 200 0.264512055045 Henry Cohn, 2026, needs more optimization.
15 201 0.264668164947 Henry Cohn, 2026, needs more optimization.
15 202 0.264803103408 Henry Cohn, 2026, needs more optimization.
15 203 0.264943839494 Henry Cohn, 2026, needs more optimization.
15 204 0.265065613540 Henry Cohn, 2026, needs more optimization.
15 205 0.265251543999 Henry Cohn, 2026, needs more optimization.
15 206 0.265354276627 Henry Cohn, 2026, needs more optimization.
15 207 0.265450291555 Henry Cohn, 2026, needs more optimization.
15 208 0.265531313478 Henry Cohn, 2026, needs more optimization.
15 209 0.265670383097 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 0.266440725809 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 0.284149290156 Henry Cohn, 2026, needs more optimization.
15 223 0.284251932264 Henry Cohn, 2026, needs more optimization.
15 224 0.284363380791 Henry Cohn, 2026, needs more optimization.
15 225 0.285451553881 Henry Cohn, 2026, needs more optimization.
15 229 0.285514881221 Henry Cohn, 2026, needs more optimization.
15 230 0.285521870177 Henry Cohn, 2026, needs more optimization.
15 231 0.285525146333 Henry Cohn, 2026, needs more optimization.
15 232 0.285531264951 Henry Cohn, 2026, needs more optimization.
15 233 0.285536309219 Henry Cohn, 2026, needs more optimization.
15 234 0.285542915060 Henry Cohn, 2026, needs more optimization.
15 235 0.285555326932 Henry Cohn, 2026, needs more optimization.
15 236 0.285562819368 Henry Cohn, 2026, needs more optimization.
15 237 0.285573203155 Henry Cohn, 2026, needs more optimization.
15 238 0.285588459516 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 0.285655742546 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 0.286935827711 Henry Cohn, 2026, needs more optimization.
15 245 0.287258045445 Henry Cohn, 2026, needs more optimization.
15 246 0.287706774231 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 0.291752699196 Henry Cohn, 2026, needs more optimization.
15 250 0.294425817098 Henry Cohn, 2026, needs more optimization.
15 251 0.297313122488 Henry Cohn, 2026, needs more optimization.
15 252 0.297805885600 Henry Cohn, 2026, needs more optimization.
15 253 0.297826741256 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 0.302591860518 Henry Cohn, 2026, needs more optimization.
15 258 0.304745123433 Henry Cohn, 2026, needs more optimization.
15 259 0.305962151289 Henry Cohn, 2026, needs more optimization.
15 260 0.307183763306 Henry Cohn, 2026, needs more optimization.
15 261 0.308190960754 Henry Cohn, 2026, needs more optimization.
15 262 0.309418185500 Henry Cohn, 2026, needs more optimization.
15 263 0.309493764649 Henry Cohn, 2026, needs more optimization.
15 264 0.309633682945 Henry Cohn, 2026, needs more optimization.
15 265 0.312022729472 Henry Cohn, 2026, needs more optimization.
15 266 0.313594730975 Henry Cohn, 2026, needs more optimization.
15 267 0.315078890365 Henry Cohn, 2026, needs more optimization.
15 268 0.316238130503 Henry Cohn, 2026, needs more optimization.
15 269 0.316301144608 Henry Cohn, 2026, needs more optimization.
15 270 0.316564747477 Henry Cohn, 2026, needs more optimization.
15 271 0.319241988593 Henry Cohn, 2026, needs more optimization.
15 272 0.321147973182 Henry Cohn, 2026, needs more optimization.
15 273 0.323515010237 Henry Cohn, 2026, needs more optimization.
15 274 0.324908252818 Henry Cohn, 2026, needs more optimization.
15 275 0.326546912688 Henry Cohn, 2026, needs more optimization.
15 276 0.328210708533 Henry Cohn, 2026, needs more optimization.
15 277 0.329945890117 Henry Cohn, 2026, needs more optimization.
15 278 0.331067848250 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 0.339316147154 Henry Cohn, 2026, needs more optimization.
15 322 0.340375509920 Henry Cohn, 2026, needs more optimization.
15 323 0.341171188496 Henry Cohn, 2026, needs more optimization.
15 324 0.341832640216 Henry Cohn, 2026, needs more optimization.
15 325 0.342383364957 Henry Cohn, 2026, needs more optimization.
15 326 0.342763311528 Henry Cohn, 2026, needs more optimization.
15 327 0.343118170038 Henry Cohn, 2026, needs more optimization.
15 328 0.343553559073 Henry Cohn, 2026, needs more optimization.
15 329 0.343822120041 Henry Cohn, 2026, needs more optimization.
15 330 0.344488529759 Henry Cohn, 2026, needs more optimization.
15 331 0.345416265562 Henry Cohn, 2026, needs more optimization.
15 332 0.345745662209 Henry Cohn, 2026, needs more optimization.
15 333 0.346505231446 Henry Cohn, 2026, needs more optimization.
15 334 0.347021345551 Henry Cohn, 2026, needs more optimization.
15 335 0.347218367850 Henry Cohn, 2026, needs more optimization.
15 336 0.347482525642 Henry Cohn, 2026, needs more optimization.
15 337 0.347850970711 Henry Cohn, 2026, needs more optimization.
15 338 0.348004655805 Henry Cohn, 2026, needs more optimization.
15 339 0.348173231364 Henry Cohn, 2026, needs more optimization.
15 340 0.348378254432 Henry Cohn, 2026, needs more optimization.
15 341 0.348555904880 Henry Cohn, 2026, needs more optimization.
15 342 0.348838296516 Henry Cohn, 2026, needs more optimization.
15 343 0.349073471320 Henry Cohn, 2026, needs more optimization.
15 344 0.349243135652 Henry Cohn, 2026, needs more optimization.
15 345 0.349404134614 Henry Cohn, 2026, needs more optimization.
15 346 0.349619710096 Henry Cohn, 2026, needs more optimization.
15 347 0.350152503963 Henry Cohn, 2026, needs more optimization.
15 348 0.350491447423 Henry Cohn, 2026, needs more optimization.
15 349 0.350845055171 Henry Cohn, 2026, needs more optimization.
15 350 0.351111746503 Henry Cohn, 2026, needs more optimization.
15 351 0.351305853458 Henry Cohn, 2026, needs more optimization.
15 352 0.351653834758 Henry Cohn, 2026, needs more optimization.
15 353 0.352031486874 Henry Cohn, 2026, needs more optimization.
15 354 0.352277741425 Henry Cohn, 2026, needs more optimization.
15 355 0.352550570610 Henry Cohn, 2026, needs more optimization.
15 356 0.352749511740 Henry Cohn, 2026, needs more optimization.
15 357 0.352951925931 Henry Cohn, 2026, needs more optimization.
15 358 0.353282632237 Henry Cohn, 2026, needs more optimization.
15 359 0.353528584167 Henry Cohn, 2026, needs more optimization.
15 360 0.353754112116 Henry Cohn, 2026, needs more optimization.
15 362 0.355530015867 Henry Cohn, 2026, needs more optimization.
15 363 0.355537385074 Henry Cohn, 2026, needs more optimization.
15 364 0.355549886491 Henry Cohn, 2026, needs more optimization.
15 365 0.355594587259 Henry Cohn, 2026, needs more optimization.
15 366 0.355595922187 Henry Cohn, 2026, needs more optimization.
15 367 0.355640639544 Henry Cohn, 2026, needs more optimization.
15 368 0.355655745382 Henry Cohn, 2026, needs more optimization.
15 369 0.355683829492 Henry Cohn, 2026, needs more optimization.
15 370 0.355707936952 Henry Cohn, 2026, needs more optimization.
15 371 0.355772785350 Henry Cohn, 2026, needs more optimization.
15 372 0.355781418082 Henry Cohn, 2026, needs more optimization.
15 373 0.356530010635 Henry Cohn, 2026, needs more optimization.
15 374 0.356861830228 Henry Cohn, 2026, needs more optimization.
15 375 0.356861836578 Henry Cohn, 2026, needs more optimization.
15 376 0.358263884130 Henry Cohn, 2026, needs more optimization.
15 377 0.358279341514 Henry Cohn, 2026, needs more optimization.
15 378 0.358284129865 Henry Cohn, 2026, needs more optimization.
15 379 0.358286637990 Henry Cohn, 2026, needs more optimization.
15 380 0.358286811225 Henry Cohn, 2026, needs more optimization.
15 381 0.360129015117 Henry Cohn, 2026, needs more optimization.
15 382 0.360748062814 Henry Cohn, 2026, needs more optimization.
15 383 0.361404345581 Henry Cohn, 2026, needs more optimization.
15 384 0.362697097844 Henry Cohn, 2026, needs more optimization.
15 385 0.363048044816 Henry Cohn, 2026, needs more optimization.
15 386 0.363884628824 Henry Cohn, 2026, needs more optimization.
15 387 0.364559152013 Henry Cohn, 2026, needs more optimization.
15 388 0.365658751707 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 0.367234880196 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 0.370025655813 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 0.372215686269 Henry Cohn, 2026, needs more optimization.
15 427 0.373370645862 Henry Cohn, 2026, needs more optimization.
15 428 0.374921952803 Henry Cohn, 2026, needs more optimization.
15 430 0.374923176881 Henry Cohn, 2026, needs more optimization.
15 431 0.374924343573 Henry Cohn, 2026, needs more optimization.
15 432 0.374924612046 Henry Cohn, 2026, needs more optimization.
15 433 0.374965259413 Henry Cohn, 2026, needs more optimization.
15 434 0.374966099701 Henry Cohn, 2026, needs more optimization.
15 435 0.375013080432 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 0.376621782278 Henry Cohn, 2026, needs more optimization.
15 467 0.381212766274 Henry Cohn, 2026, needs more optimization.
15 468 0.382759165909 Henry Cohn, 2026, needs more optimization.
15 469 0.383972099059 Henry Cohn, 2026, needs more optimization.
15 470 0.385355256031 Henry Cohn, 2026, needs more optimization.
15 471 0.386211847732 Henry Cohn, 2026, needs more optimization.
15 472 0.386926570455 Henry Cohn, 2026, needs more optimization.
15 480 0.387504105641 Henry Cohn, 2026, needs more optimization.
15 481 0.390159535503 Henry Cohn, 2026, needs more optimization.
15 482 0.392377707112 Henry Cohn, 2026, needs more optimization.
15 483 0.392382167857 Henry Cohn, 2026, needs more optimization.
15 484 0.392387773935 Henry Cohn, 2026, needs more optimization.
15 485 0.392393957448 Henry Cohn, 2026, needs more optimization.
15 486 0.392438282260 Henry Cohn, 2026, needs more optimization.
15 487 0.392438285135 Henry Cohn, 2026, needs more optimization.
15 489 0.392502200305 Henry Cohn, 2026, needs more optimization.
15 490 0.392504710735 Henry Cohn, 2026, needs more optimization.
15 491 0.392523078417 Henry Cohn, 2026, needs more optimization.
15 492 0.392528925313 Henry Cohn, 2026, needs more optimization.
15 494 0.392693849169 Henry Cohn, 2026, needs more optimization.
15 495 0.392728539972 Henry Cohn, 2026, needs more optimization.
15 496 0.392811899506 Henry Cohn, 2026, needs more optimization.
15 497 0.392845279305 Henry Cohn, 2026, needs more optimization.
15 498 0.392845287133 Henry Cohn, 2026, needs more optimization.
15 499 0.392921523744 Henry Cohn, 2026, needs more optimization.
15 500 0.392930864366 Henry Cohn, 2026, needs more optimization.
15 501 0.392950088418 Henry Cohn, 2026, needs more optimization.
15 502 0.393004692076 Henry Cohn, 2026, needs more optimization.
15 503 0.393019791580 Henry Cohn, 2026, needs more optimization.
15 504 0.393021124492 Henry Cohn, 2026, needs more optimization.
15 505 0.393100672071 Henry Cohn, 2026, needs more optimization.
15 506 0.393179851523 Henry Cohn, 2026, needs more optimization.
15 507 0.393198757239 Henry Cohn, 2026, needs more optimization.
15 508 0.393198758448 Henry Cohn, 2026, needs more optimization.
15 509 0.393426763035 Henry Cohn, 2026, needs more optimization.
15 510 0.393865050812 Henry Cohn, 2026, needs more optimization.
15 511 0.393908451217 Henry Cohn, 2026, needs more optimization.
15 513 0.393908493614 Henry Cohn, 2026, needs more optimization.
15 514 0.394034528255 Henry Cohn, 2026, needs more optimization.
15 515 0.394060480505 Henry Cohn, 2026, needs more optimization.
15 516 0.394274409324 Henry Cohn, 2026, needs more optimization.
15 517 0.394346969805 Henry Cohn, 2026, needs more optimization.
15 518 0.394685251064 Henry Cohn, 2026, needs more optimization.
15 519 0.394892707073 Henry Cohn, 2026, needs more optimization.
15 520 0.395173206828 Henry Cohn, 2026, needs more optimization.
15 521 0.395300962762 Henry Cohn, 2026, needs more optimization.
15 522 0.395671077865 Henry Cohn, 2026, needs more optimization.
15 523 0.395966829706 Henry Cohn, 2026, needs more optimization.
15 524 0.396064932694 Henry Cohn, 2026, needs more optimization.
15 525 0.396111183172 Henry Cohn, 2026, needs more optimization.
15 526 0.396163920392 Henry Cohn, 2026, needs more optimization.
15 527 0.396559557370 Henry Cohn, 2026, needs more optimization.
15 528 0.396571524940 Henry Cohn, 2026, needs more optimization.
15 529 0.396874270763 Henry Cohn, 2026, needs more optimization.
15 530 0.396995747265 Henry Cohn, 2026, needs more optimization.
15 531 0.397105050906 Henry Cohn, 2026, needs more optimization.
15 532 0.397218607599 Henry Cohn, 2026, needs more optimization.
15 533 0.397580962829 Henry Cohn, 2026, needs more optimization.
15 534 0.397599530629 Henry Cohn, 2026, needs more optimization.
15 535 0.397773769950 Henry Cohn, 2026, needs more optimization.
15 536 0.397826376193 Henry Cohn, 2026, needs more optimization.
15 537 0.398178611743 Henry Cohn, 2026, needs more optimization.
15 538 0.398220588485 Henry Cohn, 2026, needs more optimization.
15 539 0.398438486252 Henry Cohn, 2026, needs more optimization.
15 540 0.398578855201 Henry Cohn, 2026, needs more optimization.
15 541 0.398630717529 Henry Cohn, 2026, needs more optimization.
15 542 0.398723682642 Henry Cohn, 2026, needs more optimization.
15 543 0.398805706157 Henry Cohn, 2026, needs more optimization.
15 545 0.399115526149 Henry Cohn, 2026, needs more optimization.
15 546 0.399338743026 Henry Cohn, 2026, needs more optimization.
15 547 0.399636189454 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 0.410994643940 Henry Cohn, 2026, needs more optimization.
15 692 0.413599412614 Henry Cohn, 2026, needs more optimization.
15 693 0.414199028031 Henry Cohn, 2026, needs more optimization.
15 694 0.414383606130 Henry Cohn, 2026, needs more optimization.
15 695 0.415975229133 Henry Cohn, 2026, needs more optimization.
15 696 0.416267015150 Henry Cohn, 2026, needs more optimization.
15 697 0.417437214813 Henry Cohn, 2026, needs more optimization.
15 698 0.417443616564 Henry Cohn, 2026, needs more optimization.
15 699 0.417752424320 Henry Cohn, 2026, needs more optimization.
15 700 0.417757921956 Henry Cohn, 2026, needs more optimization.
15 701 0.418073574238 Henry Cohn, 2026, needs more optimization.
15 702 0.418407645546 Henry Cohn, 2026, needs more optimization.
15 703 0.418593107799 Henry Cohn, 2026, needs more optimization.
15 704 0.419096446207 Henry Cohn, 2026, needs more optimization.
15 705 0.419264448437 Henry Cohn, 2026, needs more optimization.
15 706 0.419673031021 Henry Cohn, 2026, needs more optimization.
15 707 0.420435838777 Henry Cohn, 2026, needs more optimization.
15 709 0.420952981604 Henry Cohn, 2026, needs more optimization.
15 710 0.420988560228 Henry Cohn, 2026, needs more optimization.
15 711 0.421057280262 Henry Cohn, 2026, needs more optimization.
15 712 0.421232140727 Henry Cohn, 2026, needs more optimization.
15 713 0.421341479309 Henry Cohn, 2026, needs more optimization.
15 714 0.421453596396 Henry Cohn, 2026, needs more optimization.
15 715 0.421608850789 Henry Cohn, 2026, needs more optimization.
15 716 0.421823687847 Henry Cohn, 2026, needs more optimization.
15 717 0.422138529901 Henry Cohn, 2026, needs more optimization.
15 718 0.422339269209 Henry Cohn, 2026, needs more optimization.
15 719 0.422639832371 Henry Cohn, 2026, needs more optimization.
15 720 0.422844158201 Henry Cohn, 2026, needs more optimization.
15 721 0.423011496153 Henry Cohn, 2026, needs more optimization.
15 722 0.423261076666 Henry Cohn, 2026, needs more optimization.
15 723 0.423577311506 Henry Cohn, 2026, needs more optimization.
15 724 0.423849552930 Henry Cohn, 2026, needs more optimization.
15 725 0.424189812426 Henry Cohn, 2026, needs more optimization.
15 726 0.424355705992 Henry Cohn, 2026, needs more optimization.
15 727 0.424533246400 Henry Cohn, 2026, needs more optimization.
15 728 0.424726714774 Henry Cohn, 2026, needs more optimization.
15 729 0.425052027073 Henry Cohn, 2026, needs more optimization.
15 730 0.425144583691 Henry Cohn, 2026, needs more optimization.
15 731 0.425325418708 Henry Cohn, 2026, needs more optimization.
15 732 0.425491738217 Henry Cohn, 2026, needs more optimization.
15 733 0.425641616028 Henry Cohn, 2026, needs more optimization.
15 734 0.425823455707 Henry Cohn, 2026, needs more optimization.
15 735 0.426022784741 Henry Cohn, 2026, needs more optimization.
15 736 0.426116802300 Henry Cohn, 2026, needs more optimization.
15 737 0.426450130044 Henry Cohn, 2026, needs more optimization.
15 738 0.426665334461 Henry Cohn, 2026, needs more optimization.
15 739 0.426762660802 Henry Cohn, 2026, needs more optimization.
15 740 0.427046676037 Henry Cohn, 2026, needs more optimization.
15 741 0.427294792879 Henry Cohn, 2026, needs more optimization.
15 742 0.427408989804 Henry Cohn, 2026, needs more optimization.
15 743 0.427631384682 Henry Cohn, 2026, needs more optimization.
15 744 0.427691686586 Henry Cohn, 2026, needs more optimization.
15 745 0.427869849832 Henry Cohn, 2026, needs more optimization.
15 746 0.427963941214 Henry Cohn, 2026, needs more optimization.
15 747 0.428142740835 Henry Cohn, 2026, needs more optimization.
15 748 0.428330504485 Henry Cohn, 2026, needs more optimization.
15 749 0.428535706697 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 0.439547515377 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 0.095440859515 Henry Cohn, 2025.
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 0.127284448392 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 74 0.127284656799 Henry Cohn, 2023.
156⁢x2−12⁢x−1
16 75 0.142328493208 Henry Cohn, 2026, needs more optimization.
16 76 0.155907309887 Henry Cohn, 2026, needs more optimization.
16 77 0.156180778382 Henry Cohn, 2026, needs more optimization.
16 78 0.156330418907 Henry Cohn, 2026, needs more optimization.
16 79 0.156685153801 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 0.159473252852 Henry Cohn, 2026, needs more optimization.
16 85 0.161142075511 Henry Cohn, 2026, needs more optimization.
16 88 0.168668499420 Henry Cohn, 2025, needs more optimization.
16 89 0.168683476942 Henry Cohn, 2026, needs more optimization.
16 90 0.168684111462 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 0.168685647336 Henry Cohn, 2026, needs more optimization.
16 96 0.168685666299 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 0.179204303497 Henry Cohn, 2026, needs more optimization.
16 105 0.183408686767 Henry Cohn, 2026, needs more optimization.
16 106 0.185718877448 Henry Cohn, 2026, needs more optimization.
16 107 0.188007787990 Henry Cohn, 2026, needs more optimization.
16 108 0.190691115208 Henry Cohn, 2026, needs more optimization.
16 109 0.191595935636 Henry Cohn, 2026, needs more optimization.
16 110 0.192051708392 Henry Cohn, 2026, needs more optimization.
16 111 0.192383845859 Henry Cohn, 2026, needs more optimization.
16 112 0.192403304187 Henry Cohn, 2026, needs more optimization.
16 117 0.192450089730 Henry Cohn, 2026.
27⁢x2−1
16 118 0.192450185263 Henry Cohn, 2026, needs more optimization.
16 119 0.198884094973 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 0.199988971320 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 0.200003053739 Henry Cohn, 2026, needs more optimization.
16 132 0.200003518742 Henry Cohn, 2026, needs more optimization.
16 133 0.202554133427 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.
16 159 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 0.204975380894 Henry Cohn, 2026, needs more optimization.
16 161 0.221699648782 Henry Cohn, 2026, needs more optimization.
16 162 0.229553213271 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 0.237449050255 Henry Cohn, 2026, needs more optimization.
16 171 0.240200589073 Henry Cohn, 2026, needs more optimization.
16 172 0.240963480688 Henry Cohn, 2026, needs more optimization.
16 173 0.241855339015 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 0.244630603021 Henry Cohn, 2026, needs more optimization.
16 177 0.245304226313 Henry Cohn, 2026, needs more optimization.
16 178 0.245850014976 Henry Cohn, 2026, needs more optimization.
16 179 0.246248093795 Henry Cohn, 2026, needs more optimization.
16 180 0.246522491482 Henry Cohn, 2026, needs more optimization.
16 181 0.246842599234 Henry Cohn, 2026, needs more optimization.
16 182 0.247099711971 Henry Cohn, 2026, needs more optimization.
16 183 0.247333778002 Henry Cohn, 2026, needs more optimization.
16 184 0.247504472365 Henry Cohn, 2026, needs more optimization.
16 185 0.247624546029 Henry Cohn, 2026, needs more optimization.
16 186 0.247723155043 Henry Cohn, 2026, needs more optimization.
16 187 0.247808442421 Henry Cohn, 2026, needs more optimization.
16 188 0.247977373934 Henry Cohn, 2026, needs more optimization.
16 189 0.248090767330 Henry Cohn, 2026, needs more optimization.
16 190 0.248395459221 Henry Cohn, 2026, needs more optimization.
16 191 0.248623159659 Henry Cohn, 2026, needs more optimization.
16 192 0.248921064911 Henry Cohn, 2026, needs more optimization.
16 193 0.248982461233 Henry Cohn, 2026, needs more optimization.
16 194 0.249846753539 Henry Cohn, 2026, needs more optimization.
16 195 0.249856352769 Henry Cohn, 2026, needs more optimization.
16 196 0.249862770872 Henry Cohn, 2026, needs more optimization.
16 197 0.249882648407 Henry Cohn, 2026, needs more optimization.
16 198 0.249904734229 Henry Cohn, 2026, needs more optimization.
16 199 0.249979885198 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 0.285672450987 Henry Cohn, 2026, needs more optimization.
16 290 0.291533692690 Henry Cohn, 2026, needs more optimization.
16 291 0.295037839337 Henry Cohn, 2026, needs more optimization.
16 292 0.297747448365 Henry Cohn, 2026, needs more optimization.
16 293 0.298635801346 Henry Cohn, 2026, needs more optimization.
16 294 0.298635887769 Henry Cohn, 2026, needs more optimization.
16 295 0.298636113930 Henry Cohn, 2026, needs more optimization.
16 296 0.298636139241 Henry Cohn, 2026, needs more optimization.
16 297 0.303497658021 Henry Cohn, 2026, needs more optimization.
16 298 0.305126406293 Henry Cohn, 2026, needs more optimization.
16 299 0.305824290561 Henry Cohn, 2026, needs more optimization.
16 300 0.305902318974 Henry Cohn, 2026, needs more optimization.
16 301 0.306099919257 Henry Cohn, 2026, needs more optimization.
16 302 0.306179764089 Henry Cohn, 2026, needs more optimization.
16 303 0.308247530725 Henry Cohn, 2026, needs more optimization.
16 304 0.309281175783 Henry Cohn, 2026, needs more optimization.
16 305 0.310058497317 Henry Cohn, 2026, needs more optimization.
16 306 0.310620949406 Henry Cohn, 2026, needs more optimization.
16 307 0.311407265500 Henry Cohn, 2026, needs more optimization.
16 308 0.311688104045 Henry Cohn, 2026, needs more optimization.
16 309 0.312062389855 Henry Cohn, 2026, needs more optimization.
16 310 0.312433756348 Henry Cohn, 2026, needs more optimization.
16 311 0.313090943513 Henry Cohn, 2026, needs more optimization.
16 312 0.313486659732 Henry Cohn, 2026, needs more optimization.
16 313 0.313752906852 Henry Cohn, 2026, needs more optimization.
16 314 0.313874879902 Henry Cohn, 2026, needs more optimization.
16 315 0.313890753900 Henry Cohn, 2026, needs more optimization.
16 316 0.314260711230 Henry Cohn, 2026, needs more optimization.
16 317 0.317328608170 Henry Cohn, 2026, needs more optimization.
16 318 0.320010708093 Henry Cohn, 2026, needs more optimization.
16 319 0.321923745836 Henry Cohn, 2026, needs more optimization.
16 320 0.324179993793 Henry Cohn, 2026, needs more optimization.
16 321 0.326133635269 Henry Cohn, 2026, needs more optimization.
16 322 0.326910869963 Henry Cohn, 2026, needs more optimization.
16 323 0.327999148158 Henry Cohn, 2026, needs more optimization.
16 324 0.328128845679 Henry Cohn, 2026, needs more optimization.
16 325 0.328362524653 Henry Cohn, 2026, needs more optimization.
16 326 0.328395799112 Henry Cohn, 2026, needs more optimization.
16 327 0.328611755170 Henry Cohn, 2026, needs more optimization.
16 328 0.328645205579 Henry Cohn, 2026, needs more optimization.
16 329 0.328757279792 Henry Cohn, 2026, needs more optimization.
16 330 0.328810876267 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 0.329871735725 Henry Cohn, 2026, needs more optimization.
16 343 0.329985166428 Henry Cohn, 2026, needs more optimization.
16 344 0.330282673213 Henry Cohn, 2026, needs more optimization.
16 345 0.330455856126 Henry Cohn, 2026, needs more optimization.
16 346 0.330579823645 Henry Cohn, 2026, needs more optimization.
16 347 0.330616490834 Henry Cohn, 2026, needs more optimization.
16 348 0.330692246356 Henry Cohn, 2026, needs more optimization.
16 349 0.330774626139 Henry Cohn, 2026, needs more optimization.
16 350 0.330941268113 Henry Cohn, 2026, needs more optimization.
16 351 0.331045713757 Henry Cohn, 2026, needs more optimization.
16 352 0.331351881170 Henry Cohn, 2026, needs more optimization.
16 353 0.331441258867 Henry Cohn, 2026, needs more optimization.
16 354 0.331548752633 Henry Cohn, 2026, needs more optimization.
16 355 0.331694568390 Henry Cohn, 2026, needs more optimization.
16 356 0.331826995277 Henry Cohn, 2026, needs more optimization.
16 357 0.331865516941 Henry Cohn, 2026, needs more optimization.
16 358 0.332061008460 Henry Cohn, 2026, needs more optimization.
16 359 0.332117166062 Henry Cohn, 2026, needs more optimization.
16 360 0.332280452429 Henry Cohn, 2026, needs more optimization.
16 361 0.332537836413 Henry Cohn, 2026, needs more optimization.
16 362 0.332581531478 Henry Cohn, 2026, needs more optimization.
16 363 0.332736896309 Henry Cohn, 2026, needs more optimization.
16 364 0.332785049151 Henry Cohn, 2026, needs more optimization.
16 365 0.332954504066 Henry Cohn, 2026, needs more optimization.
16 366 0.333041949358 Henry Cohn, 2026, needs more optimization.
16 367 0.333059421215 Henry Cohn, 2026, needs more optimization.
16 368 0.333083768285 Henry Cohn, 2026, needs more optimization.
16 369 0.333206803557 Henry Cohn, 2026, needs more optimization.
16 370 0.333221481940 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 0.350806504180 Henry Cohn, 2026, needs more optimization.
16 514 0.351247620538 Henry Cohn, 2026, needs more optimization.
16 515 0.352935976309 Henry Cohn, 2026, needs more optimization.
16 516 0.356581380274 Henry Cohn, 2026, needs more optimization.
16 517 0.357859965872 Henry Cohn, 2026, needs more optimization.
16 518 0.358530397588 Henry Cohn, 2026, needs more optimization.
16 519 0.358904647544 Henry Cohn, 2026, needs more optimization.
16 520 0.359967385832 Henry Cohn, 2026, needs more optimization.
16 521 0.360665013832 Henry Cohn, 2026, needs more optimization.
16 522 0.360858409550 Henry Cohn, 2026, needs more optimization.
16 523 0.361261076091 Henry Cohn, 2026, needs more optimization.
16 524 0.362586571074 Henry Cohn, 2026, needs more optimization.
16 525 0.363013873971 Henry Cohn, 2026, needs more optimization.
16 526 0.363486459512 Henry Cohn, 2026, needs more optimization.
16 527 0.364018328894 Henry Cohn, 2026, needs more optimization.
16 528 0.364563899318 Henry Cohn, 2026, needs more optimization.
16 529 0.365214869249 Henry Cohn, 2026, needs more optimization.
16 530 0.365518902136 Henry Cohn, 2026, needs more optimization.
16 531 0.365850633798 Henry Cohn, 2026, needs more optimization.
16 532 0.366442532741 Henry Cohn, 2026, needs more optimization.
16 533 0.366985545798 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 0.367830863405 Henry Cohn, 2026, needs more optimization.
16 536 0.368179743649 Henry Cohn, 2026, needs more optimization.
16 537 0.368747267258 Henry Cohn, 2026, needs more optimization.
16 538 0.369138760586 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 0.378267243328 Henry Cohn, 2026, needs more optimization.
16 589 0.378267245022 Henry Cohn, 2026, needs more optimization.
16 593 0.378269071297 Henry Cohn, 2026, needs more optimization.
16 594 0.378269076506 Henry Cohn, 2026, needs more optimization.
16 595 0.378269076868 Henry Cohn, 2026, needs more optimization.
16 596 0.378399407763 Henry Cohn, 2026, needs more optimization.
16 597 0.378400021601 Henry Cohn, 2026, needs more optimization.
16 598 0.379364028533 Henry Cohn, 2026, needs more optimization.
16 599 0.379365191925 Henry Cohn, 2026, needs more optimization.
16 600 0.380092143448 Henry Cohn, 2026, needs more optimization.
16 601 0.380093509690 Henry Cohn, 2026, needs more optimization.
16 602 0.380184562504 Henry Cohn, 2026, needs more optimization.
16 603 0.380202008871 Henry Cohn, 2026, needs more optimization.
16 604 0.380636648277 Henry Cohn, 2026, needs more optimization.
16 605 0.380637250038 Henry Cohn, 2026, needs more optimization.
16 606 0.380719567790 Henry Cohn, 2026, needs more optimization.
16 607 0.381181707519 Henry Cohn, 2026, needs more optimization.
16 608 0.381182752173 Henry Cohn, 2026, needs more optimization.
16 609 0.381758063322 Henry Cohn, 2026, needs more optimization.
16 610 0.381998761339 Henry Cohn, 2026, needs more optimization.
16 611 0.382298202135 Henry Cohn, 2026, needs more optimization.
16 612 0.382745039306 Henry Cohn, 2026, needs more optimization.
16 613 0.383157188724 Henry Cohn, 2026, needs more optimization.
16 614 0.383467482233 Henry Cohn, 2026, needs more optimization.
16 615 0.383643505852 Henry Cohn, 2026, needs more optimization.
16 616 0.384236550107 Henry Cohn, 2026, needs more optimization.
16 617 0.384328639673 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 0.386120190330 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 0.395906823376 Henry Cohn, 2026, needs more optimization.
16 683 0.396407957447 Henry Cohn, 2026, needs more optimization.
16 684 0.396850956421 Henry Cohn, 2026, needs more optimization.
16 685 0.397222133104 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 0.398934851130 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 0.406035217936 Henry Cohn, 2026, needs more optimization.
16 775 0.406073100288 Henry Cohn, 2026, needs more optimization.
16 776 0.406214167263 Henry Cohn, 2026, needs more optimization.
16 780 0.406228932439 Henry Cohn, 2026, needs more optimization.
16 781 0.406435106735 Henry Cohn, 2026, needs more optimization.
16 782 0.407344921026 Henry Cohn, 2026, needs more optimization.
16 784 0.407588753756 Henry Cohn, 2026, needs more optimization.
16 785 0.407613343810 Henry Cohn, 2026, needs more optimization.
16 787 0.407719170823 Henry Cohn, 2026, needs more optimization.
16 788 0.408575172605 Henry Cohn, 2026, needs more optimization.
16 793 0.408628377653 Henry Cohn, 2026, needs more optimization.
16 794 0.408764999429 Henry Cohn, 2026, needs more optimization.
16 795 0.408816233562 Henry Cohn, 2026, needs more optimization.
16 796 0.408945891948 Henry Cohn, 2026, needs more optimization.
16 797 0.409048746769 Henry Cohn, 2026, needs more optimization.
16 798 0.409057854314 Henry Cohn, 2026, needs more optimization.
16 799 0.409132071019 Henry Cohn, 2026, needs more optimization.
16 800 0.409166804230 Henry Cohn, 2026, needs more optimization.
16 801 0.409186223115 Henry Cohn, 2026, needs more optimization.
16 802 0.409223463391 Henry Cohn, 2026, needs more optimization.
16 803 0.409250791283 Henry Cohn, 2026, needs more optimization.
16 804 0.409341490187 Henry Cohn, 2026, needs more optimization.
16 805 0.409357610706 Henry Cohn, 2026, needs more optimization.
16 806 0.409367879950 Henry Cohn, 2026, needs more optimization.
16 807 0.409374643538 Henry Cohn, 2026, needs more optimization.
16 808 0.409374668199 Henry Cohn, 2026, needs more optimization.
16 810 0.409374848464 Henry Cohn, 2026, needs more optimization.
16 811 0.411809283340 Henry Cohn, 2026, needs more optimization.
16 812 0.411890379303 Henry Cohn, 2026, needs more optimization.
16 813 0.411892078577 Henry Cohn, 2026, needs more optimization.
16 814 0.414325999938 Henry Cohn, 2026, needs more optimization.
16 815 0.414327691103 Henry Cohn, 2026, needs more optimization.
16 816 0.414338829480 Henry Cohn, 2026, needs more optimization.
16 817 0.414395619530 Henry Cohn, 2026, needs more optimization.
16 818 0.414401809852 Henry Cohn, 2026, needs more optimization.
16 820 0.414422372506 Henry Cohn, 2026, needs more optimization.
16 823 0.414437078854 Henry Cohn, 2026, needs more optimization.
16 826 0.414694545970 Henry Cohn, 2026, needs more optimization.
16 827 0.414695682317 Henry Cohn, 2026, needs more optimization.
16 828 0.414698292186 Henry Cohn, 2026, needs more optimization.
16 829 0.414778234763 Henry Cohn, 2026, needs more optimization.
16 830 0.414783880073 Henry Cohn, 2026, needs more optimization.
16 831 0.414863714670 Henry Cohn, 2026, needs more optimization.
16 832 0.414873777166 Henry Cohn, 2026, needs more optimization.
16 833 0.415043635056 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 0.425367310796 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 0.127206601234 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 0.142557693199 Henry Cohn, 2026, needs more optimization.
17 80 0.147987559048 Henry Cohn, 2026, needs more optimization.
17 81 0.149888911515 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 0.156529575276 Henry Cohn, 2026, needs more optimization.
17 89 0.158629733318 Henry Cohn, 2026, needs more optimization.
17 90 0.163956068864 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 0.167559748143 Henry Cohn, 2026, needs more optimization.
17 94 0.167882858371 Henry Cohn, 2026, needs more optimization.
17 95 0.168040781562 Henry Cohn, 2026, needs more optimization.
17 96 0.168354290007 Henry Cohn, 2026, needs more optimization.
17 97 0.168537119254 Henry Cohn, 2026, needs more optimization.
17 98 0.168603491172 Henry Cohn, 2026, needs more optimization.
17 99 0.168672659500 Henry Cohn, 2026, needs more optimization.
17 100 0.168675190337 Henry Cohn, 2026, needs more optimization.
17 101 0.168690039352 Henry Cohn, 2026, needs more optimization.
17 102 0.169905173965 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 0.170761750770 Henry Cohn, 2026, needs more optimization.
17 108 0.175086042960 Henry Cohn, 2026, needs more optimization.
17 109 0.179289059643 Henry Cohn, 2026, needs more optimization.
17 110 0.180274068527 Henry Cohn, 2026, needs more optimization.
17 111 0.182402680249 Henry Cohn, 2026, needs more optimization.
17 115 0.184252183279 Henry Cohn, 2026.
17 116 0.184847526050 Henry Cohn, 2026, needs more optimization.
17 117 0.186673243592 Henry Cohn, 2026, needs more optimization.
17 118 0.187744177641 Henry Cohn, 2026, needs more optimization.
17 119 0.189942532139 Henry Cohn, 2026, needs more optimization.
17 120 0.190640959908 Henry Cohn, 2026, needs more optimization.
17 121 0.192294194979 Henry Cohn, 2026, needs more optimization.
17 122 0.192377889070 Henry Cohn, 2026, needs more optimization.
17 123 0.192451522909 Henry Cohn, 2026, needs more optimization.
17 124 0.192969996450 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 0.192993362600 Henry Cohn, 2026, needs more optimization.
17 127 0.193832467986 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 0.196260829371 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 0.197524399415 Henry Cohn, 2026, needs more optimization.
17 131 0.198989508585 Henry Cohn, 2026, needs more optimization.
17 132 0.199042801573 Henry Cohn, 2026, needs more optimization.
17 133 0.199562777719 Henry Cohn, 2026, needs more optimization.
17 134 0.199818589045 Henry Cohn, 2026, needs more optimization.
17 135 0.199881115381 Henry Cohn, 2026, needs more optimization.
17 136 0.199970064678 Henry Cohn, 2026, needs more optimization.
17 137 0.199989364382 Henry Cohn, 2026, needs more optimization.
17 138 0.200018626593 Henry Cohn, 2026, needs more optimization.
17 139 0.200162735544 Henry Cohn, 2026, needs more optimization.
17 140 0.200257893204 Henry Cohn, 2026, needs more optimization.
17 141 0.202596236714 Henry Cohn, 2026, needs more optimization.
17 142 0.202851463005 Henry Cohn, 2026, needs more optimization.
17 143 0.202863811415 Henry Cohn, 2026, needs more optimization.
17 144 0.202883655957 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 0.202899805483 Henry Cohn, 2026, needs more optimization.
17 153 0.202909339588 Henry Cohn, 2026, needs more optimization.
17 155 0.202911127135 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 0.202914234009 Henry Cohn, 2026, needs more optimization.
17 164 0.202919956804 Henry Cohn, 2026, needs more optimization.
17 165 0.203272366259 Henry Cohn, 2026, needs more optimization.
17 166 0.209287488667 Henry Cohn, 2026, needs more optimization.
17 167 0.209415890905 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 0.215893819570 Henry Cohn, 2026, needs more optimization.
17 179 0.223741486613 Henry Cohn, 2026, needs more optimization.
17 180 0.224786890550 Henry Cohn, 2026, needs more optimization.
17 181 0.227607609895 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 0.233280628683 Henry Cohn, 2026, needs more optimization.
17 194 0.234605562702 Henry Cohn, 2026, needs more optimization.
17 195 0.235739062685 Henry Cohn, 2026, needs more optimization.
17 196 0.237300483965 Henry Cohn, 2026, needs more optimization.
17 197 0.238211781595 Henry Cohn, 2026, needs more optimization.
17 198 0.239200305560 Henry Cohn, 2026, needs more optimization.
17 199 0.240135704906 Henry Cohn, 2026, needs more optimization.
17 200 0.240931952759 Henry Cohn, 2026, needs more optimization.
17 201 0.241627337966 Henry Cohn, 2026, needs more optimization.
17 202 0.242708389449 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.
17 203 0.242750978304 Henry Cohn, 2026, needs more optimization.
17 204 0.243196836921 Henry Cohn, 2026, needs more optimization.
17 205 0.243887411320 Henry Cohn, 2026, needs more optimization.
17 206 0.244224425714 Henry Cohn, 2026, needs more optimization.
17 207 0.244556628798 Henry Cohn, 2026, needs more optimization.
17 208 0.244962471732 Henry Cohn, 2026, needs more optimization.
17 209 0.245151880081 Henry Cohn, 2026, needs more optimization.
17 210 0.245539768900 Henry Cohn, 2026, needs more optimization.
17 211 0.245986909922 Henry Cohn, 2026, needs more optimization.
17 212 0.246279163566 Henry Cohn, 2026, needs more optimization.
17 213 0.246456482536 Henry Cohn, 2026, needs more optimization.
17 214 0.246522870682 Henry Cohn, 2026, needs more optimization.
17 215 0.246636615529 Henry Cohn, 2026, needs more optimization.
17 216 0.246895923855 Henry Cohn, 2026, needs more optimization.
17 217 0.247045726249 Henry Cohn, 2026, needs more optimization.
17 218 0.247271558453 Henry Cohn, 2026, needs more optimization.
17 219 0.247728418805 Henry Cohn, 2026, needs more optimization.
17 220 0.247837261432 Henry Cohn, 2026, needs more optimization.
17 221 0.248075512954 Henry Cohn, 2026, needs more optimization.
17 222 0.248262594876 Henry Cohn, 2026, needs more optimization.
17 223 0.248375507251 Henry Cohn, 2026, needs more optimization.
17 224 0.248515372645 Henry Cohn, 2026, needs more optimization.
17 225 0.248648867571 Henry Cohn, 2026, needs more optimization.
17 226 0.248761060503 Henry Cohn, 2026, needs more optimization.
17 227 0.248914085018 Henry Cohn, 2026, needs more optimization.
17 228 0.249001794915 Henry Cohn, 2026, needs more optimization.
17 229 0.249286713217 Henry Cohn, 2026, needs more optimization.
17 230 0.249470193391 Henry Cohn, 2026, needs more optimization.
17 231 0.249540396401 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.
17 232 0.249576567180 Henry Cohn, 2026, needs more optimization.
17 233 0.249594583198 Henry Cohn, 2026, needs more optimization.
17 234 0.249621021206 Henry Cohn, 2026, needs more optimization.
17 235 0.249631984320 Henry Cohn, 2026, needs more optimization.
17 236 0.249660804919 Henry Cohn, 2026, needs more optimization.
17 237 0.249701044978 Henry Cohn, 2026, needs more optimization.
17 238 0.249732539042 Henry Cohn, 2026, needs more optimization.
17 239 0.249755169526 Henry Cohn, 2026, needs more optimization.
17 240 0.249767382440 Henry Cohn, 2026, needs more optimization.
17 241 0.249787714135 Henry Cohn, 2026, needs more optimization.
17 242 0.249809011984 Henry Cohn, 2026, needs more optimization.
17 243 0.249840076223 Henry Cohn, 2026, needs more optimization.
17 244 0.249849710797 Henry Cohn, 2026, needs more optimization.
17 245 0.249861344609 Henry Cohn, 2026, needs more optimization.
17 246 0.249885538804 Henry Cohn, 2026, needs more optimization.
17 247 0.249907617333 Henry Cohn, 2026, needs more optimization.
17 248 0.249919218658 Henry Cohn, 2026, needs more optimization.
17 249 0.249933310281 Henry Cohn, 2026, needs more optimization.
17 250 0.249937771453 Henry Cohn, 2026, needs more optimization.
17 251 0.249980306202 Henry Cohn, 2026, needs more optimization.
17 254 0.249997185735 Henry Cohn, 2026, needs more optimization.
17 256 0.249999175810 Henry Cohn, 2026, needs more optimization.
17 257 0.249999645115 Henry Cohn, 2026, needs more optimization.
17 259 0.249999801170 Henry Cohn, 2026, needs more optimization.
17 264 0.249999860091 Henry Cohn, 2026, needs more optimization.
17 279 0.249999996203 Henry Cohn, 2026, needs more optimization.
17 280 0.249999999449 Henry Cohn, 2026, needs more optimization.
17 281 0.249999999453 Henry Cohn, 2026, needs more optimization.
17 283 0.249999999458 Henry Cohn, 2026, needs more optimization.
17 284 0.249999999699 Henry Cohn, 2026, needs more optimization.
17 285 0.249999999747 Henry Cohn, 2026, needs more optimization.
17 292 0.25 Henry Cohn, 2026.
4⁢x−1
17 293 0.250000009139 Henry Cohn, 2026, needs more optimization.
17 294 0.250000045919 Henry Cohn, 2026, needs more optimization.
17 295 0.250779194620 Henry Cohn, 2026, needs more optimization.
17 296 0.253966131961 Henry Cohn, 2026, needs more optimization.
17 297 0.255619399072 Henry Cohn, 2026, needs more optimization.
17 298 0.259858776962 Henry Cohn, 2026, needs more optimization.
17 299 0.261085318961 Henry Cohn, 2026, needs more optimization.
17 300 0.261086247733 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 0.281925942381 Henry Cohn, 2026, needs more optimization.
17 322 0.286552864475 Henry Cohn, 2026, needs more optimization.
17 323 0.289520846315 Henry Cohn, 2026, needs more optimization.
17 324 0.291667420701 Henry Cohn, 2026, needs more optimization.
17 325 0.293614817990 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 0.303058786431 Henry Cohn, 2026, needs more optimization.
17 355 0.304369545316 Henry Cohn, 2026, needs more optimization.
17 356 0.305241240505 Henry Cohn, 2026, needs more optimization.
17 357 0.306093176694 Henry Cohn, 2026, needs more optimization.
17 358 0.306690170671 Henry Cohn, 2026, needs more optimization.
17 359 0.307433856402 Henry Cohn, 2026, needs more optimization.
17 360 0.308033908133 Henry Cohn, 2026, needs more optimization.
17 361 0.308321977495 Henry Cohn, 2026, needs more optimization.
17 362 0.308715275500 Henry Cohn, 2026, needs more optimization.
17 363 0.309147467592 Henry Cohn, 2026, needs more optimization.
17 364 0.309523763188 Henry Cohn, 2026, needs more optimization.
17 365 0.309894331803 Henry Cohn, 2026, needs more optimization.
17 366 0.310327800898 Henry Cohn, 2026, needs more optimization.
17 367 0.310572103516 Henry Cohn, 2026, needs more optimization.
17 368 0.310893594490 Henry Cohn, 2026, needs more optimization.
17 369 0.311197904033 Henry Cohn, 2026, needs more optimization.
17 370 0.311457461041 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 0.312280346373 Henry Cohn, 2026, needs more optimization.
17 374 0.312606521202 Henry Cohn, 2026, needs more optimization.
17 375 0.312912760979 Henry Cohn, 2026, needs more optimization.
17 376 0.313084599188 Henry Cohn, 2026, needs more optimization.
17 377 0.313358404817 Henry Cohn, 2026, needs more optimization.
17 378 0.313537363521 Henry Cohn, 2026, needs more optimization.
17 379 0.313733755940 Henry Cohn, 2026, needs more optimization.
17 380 0.313951257833 Henry Cohn, 2026, needs more optimization.
17 381 0.314180946924 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 0.315313000316 Henry Cohn, 2026, needs more optimization.
17 388 0.315541956525 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 0.316326039601 Henry Cohn, 2026, needs more optimization.
17 392 0.316534321137 Henry Cohn, 2026, needs more optimization.
17 393 0.316765604715 Henry Cohn, 2026, needs more optimization.
17 394 0.317038360678 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 0.317677025939 Henry Cohn, 2026, needs more optimization.
17 398 0.317838024923 Henry Cohn, 2026, needs more optimization.
17 399 0.317878555479 Henry Cohn, 2026, needs more optimization.
17 400 0.318024076481 Henry Cohn, 2026, needs more optimization.
17 401 0.318078209681 Henry Cohn, 2026, needs more optimization.
17 402 0.318212829734 Henry Cohn, 2026, needs more optimization.
17 403 0.318270658163 Henry Cohn, 2026, needs more optimization.
17 404 0.318330081452 Henry Cohn, 2026, needs more optimization.
17 405 0.318359481109 Henry Cohn, 2026, needs more optimization.
17 406 0.318521356415 Henry Cohn, 2026, needs more optimization.
17 407 0.318577095696 Henry Cohn, 2026, needs more optimization.
17 408 0.318676916121 Henry Cohn, 2026, needs more optimization.
17 409 0.318766760470 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 0.322285932475 Henry Cohn, 2026, needs more optimization.
17 437 0.322623839615 Henry Cohn, 2026, needs more optimization.
17 438 0.323530844208 Henry Cohn, 2026, needs more optimization.
17 439 0.323875331574 Henry Cohn, 2026, needs more optimization.
17 440 0.324305329550 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 0.325686184880 Henry Cohn, 2026, needs more optimization.
17 444 0.326567215579 Henry Cohn, 2026, needs more optimization.
17 445 0.327316927967 Henry Cohn, 2026, needs more optimization.
17 446 0.327345029675 Henry Cohn, 2026, needs more optimization.
17 447 0.327507562178 Henry Cohn, 2026, needs more optimization.
17 448 0.327650264115 Henry Cohn, 2026, needs more optimization.
17 449 0.327799337870 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 0.345195626857 Henry Cohn, 2026, needs more optimization.
17 580 0.345195629507 Henry Cohn, 2026, needs more optimization.
17 581 0.345199120207 Henry Cohn, 2026, needs more optimization.
17 582 0.345294865637 Henry Cohn, 2026, needs more optimization.
17 583 0.345297476159 Henry Cohn, 2026, needs more optimization.
17 586 0.345317319353 Henry Cohn, 2026, needs more optimization.
17 589 0.345321556523 Henry Cohn, 2026, needs more optimization.
17 591 0.345323856648 Henry Cohn, 2026, needs more optimization.
17 592 0.349717716250 Henry Cohn, 2026, needs more optimization.
17 594 0.349768583946 Henry Cohn, 2026, needs more optimization.
17 596 0.349774647440 Henry Cohn, 2026, needs more optimization.
17 597 0.349774647759 Henry Cohn, 2026, needs more optimization.
17 599 0.349797358058 Henry Cohn, 2026, needs more optimization.
17 600 0.350131179663 Henry Cohn, 2026, needs more optimization.
17 601 0.351987418524 Henry Cohn, 2026, needs more optimization.
17 603 0.352125072654 Henry Cohn, 2026, needs more optimization.
17 604 0.352149273384 Henry Cohn, 2026, needs more optimization.
17 605 0.352149273847 Henry Cohn, 2026, needs more optimization.
17 606 0.352360067336 Henry Cohn, 2026, needs more optimization.
17 607 0.352384473792 Henry Cohn, 2026, needs more optimization.
17 608 0.352440500107 Henry Cohn, 2026, needs more optimization.
17 609 0.352570042840 Henry Cohn, 2026, needs more optimization.
17 610 0.352570121887 Henry Cohn, 2026, needs more optimization.
17 611 0.352571374753 Henry Cohn, 2026, needs more optimization.
17 612 0.352580851679 Henry Cohn, 2026, needs more optimization.
17 613 0.353071651366 Henry Cohn, 2026, needs more optimization.
17 614 0.353105577396 Henry Cohn, 2026, needs more optimization.
17 615 0.353218820094 Henry Cohn, 2026, needs more optimization.
17 616 0.353226196534 Henry Cohn, 2026, needs more optimization.
17 617 0.353226201911 Henry Cohn, 2026, needs more optimization.
17 618 0.353226202599 Henry Cohn, 2026, needs more optimization.
17 619 0.353235833222 Henry Cohn, 2026, needs more optimization.
17 620 0.353482599419 Henry Cohn, 2026, needs more optimization.
17 622 0.353518238168 Henry Cohn, 2026, needs more optimization.
17 623 0.353978626251 Henry Cohn, 2026, needs more optimization.
17 624 0.354881713323 Henry Cohn, 2026, needs more optimization.
17 625 0.354887051466 Henry Cohn, 2026, needs more optimization.
17 626 0.354895593334 Henry Cohn, 2026, needs more optimization.
17 628 0.354947191450 Henry Cohn, 2026, needs more optimization.
17 629 0.354950449470 Henry Cohn, 2026, needs more optimization.
17 630 0.354964691947 Henry Cohn, 2026, needs more optimization.
17 631 0.354976993250 Henry Cohn, 2026, needs more optimization.
17 632 0.354980791103 Henry Cohn, 2026, needs more optimization.
17 633 0.355000747754 Henry Cohn, 2026, needs more optimization.
17 634 0.355047623974 Henry Cohn, 2026, needs more optimization.
17 635 0.355050949018 Henry Cohn, 2026, needs more optimization.
17 636 0.362871427991 Henry Cohn, 2026, needs more optimization.
17 637 0.362871473746 Henry Cohn, 2026, needs more optimization.
17 638 0.362877080312 Henry Cohn, 2026, needs more optimization.
17 640 0.362920232222 Henry Cohn, 2026, needs more optimization.
17 641 0.362920511890 Henry Cohn, 2026, needs more optimization.
17 643 0.362920703539 Henry Cohn, 2026, needs more optimization.
17 644 0.362921075898 Henry Cohn, 2026, needs more optimization.
17 645 0.362940890493 Henry Cohn, 2026, needs more optimization.
17 646 0.363007334579 Henry Cohn, 2026, needs more optimization.
17 647 0.363007342251 Henry Cohn, 2026, needs more optimization.
17 648 0.363007355361 Henry Cohn, 2026, needs more optimization.
17 649 0.363007356817 Henry Cohn, 2026, needs more optimization.
17 650 0.363007382594 Henry Cohn, 2026, needs more optimization.
17 653 0.363008773080 Henry Cohn, 2026, needs more optimization.
17 654 0.363008975491 Henry Cohn, 2026, needs more optimization.
17 655 0.363061082958 Henry Cohn, 2026, needs more optimization.
17 656 0.363061087702 Henry Cohn, 2026, needs more optimization.
17 657 0.363061088622 Henry Cohn, 2026, needs more optimization.
17 658 0.363073004856 Henry Cohn, 2026, needs more optimization.
17 659 0.363073007914 Henry Cohn, 2026, needs more optimization.
17 660 0.363073010795 Henry Cohn, 2026, needs more optimization.
17 662 0.363073014322 Henry Cohn, 2026, needs more optimization.
17 663 0.363073016272 Henry Cohn, 2026, needs more optimization.
17 664 0.363073061357 Henry Cohn, 2026, needs more optimization.
17 667 0.363089815642 Henry Cohn, 2026, needs more optimization.
17 668 0.363104989051 Henry Cohn, 2026, needs more optimization.
17 669 0.363122347769 Henry Cohn, 2026, needs more optimization.
17 670 0.363122364892 Henry Cohn, 2026, needs more optimization.
17 671 0.363122365100 Henry Cohn, 2026, needs more optimization.
17 672 0.363122368561 Henry Cohn, 2026, needs more optimization.
17 673 0.363122368936 Henry Cohn, 2026, needs more optimization.
17 674 0.363122374540 Henry Cohn, 2026, needs more optimization.
17 675 0.363170721548 Henry Cohn, 2026, needs more optimization.
17 676 0.363187256557 Henry Cohn, 2026, needs more optimization.
17 678 0.363207845231 Henry Cohn, 2026, needs more optimization.
17 682 0.363212439031 Henry Cohn, 2026, needs more optimization.
17 683 0.363223418389 Henry Cohn, 2026, needs more optimization.
17 685 0.363223572471 Henry Cohn, 2026, needs more optimization.
17 686 0.363223573943 Henry Cohn, 2026, needs more optimization.
17 687 0.363235601615 Henry Cohn, 2026, needs more optimization.
17 688 0.363251147022 Henry Cohn, 2026, needs more optimization.
17 691 0.363259889808 Henry Cohn, 2026, needs more optimization.
17 694 0.363259899530 Henry Cohn, 2026, needs more optimization.
17 695 0.363259995944 Henry Cohn, 2026, needs more optimization.
17 696 0.363271971280 Henry Cohn, 2026, needs more optimization.
17 701 0.363272626672 Henry Cohn, 2026, needs more optimization.
17 708 0.363280297473 Henry Cohn, 2026, needs more optimization.
17 709 0.363294206046 Henry Cohn, 2026, needs more optimization.
17 710 0.363294207928 Henry Cohn, 2026, needs more optimization.
17 711 0.363294210242 Henry Cohn, 2026, needs more optimization.
17 712 0.363316643717 Henry Cohn, 2026, needs more optimization.
17 714 0.363329598168 Henry Cohn, 2026, needs more optimization.
17 716 0.363330297144 Henry Cohn, 2026, needs more optimization.
17 717 0.363330315982 Henry Cohn, 2026, needs more optimization.
17 718 0.363331511503 Henry Cohn, 2026, needs more optimization.
17 720 0.363335612753 Henry Cohn, 2026, needs more optimization.
17 724 0.363335613251 Henry Cohn, 2026, needs more optimization.
17 726 0.363345199717 Henry Cohn, 2026, needs more optimization.
17 727 0.363345199985 Henry Cohn, 2026, needs more optimization.
17 728 0.363345200759 Henry Cohn, 2026, needs more optimization.
17 729 0.363347173560 Henry Cohn, 2026, needs more optimization.
17 733 0.363347173592 Henry Cohn, 2026, needs more optimization.
17 734 0.363347177005 Henry Cohn, 2026, needs more optimization.
17 735 0.363352623572 Henry Cohn, 2026, needs more optimization.
17 736 0.363352625436 Henry Cohn, 2026, needs more optimization.
17 737 0.363352629725 Henry Cohn, 2026, needs more optimization.
17 739 0.363361499847 Henry Cohn, 2026, needs more optimization.
17 742 0.363361501061 Henry Cohn, 2026, needs more optimization.
17 744 0.363361502058 Henry Cohn, 2026, needs more optimization.
17 747 0.363372514189 Henry Cohn, 2026, needs more optimization.
17 749 0.363375122701 Henry Cohn, 2026, needs more optimization.
17 751 0.363381543995 Henry Cohn, 2026, needs more optimization.
17 752 0.363383225758 Henry Cohn, 2026, needs more optimization.
17 753 0.363389713647 Henry Cohn, 2026, needs more optimization.
17 754 0.363389715885 Henry Cohn, 2026, needs more optimization.
17 755 0.371249826815 Henry Cohn, 2026, needs more optimization.
17 757 0.371415603879 Henry Cohn, 2026, needs more optimization.
17 758 0.371485114534 Henry Cohn, 2026, needs more optimization.
17 759 0.371490153574 Henry Cohn, 2026, needs more optimization.
17 760 0.371636831592 Henry Cohn, 2026, needs more optimization.
17 761 0.371638420980 Henry Cohn, 2026, needs more optimization.
17 765 0.371649019307 Henry Cohn, 2026, needs more optimization.
17 766 0.371659469193 Henry Cohn, 2026, needs more optimization.
17 767 0.378550336318 Henry Cohn, 2026, needs more optimization.
17 768 0.378552741047 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 0.084307972914 Henry Cohn, 2026, needs more optimization.
18 54 0.084331772475 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 76 0.122043871163 Henry Cohn, 2026, needs more optimization.
18 77 0.123493542007 Henry Cohn, 2026, needs more optimization.
18 78 0.125804804449 Henry Cohn, 2026, needs more optimization.
18 80 0.126224060072 Henry Cohn, 2026, needs more optimization.
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 0.132294284165 Henry Cohn, 2026, needs more optimization.
18 86 0.132700025640 Henry Cohn, 2026, needs more optimization.
18 87 0.133639154099 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 0.166082379043 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 0.169256817756 Henry Cohn, 2026, needs more optimization.
18 112 0.169849384780 Henry Cohn, 2026, needs more optimization.
18 113 0.170643157469 Henry Cohn, 2026, needs more optimization.
18 114 0.172162576941 Henry Cohn, 2026, needs more optimization.
18 115 0.172924794808 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 0.183022537901 Henry Cohn, 2026, needs more optimization.
18 119 0.184590358443 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 0.196405475604 Henry Cohn, 2026, needs more optimization.
18 142 0.196587554477 Henry Cohn, 2026, needs more optimization.
18 143 0.196786535149 Henry Cohn, 2026, needs more optimization.
18 144 0.197056948475 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 0.197852375704 Henry Cohn, 2026, needs more optimization.
18 148 0.198476467566 Henry Cohn, 2026, needs more optimization.
18 149 0.198705581136 Henry Cohn, 2026, needs more optimization.
18 150 0.199207298058 Henry Cohn, 2026, needs more optimization.
18 151 0.199550368168 Henry Cohn, 2026, needs more optimization.
18 152 0.200067519324 Henry Cohn, 2026, needs more optimization.
18 153 0.200259515899 Henry Cohn, 2026, needs more optimization.
18 154 0.200294944167 Henry Cohn, 2026, needs more optimization.
18 155 0.200732176351 Henry Cohn, 2026, needs more optimization.
18 156 0.201466840595 Henry Cohn, 2026, needs more optimization.
18 157 0.201542503054 Henry Cohn, 2026, needs more optimization.
18 158 0.201575084757 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 0.202069467300 Henry Cohn, 2026, needs more optimization.
18 162 0.202280101320 Henry Cohn, 2026, needs more optimization.
18 163 0.202373950268 Henry Cohn, 2026, needs more optimization.
18 164 0.202373954525 Henry Cohn, 2026, needs more optimization.
18 165 0.202568625209 Henry Cohn, 2026, needs more optimization.
18 166 0.202859038190 Henry Cohn, 2026, needs more optimization.
18 167 0.202892422419 Henry Cohn, 2026, needs more optimization.
18 168 0.202917908013 Henry Cohn, 2026, needs more optimization.
18 169 0.202919178685 Henry Cohn, 2026, needs more optimization.
18 170 0.202919886615 Henry Cohn, 2026, needs more optimization.
18 171 0.203076021147 Henry Cohn, 2026, needs more optimization.
18 172 0.204256926732 Henry Cohn, 2026, needs more optimization.
18 173 0.205762737106 Henry Cohn, 2026, needs more optimization.
18 174 0.208703785839 Henry Cohn, 2026, needs more optimization.
18 175 0.211757672788 Henry Cohn, 2026, needs more optimization.
18 176 0.213036382138 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.
18 177 0.214250091244 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.
18 179 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 0.214583376924 Henry Cohn, 2026, needs more optimization.
18 188 0.215551822182 Henry Cohn, 2026, needs more optimization.
18 189 0.217222032137 Henry Cohn, 2026, needs more optimization.
18 190 0.219896688620 Henry Cohn, 2026, needs more optimization.
18 191 0.221442888787 Henry Cohn, 2026, needs more optimization.
18 192 0.223219497117 Henry Cohn, 2026, needs more optimization.
18 205 0.224489795919 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.
49⁢x−11
18 206 0.227401307840 Henry Cohn, 2026, needs more optimization.
18 207 0.228475714726 Henry Cohn, 2026, needs more optimization.
18 208 0.229745808676 Henry Cohn, 2026, needs more optimization.
18 209 0.230550389594 Henry Cohn, 2026, needs more optimization.
18 210 0.230994698338 Henry Cohn, 2026, needs more optimization.
18 211 0.231265700956 Henry Cohn, 2026, needs more optimization.
18 212 0.232480944280 Henry Cohn, 2026, needs more optimization.
18 213 0.233085693972 Henry Cohn, 2026, needs more optimization.
18 214 0.233103123319 Henry Cohn, 2026, needs more optimization.
18 215 0.233477430810 Henry Cohn, 2026, needs more optimization.
18 216 0.234804813261 Henry Cohn, 2026, needs more optimization.
18 217 0.235800886161 Henry Cohn, 2026, needs more optimization.
18 218 0.236443273513 Henry Cohn, 2026, needs more optimization.
18 219 0.237603427940 Henry Cohn, 2026, needs more optimization.
18 220 0.238603975656 Henry Cohn, 2026, needs more optimization.
18 221 0.239741792009 Henry Cohn, 2026, needs more optimization.
18 222 0.240338302378 Henry Cohn, 2026, needs more optimization.
18 223 0.241184833199 Henry Cohn, 2026, needs more optimization.
18 224 0.241540052913 Henry Cohn, 2026, needs more optimization.
18 225 0.241645781628 Henry Cohn, 2026, needs more optimization.
18 226 0.241767621509 Henry Cohn, 2026, needs more optimization.
18 227 0.241903800384 Henry Cohn, 2026, needs more optimization.
18 228 0.242081607099 Henry Cohn, 2026, needs more optimization.
18 229 0.242322111897 Henry Cohn, 2026, needs more optimization.
18 230 0.242428290060 Henry Cohn, 2026, needs more optimization.
18 231 0.242552987301 Henry Cohn, 2026, needs more optimization.
18 232 0.242825492695 Henry Cohn, 2026, needs more optimization.
18 233 0.243060347694 Henry Cohn, 2026, needs more optimization.
18 234 0.243541073156 Henry Cohn, 2026, needs more optimization.
18 235 0.243842594289 Henry Cohn, 2026, needs more optimization.
18 236 0.243998417985 Henry Cohn, 2026, needs more optimization.
18 237 0.244149185536 Henry Cohn, 2026, needs more optimization.
18 238 0.244362981028 Henry Cohn, 2026, needs more optimization.
18 239 0.244808185364 Henry Cohn, 2026, needs more optimization.
18 241 0.244808193449 Henry Cohn, 2026, needs more optimization.
18 242 0.244820757641 Henry Cohn, 2026, needs more optimization.
18 243 0.244863432769 Henry Cohn, 2026, needs more optimization.
18 244 0.245126730286 Henry Cohn, 2026, needs more optimization.
18 245 0.245179121517 Henry Cohn, 2026, needs more optimization.
18 246 0.245202263433 Henry Cohn, 2026, needs more optimization.
18 247 0.245346442623 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 0.245773349800 Henry Cohn, 2026, needs more optimization.
18 252 0.245833399556 Henry Cohn, 2026, needs more optimization.
18 253 0.245968562741 Henry Cohn, 2026, needs more optimization.
18 254 0.245970143872 Henry Cohn, 2026, needs more optimization.
18 255 0.246025729757 Henry Cohn, 2026, needs more optimization.
18 256 0.246067070343 Henry Cohn, 2026, needs more optimization.
18 257 0.246124014700 Henry Cohn, 2026, needs more optimization.
18 258 0.246156886667 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 0.246411648651 Henry Cohn, 2026, needs more optimization.
18 263 0.246433997538 Henry Cohn, 2026, needs more optimization.
18 264 0.246479235048 Henry Cohn, 2026, needs more optimization.
18 265 0.246931153699 Henry Cohn, 2026, needs more optimization.
18 266 0.246962330627 Henry Cohn, 2026, needs more optimization.
18 267 0.246980828734 Henry Cohn, 2026, needs more optimization.
18 268 0.247076619076 Henry Cohn, 2026, needs more optimization.
18 269 0.247474141730 Henry Cohn, 2026, needs more optimization.
18 270 0.247485365255 Henry Cohn, 2026, needs more optimization.
18 271 0.247527103295 Henry Cohn, 2026, needs more optimization.
18 272 0.247574167266 Henry Cohn, 2026, needs more optimization.
18 273 0.247582005651 Henry Cohn, 2026, needs more optimization.
18 274 0.247594186788 Henry Cohn, 2026, needs more optimization.
18 275 0.247626131163 Henry Cohn, 2026, needs more optimization.
18 276 0.247646419025 Henry Cohn, 2026, needs more optimization.
18 277 0.247700627359 Henry Cohn, 2026, needs more optimization.
18 278 0.247719852041 Henry Cohn, 2026, needs more optimization.
18 279 0.247739691570 Henry Cohn, 2026, needs more optimization.
18 280 0.247741668984 Henry Cohn, 2026, needs more optimization.
18 281 0.247790622328 Henry Cohn, 2026, needs more optimization.
18 282 0.247800395597 Henry Cohn, 2026, needs more optimization.
18 283 0.247855354547 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 0.248232017047 Henry Cohn, 2026, needs more optimization.
18 288 0.248891217838 Henry Cohn, 2026, needs more optimization.
18 289 0.248926097900 Henry Cohn, 2026, needs more optimization.
18 290 0.249118685347 Henry Cohn, 2026, needs more optimization.
18 291 0.249401342868 Henry Cohn, 2026, needs more optimization.
18 292 0.249404789429 Henry Cohn, 2026, needs more optimization.
18 293 0.249656851737 Henry Cohn, 2026, needs more optimization.
18 294 0.249877634835 Henry Cohn, 2026, needs more optimization.
18 295 0.249879673227 Henry Cohn, 2026, needs more optimization.
18 296 0.249939798851 Henry Cohn, 2026, needs more optimization.
18 297 0.250007337302 Henry Cohn, 2026, needs more optimization.
18 298 0.250007368329 Henry Cohn, 2026, needs more optimization.
18 299 0.250007418111 Henry Cohn, 2026, needs more optimization.
18 300 0.250010271603 Henry Cohn, 2026, needs more optimization.
18 301 0.250010274393 Henry Cohn, 2026, needs more optimization.
18 302 0.250011641758 Henry Cohn, 2026, needs more optimization.
18 303 0.250020031975 Henry Cohn, 2026, needs more optimization.
18 304 0.250020035004 Henry Cohn, 2026, needs more optimization.
18 305 0.250034474304 Henry Cohn, 2026, needs more optimization.
18 306 0.250148540992 Henry Cohn, 2026, needs more optimization.
18 307 0.251213201805 Henry Cohn, 2026, needs more optimization.
18 308 0.251984897189 Henry Cohn, 2026, needs more optimization.
18 309 0.252629433856 Henry Cohn, 2026, needs more optimization.
18 310 0.253790207216 Henry Cohn, 2026, needs more optimization.
18 311 0.254844687402 Henry Cohn, 2026, needs more optimization.
18 312 0.256229957148 Henry Cohn, 2026, needs more optimization.
18 313 0.256882299630 Henry Cohn, 2026, needs more optimization.
18 314 0.258109718504 Henry Cohn, 2026, needs more optimization.
18 315 0.258840381823 Henry Cohn, 2026, needs more optimization.
18 316 0.258854888649 Henry Cohn, 2026, needs more optimization.
18 317 0.258942740518 Henry Cohn, 2026, needs more optimization.
18 318 0.258951989857 Henry Cohn, 2026, needs more optimization.
18 319 0.259067816679 Henry Cohn, 2026, needs more optimization.
18 320 0.259176089262 Henry Cohn, 2026, needs more optimization.
18 321 0.259178245351 Henry Cohn, 2026, needs more optimization.
18 322 0.259194786174 Henry Cohn, 2026, needs more optimization.
18 323 0.259207617837 Henry Cohn, 2026, needs more optimization.
18 324 0.259395714308 Henry Cohn, 2026, needs more optimization.
18 325 0.259865500796 Henry Cohn, 2026, needs more optimization.
18 326 0.259930149781 Henry Cohn, 2026, needs more optimization.
18 327 0.260109235989 Henry Cohn, 2026, needs more optimization.
18 328 0.260221037859 Henry Cohn, 2026, needs more optimization.
18 329 0.260419005496 Henry Cohn, 2026, needs more optimization.
18 330 0.260721167937 Henry Cohn, 2026, needs more optimization.
18 331 0.260721198683 Henry Cohn, 2026, needs more optimization.
18 332 0.260721228034 Henry Cohn, 2026, needs more optimization.
18 333 0.260738025797 Henry Cohn, 2026, needs more optimization.
18 334 0.260760348100 Henry Cohn, 2026, needs more optimization.
18 335 0.260773829830 Henry Cohn, 2026, needs more optimization.
18 336 0.260785690432 Henry Cohn, 2026, needs more optimization.
18 337 0.260830682003 Henry Cohn, 2026, needs more optimization.
18 338 0.260833371280 Henry Cohn, 2026, needs more optimization.
18 339 0.260845291658 Henry Cohn, 2026, needs more optimization.
18 340 0.260849523386 Henry Cohn, 2026, needs more optimization.
18 341 0.260873673696 Henry Cohn, 2026, needs more optimization.
18 342 0.260875493480 Henry Cohn, 2026, needs more optimization.
18 343 0.260886776751 Henry Cohn, 2026, needs more optimization.
18 344 0.260915745765 Henry Cohn, 2026, needs more optimization.
18 345 0.260934270111 Henry Cohn, 2026, needs more optimization.
18 346 0.260944913122 Henry Cohn, 2026, needs more optimization.
18 347 0.260947885704 Henry Cohn, 2026, needs more optimization.
18 348 0.260966218928 Henry Cohn, 2026, needs more optimization.
18 349 0.260970353568 Henry Cohn, 2026, needs more optimization.
18 350 0.260999686460 Henry Cohn, 2026, needs more optimization.
18 351 0.261022624127 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.
18 352 0.261046365090 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 0.277865999646 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 0.284721427051 Henry Cohn, 2026, needs more optimization.
18 357 0.287886955460 Henry Cohn, 2026, needs more optimization.
18 358 0.290352483425 Henry Cohn, 2026, needs more optimization.
18 359 0.291557165226 Henry Cohn, 2026, needs more optimization.
18 360 0.292848400416 Henry Cohn, 2026, needs more optimization.
18 364 0.294119196950 Henry Cohn, 2026, needs more optimization.
18 366 0.294119197711 Henry Cohn, 2026, needs more optimization.
18 368 0.294119210134 Henry Cohn, 2026, needs more optimization.
18 369 0.294119228286 Henry Cohn, 2026, needs more optimization.
18 372 0.294119238701 Henry Cohn, 2026, needs more optimization.
18 373 0.294119240172 Henry Cohn, 2026, needs more optimization.
18 374 0.294119240811 Henry Cohn, 2026, needs more optimization.
18 379 0.294119247715 Henry Cohn, 2026, needs more optimization.
18 393 0.294119251646 Henry Cohn, 2026, needs more optimization.
18 399 0.294119252187 Henry Cohn, 2026, needs more optimization.
18 401 0.294119252294 Henry Cohn, 2026, needs more optimization.
18 402 0.294119252783 Henry Cohn, 2026, needs more optimization.
18 404 0.294119252970 Henry Cohn, 2026, needs more optimization.
18 405 0.294119253316 Henry Cohn, 2026, needs more optimization.
18 406 0.294120921039 Henry Cohn, 2026, needs more optimization.
18 407 0.294120921085 Henry Cohn, 2026, needs more optimization.
18 408 0.294120921338 Henry Cohn, 2026, needs more optimization.
18 411 0.294121694310 Henry Cohn, 2026, needs more optimization.
18 412 0.294121698903 Henry Cohn, 2026, needs more optimization.
18 413 0.294121700834 Henry Cohn, 2026, needs more optimization.
18 414 0.294166887283 Henry Cohn, 2026, needs more optimization.
18 415 0.295551092009 Henry Cohn, 2026, needs more optimization.
18 416 0.295553975936 Henry Cohn, 2026, needs more optimization.
18 417 0.295882704075 Henry Cohn, 2026, needs more optimization.
18 418 0.295913976803 Henry Cohn, 2026, needs more optimization.
18 419 0.295913991360 Henry Cohn, 2026, needs more optimization.
18 420 0.295925935166 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 0.300184185595 Henry Cohn, 2026, needs more optimization.
18 483 0.301458682605 Henry Cohn, 2026, needs more optimization.
18 484 0.302688058870 Henry Cohn, 2026, needs more optimization.
18 485 0.303484901130 Henry Cohn, 2026, needs more optimization.
18 486 0.305668044309 Henry Cohn, 2026, needs more optimization.
18 487 0.307366851086 Henry Cohn, 2026, needs more optimization.
18 488 0.309235015123 Henry Cohn, 2026, needs more optimization.
18 489 0.309499831737 Henry Cohn, 2026, needs more optimization.
18 490 0.309610324350 Henry Cohn, 2026, needs more optimization.
18 491 0.309888815500 Henry Cohn, 2026, needs more optimization.
18 492 0.310043426507 Henry Cohn, 2026, needs more optimization.
18 493 0.311352159718 Henry Cohn, 2026, needs more optimization.
18 494 0.312284319997 Henry Cohn, 2026, needs more optimization.
18 495 0.313010698401 Henry Cohn, 2026, needs more optimization.
18 496 0.313641478702 Henry Cohn, 2026, needs more optimization.
18 497 0.313716307597 Henry Cohn, 2026, needs more optimization.
18 498 0.313820606747 Henry Cohn, 2026, needs more optimization.
18 499 0.314051184042 Henry Cohn, 2026, needs more optimization.
18 500 0.315421256277 Henry Cohn, 2026, needs more optimization.
18 501 0.315965913663 Henry Cohn, 2026, needs more optimization.
18 502 0.316381987440 Henry Cohn, 2026, needs more optimization.
18 503 0.316632133189 Henry Cohn, 2026, needs more optimization.
18 504 0.316745119996 Henry Cohn, 2026, needs more optimization.
18 505 0.317114906410 Henry Cohn, 2026, needs more optimization.
18 506 0.317438171293 Henry Cohn, 2026, needs more optimization.
18 507 0.317887617514 Henry Cohn, 2026, needs more optimization.
18 508 0.318380748703 Henry Cohn, 2026, needs more optimization.
18 509 0.318728560948 Henry Cohn, 2026, needs more optimization.
18 510 0.318851434288 Henry Cohn, 2026, needs more optimization.
18 511 0.318939157930 Henry Cohn, 2026, needs more optimization.
18 512 0.319263997722 Henry Cohn, 2026, needs more optimization.
18 513 0.319299734660 Henry Cohn, 2026, needs more optimization.
18 514 0.319653578750 Henry Cohn, 2026, needs more optimization.
18 515 0.319705644680 Henry Cohn, 2026, needs more optimization.
18 516 0.320272132106 Henry Cohn, 2026, needs more optimization.
18 517 0.320525933016 Henry Cohn, 2026, needs more optimization.
18 518 0.321028919448 Henry Cohn, 2026, needs more optimization.
18 519 0.321690136050 Henry Cohn, 2026, needs more optimization.
18 520 0.321869820347 Henry Cohn, 2026, needs more optimization.
18 521 0.322013647079 Henry Cohn, 2026, needs more optimization.
18 522 0.323088444126 Henry Cohn, 2026, needs more optimization.
18 523 0.323118087089 Henry Cohn, 2026, needs more optimization.
18 524 0.323178881408 Henry Cohn, 2026, needs more optimization.
18 525 0.323756648612 Henry Cohn, 2026, needs more optimization.
18 526 0.323962431761 Henry Cohn, 2026, needs more optimization.
18 527 0.324378629865 Henry Cohn, 2026, needs more optimization.
18 528 0.324654658054 Henry Cohn, 2026, needs more optimization.
18 529 0.324931214596 Henry Cohn, 2026, needs more optimization.
18 530 0.324944564190 Henry Cohn, 2026, needs more optimization.
18 531 0.325276407385 Henry Cohn, 2026, needs more optimization.
18 532 0.325701066065 Henry Cohn, 2026, needs more optimization.
18 533 0.326013688480 Henry Cohn, 2026, needs more optimization.
18 534 0.326345542701 Henry Cohn, 2026, needs more optimization.
18 535 0.326584366306 Henry Cohn, 2026, needs more optimization.
18 536 0.326886671349 Henry Cohn, 2026, needs more optimization.
18 537 0.327123223845 Henry Cohn, 2026, needs more optimization.
18 538 0.327735911450 Henry Cohn, 2026, needs more optimization.
18 539 0.327922720368 Henry Cohn, 2026, needs more optimization.
18 540 0.328319330609 Henry Cohn, 2026, needs more optimization.
18 541 0.328723318299 Henry Cohn, 2026, needs more optimization.
18 542 0.329000614334 Henry Cohn, 2026, needs more optimization.
18 543 0.329077058039 Henry Cohn, 2026, needs more optimization.
18 544 0.329528718756 Henry Cohn, 2026, needs more optimization.
18 545 0.329678935522 Henry Cohn, 2026, needs more optimization.
18 546 0.330035533356 Henry Cohn, 2026, needs more optimization.
18 547 0.330251103688 Henry Cohn, 2026, needs more optimization.
18 548 0.330500871040 Henry Cohn, 2026, needs more optimization.
18 549 0.330858484403 Henry Cohn, 2026, needs more optimization.
18 550 0.331292145452 Henry Cohn, 2026, needs more optimization.
18 551 0.331652848305 Henry Cohn, 2026, needs more optimization.
18 552 0.331946826468 Henry Cohn, 2026, needs more optimization.
18 553 0.332358465974 Henry Cohn, 2026, needs more optimization.
18 554 0.332435931514 Henry Cohn, 2026, needs more optimization.
18 555 0.332569072773 Henry Cohn, 2026, needs more optimization.
18 556 0.332863052533 Henry Cohn, 2026, needs more optimization.
18 557 0.332981743443 Henry Cohn, 2026, needs more optimization.
18 558 0.333177871361 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 0.342211631844 Henry Cohn, 2026, needs more optimization.
18 706 0.343283576531 Henry Cohn, 2026, needs more optimization.
18 707 0.344654843800 Henry Cohn, 2026, needs more optimization.
18 708 0.345480696939 Henry Cohn, 2026, needs more optimization.
18 709 0.346125233919 Henry Cohn, 2026, needs more optimization.
18 710 0.346671672838 Henry Cohn, 2026, needs more optimization.
18 711 0.347197455599 Henry Cohn, 2026, needs more optimization.
18 712 0.347599469663 Henry Cohn, 2026, needs more optimization.
18 713 0.348065381431 Henry Cohn, 2026, needs more optimization.
18 714 0.348522289637 Henry Cohn, 2026, needs more optimization.
18 715 0.348829275535 Henry Cohn, 2026, needs more optimization.
18 716 0.348927999358 Henry Cohn, 2026, needs more optimization.
18 717 0.349216861744 Henry Cohn, 2026, needs more optimization.
18 718 0.349491909384 Henry Cohn, 2026, needs more optimization.
18 719 0.349816004347 Henry Cohn, 2026, needs more optimization.
18 720 0.350032942723 Henry Cohn, 2026, needs more optimization.
18 721 0.350305300204 Henry Cohn, 2026, needs more optimization.
18 722 0.350578883219 Henry Cohn, 2026, needs more optimization.
18 723 0.350634141032 Henry Cohn, 2026, needs more optimization.
18 724 0.350853782576 Henry Cohn, 2026, needs more optimization.
18 725 0.350973686974 Henry Cohn, 2026, needs more optimization.
18 726 0.351043287117 Henry Cohn, 2026, needs more optimization.
18 727 0.351254725975 Henry Cohn, 2026, needs more optimization.
18 728 0.351405722515 Henry Cohn, 2026, needs more optimization.
18 729 0.351541844256 Henry Cohn, 2026, needs more optimization.
18 730 0.351730773879 Henry Cohn, 2026, needs more optimization.
18 731 0.351799730346 Henry Cohn, 2026, needs more optimization.
18 733 0.351912227073 Henry Cohn, 2026, needs more optimization.
18 734 0.351917086588 Henry Cohn, 2026, needs more optimization.
18 736 0.351919967133 Henry Cohn, 2026, needs more optimization.
18 737 0.351921724819 Henry Cohn, 2026, needs more optimization.
18 740 0.351925183806 Henry Cohn, 2026, needs more optimization.
18 742 0.351928065471 Henry Cohn, 2026, needs more optimization.
18 743 0.351929876856 Henry Cohn, 2026, needs more optimization.
18 744 0.351950666337 Henry Cohn, 2026, needs more optimization.
18 745 0.351959722758 Henry Cohn, 2026, needs more optimization.
18 746 0.351960044892 Henry Cohn, 2026, needs more optimization.
18 747 0.351971833161 Henry Cohn, 2026, needs more optimization.
18 749 0.351983249900 Henry Cohn, 2026, needs more optimization.
18 750 0.351993298264 Henry Cohn, 2026, needs more optimization.
18 752 0.351993555186 Henry Cohn, 2026, needs more optimization.
18 753 0.351997794642 Henry Cohn, 2026, needs more optimization.
18 754 0.352002308948 Henry Cohn, 2026, needs more optimization.
18 755 0.352007691788 Henry Cohn, 2026, needs more optimization.
18 756 0.352010670883 Henry Cohn, 2026, needs more optimization.
18 757 0.352011476322 Henry Cohn, 2026, needs more optimization.
18 758 0.352018619166 Henry Cohn, 2026, needs more optimization.
18 760 0.352022642216 Henry Cohn, 2026, needs more optimization.
18 761 0.352035583138 Henry Cohn, 2026, needs more optimization.
18 762 0.352039756313 Henry Cohn, 2026, needs more optimization.
18 764 0.352039857410 Henry Cohn, 2026, needs more optimization.
18 765 0.352040702426 Henry Cohn, 2026, needs more optimization.
18 767 0.352043393155 Henry Cohn, 2026, needs more optimization.
18 768 0.352044708261 Henry Cohn, 2026, needs more optimization.
18 769 0.352047697796 Henry Cohn, 2026, needs more optimization.
18 771 0.352054352949 Henry Cohn, 2026, needs more optimization.
18 772 0.356485678504 Henry Cohn, 2026, needs more optimization.
18 773 0.356645163698 Henry Cohn, 2026, needs more optimization.
18 774 0.356826361255 Henry Cohn, 2026, needs more optimization.
18 775 0.356975722620 Henry Cohn, 2026, needs more optimization.
18 776 0.357124466688 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 0.373247107047 Henry Cohn, 2026, needs more optimization.
18 869 0.373268911243 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 0.084523429909 Henry Cohn, 2026, needs more optimization.
19 58 0.088502538618 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 0.104236937608 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 0.112769027873 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 0.133875538274 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 0.175005727194 Henry Cohn, 2026, needs more optimization.
19 136 0.175551912619 Henry Cohn, 2026, needs more optimization.
19 137 0.176552733641 Henry Cohn, 2026, needs more optimization.
19 138 0.177160791714 Henry Cohn, 2026, needs more optimization.
19 139 0.177608187220 Henry Cohn, 2026, needs more optimization.
19 140 0.178022647099 Henry Cohn, 2026, needs more optimization.
19 141 0.178307267136 Henry Cohn, 2026, needs more optimization.
19 142 0.178659456328 Henry Cohn, 2026, needs more optimization.
19 143 0.179134157824 Henry Cohn, 2026, needs more optimization.
19 144 0.179750083872 Henry Cohn, 2026, needs more optimization.
19 145 0.180462993720 Henry Cohn, 2026, needs more optimization.
19 146 0.180712993615 Henry Cohn, 2026, needs more optimization.
19 147 0.182338171375 Henry Cohn, 2026, needs more optimization.
19 148 0.183295513736 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 0.195467892411 Henry Cohn, 2026, needs more optimization.
19 180 0.195821119719 Henry Cohn, 2026, needs more optimization.
19 181 0.196900143928 Henry Cohn, 2026, needs more optimization.
19 182 0.197623509862 Henry Cohn, 2026, needs more optimization.
19 183 0.198453416125 Henry Cohn, 2026, needs more optimization.
19 184 0.199206619499 Henry Cohn, 2026, needs more optimization.
19 185 0.199768592021 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 0.207110961337 Henry Cohn, 2026, needs more optimization.
19 196 0.208040818646 Henry Cohn, 2026, needs more optimization.
19 197 0.208692896054 Henry Cohn, 2026, needs more optimization.
19 198 0.209394082875 Henry Cohn, 2026, needs more optimization.
19 199 0.209808203408 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 0.212023097497 Henry Cohn, 2026, needs more optimization.
19 204 0.212310394003 Henry Cohn, 2026, needs more optimization.
19 205 0.212685452332 Henry Cohn, 2026, needs more optimization.
19 206 0.212895489764 Henry Cohn, 2026, needs more optimization.
19 207 0.213597080177 Henry Cohn, 2026, needs more optimization.
19 208 0.214192896568 Henry Cohn, 2026, needs more optimization.
19 209 0.214628062189 Henry Cohn, 2026, needs more optimization.
19 210 0.214968827345 Henry Cohn, 2026, needs more optimization.
19 211 0.215406279711 Henry Cohn, 2026, needs more optimization.
19 212 0.215588801261 Henry Cohn, 2026, needs more optimization.
19 213 0.216096173073 Henry Cohn, 2026, needs more optimization.
19 214 0.216351820619 Henry Cohn, 2026, needs more optimization.
19 215 0.216868092043 Henry Cohn, 2026, needs more optimization.
19 216 0.217390605595 Henry Cohn, 2026, needs more optimization.
19 217 0.217556764905 Henry Cohn, 2026, needs more optimization.
19 218 0.218609270490 Henry Cohn, 2026, needs more optimization.
19 219 0.219122752988 Henry Cohn, 2026, needs more optimization.
19 220 0.219988040738 Henry Cohn, 2026, needs more optimization.
19 221 0.221051336970 Henry Cohn, 2026, needs more optimization.
19 222 0.222168627744 Henry Cohn, 2026, needs more optimization.
19 223 0.222377520406 Henry Cohn, 2026, needs more optimization.
19 224 0.222485333706 Henry Cohn, 2026, needs more optimization.
19 225 0.223302029953 Henry Cohn, 2026, needs more optimization.
19 226 0.223551190480 Henry Cohn, 2026, needs more optimization.
19 227 0.223958615227 Henry Cohn, 2026, needs more optimization.
19 228 0.224163263546 Henry Cohn, 2026, needs more optimization.
19 229 0.224213736661 Henry Cohn, 2026, needs more optimization.
19 230 0.224318199329 Henry Cohn, 2026, needs more optimization.
19 231 0.224475299223 Henry Cohn, 2026, needs more optimization.
19 232 0.224536470617 Henry Cohn, 2026, needs more optimization.
19 233 0.224693989110 Henry Cohn, 2026, needs more optimization.
19 234 0.224750554416 Henry Cohn, 2026, needs more optimization.
19 235 0.225176658547 Henry Cohn, 2026, needs more optimization.
19 236 0.225834184446 Henry Cohn, 2026, needs more optimization.
19 237 0.225936940222 Henry Cohn, 2026, needs more optimization.
19 238 0.225971570647 Henry Cohn, 2026, needs more optimization.
19 239 0.225984713327 Henry Cohn, 2026, needs more optimization.
19 240 0.226450369977 Henry Cohn, 2026, needs more optimization.
19 241 0.226628453027 Henry Cohn, 2026, needs more optimization.
19 242 0.226793132579 Henry Cohn, 2026, needs more optimization.
19 243 0.227021153563 Henry Cohn, 2026, needs more optimization.
19 244 0.227637650541 Henry Cohn, 2026, needs more optimization.
19 245 0.228808982230 Henry Cohn, 2026, needs more optimization.
19 246 0.229514527896 Henry Cohn, 2026, needs more optimization.
19 247 0.229945104880 Henry Cohn, 2026, needs more optimization.
19 248 0.230600575811 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.
19 277 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 0.235888485025 Henry Cohn, 2026, needs more optimization.
19 279 0.237140700588 Henry Cohn, 2026, needs more optimization.
19 280 0.238262890905 Henry Cohn, 2026, needs more optimization.
19 291 0.238519273263 Henry Cohn, 2026, needs more optimization.
19 292 0.240769288986 Henry Cohn, 2026, needs more optimization.
19 293 0.242312780003 Henry Cohn, 2026, needs more optimization.
19 294 0.243950308167 Henry Cohn, 2026, needs more optimization.
19 295 0.244497921293 Henry Cohn, 2026, needs more optimization.
19 296 0.244865473606 Henry Cohn, 2026, needs more optimization.
19 297 0.246209839732 Henry Cohn, 2026, needs more optimization.
19 298 0.246213575015 Henry Cohn, 2026, needs more optimization.
19 299 0.246672441625 Henry Cohn, 2026, needs more optimization.
19 300 0.247519635899 Henry Cohn, 2026, needs more optimization.
19 301 0.248421468889 Henry Cohn, 2026, needs more optimization.
19 302 0.249119347636 Henry Cohn, 2026, needs more optimization.
19 303 0.249356881159 Henry Cohn, 2026, needs more optimization.
19 304 0.249882978891 Henry Cohn, 2026, needs more optimization.
19 305 0.249947980503 Henry Cohn, 2026, needs more optimization.
19 306 0.249947981193 Henry Cohn, 2026, needs more optimization.
19 307 0.249947982313 Henry Cohn, 2026, needs more optimization.
19 308 0.249950192452 Henry Cohn, 2026, needs more optimization.
19 309 0.249950193877 Henry Cohn, 2026, needs more optimization.
19 310 0.249950196711 Henry Cohn, 2026, needs more optimization.
19 311 0.249950198093 Henry Cohn, 2026, needs more optimization.
19 312 0.249968084148 Henry Cohn, 2026, needs more optimization.
19 313 0.249968676785 Henry Cohn, 2026, needs more optimization.
19 314 0.249969275151 Henry Cohn, 2026, needs more optimization.
19 315 0.249969368804 Henry Cohn, 2026, needs more optimization.
19 318 0.249975123762 Henry Cohn, 2026, needs more optimization.
19 319 0.249987176843 Henry Cohn, 2026, needs more optimization.
19 320 0.249996452512 Henry Cohn, 2026, needs more optimization.
19 321 0.250000860148 Henry Cohn, 2026, needs more optimization.
19 322 0.250006332606 Henry Cohn, 2026, needs more optimization.
19 323 0.250010279232 Henry Cohn, 2026, needs more optimization.
19 324 0.250034755621 Henry Cohn, 2026, needs more optimization.
19 325 0.250072608555 Henry Cohn, 2026, needs more optimization.
19 326 0.250179701358 Henry Cohn, 2026, needs more optimization.
19 327 0.250738853742 Henry Cohn, 2026, needs more optimization.
19 328 0.251791316363 Henry Cohn, 2026, needs more optimization.
19 329 0.252779456455 Henry Cohn, 2026, needs more optimization.
19 330 0.253232980602 Henry Cohn, 2026, needs more optimization.
19 331 0.254217643921 Henry Cohn, 2026, needs more optimization.
19 332 0.255673657730 Henry Cohn, 2026, needs more optimization.
19 333 0.256803830370 Henry Cohn, 2026, needs more optimization.
19 334 0.258015102587 Henry Cohn, 2026, needs more optimization.
19 335 0.258053261017 Henry Cohn, 2026, needs more optimization.
19 336 0.258149862516 Henry Cohn, 2026, needs more optimization.
19 337 0.258243184818 Henry Cohn, 2026, needs more optimization.
19 338 0.258285570803 Henry Cohn, 2026, needs more optimization.
19 339 0.258401566530 Henry Cohn, 2026, needs more optimization.
19 340 0.258508987170 Henry Cohn, 2026, needs more optimization.
19 341 0.258571492729 Henry Cohn, 2026, needs more optimization.
19 342 0.258651884976 Henry Cohn, 2026, needs more optimization.
19 343 0.258843539894 Henry Cohn, 2026, needs more optimization.
19 344 0.258848573369 Henry Cohn, 2026, needs more optimization.
19 345 0.258854957151 Henry Cohn, 2026, needs more optimization.
19 346 0.258874704078 Henry Cohn, 2026, needs more optimization.
19 347 0.258901311682 Henry Cohn, 2026, needs more optimization.
19 348 0.258915945706 Henry Cohn, 2026, needs more optimization.
19 349 0.258972593847 Henry Cohn, 2026, needs more optimization.
19 350 0.259103178868 Henry Cohn, 2026, needs more optimization.
19 351 0.259201944893 Henry Cohn, 2026, needs more optimization.
19 352 0.259269040963 Henry Cohn, 2026, needs more optimization.
19 353 0.259348214021 Henry Cohn, 2026, needs more optimization.
19 354 0.259390023792 Henry Cohn, 2026, needs more optimization.
19 355 0.259497901423 Henry Cohn, 2026, needs more optimization.
19 356 0.259544422609 Henry Cohn, 2026, needs more optimization.
19 357 0.259655209838 Henry Cohn, 2026, needs more optimization.
19 358 0.259909506493 Henry Cohn, 2026, needs more optimization.
19 359 0.260020498471 Henry Cohn, 2026, needs more optimization.
19 360 0.260618976516 Henry Cohn, 2026, needs more optimization.
19 361 0.261503162698 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 0.263803628501 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 0.265639077728 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 0.267119495412 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.
19 365 0.268790607415 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.
19 366 0.268878984251 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 0.270085196538 Henry Cohn, 2026, needs more optimization.
19 368 0.270348286989 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 0.271660319184 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 0.281139421667 Henry Cohn, 2026, needs more optimization.
19 408 0.281658893357 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 0.282457394610 Henry Cohn, 2026, needs more optimization.
19 411 0.282667166242 Henry Cohn, 2026, needs more optimization.
19 412 0.282900032948 Henry Cohn, 2026, needs more optimization.
19 413 0.283125734480 Henry Cohn, 2026, needs more optimization.
19 414 0.283382545484 Henry Cohn, 2026, needs more optimization.
19 415 0.286050262962 Henry Cohn, 2026, needs more optimization.
19 416 0.286355519995 Henry Cohn, 2026, needs more optimization.
19 417 0.287130266858 Henry Cohn, 2026, needs more optimization.
19 464 0.287671232877 Henry Cohn, 2026.
73⁢x−21
19 465 0.287702014266 Henry Cohn, 2026, needs more optimization.
19 466 0.287786930204 Henry Cohn, 2026, needs more optimization.
19 467 0.287879499984 Henry Cohn, 2026, needs more optimization.
19 468 0.287885853166 Henry Cohn, 2026, needs more optimization.
19 469 0.287893259419 Henry Cohn, 2026, needs more optimization.
19 470 0.287893315074 Henry Cohn, 2026, needs more optimization.
19 471 0.287893806499 Henry Cohn, 2026, needs more optimization.
19 472 0.287903411472 Henry Cohn, 2026, needs more optimization.
19 473 0.287905481405 Henry Cohn, 2026, needs more optimization.
19 474 0.287907506738 Henry Cohn, 2026, needs more optimization.
19 476 0.287908365488 Henry Cohn, 2026, needs more optimization.
19 477 0.287910514825 Henry Cohn, 2026, needs more optimization.
19 478 0.287918746609 Henry Cohn, 2026, needs more optimization.
19 479 0.287928758084 Henry Cohn, 2026, needs more optimization.
19 480 0.287940409494 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 0.295155563022 Henry Cohn, 2026, needs more optimization.
19 580 0.296103976695 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 0.296715828924 Henry Cohn, 2026, needs more optimization.
19 584 0.296838990229 Henry Cohn, 2026, needs more optimization.
19 585 0.296935608399 Henry Cohn, 2026, needs more optimization.
19 586 0.297170050634 Henry Cohn, 2026, needs more optimization.
19 587 0.297367505033 Henry Cohn, 2026, needs more optimization.
19 588 0.297839567164 Henry Cohn, 2026, needs more optimization.
19 589 0.298140514227 Henry Cohn, 2026, needs more optimization.
19 590 0.298508818114 Henry Cohn, 2026, needs more optimization.
19 591 0.298845856714 Henry Cohn, 2026, needs more optimization.
19 592 0.299191134776 Henry Cohn, 2026, needs more optimization.
19 593 0.299289294928 Henry Cohn, 2026, needs more optimization.
19 594 0.299542095599 Henry Cohn, 2026, needs more optimization.
19 595 0.299675680441 Henry Cohn, 2026, needs more optimization.
19 596 0.299856934586 Henry Cohn, 2026, needs more optimization.
19 597 0.300027170013 Henry Cohn, 2026, needs more optimization.
19 598 0.300229918437 Henry Cohn, 2026, needs more optimization.
19 599 0.300370463145 Henry Cohn, 2026, needs more optimization.
19 600 0.300510384695 Henry Cohn, 2026, needs more optimization.
19 601 0.300647050393 Henry Cohn, 2026, needs more optimization.
19 602 0.300856867836 Henry Cohn, 2026, needs more optimization.
19 603 0.301013105968 Henry Cohn, 2026, needs more optimization.
19 604 0.301362908351 Henry Cohn, 2026, needs more optimization.
19 605 0.301640858340 Henry Cohn, 2026, needs more optimization.
19 606 0.301901527824 Henry Cohn, 2026, needs more optimization.
19 607 0.302118685161 Henry Cohn, 2026, needs more optimization.
19 608 0.302347335405 Henry Cohn, 2026, needs more optimization.
19 609 0.302596531027 Henry Cohn, 2026, needs more optimization.
19 610 0.302854777118 Henry Cohn, 2026, needs more optimization.
19 611 0.303044628279 Henry Cohn, 2026, needs more optimization.
19 612 0.303242406990 Henry Cohn, 2026, needs more optimization.
19 613 0.303380222190 Henry Cohn, 2026, needs more optimization.
19 614 0.303618021788 Henry Cohn, 2026, needs more optimization.
19 615 0.303774512794 Henry Cohn, 2026, needs more optimization.
19 616 0.303871577379 Henry Cohn, 2026, needs more optimization.
19 617 0.304058762666 Henry Cohn, 2026, needs more optimization.
19 618 0.304189048574 Henry Cohn, 2026, needs more optimization.
19 619 0.304256610189 Henry Cohn, 2026, needs more optimization.
19 620 0.304352811591 Henry Cohn, 2026, needs more optimization.
19 621 0.304456155774 Henry Cohn, 2026, needs more optimization.
19 622 0.304557170025 Henry Cohn, 2026, needs more optimization.
19 623 0.305093014896 Henry Cohn, 2026, needs more optimization.
19 624 0.305096470806 Henry Cohn, 2026, needs more optimization.
19 625 0.305097691509 Henry Cohn, 2026, needs more optimization.
19 626 0.305107199877 Henry Cohn, 2026, needs more optimization.
19 627 0.305114658380 Henry Cohn, 2026, needs more optimization.
19 628 0.305118696370 Henry Cohn, 2026, needs more optimization.
19 629 0.305123988522 Henry Cohn, 2026, needs more optimization.
19 630 0.305129782373 Henry Cohn, 2026, needs more optimization.
19 631 0.305138075269 Henry Cohn, 2026, needs more optimization.
19 632 0.305145133112 Henry Cohn, 2026, needs more optimization.
19 633 0.305148298074 Henry Cohn, 2026, needs more optimization.
19 634 0.305152979658 Henry Cohn, 2026, needs more optimization.
19 635 0.305156067349 Henry Cohn, 2026, needs more optimization.
19 636 0.305161231404 Henry Cohn, 2026, needs more optimization.
19 637 0.305164805186 Henry Cohn, 2026, needs more optimization.
19 638 0.305169098451 Henry Cohn, 2026, needs more optimization.
19 639 0.305172840725 Henry Cohn, 2026, needs more optimization.
19 640 0.305174895044 Henry Cohn, 2026, needs more optimization.
19 642 0.308282507428 Henry Cohn, 2026, needs more optimization.
19 643 0.308282789617 Henry Cohn, 2026, needs more optimization.
19 644 0.309146552922 Henry Cohn, 2026, needs more optimization.
19 645 0.309758777341 Henry Cohn, 2026, needs more optimization.
19 646 0.309759313059 Henry Cohn, 2026, needs more optimization.
19 647 0.310680241285 Henry Cohn, 2026, needs more optimization.
19 648 0.310963490036 Henry Cohn, 2026, needs more optimization.
19 649 0.311342528373 Henry Cohn, 2026, needs more optimization.
19 650 0.311464042184 Henry Cohn, 2026, needs more optimization.
19 651 0.311961356180 Henry Cohn, 2026, needs more optimization.
19 652 0.312217752643 Henry Cohn, 2026, needs more optimization.
19 653 0.312273712698 Henry Cohn, 2026, needs more optimization.
19 654 0.312736385307 Henry Cohn, 2026, needs more optimization.
19 655 0.312985718012 Henry Cohn, 2026, needs more optimization.
19 656 0.313155994662 Henry Cohn, 2026, needs more optimization.
19 657 0.313584057029 Henry Cohn, 2026, needs more optimization.
19 658 0.313803747823 Henry Cohn, 2026, needs more optimization.
19 659 0.314015508600 Henry Cohn, 2026, needs more optimization.
19 660 0.314167962731 Henry Cohn, 2026, needs more optimization.
19 661 0.314400368988 Henry Cohn, 2026, needs more optimization.
19 662 0.314549464487 Henry Cohn, 2026, needs more optimization.
19 663 0.314814798809 Henry Cohn, 2026, needs more optimization.
19 664 0.314978568657 Henry Cohn, 2026, needs more optimization.
19 665 0.315229718723 Henry Cohn, 2026, needs more optimization.
19 666 0.315360567645 Henry Cohn, 2026, needs more optimization.
19 667 0.315395911012 Henry Cohn, 2026, needs more optimization.
19 668 0.315680524245 Henry Cohn, 2026, needs more optimization.
19 669 0.315856263427 Henry Cohn, 2026, needs more optimization.
19 670 0.316109853252 Henry Cohn, 2026, needs more optimization.
19 671 0.316458681452 Henry Cohn, 2026, needs more optimization.
19 672 0.316549664317 Henry Cohn, 2026, needs more optimization.
19 673 0.316706086567 Henry Cohn, 2026, needs more optimization.
19 674 0.316968917526 Henry Cohn, 2026, needs more optimization.
19 675 0.317122886634 Henry Cohn, 2026, needs more optimization.
19 676 0.317251187624 Henry Cohn, 2026, needs more optimization.
19 677 0.317323385363 Henry Cohn, 2026, needs more optimization.
19 678 0.317580609774 Henry Cohn, 2026, needs more optimization.
19 679 0.317934446864 Henry Cohn, 2026, needs more optimization.
19 680 0.318239617481 Henry Cohn, 2026, needs more optimization.
19 681 0.318372139906 Henry Cohn, 2026, needs more optimization.
19 682 0.318728290217 Henry Cohn, 2026, needs more optimization.
19 683 0.318991975401 Henry Cohn, 2026, needs more optimization.
19 684 0.319321484831 Henry Cohn, 2026, needs more optimization.
19 685 0.319457530426 Henry Cohn, 2026, needs more optimization.
19 686 0.319681881672 Henry Cohn, 2026, needs more optimization.
19 687 0.319792373253 Henry Cohn, 2026, needs more optimization.
19 688 0.320180459037 Henry Cohn, 2026, needs more optimization.
19 689 0.320288088795 Henry Cohn, 2026, needs more optimization.
19 690 0.320495094308 Henry Cohn, 2026, needs more optimization.
19 691 0.320736991097 Henry Cohn, 2026, needs more optimization.
19 692 0.321075133537 Henry Cohn, 2026, needs more optimization.
19 693 0.321293119735 Henry Cohn, 2026, needs more optimization.
19 694 0.321412418423 Henry Cohn, 2026, needs more optimization.
19 695 0.321762361036 Henry Cohn, 2026, needs more optimization.
19 696 0.321908440005 Henry Cohn, 2026, needs more optimization.
19 697 0.322140611100 Henry Cohn, 2026, needs more optimization.
19 698 0.322375924759 Henry Cohn, 2026, needs more optimization.
19 699 0.322548450410 Henry Cohn, 2026, needs more optimization.
19 700 0.322614653673 Henry Cohn, 2026, needs more optimization.
19 701 0.322691700735 Henry Cohn, 2026, needs more optimization.
19 702 0.322926542677 Henry Cohn, 2026, needs more optimization.
19 703 0.323195420789 Henry Cohn, 2026, needs more optimization.
19 704 0.323570393445 Henry Cohn, 2026, needs more optimization.
19 705 0.323714565781 Henry Cohn, 2026, needs more optimization.
19 706 0.323808091299 Henry Cohn, 2026, needs more optimization.
19 707 0.323994243405 Henry Cohn, 2026, needs more optimization.
19 708 0.324138944647 Henry Cohn, 2026, needs more optimization.
19 709 0.324311300334 Henry Cohn, 2026, needs more optimization.
19 710 0.324385507578 Henry Cohn, 2026, needs more optimization.
19 711 0.324475804518 Henry Cohn, 2026, needs more optimization.
19 712 0.324555827067 Henry Cohn, 2026, needs more optimization.
19 713 0.324827445699 Henry Cohn, 2026, needs more optimization.
19 714 0.324923991255 Henry Cohn, 2026, needs more optimization.
19 715 0.325146068062 Henry Cohn, 2026, needs more optimization.
19 716 0.325367769683 Henry Cohn, 2026, needs more optimization.
19 717 0.325619558049 Henry Cohn, 2026, needs more optimization.
19 718 0.325809541970 Henry Cohn, 2026, needs more optimization.
19 719 0.326042953422 Henry Cohn, 2026, needs more optimization.
19 720 0.326210323019 Henry Cohn, 2026, needs more optimization.
19 721 0.326328548917 Henry Cohn, 2026, needs more optimization.
19 722 0.326532016872 Henry Cohn, 2026, needs more optimization.
19 723 0.326640743684 Henry Cohn, 2026, needs more optimization.
19 724 0.326716191805 Henry Cohn, 2026, needs more optimization.
19 725 0.326822964839 Henry Cohn, 2026, needs more optimization.
19 726 0.326990728140 Henry Cohn, 2026, needs more optimization.
19 727 0.327099335394 Henry Cohn, 2026, needs more optimization.
19 728 0.327263177269 Henry Cohn, 2026, needs more optimization.
19 729 0.327408109270 Henry Cohn, 2026, needs more optimization.
19 730 0.327712272264 Henry Cohn, 2026, needs more optimization.
19 731 0.327805625649 Henry Cohn, 2026, needs more optimization.
19 732 0.327942119406 Henry Cohn, 2026, needs more optimization.
19 733 0.328136307784 Henry Cohn, 2026, needs more optimization.
19 734 0.328261055641 Henry Cohn, 2026, needs more optimization.
19 735 0.328431867468 Henry Cohn, 2026, needs more optimization.
19 736 0.328575124395 Henry Cohn, 2026, needs more optimization.
19 737 0.328765213909 Henry Cohn, 2026, needs more optimization.
19 738 0.328953094444 Henry Cohn, 2026, needs more optimization.
19 739 0.329147348982 Henry Cohn, 2026, needs more optimization.
19 740 0.329454891020 Henry Cohn, 2026, needs more optimization.
19 741 0.329764331827 Henry Cohn, 2026, needs more optimization.
19 742 0.329880412887 Henry Cohn, 2026, needs more optimization.
19 743 0.330140591531 Henry Cohn, 2026, needs more optimization.
19 744 0.330405319207 Henry Cohn, 2026, needs more optimization.
19 745 0.330494421354 Henry Cohn, 2026, needs more optimization.
19 746 0.330747893598 Henry Cohn, 2026, needs more optimization.
19 747 0.330840957159 Henry Cohn, 2026, needs more optimization.
19 748 0.331096336913 Henry Cohn, 2026, needs more optimization.
19 749 0.331229969553 Henry Cohn, 2026, needs more optimization.
19 750 0.331424839109 Henry Cohn, 2026, needs more optimization.
19 751 0.331654262166 Henry Cohn, 2026, needs more optimization.
19 752 0.331887267184 Henry Cohn, 2026, needs more optimization.
19 753 0.332153134208 Henry Cohn, 2026, needs more optimization.
19 754 0.332352276592 Henry Cohn, 2026, needs more optimization.
19 755 0.332679404393 Henry Cohn, 2026, needs more optimization.
19 756 0.332865353739 Henry Cohn, 2026, needs more optimization.
19 757 0.333062968807 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 0.339478001214 Henry Cohn, 2026, needs more optimization.
19 898 0.341210512523 Henry Cohn, 2026, needs more optimization.
19 899 0.342635710189 Henry Cohn, 2026, needs more optimization.
19 900 0.344034361226 Henry Cohn, 2026, needs more optimization.
19 901 0.345535746937 Henry Cohn, 2026, needs more optimization.
19 902 0.346053888916 Henry Cohn, 2026, needs more optimization.
19 903 0.346840660246 Henry Cohn, 2026, needs more optimization.
19 904 0.347406812645 Henry Cohn, 2026, needs more optimization.
19 905 0.347934873486 Henry Cohn, 2026, needs more optimization.
19 906 0.348384797653 Henry Cohn, 2026, needs more optimization.
19 907 0.349044229079 Henry Cohn, 2026, needs more optimization.
19 908 0.349300035473 Henry Cohn, 2026, needs more optimization.
19 909 0.349727293987 Henry Cohn, 2026, needs more optimization.
19 910 0.350005730178 Henry Cohn, 2026, needs more optimization.
19 911 0.350115815876 Henry Cohn, 2026, needs more optimization.
19 912 0.350857266972 Henry Cohn, 2026, needs more optimization.
19 913 0.350990698890 Henry Cohn, 2026, needs more optimization.
19 914 0.351387209306 Henry Cohn, 2026, needs more optimization.
19 915 0.351468606214 Henry Cohn, 2026, needs more optimization.
19 916 0.351531037919 Henry Cohn, 2026, needs more optimization.
19 917 0.351619501177 Henry Cohn, 2026, needs more optimization.
19 918 0.351664590736 Henry Cohn, 2026, needs more optimization.
19 919 0.351800276323 Henry Cohn, 2026, needs more optimization.
19 920 0.351920189806 Henry Cohn, 2026, needs more optimization.
19 921 0.352111996445 Henry Cohn, 2026, needs more optimization.
19 922 0.352196164486 Henry Cohn, 2026, needs more optimization.
19 923 0.352273788968 Henry Cohn, 2026, needs more optimization.
19 924 0.352470887912 Henry Cohn, 2026, needs more optimization.
19 925 0.352538293073 Henry Cohn, 2026, needs more optimization.
19 926 0.352739963180 Henry Cohn, 2026, needs more optimization.
19 927 0.352997840595 Henry Cohn, 2026, needs more optimization.
19 928 0.353090955728 Henry Cohn, 2026, needs more optimization.
19 929 0.353230386723 Henry Cohn, 2026, needs more optimization.
19 930 0.353435073471 Henry Cohn, 2026, needs more optimization.
19 931 0.353686676395 Henry Cohn, 2026, needs more optimization.
19 932 0.353782722464 Henry Cohn, 2026, needs more optimization.
19 933 0.353871220837 Henry Cohn, 2026, needs more optimization.
19 934 0.354038520919 Henry Cohn, 2026, needs more optimization.
19 935 0.354198526547 Henry Cohn, 2026, needs more optimization.
19 936 0.354343602758 Henry Cohn, 2026, needs more optimization.
19 937 0.354523449498 Henry Cohn, 2026, needs more optimization.
19 938 0.354688800956 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 0.096786110818 Henry Cohn, 2026, needs more optimization.
20 70 0.097921327696 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 0.149706562630 Henry Cohn, 2026, needs more optimization.
20 128 0.149901784883 Henry Cohn, 2026, needs more optimization.
20 129 0.150201699198 Henry Cohn, 2026, needs more optimization.
20 130 0.150479940773 Henry Cohn, 2026, needs more optimization.
20 132 0.150515983244 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 0.153058909203 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 0.154382441970 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 0.166621820001 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 0.187888037362 Henry Cohn, 2026, needs more optimization.
20 173 0.189190364505 Henry Cohn, 2026, needs more optimization.
20 174 0.189190374168 Henry Cohn, 2026, needs more optimization.
20 175 0.189190391311 Henry Cohn, 2026, needs more optimization.
20 176 0.189190436919 Henry Cohn, 2026, needs more optimization.
20 181 0.189190442690 Henry Cohn, 2026, needs more optimization.
20 182 0.189190515564 Henry Cohn, 2026, needs more optimization.
20 184 0.189190526077 Henry Cohn, 2026, needs more optimization.
20 185 0.189190769596 Henry Cohn, 2026, needs more optimization.
20 186 0.189190778946 Henry Cohn, 2026, needs more optimization.
20 187 0.189190793487 Henry Cohn, 2026, needs more optimization.
20 188 0.189190794573 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 0.189190795539 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 0.189190796509 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 0.189282096491 Henry Cohn, 2026, needs more optimization.
20 194 0.191919197995 Henry Cohn, 2026, needs more optimization.
20 195 0.191919201071 Henry Cohn, 2026, needs more optimization.
20 196 0.191919201083 Henry Cohn, 2026, needs more optimization.
20 201 0.191919201146 Henry Cohn, 2026, needs more optimization.
20 202 0.191919616754 Henry Cohn, 2026, needs more optimization.
20 203 0.191920114214 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 0.205920911961 Henry Cohn, 2026, needs more optimization.
20 259 0.207516721309 Henry Cohn, 2026, needs more optimization.
20 262 0.208386799892 Henry Cohn, 2026, needs more optimization.
20 263 0.208832108446 Henry Cohn, 2026, needs more optimization.
20 264 0.208834164080 Henry Cohn, 2026, needs more optimization.
20 265 0.212161795908 Henry Cohn, 2026, needs more optimization.
20 266 0.212395793509 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 0.213339621098 Henry Cohn, 2026, needs more optimization.
20 270 0.213414106630 Henry Cohn, 2026, needs more optimization.
20 271 0.213859612521 Henry Cohn, 2026, needs more optimization.
20 272 0.214208524590 Henry Cohn, 2026, needs more optimization.
20 273 0.214555919761 Henry Cohn, 2026, needs more optimization.
20 274 0.215049159680 Henry Cohn, 2026, needs more optimization.
20 275 0.215348191781 Henry Cohn, 2026, needs more optimization.
20 276 0.215672663165 Henry Cohn, 2026, needs more optimization.
20 277 0.215979876934 Henry Cohn, 2026, needs more optimization.
20 278 0.216159262784 Henry Cohn, 2026, needs more optimization.
20 279 0.216311755346 Henry Cohn, 2026, needs more optimization.
20 280 0.216551717165 Henry Cohn, 2026, needs more optimization.
20 281 0.216764550369 Henry Cohn, 2026, needs more optimization.
20 282 0.217059838950 Henry Cohn, 2026, needs more optimization.
20 283 0.217450078299 Henry Cohn, 2026, needs more optimization.
20 284 0.217805770585 Henry Cohn, 2026, needs more optimization.
20 285 0.218259104730 Henry Cohn, 2026, needs more optimization.
20 286 0.218626301596 Henry Cohn, 2026, needs more optimization.
20 287 0.218962732232 Henry Cohn, 2026, needs more optimization.
20 288 0.219467289582 Henry Cohn, 2026, needs more optimization.
20 289 0.219988791798 Henry Cohn, 2026, needs more optimization.
20 290 0.220495424604 Henry Cohn, 2026, needs more optimization.
20 291 0.220669072816 Henry Cohn, 2026, needs more optimization.
20 293 0.220692466681 Henry Cohn, 2026, needs more optimization.
20 294 0.220694635151 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 0.236122066567 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 0.242466509016 Henry Cohn, 2026, needs more optimization.
20 380 0.242513034379 Henry Cohn, 2026, needs more optimization.
20 381 0.242576659861 Henry Cohn, 2026, needs more optimization.
20 382 0.242653603817 Henry Cohn, 2026, needs more optimization.
20 383 0.242718590254 Henry Cohn, 2026, needs more optimization.
20 384 0.242794407473 Henry Cohn, 2026, needs more optimization.
20 385 0.242884083200 Henry Cohn, 2026, needs more optimization.
20 386 0.242986730349 Henry Cohn, 2026, needs more optimization.
20 387 0.242996267501 Henry Cohn, 2026, needs more optimization.
20 388 0.243023230544 Henry Cohn, 2026, needs more optimization.
20 389 0.243115202481 Henry Cohn, 2026, needs more optimization.
20 390 0.243171239031 Henry Cohn, 2026, needs more optimization.
20 391 0.243223804298 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 0.264990822549 Henry Cohn, 2026, needs more optimization.
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 474 0.269857120652 Henry Cohn, 2026, needs more optimization.
20 475 0.270935841507 Henry Cohn, 2026, needs more optimization.
20 476 0.272600437514 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 0.280559617935 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 1004 0.323086756637 Henry Cohn, 2026, needs more optimization.
20 1005 0.323087020599 Henry Cohn, 2026, needs more optimization.
20 1006 0.323087182312 Henry Cohn, 2026, needs more optimization.
20 1007 0.323180719200 Henry Cohn, 2026, needs more optimization.
20 1008 0.323180832190 Henry Cohn, 2026, needs more optimization.
20 1009 0.323475770784 Henry Cohn, 2026, needs more optimization.
20 1010 0.323476061558 Henry Cohn, 2026, needs more optimization.
20 1011 0.323879775523 Henry Cohn, 2026, needs more optimization.
20 1012 0.323881793772 Henry Cohn, 2026, needs more optimization.
20 1014 0.323882411085 Henry Cohn, 2026, needs more optimization.
20 1015 0.323884114164 Henry Cohn, 2026, needs more optimization.
20 1017 0.323980157633 Henry Cohn, 2026, needs more optimization.
20 1019 0.324109719015 Henry Cohn, 2026, needs more optimization.
20 1020 0.324111843878 Henry Cohn, 2026, needs more optimization.
20 1021 0.324197591105 Henry Cohn, 2026, needs more optimization.
20 1022 0.324201466745 Henry Cohn, 2026, needs more optimization.
20 1023 0.324717721382 Henry Cohn, 2026, needs more optimization.
20 1024 0.324719800221 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 0.066665077400 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 86 0.104649382361 Henry Cohn, 2026, needs more optimization.
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 0.139345069179 Henry Cohn, 2026, needs more optimization.
21 121 0.139345416660 Henry Cohn, 2026, needs more optimization.
21 122 0.139345447737 Henry Cohn, 2026, needs more optimization.
21 123 0.139389999185 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 0.160001480487 Henry Cohn, 2026, needs more optimization.
21 165 0.160006331956 Henry Cohn, 2026, needs more optimization.
21 166 0.160898987282 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 0.174790480683 Henry Cohn, 2026, needs more optimization.
21 201 0.174791437408 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 0.177468399015 Henry Cohn, 2026, needs more optimization.
21 221 0.177481029937 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 0.190603593058 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 0.194543172358 Henry Cohn, 2026, needs more optimization.
21 237 0.195353623216 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
21 379 0.227586206897 Henry Cohn, 2026.
145⁢x−33
21 380 0.228034577480 Henry Cohn, 2026, needs more optimization.
21 381 0.228389772581 Henry Cohn, 2026, needs more optimization.
21 383 0.228663101723 Henry Cohn, 2026, needs more optimization.
21 384 0.228738654103 Henry Cohn, 2026, needs more optimization.
21 385 0.228924606398 Henry Cohn, 2026, needs more optimization.
21 386 0.228989465698 Henry Cohn, 2026, needs more optimization.
21 387 0.229011990478 Henry Cohn, 2026, needs more optimization.
21 388 0.229067337792 Henry Cohn, 2026, needs more optimization.
21 394 0.230769230770 Henry Cohn, 2026.
13⁢x−3
21 395 0.230774988348 Henry Cohn, 2026, needs more optimization.
21 396 0.232550681867 Henry Cohn, 2026, needs more optimization.
21 397 0.237334086070 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 0.253543777367 Henry Cohn, 2026, needs more optimization.
21 569 0.254511286763 Henry Cohn, 2026, needs more optimization.
21 570 0.255070132572 Henry Cohn, 2026, needs more optimization.
21 571 0.255481947998 Henry Cohn, 2026, needs more optimization.
21 572 0.255808353810 Henry Cohn, 2026, needs more optimization.
21 573 0.256126365132 Henry Cohn, 2026, needs more optimization.
21 574 0.256387279370 Henry Cohn, 2026, needs more optimization.
21 575 0.256604060044 Henry Cohn, 2026, needs more optimization.
21 576 0.256820655559 Henry Cohn, 2026, needs more optimization.
21 577 0.257069076834 Henry Cohn, 2026, needs more optimization.
21 578 0.257280701046 Henry Cohn, 2026, needs more optimization.
21 579 0.257426614447 Henry Cohn, 2026, needs more optimization.
21 580 0.257578221462 Henry Cohn, 2026, needs more optimization.
21 581 0.257698293985 Henry Cohn, 2026, needs more optimization.
21 582 0.257817542946 Henry Cohn, 2026, needs more optimization.
21 583 0.257904037908 Henry Cohn, 2026, needs more optimization.
21 584 0.258018684231 Henry Cohn, 2026, needs more optimization.
21 585 0.258109281557 Henry Cohn, 2026, needs more optimization.
21 586 0.258238070869 Henry Cohn, 2026, needs more optimization.
21 587 0.258303970870 Henry Cohn, 2026, needs more optimization.
21 588 0.258375804009 Henry Cohn, 2026, needs more optimization.
21 589 0.258446650596 Henry Cohn, 2026, needs more optimization.
21 590 0.258602339010 Henry Cohn, 2026, needs more optimization.
21 591 0.258702771284 Henry Cohn, 2026, needs more optimization.
21 592 0.258737073170 Henry Cohn, 2026, needs more optimization.
21 593 0.258974580512 Henry Cohn, 2026, needs more optimization.
21 594 0.259207708524 Henry Cohn, 2026, needs more optimization.
21 595 0.259319632944 Henry Cohn, 2026, needs more optimization.
21 596 0.259394659413 Henry Cohn, 2026, needs more optimization.
21 597 0.259464624852 Henry Cohn, 2026, needs more optimization.
21 598 0.259601699033 Henry Cohn, 2026, needs more optimization.
21 599 0.259676120054 Henry Cohn, 2026, needs more optimization.
21 600 0.259741523167 Henry Cohn, 2026, needs more optimization.
21 601 0.259793025469 Henry Cohn, 2026, needs more optimization.
21 602 0.259831776045 Henry Cohn, 2026, needs more optimization.
21 603 0.259908109680 Henry Cohn, 2026, needs more optimization.
21 604 0.259940382464 Henry Cohn, 2026, needs more optimization.
21 605 0.260045468858 Henry Cohn, 2026, needs more optimization.
21 606 0.260136047727 Henry Cohn, 2026, needs more optimization.
21 607 0.260230577367 Henry Cohn, 2026, needs more optimization.
21 608 0.260275965760 Henry Cohn, 2026, needs more optimization.
21 609 0.260316619220 Henry Cohn, 2026, needs more optimization.
21 610 0.260499647720 Henry Cohn, 2026, needs more optimization.
21 611 0.260604262564 Henry Cohn, 2026, needs more optimization.
21 612 0.260665667133 Henry Cohn, 2026, needs more optimization.
21 613 0.260787740386 Henry Cohn, 2026, needs more optimization.
21 614 0.260879320147 Henry Cohn, 2026, needs more optimization.
21 615 0.260938563634 Henry Cohn, 2026, needs more optimization.
21 616 0.261029043878 Henry Cohn, 2026, needs more optimization.
21 617 0.261086301936 Henry Cohn, 2026, needs more optimization.
21 618 0.261163226084 Henry Cohn, 2026, needs more optimization.
21 619 0.261230697094 Henry Cohn, 2026, needs more optimization.
21 620 0.261271830730 Henry Cohn, 2026, needs more optimization.
21 621 0.261308763126 Henry Cohn, 2026, needs more optimization.
21 622 0.261349222771 Henry Cohn, 2026, needs more optimization.
21 623 0.261394167455 Henry Cohn, 2026, needs more optimization.
21 624 0.261428974530 Henry Cohn, 2026, needs more optimization.
21 625 0.261463105275 Henry Cohn, 2026, needs more optimization.
21 626 0.261504697804 Henry Cohn, 2026, needs more optimization.
21 627 0.261576710205 Henry Cohn, 2026, needs more optimization.
21 628 0.261631777024 Henry Cohn, 2026, needs more optimization.
21 629 0.261686034648 Henry Cohn, 2026, needs more optimization.
21 630 0.262077336289 Henry Cohn, 2026, needs more optimization.
21 631 0.262329765914 Henry Cohn, 2026, needs more optimization.
21 632 0.262518594583 Henry Cohn, 2026, needs more optimization.
21 633 0.262617969613 Henry Cohn, 2026, needs more optimization.
21 634 0.262688844722 Henry Cohn, 2026, needs more optimization.
21 635 0.262739759239 Henry Cohn, 2026, needs more optimization.
21 636 0.262890501196 Henry Cohn, 2026, needs more optimization.
21 637 0.263011355843 Henry Cohn, 2026, needs more optimization.
21 638 0.263141564004 Henry Cohn, 2026, needs more optimization.
21 639 0.263230971011 Henry Cohn, 2026, needs more optimization.
21 640 0.263330017779 Henry Cohn, 2026, needs more optimization.
21 641 0.263418463688 Henry Cohn, 2026, needs more optimization.
21 642 0.263580378648 Henry Cohn, 2026, needs more optimization.
21 643 0.263705753873 Henry Cohn, 2026, needs more optimization.
21 644 0.263828129834 Henry Cohn, 2026, needs more optimization.
21 645 0.263936395449 Henry Cohn, 2026, needs more optimization.
21 646 0.263974385850 Henry Cohn, 2026, needs more optimization.
21 647 0.264051415474 Henry Cohn, 2026, needs more optimization.
21 648 0.264127202435 Henry Cohn, 2026, needs more optimization.
21 649 0.264188474001 Henry Cohn, 2026, needs more optimization.
21 650 0.264295473364 Henry Cohn, 2026, needs more optimization.
21 651 0.264368850677 Henry Cohn, 2026, needs more optimization.
21 652 0.264439809533 Henry Cohn, 2026, needs more optimization.
21 653 0.264507351311 Henry Cohn, 2026, needs more optimization.
21 654 0.264560394642 Henry Cohn, 2026, needs more optimization.
21 655 0.264636306189 Henry Cohn, 2026, needs more optimization.
21 656 0.264735069816 Henry Cohn, 2026, needs more optimization.
21 657 0.264804417358 Henry Cohn, 2026, needs more optimization.
21 658 0.264896559090 Henry Cohn, 2026, needs more optimization.
21 659 0.264990511711 Henry Cohn, 2026, needs more optimization.
21 660 0.265125866466 Henry Cohn, 2026, needs more optimization.
21 661 0.265181054985 Henry Cohn, 2026, needs more optimization.
21 662 0.265232741774 Henry Cohn, 2026, needs more optimization.
21 663 0.265297895344 Henry Cohn, 2026, needs more optimization.
21 664 0.265376329244 Henry Cohn, 2026, needs more optimization.
21 665 0.265449359904 Henry Cohn, 2026, needs more optimization.
21 666 0.265522530057 Henry Cohn, 2026, needs more optimization.
21 667 0.265560100826 Henry Cohn, 2026, needs more optimization.
21 668 0.265605810210 Henry Cohn, 2026, needs more optimization.
21 669 0.265633081210 Henry Cohn, 2026, needs more optimization.
21 670 0.265669078492 Henry Cohn, 2026, needs more optimization.
21 671 0.265732577571 Henry Cohn, 2026, needs more optimization.
21 672 0.265770747149 Henry Cohn, 2026, needs more optimization.
21 673 0.265853816409 Henry Cohn, 2026, needs more optimization.
21 674 0.265902370373 Henry Cohn, 2026, needs more optimization.
21 675 0.265960677245 Henry Cohn, 2026, needs more optimization.
21 676 0.266028340242 Henry Cohn, 2026, needs more optimization.
21 677 0.266080563724 Henry Cohn, 2026, needs more optimization.
21 678 0.266136777582 Henry Cohn, 2026, needs more optimization.
21 679 0.266167863374 Henry Cohn, 2026, needs more optimization.
21 680 0.266224683365 Henry Cohn, 2026, needs more optimization.
21 681 0.266280377778 Henry Cohn, 2026, needs more optimization.
21 682 0.266343579024 Henry Cohn, 2026, needs more optimization.
21 683 0.266505569797 Henry Cohn, 2026, needs more optimization.
21 684 0.266586819377 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, needs more optimization.
21 729 0.267261241913 Henry Cohn, 2026.
14⁢x2−1
21 730 0.277255487237 Henry Cohn, 2026, needs more optimization.
21 731 0.282349171777 Henry Cohn, 2026, needs more optimization.
21 732 0.284704896206 Henry Cohn, 2026, needs more optimization.
21 850 0.285714285715 Henry Cohn, 2026.
7⁢x−2
21 851 0.290297899281 Henry Cohn, 2026, needs more optimization.
21 852 0.291096848946 Henry Cohn, 2026, needs more optimization.
21 853 0.291723399992 Henry Cohn, 2026, needs more optimization.
21 854 0.292109512003 Henry Cohn, 2026, needs more optimization.
21 855 0.292435594190 Henry Cohn, 2026, needs more optimization.
21 856 0.292768184046 Henry Cohn, 2026, needs more optimization.
21 857 0.293060004621 Henry Cohn, 2026, needs more optimization.
21 858 0.293325013893 Henry Cohn, 2026, needs more optimization.
21 859 0.293640633169 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 0.299223644580 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 0.066447990775 Henry Cohn, 2026, needs more optimization.
22 57 0.066559109857 Henry Cohn, 2026.
22 58 0.066626702518 Henry Cohn, 2026, needs more optimization.
22 59 0.066653898230 Henry Cohn, 2026, needs more optimization.
22 60 0.066662323881 Henry Cohn, 2026, needs more optimization.
22 61 0.069638781740 Henry Cohn, 2026, needs more optimization.
22 62 0.071702992547 Henry Cohn, 2026, needs more optimization.
22 63 0.076904418853 Henry Cohn, 2026, needs more optimization.
22 64 0.076919638870 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 0.079295785727 Henry Cohn, 2026, needs more optimization.
22 68 0.080927905651 Henry Cohn, 2026.
22 69 0.083022936401 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.
22 117 0.122810717150 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 0.135518337350 Henry Cohn, 2026, needs more optimization.
22 143 0.137954008389 Henry Cohn, 2026, needs more optimization.
22 144 0.139626854227 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 0.158305577233 Henry Cohn, 2026, needs more optimization.
22 173 0.159107132818 Henry Cohn, 2026, needs more optimization.
22 174 0.161511269865 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 0.165619332566 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 0.185915282328 Henry Cohn, 2026, needs more optimization.
22 278 0.189292456068 Henry Cohn, 2026, needs more optimization.
22 279 0.191593425441 Henry Cohn, 2026, needs more optimization.
22 280 0.193243505801 Henry Cohn, 2026, needs more optimization.
22 281 0.194531534954 Henry Cohn, 2026, needs more optimization.
22 282 0.195731103204 Henry Cohn, 2026, needs more optimization.
22 283 0.196337922150 Henry Cohn, 2026, needs more optimization.
22 284 0.196353308882 Henry Cohn, 2026, needs more optimization.
22 286 0.196362023436 Henry Cohn, 2026, needs more optimization.
22 287 0.199274673366 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 0.204058373793 Henry Cohn, 2026, needs more optimization.
22 358 0.204059171295 Henry Cohn, 2026, needs more optimization.
22 359 0.204489355211 Henry Cohn, 2026, needs more optimization.
22 374 0.204624019941 Henry Cohn, 2026.
22 375 0.205726049225 Henry Cohn, 2026, needs more optimization.
22 376 0.206395598566 Henry Cohn, 2026, needs more optimization.
22 377 0.206700683411 Henry Cohn, 2026, needs more optimization.
22 378 0.206884760646 Henry Cohn, 2026, needs more optimization.
22 379 0.207061271088 Henry Cohn, 2026, needs more optimization.
22 380 0.207123750072 Henry Cohn, 2026, needs more optimization.
22 381 0.207166777411 Henry Cohn, 2026, needs more optimization.
22 382 0.207174908612 Henry Cohn, 2026, needs more optimization.
22 383 0.207175677901 Henry Cohn, 2026, needs more optimization.
22 384 0.207175745662 Henry Cohn, 2026, needs more optimization.
22 385 0.207175810802 Henry Cohn, 2026, needs more optimization.
22 386 0.207175832327 Henry Cohn, 2026, needs more optimization.
22 387 0.207175868284 Henry Cohn, 2026, needs more optimization.
22 388 0.207175892695 Henry Cohn, 2026, needs more optimization.
22 389 0.207175920417 Henry Cohn, 2026, needs more optimization.
22 390 0.207175940326 Henry Cohn, 2026, needs more optimization.
22 391 0.208467186721 Henry Cohn, 2026, needs more optimization.
22 392 0.208827617136 Henry Cohn, 2026, needs more optimization.
22 393 0.209043529544 Henry Cohn, 2026, needs more optimization.
22 394 0.209110265249 Henry Cohn, 2026, needs more optimization.
22 395 0.209395085784 Henry Cohn, 2026, needs more optimization.
22 396 0.209529365577 Henry Cohn, 2026, needs more optimization.
22 397 0.209579968278 Henry Cohn, 2026, needs more optimization.
22 398 0.209592508087 Henry Cohn, 2026, needs more optimization.
22 399 0.209595614148 Henry Cohn, 2026, needs more optimization.
22 400 0.209598718449 Henry Cohn, 2026, needs more optimization.
22 401 0.209600130303 Henry Cohn, 2026, needs more optimization.
22 402 0.209617009203 Henry Cohn, 2026, needs more optimization.
22 403 0.209619548399 Henry Cohn, 2026, needs more optimization.
22 404 0.209688932806 Henry Cohn, 2026, needs more optimization.
22 405 0.209706920744 Henry Cohn, 2026, needs more optimization.
22 415 0.209711494419 Henry Cohn, 2026, needs more optimization.
22 416 0.209814768597 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 0.211663343138 Henry Cohn, 2026, needs more optimization.
22 433 0.212039741267 Henry Cohn, 2026, needs more optimization.
22 436 0.212148697334 Henry Cohn, 2026, needs more optimization.
22 437 0.212406691088 Henry Cohn, 2026, needs more optimization.
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 0.238096309349 Henry Cohn, 2026, needs more optimization.
22 558 0.238098899014 Henry Cohn, 2026, needs more optimization.
22 559 0.238227252158 Henry Cohn, 2026, needs more optimization.
22 560 0.238532821297 Henry Cohn, 2026, needs more optimization.
22 561 0.240731002620 Henry Cohn, 2026, needs more optimization.
22 562 0.244022975511 Henry Cohn, 2026, needs more optimization.
22 563 0.246130742175 Henry Cohn, 2026, needs more optimization.
22 564 0.248017614034 Henry Cohn, 2026, needs more optimization.
22 565 0.249760606268 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 0.064488033251 Henry Cohn, 2026, needs more optimization.
23 59 0.065950754079 Henry Cohn, 2026, needs more optimization.
23 60 0.066276673588 Henry Cohn, 2026, needs more optimization.
23 61 0.066464177095 Henry Cohn, 2026, needs more optimization.
23 62 0.066565580256 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 0.076897666572 Henry Cohn, 2026, needs more optimization.
23 69 0.077605236851 Henry Cohn, 2026, needs more optimization.
23 70 0.077985696565 Henry Cohn, 2026, needs more optimization.
23 71 0.079522620309 Henry Cohn, 2026.
23 72 0.080064660878 Henry Cohn, 2026.
23 73 0.081989242399 Henry Cohn, 2026, needs more optimization.
23 74 0.083306336565 Henry Cohn, 2026, needs more optimization.
23 75 0.083317601017 Henry Cohn, 2026, needs more optimization.
23 76 0.083320662955 Henry Cohn, 2026, needs more optimization.
23 77 0.083331616679 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 0.083366092221 Henry Cohn, 2026, needs more optimization.
23 83 0.087272831288 Henry Cohn, 2026, needs more optimization.
23 84 0.089253587948 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 0.111111109515 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 0.111112082211 Henry Cohn, 2026, needs more optimization.
23 118 0.111112859878 Henry Cohn, 2026, needs more optimization.
23 119 0.115910206677 Henry Cohn, 2026, needs more optimization.
23 120 0.119779726144 Henry Cohn, 2026, needs more optimization.
23 121 0.124496233065 Henry Cohn, 2026, needs more optimization.
23 122 0.124528091734 Henry Cohn, 2026, needs more optimization.
23 123 0.130494915612 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 0.131783955568 Henry Cohn, 2026, needs more optimization.
23 131 0.132069368312 Henry Cohn, 2026, needs more optimization.
23 132 0.134227406740 Henry Cohn, 2026, needs more optimization.
23 133 0.134738936814 Henry Cohn, 2026, needs more optimization.
23 134 0.135040673450 Henry Cohn, 2026, needs more optimization.
23 147 0.135135135136 Henry Cohn, 2026.
37⁢x−5
23 148 0.135336599799 Henry Cohn, 2026, needs more optimization.
23 149 0.136614607366 Henry Cohn, 2026, needs more optimization.
23 150 0.136648192147 Henry Cohn, 2026, needs more optimization.
23 151 0.137558642772 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 0.145096871936 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 0.146719321096 Henry Cohn, 2026, needs more optimization.
23 175 0.150598541170 Henry Cohn, 2026, needs more optimization.
23 176 0.153575428866 Henry Cohn, 2026, needs more optimization.
23 177 0.154912239832 Henry Cohn, 2026, needs more optimization.
23 178 0.155965625586 Henry Cohn, 2026, needs more optimization.
23 179 0.156306715649 Henry Cohn, 2026, needs more optimization.
23 180 0.158780166461 Henry Cohn, 2026, needs more optimization.
23 181 0.159255831194 Henry Cohn, 2026, needs more optimization.
23 182 0.160920676160 Henry Cohn, 2026, needs more optimization.
23 183 0.161398498043 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 0.161967368062 Henry Cohn, 2026, needs more optimization.
23 209 0.164064848062 Henry Cohn, 2026, needs more optimization.
23 210 0.164972218848 Henry Cohn, 2026, needs more optimization.
23 211 0.165538251191 Henry Cohn, 2026, needs more optimization.
23 212 0.166146598364 Henry Cohn, 2026, needs more optimization.
23 213 0.166459737773 Henry Cohn, 2026, needs more optimization.
23 214 0.166608278148 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 0.174237305553 Henry Cohn, 2026, needs more optimization.
23 281 0.178768448153 Henry Cohn, 2026, needs more optimization.
23 282 0.181992133251 Henry Cohn, 2026, needs more optimization.
23 283 0.183321196593 Henry Cohn, 2026, needs more optimization.
23 284 0.185743465077 Henry Cohn, 2026, needs more optimization.
23 285 0.186050050539 Henry Cohn, 2026, needs more optimization.
23 286 0.187604482459 Henry Cohn, 2026, needs more optimization.
23 287 0.188056260894 Henry Cohn, 2026, needs more optimization.
23 288 0.188347287247 Henry Cohn, 2026, needs more optimization.
23 289 0.189204157091 Henry Cohn, 2026, needs more optimization.
23 290 0.189391900626 Henry Cohn, 2026, needs more optimization.
23 291 0.189516425398 Henry Cohn, 2026, needs more optimization.
23 292 0.189589581149 Henry Cohn, 2026, needs more optimization.
23 293 0.189631904250 Henry Cohn, 2026, needs more optimization.
23 295 0.189658270853 Henry Cohn, 2026, needs more optimization.
23 296 0.189658313116 Henry Cohn, 2026, needs more optimization.
23 297 0.189658521106 Henry Cohn, 2026, needs more optimization.
23 298 0.189662294055 Henry Cohn, 2026, needs more optimization.
23 299 0.189662978436 Henry Cohn, 2026, needs more optimization.
23 300 0.189663361301 Henry Cohn, 2026, needs more optimization.
23 301 0.190663699434 Henry Cohn, 2026, needs more optimization.
23 302 0.193051848734 Henry Cohn, 2026, needs more optimization.
23 303 0.194191902687 Henry Cohn, 2026, needs more optimization.
23 304 0.195463119805 Henry Cohn, 2026, needs more optimization.
23 305 0.196324654250 Henry Cohn, 2026, needs more optimization.
23 306 0.197503700342 Henry Cohn, 2026, needs more optimization.
23 307 0.198616198339 Henry Cohn, 2026, needs more optimization.
23 308 0.199027896724 Henry Cohn, 2026, needs more optimization.
23 309 0.199277388212 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 0.235338768327 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 0.238096306925 Henry Cohn, 2026, needs more optimization.
23 560 0.238096881595 Henry Cohn, 2026, needs more optimization.
23 562 0.238097142063 Henry Cohn, 2026, needs more optimization.
23 563 0.238097285102 Henry Cohn, 2026, needs more optimization.
23 564 0.238106732003 Henry Cohn, 2026, needs more optimization.
23 565 0.238106734396 Henry Cohn, 2026, needs more optimization.
23 566 0.238106734799 Henry Cohn, 2026, needs more optimization.
23 567 0.238804869842 Henry Cohn, 2026, needs more optimization.
23 568 0.238804872281 Henry Cohn, 2026, needs more optimization.
23 569 0.238804872362 Henry Cohn, 2026, needs more optimization.
23 570 0.238809828069 Henry Cohn, 2026, needs more optimization.
23 571 0.238809829481 Henry Cohn, 2026, needs more optimization.
23 572 0.238827175020 Henry Cohn, 2026, needs more optimization.
23 573 0.239247505807 Henry Cohn, 2026, needs more optimization.
23 574 0.240095760727 Henry Cohn, 2026, needs more optimization.
23 575 0.241056153008 Henry Cohn, 2026, needs more optimization.
23 576 0.241377557874 Henry Cohn, 2026, needs more optimization.
23 577 0.241650129075 Henry Cohn, 2026, needs more optimization.
23 578 0.242850291456 Henry Cohn, 2026, needs more optimization.
23 579 0.242864806636 Henry Cohn, 2026, needs more optimization.
23 581 0.243332306461 Henry Cohn, 2026, needs more optimization.
23 582 0.243685404355 Henry Cohn, 2026, needs more optimization.
23 583 0.244284695722 Henry Cohn, 2026, needs more optimization.
23 584 0.244904498846 Henry Cohn, 2026, needs more optimization.
23 585 0.245360601837 Henry Cohn, 2026, needs more optimization.
23 586 0.245660346300 Henry Cohn, 2026, needs more optimization.
23 587 0.245917978342 Henry Cohn, 2026, needs more optimization.
23 588 0.245957347897 Henry Cohn, 2026, needs more optimization.
23 589 0.246207646558 Henry Cohn, 2026, needs more optimization.
23 590 0.246224424982 Henry Cohn, 2026, needs more optimization.
23 591 0.246495431097 Henry Cohn, 2026, needs more optimization.
23 592 0.246519178141 Henry Cohn, 2026, needs more optimization.
23 593 0.247123168051 Henry Cohn, 2026, needs more optimization.
23 594 0.247172249082 Henry Cohn, 2026, needs more optimization.
23 595 0.247330925391 Henry Cohn, 2026, needs more optimization.
23 596 0.247682016887 Henry Cohn, 2026, needs more optimization.
23 597 0.247989649787 Henry Cohn, 2026, needs more optimization.
23 598 0.248493536094 Henry Cohn, 2026, needs more optimization.
23 599 0.248765068734 Henry Cohn, 2026, needs more optimization.
23 600 0.248917637485 Henry Cohn, 2026, needs more optimization.
23 601 0.249315469345 Henry Cohn, 2026, needs more optimization.
23 602 0.249509601137 Henry Cohn, 2026, needs more optimization.
23 603 0.249662315731 Henry Cohn, 2026, needs more optimization.
23 604 0.249671494892 Henry Cohn, 2026, needs more optimization.
23 605 0.249861573592 Henry Cohn, 2026, needs more optimization.
23 894 0.25 Henry Cohn, 2026.
4⁢x−1
23 895 0.250006612958 Henry Cohn, 2026, needs more optimization.
23 896 0.252693959928 Henry Cohn, 2026, needs more optimization.
23 897 0.254330291203 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 0.256378509210 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 0.256933448151 Henry Cohn, 2026, needs more optimization.
23 903 0.258016508533 Henry Cohn, 2026, needs more optimization.
23 904 0.258529222862 Henry Cohn, 2026, needs more optimization.
23 905 0.259255674938 Henry Cohn, 2026, needs more optimization.
23 906 0.259478936604 Henry Cohn, 2026, needs more optimization.
23 907 0.261483346476 Henry Cohn, 2026, needs more optimization.
23 908 0.264865981158 Henry Cohn, 2026, needs more optimization.
23 909 0.265187671461 Henry Cohn, 2026, needs more optimization.
23 910 0.265383120804 Henry Cohn, 2026, needs more optimization.
23 911 0.266018128768 Henry Cohn, 2026, needs more optimization.
23 912 0.267152478138 Henry Cohn, 2026, needs more optimization.
23 913 0.268036436944 Henry Cohn, 2026, needs more optimization.
23 914 0.268697859763 Henry Cohn, 2026, needs more optimization.
23 915 0.268794567313 Henry Cohn, 2026, needs more optimization.
23 916 0.269617966910 Henry Cohn, 2026, needs more optimization.
23 917 0.270155376409 Henry Cohn, 2026, needs more optimization.
23 918 0.270693200728 Henry Cohn, 2026, needs more optimization.
23 919 0.271142093065 Henry Cohn, 2026, needs more optimization.
23 920 0.271436534573 Henry Cohn, 2026, needs more optimization.
23 921 0.272121453400 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 0.065062155849 Henry Cohn, 2026, needs more optimization.
24 63 0.065495639999 Henry Cohn, 2026, needs more optimization.
24 64 0.065897872223 Henry Cohn, 2026, needs more optimization.
24 65 0.066587625359 Henry Cohn, 2026, needs more optimization.
24 66 0.068180518549 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 0.076553856244 Henry Cohn, 2026, needs more optimization.
24 71 0.076921807212 Henry Cohn, 2026, needs more optimization.
24 72 0.077412163748 Henry Cohn, 2026, needs more optimization.
24 73 0.077740721388 Henry Cohn, 2026, needs more optimization.
24 74 0.077908661685 Henry Cohn, 2026, needs more optimization.
24 75 0.078509013013 Henry Cohn, 2026, needs more optimization.
24 76 0.078850061999 Henry Cohn, 2026, needs more optimization.
24 77 0.081783796076 Henry Cohn, 2026, needs more optimization.
24 78 0.082768278745 Henry Cohn, 2026, needs more optimization.
24 79 0.083210437922 Henry Cohn, 2026, needs more optimization.
24 80 0.083247399265 Henry Cohn, 2026, needs more optimization.
24 81 0.083292973468 Henry Cohn, 2026, needs more optimization.
24 83 0.083316966042 Henry Cohn, 2026, needs more optimization.
24 84 0.083328203539 Henry Cohn, 2026, needs more optimization.
24 85 0.083328479334 Henry Cohn, 2026, needs more optimization.
24 86 0.086223271025 Henry Cohn, 2026, needs more optimization.
24 87 0.088144386954 Henry Cohn, 2026, needs more optimization.
24 88 0.089551873680 Henry Cohn, 2026, needs more optimization.
24 89 0.090178502141 Henry Cohn, 2026, needs more optimization.
24 90 0.090580720563 Henry Cohn, 2026, needs more optimization.
24 91 0.090714014441 Henry Cohn, 2026, needs more optimization.
24 92 0.090834706154 Henry Cohn, 2026, needs more optimization.
24 93 0.090893762882 Henry Cohn, 2026, needs more optimization.
24 97 0.090909090540 Henry Cohn, 2026, needs more optimization.
24 98 0.090909090558 Henry Cohn, 2026, needs more optimization.
24 103 0.090909090571 Henry Cohn, 2026, needs more optimization.
24 104 0.090909090572 Henry Cohn, 2026, needs more optimization.
24 105 0.091495718519 Henry Cohn, 2026, needs more optimization.
24 106 0.095233377765 Henry Cohn, 2026, needs more optimization.
24 107 0.100955645140 Henry Cohn, 2026, needs more optimization.
24 108 0.105658117445 Henry Cohn, 2026, needs more optimization.
24 109 0.110679598438 Henry Cohn, 2026, needs more optimization.
24 110 0.110683766415 Henry Cohn, 2026, needs more optimization.
24 111 0.110692488325 Henry Cohn, 2026, needs more optimization.
24 112 0.110697293007 Henry Cohn, 2026, needs more optimization.
24 113 0.110871826067 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 0.112099611176 Henry Cohn, 2026, needs more optimization.
24 123 0.116166510191 Henry Cohn, 2026, needs more optimization.
24 124 0.117892571779 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 0.131755624852 Henry Cohn, 2026, needs more optimization.
24 128 0.131763931495 Henry Cohn, 2026, needs more optimization.
24 130 0.131766032690 Henry Cohn, 2026, needs more optimization.
24 131 0.131776134506 Henry Cohn, 2026, needs more optimization.
24 132 0.131778295943 Henry Cohn, 2026, needs more optimization.
24 133 0.131782548713 Henry Cohn, 2026, needs more optimization.
24 134 0.131788208520 Henry Cohn, 2026, needs more optimization.
24 135 0.131961780737 Henry Cohn, 2026, needs more optimization.
24 136 0.132224356128 Henry Cohn, 2026, needs more optimization.
24 137 0.132938415907 Henry Cohn, 2026, needs more optimization.
24 138 0.133280031626 Henry Cohn, 2026, needs more optimization.
24 139 0.134268142687 Henry Cohn, 2026, needs more optimization.
24 140 0.134412528083 Henry Cohn, 2026, needs more optimization.
24 141 0.134832710099 Henry Cohn, 2026, needs more optimization.
24 142 0.134968637794 Henry Cohn, 2026, needs more optimization.
24 143 0.135116030496 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.
24 154 0.136268204927 Henry Cohn, 2026, needs more optimization.
24 155 0.137117500838 Henry Cohn, 2026, needs more optimization.
24 156 0.139165227847 Henry Cohn, 2026, needs more optimization.
24 157 0.141140418081 Henry Cohn, 2026, needs more optimization.
24 158 0.142857107111 Henry Cohn, 2026, needs more optimization.
24 159 0.142857110879 Henry Cohn, 2026, needs more optimization.
24 160 0.142857110902 Henry Cohn, 2026, needs more optimization.
24 162 0.142857110917 Henry Cohn, 2026, needs more optimization.
24 164 0.142857116293 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 0.143424529295 Henry Cohn, 2026, needs more optimization.
24 176 0.145882911833 Henry Cohn, 2026, needs more optimization.
24 177 0.145885113127 Henry Cohn, 2026, needs more optimization.
24 178 0.145890106675 Henry Cohn, 2026, needs more optimization.
24 179 0.146024314632 Henry Cohn, 2026, needs more optimization.
24 180 0.147287921637 Henry Cohn, 2026, needs more optimization.
24 181 0.147690664596 Henry Cohn, 2026, needs more optimization.
24 182 0.148124226265 Henry Cohn, 2026, needs more optimization.
24 183 0.148206023642 Henry Cohn, 2026, needs more optimization.
24 184 0.148269609570 Henry Cohn, 2026, needs more optimization.
24 186 0.148728163557 Henry Cohn, 2026, needs more optimization.
24 187 0.152046153399 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 0.153303130748 Henry Cohn, 2026, needs more optimization.
24 191 0.155109763032 Henry Cohn, 2026, needs more optimization.
24 192 0.155159414693 Henry Cohn, 2026, needs more optimization.
24 193 0.155183400090 Henry Cohn, 2026, needs more optimization.
24 194 0.157480793263 Henry Cohn, 2026, needs more optimization.
24 195 0.157764421768 Henry Cohn, 2026, needs more optimization.
24 196 0.159099752743 Henry Cohn, 2026, needs more optimization.
24 197 0.160026764089 Henry Cohn, 2026, needs more optimization.
24 198 0.160191592559 Henry Cohn, 2026, needs more optimization.
24 199 0.161380243149 Henry Cohn, 2026, needs more optimization.
24 200 0.161478355579 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 0.161904778792 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 0.162016792194 Henry Cohn, 2026, needs more optimization.
24 215 0.162171536904 Henry Cohn, 2026, needs more optimization.
24 216 0.163087886787 Henry Cohn, 2026, needs more optimization.
24 217 0.163193194144 Henry Cohn, 2026, needs more optimization.
24 218 0.164162364974 Henry Cohn, 2026, needs more optimization.
24 219 0.164910774326 Henry Cohn, 2026, needs more optimization.
24 220 0.165014741266 Henry Cohn, 2026, needs more optimization.
24 221 0.165554118437 Henry Cohn, 2026, needs more optimization.
24 222 0.165856255427 Henry Cohn, 2026, needs more optimization.
24 223 0.166165751860 Henry Cohn, 2026, needs more optimization.
24 224 0.166460795782 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 0.166833231663 Henry Cohn, 2026, needs more optimization.
24 285 0.170025182790 Henry Cohn, 2026, needs more optimization.
24 286 0.171406765728 Henry Cohn, 2026, needs more optimization.
24 287 0.174968784827 Henry Cohn, 2026, needs more optimization.
24 288 0.177021421132 Henry Cohn, 2026, needs more optimization.
24 289 0.179249908730 Henry Cohn, 2026, needs more optimization.
24 290 0.181630318081 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 0.182046028439 Henry Cohn, 2026, needs more optimization.
24 315 0.186814383316 Henry Cohn, 2026, needs more optimization.
24 316 0.189754416876 Henry Cohn, 2026, needs more optimization.
24 317 0.191049006482 Henry Cohn, 2026, needs more optimization.
24 318 0.192016025498 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 0.200816707687 Henry Cohn, 2026, needs more optimization.
24 557 0.206713553594 Henry Cohn, 2026, needs more optimization.
24 558 0.213706000279 Henry Cohn, 2026, needs more optimization.
24 559 0.216973154923 Henry Cohn, 2026, needs more optimization.
24 560 0.219742116932 Henry Cohn, 2026, needs more optimization.
24 561 0.222365722579 Henry Cohn, 2026, needs more optimization.
24 562 0.222685164528 Henry Cohn, 2026, needs more optimization.
24 563 0.224134706215 Henry Cohn, 2026, needs more optimization.
24 564 0.225347255834 Henry Cohn, 2026, needs more optimization.
24 565 0.226575205575 Henry Cohn, 2026, needs more optimization.
24 566 0.228203418502 Henry Cohn, 2026, needs more optimization.
24 567 0.229118407180 Henry Cohn, 2026, needs more optimization.
24 568 0.230515843851 Henry Cohn, 2026, needs more optimization.
24 569 0.231660525138 Henry Cohn, 2026, needs more optimization.
24 570 0.231807864887 Henry Cohn, 2026, needs more optimization.
24 571 0.232161973258 Henry Cohn, 2026, needs more optimization.
24 572 0.232367830123 Henry Cohn, 2026, needs more optimization.
24 573 0.233009785272 Henry Cohn, 2026, needs more optimization.
24 574 0.233355084696 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 0.234572039208 Henry Cohn, 2026, needs more optimization.
24 583 0.234575066525 Henry Cohn, 2026, needs more optimization.
24 584 0.234982999764 Henry Cohn, 2026, needs more optimization.
24 585 0.235421837824 Henry Cohn, 2026, needs more optimization.
24 586 0.235879731652 Henry Cohn, 2026, needs more optimization.
24 587 0.238388502500 Henry Cohn, 2026, needs more optimization.
24 590 0.238527037797 Henry Cohn, 2026, needs more optimization.
24 592 0.238527339591 Henry Cohn, 2026, needs more optimization.
24 593 0.238527579281 Henry Cohn, 2026, needs more optimization.
24 594 0.238810344398 Henry Cohn, 2026, needs more optimization.
24 595 0.239812069239 Henry Cohn, 2026, needs more optimization.
24 596 0.239971577269 Henry Cohn, 2026, needs more optimization.
24 597 0.239972723405 Henry Cohn, 2026, needs more optimization.
24 598 0.240411946656 Henry Cohn, 2026, needs more optimization.
24 599 0.240584336446 Henry Cohn, 2026, needs more optimization.
24 600 0.241471568127 Henry Cohn, 2026, needs more optimization.
24 601 0.241686393106 Henry Cohn, 2026, needs more optimization.
24 602 0.241699216661 Henry Cohn, 2026, needs more optimization.
24 603 0.242062315481 Henry Cohn, 2026, needs more optimization.
24 604 0.242331620323 Henry Cohn, 2026, needs more optimization.
24 605 0.242333059427 Henry Cohn, 2026, needs more optimization.
24 606 0.242334551551 Henry Cohn, 2026, needs more optimization.
24 607 0.242818686922 Henry Cohn, 2026, needs more optimization.
24 608 0.243339023579 Henry Cohn, 2026, needs more optimization.
24 609 0.243532312333 Henry Cohn, 2026, needs more optimization.
24 610 0.243744489641 Henry Cohn, 2026, needs more optimization.
24 611 0.244196721224 Henry Cohn, 2026, needs more optimization.
24 612 0.244499341446 Henry Cohn, 2026, needs more optimization.
24 613 0.245134541296 Henry Cohn, 2026, needs more optimization.
24 614 0.245540901983 Henry Cohn, 2026, needs more optimization.
24 615 0.245698174583 Henry Cohn, 2026, needs more optimization.
24 616 0.246266713572 Henry Cohn, 2026, needs more optimization.
24 617 0.246770421407 Henry Cohn, 2026, needs more optimization.
24 618 0.247151865099 Henry Cohn, 2026, needs more optimization.
24 619 0.247523199486 Henry Cohn, 2026, needs more optimization.
24 620 0.247693350044 Henry Cohn, 2026, needs more optimization.
24 621 0.247761313934 Henry Cohn, 2026, needs more optimization.
24 622 0.248181878832 Henry Cohn, 2026, needs more optimization.
24 623 0.248450230531 Henry Cohn, 2026, needs more optimization.
24 624 0.248895246850 Henry Cohn, 2026, needs more optimization.
24 625 0.249118010779 Henry Cohn, 2026, needs more optimization.
24 626 0.249488744670 Henry Cohn, 2026, needs more optimization.
24 627 0.249564200978 Henry Cohn, 2026, needs more optimization.
24 628 0.249694550722 Henry Cohn, 2026, needs more optimization.
24 629 0.249808155448 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 0.250004135130 Henry Cohn, 2026, needs more optimization.
24 898 0.250032415364 Henry Cohn, 2026, needs more optimization.
24 899 0.250034754904 Henry Cohn, 2026, needs more optimization.
24 900 0.250041122821 Henry Cohn, 2026, needs more optimization.
24 901 0.250052235090 Henry Cohn, 2026, needs more optimization.
24 902 0.250128927111 Henry Cohn, 2026, needs more optimization.
24 903 0.250128927941 Henry Cohn, 2026, needs more optimization.
24 904 0.250128976805 Henry Cohn, 2026, needs more optimization.
24 905 0.250148294419 Henry Cohn, 2026, needs more optimization.
24 906 0.250199788895 Henry Cohn, 2026, needs more optimization.
24 907 0.250258793973 Henry Cohn, 2026, needs more optimization.
24 908 0.251096516357 Henry Cohn, 2026, needs more optimization.
24 909 0.251304187630 Henry Cohn, 2026, needs more optimization.
24 910 0.251770745394 Henry Cohn, 2026, needs more optimization.
24 911 0.254924922608 Henry Cohn, 2026, needs more optimization.
24 912 0.255901252299 Henry Cohn, 2026, needs more optimization.
24 913 0.255978391137 Henry Cohn, 2026, needs more optimization.
24 914 0.256272810524 Henry Cohn, 2026, needs more optimization.
24 915 0.256464607534 Henry Cohn, 2026, needs more optimization.
24 916 0.256467521201 Henry Cohn, 2026, needs more optimization.
24 917 0.256483350032 Henry Cohn, 2026, needs more optimization.
24 918 0.256484677308 Henry Cohn, 2026, needs more optimization.
24 919 0.256811410627 Henry Cohn, 2026, needs more optimization.
24 920 0.257090626421 Henry Cohn, 2026, needs more optimization.
24 921 0.257615424203 Henry Cohn, 2026, needs more optimization.
24 922 0.258317934796 Henry Cohn, 2026, needs more optimization.
24 923 0.258836382179 Henry Cohn, 2026, needs more optimization.
24 924 0.259353708473 Henry Cohn, 2026, needs more optimization.
24 925 0.259370486284 Henry Cohn, 2026, needs more optimization.
24 926 0.261291224942 Henry Cohn, 2026, needs more optimization.
24 927 0.262273961681 Henry Cohn, 2026, needs more optimization.
24 928 0.262650826151 Henry Cohn, 2026, needs more optimization.
24 929 0.263676903408 Henry Cohn, 2026, needs more optimization.
24 930 0.264017905363 Henry Cohn, 2026, needs more optimization.
24 931 0.264470170253 Henry Cohn, 2026, needs more optimization.
24 932 0.265244675322 Henry Cohn, 2026, needs more optimization.
24 933 0.265476549776 Henry Cohn, 2026, needs more optimization.
24 934 0.266505456500 Henry Cohn, 2026, needs more optimization.
24 935 0.266817629875 Henry Cohn, 2026, needs more optimization.
24 936 0.267137403707 Henry Cohn, 2026, needs more optimization.
24 937 0.267566067321 Henry Cohn, 2026, needs more optimization.
24 938 0.267992036516 Henry Cohn, 2026, needs more optimization.
24 939 0.267992294015 Henry Cohn, 2026, needs more optimization.
24 940 0.268439995229 Henry Cohn, 2026, needs more optimization.
24 941 0.268933124004 Henry Cohn, 2026, needs more optimization.
24 942 0.269134886916 Henry Cohn, 2026, needs more optimization.
24 943 0.270084123426 Henry Cohn, 2026, needs more optimization.
24 945 0.270915120557 Henry Cohn, 2026, needs more optimization.
24 946 0.271356484913 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 0.046836760422 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 0.065042073071 Henry Cohn, 2026, needs more optimization.
25 66 0.065052412052 Henry Cohn, 2026, needs more optimization.
25 67 0.066213037727 Henry Cohn, 2026, needs more optimization.
25 68 0.066469688724 Henry Cohn, 2026, needs more optimization.
25 69 0.068627707329 Henry Cohn, 2026.
25 70 0.071055411990 Henry Cohn, 2026.
25 71 0.071792639031 Henry Cohn, 2026, needs more optimization.
25 72 0.073329992511 Henry Cohn, 2026, needs more optimization.
25 73 0.076172580466 Henry Cohn, 2026, needs more optimization.
25 74 0.076833417558 Henry Cohn, 2026, needs more optimization.
25 76 0.076923160984 Henry Cohn, 2026, needs more optimization.
25 77 0.077469943039 Henry Cohn, 2026, needs more optimization.
25 78 0.077920644306 Henry Cohn, 2026, needs more optimization.
25 79 0.078551973902 Henry Cohn, 2026, needs more optimization.
25 80 0.080796015136 Henry Cohn, 2026, needs more optimization.
25 81 0.082102608920 Henry Cohn, 2026, needs more optimization.
25 82 0.082605310909 Henry Cohn, 2026, needs more optimization.
25 83 0.082978456054 Henry Cohn, 2026, needs more optimization.
25 85 0.083095965795 Henry Cohn, 2026, needs more optimization.
25 86 0.083271833347 Henry Cohn, 2026, needs more optimization.
25 87 0.083304914387 Henry Cohn, 2026, needs more optimization.
25 88 0.083317142846 Henry Cohn, 2026, needs more optimization.
25 89 0.085168760181 Henry Cohn, 2026, needs more optimization.
25 90 0.087169375561 Henry Cohn, 2026, needs more optimization.
25 91 0.087278836679 Henry Cohn, 2026, needs more optimization.
25 92 0.088771794421 Henry Cohn, 2026, needs more optimization.
25 93 0.089638353165 Henry Cohn, 2026, needs more optimization.
25 94 0.089925041041 Henry Cohn, 2026, needs more optimization.
25 95 0.090447099682 Henry Cohn, 2026, needs more optimization.
25 96 0.090646506346 Henry Cohn, 2026, needs more optimization.
25 97 0.090830592731 Henry Cohn, 2026, needs more optimization.
25 98 0.090837311876 Henry Cohn, 2026, needs more optimization.
25 99 0.090896960218 Henry Cohn, 2026, needs more optimization.
25 100 0.090907038619 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 0.090909472483 Henry Cohn, 2026, needs more optimization.
25 108 0.090911537399 Henry Cohn, 2026, needs more optimization.
25 109 0.095542644965 Henry Cohn, 2026, needs more optimization.
25 110 0.099775964507 Henry Cohn, 2026, needs more optimization.
25 111 0.102646514984 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 0.108645354906 Henry Cohn, 2026, needs more optimization.
25 120 0.108646695668 Henry Cohn, 2026, needs more optimization.
25 121 0.109297308116 Henry Cohn, 2026, needs more optimization.
25 122 0.109493478726 Henry Cohn, 2026, needs more optimization.
25 123 0.109880170269 Henry Cohn, 2026, needs more optimization.
25 124 0.111035245720 Henry Cohn, 2026, needs more optimization.
25 125 0.111109898181 Henry Cohn, 2026, needs more optimization.
25 126 0.111125331379 Henry Cohn, 2026, needs more optimization.
25 127 0.111143895741 Henry Cohn, 2026, needs more optimization.
25 128 0.111341725328 Henry Cohn, 2026, needs more optimization.
25 129 0.117080391687 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 0.123583659378 Henry Cohn, 2026, needs more optimization.
25 133 0.124981451545 Henry Cohn, 2026, needs more optimization.
25 134 0.126246752801 Henry Cohn, 2026, needs more optimization.
25 135 0.128192665800 Henry Cohn, 2026, needs more optimization.
25 136 0.129707611770 Henry Cohn, 2026, needs more optimization.
25 137 0.131708952828 Henry Cohn, 2026, needs more optimization.
25 138 0.131741336271 Henry Cohn, 2026, needs more optimization.
25 139 0.131775618812 Henry Cohn, 2026, needs more optimization.
25 140 0.131785190339 Henry Cohn, 2026, needs more optimization.
25 141 0.131835079958 Henry Cohn, 2026, needs more optimization.
25 142 0.132268771069 Henry Cohn, 2026, needs more optimization.
25 143 0.132845346884 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 0.135174272972 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 0.139854996394 Henry Cohn, 2026, needs more optimization.
25 161 0.141385127293 Henry Cohn, 2026, needs more optimization.
25 162 0.142809843814 Henry Cohn, 2026, needs more optimization.
25 163 0.142823633182 Henry Cohn, 2026, needs more optimization.
25 164 0.142834850360 Henry Cohn, 2026, needs more optimization.
25 165 0.142839570492 Henry Cohn, 2026, needs more optimization.
25 166 0.142840690309 Henry Cohn, 2026, needs more optimization.
25 167 0.142841302577 Henry Cohn, 2026, needs more optimization.
25 168 0.142847398228 Henry Cohn, 2026, needs more optimization.
25 169 0.142851851632 Henry Cohn, 2026, needs more optimization.
25 171 0.142851851745 Henry Cohn, 2026, needs more optimization.
25 172 0.142852511902 Henry Cohn, 2026, needs more optimization.
25 174 0.142856504618 Henry Cohn, 2026, needs more optimization.
25 175 0.142856629822 Henry Cohn, 2026, needs more optimization.
25 176 0.142856692726 Henry Cohn, 2026, needs more optimization.
25 177 0.142860860274 Henry Cohn, 2026, needs more optimization.
25 178 0.142889902940 Henry Cohn, 2026, needs more optimization.
25 179 0.142927110572 Henry Cohn, 2026, needs more optimization.
25 180 0.143255116269 Henry Cohn, 2026, needs more optimization.
25 181 0.144736691150 Henry Cohn, 2026, needs more optimization.
25 182 0.144743776969 Henry Cohn, 2026, needs more optimization.
25 183 0.145949200217 Henry Cohn, 2026, needs more optimization.
25 184 0.145984806552 Henry Cohn, 2026, needs more optimization.
25 185 0.146042911647 Henry Cohn, 2026, needs more optimization.
25 186 0.146184366348 Henry Cohn, 2026, needs more optimization.
25 187 0.146201165134 Henry Cohn, 2026, needs more optimization.
25 188 0.146794694519 Henry Cohn, 2026, needs more optimization.
25 189 0.147165649084 Henry Cohn, 2026, needs more optimization.
25 190 0.147307293395 Henry Cohn, 2026, needs more optimization.
25 191 0.147378457086 Henry Cohn, 2026, needs more optimization.
25 192 0.147678243835 Henry Cohn, 2026, needs more optimization.
25 193 0.150402183815 Henry Cohn, 2026, needs more optimization.
25 194 0.151356044218 Henry Cohn, 2026, needs more optimization.
25 195 0.152366584908 Henry Cohn, 2026, needs more optimization.
25 196 0.152641577978 Henry Cohn, 2026, needs more optimization.
25 197 0.152650007072 Henry Cohn, 2026, needs more optimization.
25 198 0.152723832338 Henry Cohn, 2026, needs more optimization.
25 199 0.152733485408 Henry Cohn, 2026, needs more optimization.
25 200 0.153212008046 Henry Cohn, 2026, needs more optimization.
25 201 0.153219894026 Henry Cohn, 2026, needs more optimization.
25 202 0.153817565408 Henry Cohn, 2026, needs more optimization.
25 203 0.153830617080 Henry Cohn, 2026, needs more optimization.
25 204 0.155259710187 Henry Cohn, 2026, needs more optimization.
25 205 0.155260425681 Henry Cohn, 2026, needs more optimization.
25 206 0.155400169322 Henry Cohn, 2026, needs more optimization.
25 207 0.155400201193 Henry Cohn, 2026, needs more optimization.
25 208 0.155400216826 Henry Cohn, 2026, needs more optimization.
25 209 0.156577660252 Henry Cohn, 2026, needs more optimization.
25 210 0.157317398499 Henry Cohn, 2026, needs more optimization.
25 211 0.158570941464 Henry Cohn, 2026, needs more optimization.
25 212 0.158679438992 Henry Cohn, 2026, needs more optimization.
25 214 0.159266813602 Henry Cohn, 2026, needs more optimization.
25 215 0.159273026237 Henry Cohn, 2026, needs more optimization.
25 216 0.159814926152 Henry Cohn, 2026, needs more optimization.
25 217 0.159873574325 Henry Cohn, 2026, needs more optimization.
25 218 0.160726791473 Henry Cohn, 2026, needs more optimization.
25 219 0.160865515745 Henry Cohn, 2026, needs more optimization.
25 220 0.161526347181 Henry Cohn, 2026, needs more optimization.
25 221 0.161932022294 Henry Cohn, 2026, needs more optimization.
25 222 0.161935007144 Henry Cohn, 2026, needs more optimization.
25 223 0.162163211000 Henry Cohn, 2026, needs more optimization.
25 224 0.162640880037 Henry Cohn, 2026, needs more optimization.
25 225 0.162916999693 Henry Cohn, 2026, needs more optimization.
25 226 0.163594629638 Henry Cohn, 2026, needs more optimization.
25 227 0.164307117757 Henry Cohn, 2026, needs more optimization.
25 228 0.164662104304 Henry Cohn, 2026, needs more optimization.
25 229 0.165090264914 Henry Cohn, 2026, needs more optimization.
25 230 0.165424935552 Henry Cohn, 2026, needs more optimization.
25 231 0.165873867712 Henry Cohn, 2026, needs more optimization.
25 232 0.165979861670 Henry Cohn, 2026, needs more optimization.
25 233 0.166221927797 Henry Cohn, 2026, needs more optimization.
25 234 0.166401738781 Henry Cohn, 2026, needs more optimization.
25 235 0.166469464470 Henry Cohn, 2026, needs more optimization.
25 236 0.166548274417 Henry Cohn, 2026, needs more optimization.
25 237 0.166588441663 Henry Cohn, 2026, needs more optimization.
25 238 0.166599122257 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.
25 287 0.166669134290 Henry Cohn, 2026, needs more optimization.
25 288 0.166669134583 Henry Cohn, 2026, needs more optimization.
25 289 0.166670194654 Henry Cohn, 2026, needs more optimization.
25 290 0.166713251050 Henry Cohn, 2026, needs more optimization.
25 291 0.167655799636 Henry Cohn, 2026, needs more optimization.
25 292 0.169494605369 Henry Cohn, 2026, needs more optimization.
25 293 0.170002498513 Henry Cohn, 2026, needs more optimization.
25 294 0.172051188137 Henry Cohn, 2026, needs more optimization.
25 295 0.173780949886 Henry Cohn, 2026, needs more optimization.
25 296 0.175896140273 Henry Cohn, 2026, needs more optimization.
25 297 0.177353772816 Henry Cohn, 2026, needs more optimization.
25 298 0.178941452848 Henry Cohn, 2026, needs more optimization.
25 299 0.180504922062 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 0.181819695852 Henry Cohn, 2026, needs more optimization.
25 319 0.181821795449 Henry Cohn, 2026, needs more optimization.
25 320 0.181824070779 Henry Cohn, 2026, needs more optimization.
25 321 0.181832585085 Henry Cohn, 2026, needs more optimization.
25 322 0.183682922025 Henry Cohn, 2026, needs more optimization.
25 323 0.184810853866 Henry Cohn, 2026, needs more optimization.
25 324 0.185427198466 Henry Cohn, 2026, needs more optimization.
25 325 0.187079836777 Henry Cohn, 2026, needs more optimization.
25 326 0.187757966520 Henry Cohn, 2026, needs more optimization.
25 327 0.189845005137 Henry Cohn, 2026, needs more optimization.
25 328 0.191171261187 Henry Cohn, 2026, needs more optimization.
25 329 0.192106826887 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 0.193555507016 Henry Cohn, 2026, needs more optimization.
25 335 0.193906347049 Henry Cohn, 2026, needs more optimization.
25 340 0.194120819402 Henry Cohn, 2026, needs more optimization.
25 341 0.196571592512 Henry Cohn, 2026, needs more optimization.
25 342 0.198084564152 Henry Cohn, 2026, needs more optimization.
25 343 0.199529960364 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
25 558 0.200001673967 Henry Cohn, 2026, needs more optimization.
25 559 0.200003466557 Henry Cohn, 2026, needs more optimization.
25 560 0.200003479054 Henry Cohn, 2026, needs more optimization.
25 561 0.200004266559 Henry Cohn, 2026, needs more optimization.
25 562 0.200012990697 Henry Cohn, 2026, needs more optimization.
25 563 0.200255452669 Henry Cohn, 2026, needs more optimization.
25 564 0.201407581150 Henry Cohn, 2026, needs more optimization.
25 565 0.203397506258 Henry Cohn, 2026, needs more optimization.
25 566 0.207011458874 Henry Cohn, 2026, needs more optimization.
25 567 0.209925670980 Henry Cohn, 2026, needs more optimization.
25 568 0.211779922933 Henry Cohn, 2026, needs more optimization.
25 569 0.214515545404 Henry Cohn, 2026, needs more optimization.
25 570 0.216520028275 Henry Cohn, 2026, needs more optimization.
25 571 0.218023632380 Henry Cohn, 2026, needs more optimization.
25 572 0.219554252938 Henry Cohn, 2026, needs more optimization.
25 573 0.221366248592 Henry Cohn, 2026, needs more optimization.
25 574 0.222279639300 Henry Cohn, 2026, needs more optimization.
25 575 0.223748791616 Henry Cohn, 2026, needs more optimization.
25 576 0.224716262430 Henry Cohn, 2026, needs more optimization.
25 577 0.226321589620 Henry Cohn, 2026, needs more optimization.
25 578 0.226429510430 Henry Cohn, 2026, needs more optimization.
25 579 0.227412712131 Henry Cohn, 2026, needs more optimization.
25 580 0.228342082563 Henry Cohn, 2026, needs more optimization.
25 581 0.229108003522 Henry Cohn, 2026, needs more optimization.
25 582 0.229604597370 Henry Cohn, 2026, needs more optimization.
25 583 0.230810779699 Henry Cohn, 2026, needs more optimization.
25 584 0.231790842185 Henry Cohn, 2026, needs more optimization.
25 585 0.232067151158 Henry Cohn, 2026, needs more optimization.
25 586 0.233002968106 Henry Cohn, 2026, needs more optimization.
25 587 0.233554689760 Henry Cohn, 2026, needs more optimization.
25 588 0.234226942884 Henry Cohn, 2026, needs more optimization.
25 589 0.235074883256 Henry Cohn, 2026, needs more optimization.
25 590 0.235693617492 Henry Cohn, 2026, needs more optimization.
25 591 0.236501235301 Henry Cohn, 2026, needs more optimization.
25 592 0.237429680667 Henry Cohn, 2026, needs more optimization.
25 593 0.237509479302 Henry Cohn, 2026, needs more optimization.
25 594 0.237760328734 Henry Cohn, 2026, needs more optimization.
25 596 0.238098536296 Henry Cohn, 2026, needs more optimization.
25 597 0.238099717062 Henry Cohn, 2026, needs more optimization.
25 599 0.238100055939 Henry Cohn, 2026, needs more optimization.
25 603 0.238102783060 Henry Cohn, 2026, needs more optimization.
25 606 0.238102783882 Henry Cohn, 2026, needs more optimization.
25 607 0.238107708361 Henry Cohn, 2026, needs more optimization.
25 608 0.238113139041 Henry Cohn, 2026, needs more optimization.
25 609 0.238113139397 Henry Cohn, 2026, needs more optimization.
25 611 0.238130470569 Henry Cohn, 2026, needs more optimization.
25 612 0.238141979430 Henry Cohn, 2026, needs more optimization.
25 613 0.238142009313 Henry Cohn, 2026, needs more optimization.
25 614 0.238441396639 Henry Cohn, 2026, needs more optimization.
25 615 0.238549402592 Henry Cohn, 2026, needs more optimization.
25 616 0.238706417200 Henry Cohn, 2026, needs more optimization.
25 617 0.238999754916 Henry Cohn, 2026, needs more optimization.
25 618 0.239202485579 Henry Cohn, 2026, needs more optimization.
25 620 0.239405703092 Henry Cohn, 2026, needs more optimization.
25 621 0.239874005984 Henry Cohn, 2026, needs more optimization.
25 622 0.240295239966 Henry Cohn, 2026, needs more optimization.
25 623 0.240977507109 Henry Cohn, 2026, needs more optimization.
25 624 0.241438238100 Henry Cohn, 2026, needs more optimization.
25 625 0.241765304109 Henry Cohn, 2026, needs more optimization.
25 626 0.241929258004 Henry Cohn, 2026, needs more optimization.
25 627 0.247325905020 Henry Cohn, 2026, needs more optimization.
25 628 0.247660611788 Henry Cohn, 2026, needs more optimization.
25 630 0.247809380356 Henry Cohn, 2026, needs more optimization.
25 631 0.247987592997 Henry Cohn, 2026, needs more optimization.
25 632 0.248220073412 Henry Cohn, 2026, needs more optimization.
25 633 0.248325470820 Henry Cohn, 2026, needs more optimization.
25 634 0.248396405953 Henry Cohn, 2026, needs more optimization.
25 637 0.248484232672 Henry Cohn, 2026, needs more optimization.
25 638 0.248507731529 Henry Cohn, 2026, needs more optimization.
25 639 0.248611042913 Henry Cohn, 2026, needs more optimization.
25 640 0.248801878290 Henry Cohn, 2026, needs more optimization.
25 641 0.248889901128 Henry Cohn, 2026, needs more optimization.
25 642 0.248938371492 Henry Cohn, 2026, needs more optimization.
25 645 0.248938373336 Henry Cohn, 2026, needs more optimization.
25 646 0.248938377263 Henry Cohn, 2026, needs more optimization.
25 647 0.248938387602 Henry Cohn, 2026, needs more optimization.
25 648 0.249107043937 Henry Cohn, 2026, needs more optimization.
25 650 0.249125605991 Henry Cohn, 2026, needs more optimization.
25 651 0.249169426655 Henry Cohn, 2026, needs more optimization.
25 652 0.249175019223 Henry Cohn, 2026, needs more optimization.
25 653 0.249229130797 Henry Cohn, 2026, needs more optimization.
25 654 0.249240965351 Henry Cohn, 2026, needs more optimization.
25 655 0.249257165122 Henry Cohn, 2026, needs more optimization.
25 656 0.249294374835 Henry Cohn, 2026, needs more optimization.
25 657 0.249346622144 Henry Cohn, 2026, needs more optimization.
25 658 0.249352892716 Henry Cohn, 2026, needs more optimization.
25 659 0.249446653318 Henry Cohn, 2026, needs more optimization.
25 660 0.249484817481 Henry Cohn, 2026, needs more optimization.
25 661 0.249505156101 Henry Cohn, 2026, needs more optimization.
25 662 0.249539382327 Henry Cohn, 2026, needs more optimization.
25 663 0.249557003830 Henry Cohn, 2026, needs more optimization.
25 664 0.249596536735 Henry Cohn, 2026, needs more optimization.
25 665 0.249628337737 Henry Cohn, 2026, needs more optimization.
25 666 0.249689246647 Henry Cohn, 2026, needs more optimization.
25 667 0.249689249585 Henry Cohn, 2026, needs more optimization.
25 669 0.249724509313 Henry Cohn, 2026, needs more optimization.
25 670 0.249772765919 Henry Cohn, 2026, needs more optimization.
25 671 0.249802170446 Henry Cohn, 2026, needs more optimization.
25 672 0.249831088638 Henry Cohn, 2026, needs more optimization.
25 673 0.249858787504 Henry Cohn, 2026, needs more optimization.
25 674 0.249889355528 Henry Cohn, 2026, needs more optimization.
25 675 0.249910504141 Henry Cohn, 2026, needs more optimization.
25 676 0.249913554117 Henry Cohn, 2026, needs more optimization.
25 677 0.249941679842 Henry Cohn, 2026, needs more optimization.
25 900 0.25 Henry Cohn, 2025.
4⁢x−1
25 901 0.250007185794 Henry Cohn, 2026, needs more optimization.
25 902 0.250007186219 Henry Cohn, 2026, needs more optimization.
25 905 0.250007189362 Henry Cohn, 2026, needs more optimization.
25 908 0.250007190161 Henry Cohn, 2026, needs more optimization.
25 909 0.250007192636 Henry Cohn, 2026, needs more optimization.
25 911 0.250008870235 Henry Cohn, 2026, needs more optimization.
25 914 0.250008870608 Henry Cohn, 2026, needs more optimization.
25 915 0.250008874152 Henry Cohn, 2026, needs more optimization.
25 916 0.250012169489 Henry Cohn, 2026, needs more optimization.
25 917 0.250021689628 Henry Cohn, 2026, needs more optimization.
25 918 0.250046372513 Henry Cohn, 2026, needs more optimization.
25 919 0.250255801633 Henry Cohn, 2026, needs more optimization.
25 920 0.250277508022 Henry Cohn, 2026, needs more optimization.
25 921 0.250386611029 Henry Cohn, 2026, needs more optimization.
25 922 0.250798613932 Henry Cohn, 2026, needs more optimization.
25 923 0.251013421969 Henry Cohn, 2026, needs more optimization.
25 925 0.251295775379 Henry Cohn, 2026, needs more optimization.
25 926 0.251570348978 Henry Cohn, 2026, needs more optimization.
25 927 0.251808135733 Henry Cohn, 2026, needs more optimization.
25 928 0.252560486742 Henry Cohn, 2026, needs more optimization.
25 929 0.253494913204 Henry Cohn, 2026, needs more optimization.
25 930 0.253792165918 Henry Cohn, 2026, needs more optimization.
25 931 0.254356565441 Henry Cohn, 2026, needs more optimization.
25 932 0.254762054807 Henry Cohn, 2026, needs more optimization.
25 933 0.255099177875 Henry Cohn, 2026, needs more optimization.
25 934 0.255710150595 Henry Cohn, 2026, needs more optimization.
25 935 0.256139750991 Henry Cohn, 2026, needs more optimization.
25 936 0.256850121127 Henry Cohn, 2026, needs more optimization.
25 937 0.257407597388 Henry Cohn, 2026, needs more optimization.
25 938 0.257776666122 Henry Cohn, 2026, needs more optimization.
25 939 0.258043517804 Henry Cohn, 2026, needs more optimization.
25 940 0.258439564021 Henry Cohn, 2026, needs more optimization.
25 941 0.259017852997 Henry Cohn, 2026, needs more optimization.
25 942 0.259734265582 Henry Cohn, 2026, needs more optimization.
25 943 0.259972262070 Henry Cohn, 2026, needs more optimization.
25 944 0.260413259538 Henry Cohn, 2026, needs more optimization.
25 945 0.260975766530 Henry Cohn, 2026, needs more optimization.
25 946 0.261512240997 Henry Cohn, 2026, needs more optimization.
25 947 0.261735261159 Henry Cohn, 2026, needs more optimization.
25 948 0.262064361280 Henry Cohn, 2026, needs more optimization.
25 949 0.262795134595 Henry Cohn, 2026, needs more optimization.
25 950 0.263448454948 Henry Cohn, 2026, needs more optimization.
25 951 0.263616161105 Henry Cohn, 2026, needs more optimization.
25 952 0.264016297148 Henry Cohn, 2026, needs more optimization.
25 953 0.264326923181 Henry Cohn, 2026, needs more optimization.
25 954 0.264546250345 Henry Cohn, 2026, needs more optimization.
25 955 0.265047041749 Henry Cohn, 2026, needs more optimization.
25 956 0.265752519704 Henry Cohn, 2026, needs more optimization.
25 957 0.266159188835 Henry Cohn, 2026, needs more optimization.
25 958 0.266540938074 Henry Cohn, 2026, needs more optimization.
25 959 0.266988645323 Henry Cohn, 2026, needs more optimization.
25 960 0.267307761262 Henry Cohn, 2026, needs more optimization.
25 961 0.267558291729 Henry Cohn, 2026, needs more optimization.
25 962 0.267615564214 Henry Cohn, 2026, needs more optimization.
25 963 0.267845144561 Henry Cohn, 2026, needs more optimization.
25 964 0.268209427546 Henry Cohn, 2026, needs more optimization.
25 965 0.268588290254 Henry Cohn, 2026, needs more optimization.
25 966 0.268945375740 Henry Cohn, 2026, needs more optimization.
25 967 0.269311833947 Henry Cohn, 2026, needs more optimization.
25 968 0.269564437248 Henry Cohn, 2026, needs more optimization.
25 969 0.269847683165 Henry Cohn, 2026, needs more optimization.
25 970 0.269895061720 Henry Cohn, 2026, needs more optimization.
25 971 0.270382793662 Henry Cohn, 2026, needs more optimization.
25 973 0.270694771945 Henry Cohn, 2026, needs more optimization.
25 974 0.270858310371 Henry Cohn, 2026, needs more optimization.
25 975 0.271552956302 Henry Cohn, 2026, needs more optimization.
25 976 0.271780364629 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 0.039998970516 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 0.063559232577 Henry Cohn, 2026, needs more optimization.
26 68 0.063600411316 Henry Cohn, 2026, needs more optimization.
26 69 0.064916627337 Henry Cohn, 2026, needs more optimization.
26 70 0.065400189134 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 0.073191111903 Henry Cohn, 2026, needs more optimization.
26 75 0.074028141305 Henry Cohn, 2026, needs more optimization.
26 76 0.075372291887 Henry Cohn, 2026, needs more optimization.
26 77 0.076354800296 Henry Cohn, 2026, needs more optimization.
26 78 0.076863706138 Henry Cohn, 2026, needs more optimization.
26 79 0.076920014415 Henry Cohn, 2026, needs more optimization.
26 80 0.076959313473 Henry Cohn, 2026, needs more optimization.
26 81 0.077577278370 Henry Cohn, 2026, needs more optimization.
26 82 0.077924828163 Henry Cohn, 2026, needs more optimization.
26 83 0.078211449604 Henry Cohn, 2026, needs more optimization.
26 84 0.078381128167 Henry Cohn, 2026, needs more optimization.
26 85 0.078756323799 Henry Cohn, 2026, needs more optimization.
26 86 0.079374579828 Henry Cohn, 2026, needs more optimization.
26 94 0.080685003328 Henry Cohn, 2026.
575⁢x2−34⁢x−1
26 95 0.082981805763 Henry Cohn, 2026, needs more optimization.
26 96 0.085914566489 Henry Cohn, 2026, needs more optimization.
26 97 0.089166971683 Henry Cohn, 2026, needs more optimization.
26 98 0.089782605388 Henry Cohn, 2026, needs more optimization.
26 99 0.090058550629 Henry Cohn, 2026, needs more optimization.
26 100 0.090312517989 Henry Cohn, 2026, needs more optimization.
26 101 0.090543829677 Henry Cohn, 2026, needs more optimization.
26 102 0.090686733783 Henry Cohn, 2026, needs more optimization.
26 103 0.090772374883 Henry Cohn, 2026, needs more optimization.
26 104 0.090847260108 Henry Cohn, 2026, needs more optimization.
26 105 0.090867443639 Henry Cohn, 2026, needs more optimization.
26 106 0.090898073253 Henry Cohn, 2026, needs more optimization.
26 108 0.090899908460 Henry Cohn, 2026, needs more optimization.
26 109 0.090904435391 Henry Cohn, 2026, needs more optimization.
26 110 0.090909315674 Henry Cohn, 2026, needs more optimization.
26 111 0.091755838344 Henry Cohn, 2026, needs more optimization.
26 112 0.094492508573 Henry Cohn, 2026, needs more optimization.
26 113 0.097432419031 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 0.105414239527 Henry Cohn, 2026, needs more optimization.
26 123 0.106264062113 Henry Cohn, 2026, needs more optimization.
26 124 0.107119100710 Henry Cohn, 2026, needs more optimization.
26 125 0.107685811674 Henry Cohn, 2026, needs more optimization.
26 126 0.108555360076 Henry Cohn, 2026, needs more optimization.
26 127 0.109072968564 Henry Cohn, 2026, needs more optimization.
26 128 0.111062131392 Henry Cohn, 2026, needs more optimization.
26 129 0.111064080581 Henry Cohn, 2026, needs more optimization.
26 130 0.111084228112 Henry Cohn, 2026, needs more optimization.
26 131 0.111106517778 Henry Cohn, 2026, needs more optimization.
26 132 0.112890660390 Henry Cohn, 2026, needs more optimization.
26 133 0.114542503346 Henry Cohn, 2026, needs more optimization.
26 134 0.115296571767 Henry Cohn, 2026, needs more optimization.
26 135 0.116308909440 Henry Cohn, 2026, needs more optimization.
26 136 0.116455213976 Henry Cohn, 2026, needs more optimization.
26 137 0.117070718711 Henry Cohn, 2026, needs more optimization.
26 138 0.118625425485 Henry Cohn, 2026, needs more optimization.
26 139 0.122355015097 Henry Cohn, 2026, needs more optimization.
26 140 0.125308839236 Henry Cohn, 2026, needs more optimization.
26 141 0.127924296559 Henry Cohn, 2026, needs more optimization.
26 142 0.130226435800 Henry Cohn, 2026, needs more optimization.
26 143 0.131454472130 Henry Cohn, 2026, needs more optimization.
26 144 0.131615150498 Henry Cohn, 2026, needs more optimization.
26 145 0.131728241353 Henry Cohn, 2026, needs more optimization.
26 146 0.131788303637 Henry Cohn, 2026, needs more optimization.
26 147 0.131911831173 Henry Cohn, 2026, needs more optimization.
26 148 0.132083314999 Henry Cohn, 2026, needs more optimization.
26 149 0.132351695980 Henry Cohn, 2026, needs more optimization.
26 150 0.133024375407 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 0.135129077869 Henry Cohn, 2026, needs more optimization.
26 162 0.135323044627 Henry Cohn, 2026, needs more optimization.
26 163 0.136053470094 Henry Cohn, 2026, needs more optimization.
26 164 0.136697655146 Henry Cohn, 2026, needs more optimization.
26 165 0.137900513245 Henry Cohn, 2026, needs more optimization.
26 166 0.138941425001 Henry Cohn, 2026, needs more optimization.
26 167 0.139937937886 Henry Cohn, 2026, needs more optimization.
26 168 0.141037807262 Henry Cohn, 2026, needs more optimization.
26 169 0.142695725222 Henry Cohn, 2026, needs more optimization.
26 170 0.142711000645 Henry Cohn, 2026, needs more optimization.
26 171 0.142714428190 Henry Cohn, 2026, needs more optimization.
26 172 0.142738185676 Henry Cohn, 2026, needs more optimization.
26 173 0.142750494327 Henry Cohn, 2026, needs more optimization.
26 174 0.142779975817 Henry Cohn, 2026, needs more optimization.
26 175 0.142802809351 Henry Cohn, 2026, needs more optimization.
26 176 0.142803307099 Henry Cohn, 2026, needs more optimization.
26 177 0.142811398433 Henry Cohn, 2026, needs more optimization.
26 178 0.142817871102 Henry Cohn, 2026, needs more optimization.
26 179 0.142818251116 Henry Cohn, 2026, needs more optimization.
26 180 0.142818252545 Henry Cohn, 2026, needs more optimization.
26 181 0.142837223630 Henry Cohn, 2026, needs more optimization.
26 182 0.142851452386 Henry Cohn, 2026, needs more optimization.
26 183 0.142856479834 Henry Cohn, 2026, needs more optimization.
26 184 0.142861573726 Henry Cohn, 2026, needs more optimization.
26 185 0.142903374967 Henry Cohn, 2026, needs more optimization.
26 186 0.143134811251 Henry Cohn, 2026, needs more optimization.
26 187 0.143817566258 Henry Cohn, 2026, needs more optimization.
26 188 0.145218765627 Henry Cohn, 2026, needs more optimization.
26 189 0.145511068993 Henry Cohn, 2026, needs more optimization.
26 190 0.145783353595 Henry Cohn, 2026, needs more optimization.
26 191 0.146056372389 Henry Cohn, 2026, needs more optimization.
26 192 0.146464874760 Henry Cohn, 2026, needs more optimization.
26 193 0.146644347544 Henry Cohn, 2026, needs more optimization.
26 194 0.146839864755 Henry Cohn, 2026, needs more optimization.
26 195 0.146895420104 Henry Cohn, 2026, needs more optimization.
26 196 0.147013537038 Henry Cohn, 2026, needs more optimization.
26 197 0.147013820918 Henry Cohn, 2026, needs more optimization.
26 198 0.147017495011 Henry Cohn, 2026, needs more optimization.
26 199 0.147132872525 Henry Cohn, 2026, needs more optimization.
26 200 0.147198573328 Henry Cohn, 2026, needs more optimization.
26 201 0.147504247956 Henry Cohn, 2026, needs more optimization.
26 202 0.147505089214 Henry Cohn, 2026, needs more optimization.
26 203 0.148221352153 Henry Cohn, 2026, needs more optimization.
26 204 0.148920087354 Henry Cohn, 2026, needs more optimization.
26 205 0.149240960729 Henry Cohn, 2026, needs more optimization.
26 206 0.149266002839 Henry Cohn, 2026, needs more optimization.
26 207 0.149979668489 Henry Cohn, 2026, needs more optimization.
26 208 0.150272455871 Henry Cohn, 2026, needs more optimization.
26 209 0.150330683598 Henry Cohn, 2026, needs more optimization.
26 210 0.150472435359 Henry Cohn, 2026, needs more optimization.
26 211 0.150474432769 Henry Cohn, 2026, needs more optimization.
26 212 0.151001057928 Henry Cohn, 2026, needs more optimization.
26 213 0.151228789497 Henry Cohn, 2026, needs more optimization.
26 214 0.151285780664 Henry Cohn, 2026, needs more optimization.
26 215 0.151285788991 Henry Cohn, 2026, needs more optimization.
26 216 0.151843941829 Henry Cohn, 2026, needs more optimization.
26 217 0.151843942036 Henry Cohn, 2026, needs more optimization.
26 218 0.151936916598 Henry Cohn, 2026, needs more optimization.
26 219 0.151940609511 Henry Cohn, 2026, needs more optimization.
26 220 0.152490829209 Henry Cohn, 2026, needs more optimization.
26 221 0.154085209485 Henry Cohn, 2026, needs more optimization.
26 222 0.154408970162 Henry Cohn, 2026, needs more optimization.
26 223 0.154620026728 Henry Cohn, 2026, needs more optimization.
26 224 0.155109750213 Henry Cohn, 2026, needs more optimization.
26 225 0.156464864313 Henry Cohn, 2026, needs more optimization.
26 226 0.156930235260 Henry Cohn, 2026, needs more optimization.
26 227 0.157305249598 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 0.159338322994 Henry Cohn, 2026, needs more optimization.
26 231 0.160253268391 Henry Cohn, 2026, needs more optimization.
26 232 0.161975017532 Henry Cohn, 2026, needs more optimization.
26 233 0.162067860150 Henry Cohn, 2026, needs more optimization.
26 234 0.162559224570 Henry Cohn, 2026, needs more optimization.
26 235 0.162933918121 Henry Cohn, 2026, needs more optimization.
26 236 0.163196819352 Henry Cohn, 2026, needs more optimization.
26 237 0.163408784343 Henry Cohn, 2026, needs more optimization.
26 238 0.163931115881 Henry Cohn, 2026, needs more optimization.
26 239 0.164441237857 Henry Cohn, 2026, needs more optimization.
26 240 0.164547586288 Henry Cohn, 2026, needs more optimization.
26 241 0.165094605578 Henry Cohn, 2026, needs more optimization.
26 242 0.165352547753 Henry Cohn, 2026, needs more optimization.
26 243 0.165687372342 Henry Cohn, 2026, needs more optimization.
26 244 0.165899196623 Henry Cohn, 2026, needs more optimization.
26 245 0.166008320418 Henry Cohn, 2026, needs more optimization.
26 246 0.166238837590 Henry Cohn, 2026, needs more optimization.
26 247 0.166374903928 Henry Cohn, 2026, needs more optimization.
26 248 0.166435732411 Henry Cohn, 2026, needs more optimization.
26 249 0.166445772274 Henry Cohn, 2026, needs more optimization.
26 250 0.166448522572 Henry Cohn, 2026, needs more optimization.
26 251 0.166518189014 Henry Cohn, 2026, needs more optimization.
26 252 0.166518772673 Henry Cohn, 2026, needs more optimization.
26 253 0.166620656377 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.
26 290 0.166668813579 Henry Cohn, 2026, needs more optimization.
26 291 0.166670194182 Henry Cohn, 2026, needs more optimization.
26 292 0.166671465846 Henry Cohn, 2026, needs more optimization.
26 293 0.166672346911 Henry Cohn, 2026, needs more optimization.
26 294 0.166674133224 Henry Cohn, 2026, needs more optimization.
26 295 0.166683336754 Henry Cohn, 2026, needs more optimization.
26 296 0.166705499733 Henry Cohn, 2026, needs more optimization.
26 297 0.166898110511 Henry Cohn, 2026, needs more optimization.
26 298 0.167314292940 Henry Cohn, 2026, needs more optimization.
26 299 0.168433747999 Henry Cohn, 2026, needs more optimization.
26 300 0.169922367138 Henry Cohn, 2026, needs more optimization.
26 301 0.170974694049 Henry Cohn, 2026, needs more optimization.
26 302 0.172075485199 Henry Cohn, 2026, needs more optimization.
26 303 0.173858762643 Henry Cohn, 2026, needs more optimization.
26 304 0.175654019415 Henry Cohn, 2026, needs more optimization.
26 305 0.176574312719 Henry Cohn, 2026, needs more optimization.
26 306 0.178314173048 Henry Cohn, 2026, needs more optimization.
26 307 0.179623578135 Henry Cohn, 2026, needs more optimization.
26 308 0.180450472975 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 0.181819184362 Henry Cohn, 2026, needs more optimization.
26 323 0.181819351767 Henry Cohn, 2026, needs more optimization.
26 325 0.181819351818 Henry Cohn, 2026, needs more optimization.
26 326 0.181820070788 Henry Cohn, 2026, needs more optimization.
26 327 0.181820071074 Henry Cohn, 2026, needs more optimization.
26 328 0.181822165196 Henry Cohn, 2026, needs more optimization.
26 329 0.181823631607 Henry Cohn, 2026, needs more optimization.
26 330 0.181829833054 Henry Cohn, 2026, needs more optimization.
26 331 0.182100354132 Henry Cohn, 2026, needs more optimization.
26 332 0.182715021522 Henry Cohn, 2026, needs more optimization.
26 333 0.184017312231 Henry Cohn, 2026, needs more optimization.
26 334 0.185148866288 Henry Cohn, 2026, needs more optimization.
26 335 0.185785550104 Henry Cohn, 2026, needs more optimization.
26 336 0.187159599080 Henry Cohn, 2026, needs more optimization.
26 337 0.187955825609 Henry Cohn, 2026, needs more optimization.
26 338 0.188847042917 Henry Cohn, 2026, needs more optimization.
26 339 0.190011133108 Henry Cohn, 2026, needs more optimization.
26 340 0.190318158249 Henry Cohn, 2026, needs more optimization.
26 341 0.192165848579 Henry Cohn, 2026, needs more optimization.
26 342 0.192571440729 Henry Cohn, 2026, needs more optimization.
26 343 0.193221523562 Henry Cohn, 2026, needs more optimization.
26 344 0.194472646704 Henry Cohn, 2026, needs more optimization.
26 345 0.195190997726 Henry Cohn, 2026, needs more optimization.
26 346 0.196308037258 Henry Cohn, 2026, needs more optimization.
26 347 0.196469231789 Henry Cohn, 2026, needs more optimization.
26 348 0.196589347721 Henry Cohn, 2026, needs more optimization.
26 349 0.196681842978 Henry Cohn, 2026, needs more optimization.
26 350 0.196921764004 Henry Cohn, 2026, needs more optimization.
26 351 0.196993722234 Henry Cohn, 2026, needs more optimization.
26 352 0.197129613093 Henry Cohn, 2026, needs more optimization.
26 353 0.197261114207 Henry Cohn, 2026, needs more optimization.
26 354 0.197347984144 Henry Cohn, 2026, needs more optimization.
26 355 0.197428886008 Henry Cohn, 2026, needs more optimization.
26 356 0.197696394451 Henry Cohn, 2026, needs more optimization.
26 357 0.197777882400 Henry Cohn, 2026, needs more optimization.
26 358 0.197872370552 Henry Cohn, 2026, needs more optimization.
26 359 0.198059550806 Henry Cohn, 2026, needs more optimization.
26 360 0.198138412161 Henry Cohn, 2026, needs more optimization.
26 361 0.198237686693 Henry Cohn, 2026, needs more optimization.
26 362 0.198298582562 Henry Cohn, 2026, needs more optimization.
26 363 0.198350768350 Henry Cohn, 2026, needs more optimization.
26 364 0.198444924118 Henry Cohn, 2026, needs more optimization.
26 365 0.198518607452 Henry Cohn, 2026, needs more optimization.
26 366 0.198564394666 Henry Cohn, 2026, needs more optimization.
26 367 0.198672566563 Henry Cohn, 2026, needs more optimization.
26 368 0.198719186820 Henry Cohn, 2026, needs more optimization.
26 369 0.198824471342 Henry Cohn, 2026, needs more optimization.
26 370 0.198895382020 Henry Cohn, 2026, needs more optimization.
26 371 0.199051295855 Henry Cohn, 2026, needs more optimization.
26 372 0.199093512329 Henry Cohn, 2026, needs more optimization.
26 373 0.199115006742 Henry Cohn, 2026, needs more optimization.
26 374 0.199218933635 Henry Cohn, 2026, needs more optimization.
26 375 0.199283369783 Henry Cohn, 2026, needs more optimization.
26 376 0.199332716345 Henry Cohn, 2026, needs more optimization.
26 377 0.199365050476 Henry Cohn, 2026, needs more optimization.
26 378 0.199426245527 Henry Cohn, 2026, needs more optimization.
26 379 0.199489854802 Henry Cohn, 2026, needs more optimization.
26 380 0.199535252268 Henry Cohn, 2026, needs more optimization.
26 381 0.199535277055 Henry Cohn, 2026, needs more optimization.
26 382 0.199543269379 Henry Cohn, 2026, needs more optimization.
26 383 0.199559483111 Henry Cohn, 2026, needs more optimization.
26 384 0.199589827589 Henry Cohn, 2026, needs more optimization.
26 385 0.199633182062 Henry Cohn, 2026, needs more optimization.
26 386 0.199677645365 Henry Cohn, 2026, needs more optimization.
26 387 0.199715484615 Henry Cohn, 2026, needs more optimization.
26 388 0.199739169347 Henry Cohn, 2026, needs more optimization.
26 389 0.199776809843 Henry Cohn, 2026, needs more optimization.
26 390 0.199838152142 Henry Cohn, 2026, needs more optimization.
26 391 0.199838153062 Henry Cohn, 2026, needs more optimization.
26 392 0.199849173127 Henry Cohn, 2026, needs more optimization.
26 393 0.199868936517 Henry Cohn, 2026, needs more optimization.
26 394 0.199888540394 Henry Cohn, 2026, needs more optimization.
26 395 0.199917602204 Henry Cohn, 2026, needs more optimization.
26 396 0.199936337027 Henry Cohn, 2026, needs more optimization.
26 397 0.199956117616 Henry Cohn, 2026, needs more optimization.
26 398 0.199974184531 Henry Cohn, 2026, needs more optimization.
26 399 0.199975832779 Henry Cohn, 2026, needs more optimization.
26 400 0.199982364119 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
26 560 0.200001673967 Orthogonal union of 558 points in 25 dimensions and 2 points in 1 dimension.
26 561 0.200002572951 Henry Cohn, 2026, needs more optimization.
26 563 0.200002573034 Henry Cohn, 2026, needs more optimization.
26 565 0.200003051605 Henry Cohn, 2026, needs more optimization.
26 567 0.200003052344 Henry Cohn, 2026, needs more optimization.
26 568 0.200003276382 Henry Cohn, 2026, needs more optimization.
26 569 0.200022245266 Henry Cohn, 2026, needs more optimization.
26 570 0.200057349130 Henry Cohn, 2026, needs more optimization.
26 571 0.200520789616 Henry Cohn, 2026, needs more optimization.
26 572 0.200737142705 Henry Cohn, 2026, needs more optimization.
26 573 0.201312782140 Henry Cohn, 2026, needs more optimization.
26 574 0.202335108561 Henry Cohn, 2026, needs more optimization.
26 575 0.204471161215 Henry Cohn, 2026, needs more optimization.
26 576 0.205549841635 Henry Cohn, 2026, needs more optimization.
26 577 0.208783685333 Henry Cohn, 2026, needs more optimization.
26 578 0.210061028536 Henry Cohn, 2026, needs more optimization.
26 579 0.211552414589 Henry Cohn, 2026, needs more optimization.
26 580 0.212552860669 Henry Cohn, 2026, needs more optimization.
26 581 0.214573057127 Henry Cohn, 2026, needs more optimization.
26 582 0.216174077318 Henry Cohn, 2026, needs more optimization.
26 583 0.216923177091 Henry Cohn, 2026, needs more optimization.
26 584 0.217525749456 Henry Cohn, 2026, needs more optimization.
26 585 0.218852142466 Henry Cohn, 2026, needs more optimization.
26 586 0.219438898835 Henry Cohn, 2026, needs more optimization.
26 587 0.220741544130 Henry Cohn, 2026, needs more optimization.
26 588 0.221634434895 Henry Cohn, 2026, needs more optimization.
26 589 0.222136163409 Henry Cohn, 2026, needs more optimization.
26 590 0.222962090864 Henry Cohn, 2026, needs more optimization.
26 591 0.224056001801 Henry Cohn, 2026, needs more optimization.
26 592 0.224578821740 Henry Cohn, 2026, needs more optimization.
26 593 0.225013788784 Henry Cohn, 2026, needs more optimization.
26 594 0.225958832729 Henry Cohn, 2026, needs more optimization.
26 595 0.226234976650 Henry Cohn, 2026, needs more optimization.
26 596 0.226579417602 Henry Cohn, 2026, needs more optimization.
26 602 0.238096469173 Henry Cohn, 2026, needs more optimization.
26 603 0.238098422334 Henry Cohn, 2026, needs more optimization.
26 609 0.238098678714 Henry Cohn, 2026, needs more optimization.
26 610 0.238098678719 Henry Cohn, 2026, needs more optimization.
26 613 0.238099258105 Henry Cohn, 2026, needs more optimization.
26 614 0.238099258153 Henry Cohn, 2026, needs more optimization.
26 615 0.238099854383 Henry Cohn, 2026, needs more optimization.
26 619 0.238099854441 Henry Cohn, 2026, needs more optimization.
26 620 0.238103826563 Henry Cohn, 2026, needs more optimization.
26 622 0.238107788229 Henry Cohn, 2026, needs more optimization.
26 623 0.238107788258 Henry Cohn, 2026, needs more optimization.
26 625 0.238115031836 Henry Cohn, 2026, needs more optimization.
26 626 0.238115037867 Henry Cohn, 2026, needs more optimization.
26 627 0.238115038371 Henry Cohn, 2026, needs more optimization.
26 628 0.238138900925 Henry Cohn, 2026, needs more optimization.
26 629 0.238685692784 Henry Cohn, 2026, needs more optimization.
26 630 0.238685818773 Henry Cohn, 2026, needs more optimization.
26 631 0.238780486478 Henry Cohn, 2026, needs more optimization.
26 632 0.239750288361 Henry Cohn, 2026, needs more optimization.
26 633 0.240404610766 Henry Cohn, 2026, needs more optimization.
26 634 0.240438183926 Henry Cohn, 2026, needs more optimization.
26 635 0.241312824700 Henry Cohn, 2026, needs more optimization.
26 636 0.241525724642 Henry Cohn, 2026, needs more optimization.
26 637 0.241698939238 Henry Cohn, 2026, needs more optimization.
26 638 0.241698939591 Henry Cohn, 2026, needs more optimization.
26 639 0.242546964455 Henry Cohn, 2026, needs more optimization.
26 640 0.243056357329 Henry Cohn, 2026, needs more optimization.
26 641 0.244052296444 Henry Cohn, 2026, needs more optimization.
26 642 0.244171845087 Henry Cohn, 2026, needs more optimization.
26 643 0.244260463752 Henry Cohn, 2026, needs more optimization.
26 644 0.244565896554 Henry Cohn, 2026, needs more optimization.
26 645 0.245569478481 Henry Cohn, 2026, needs more optimization.
26 646 0.245944081932 Henry Cohn, 2026, needs more optimization.
26 647 0.246069542415 Henry Cohn, 2026, needs more optimization.
26 648 0.246069559353 Henry Cohn, 2026, needs more optimization.
26 649 0.246069588000 Henry Cohn, 2026, needs more optimization.
26 650 0.246069592690 Henry Cohn, 2026, needs more optimization.
26 651 0.246715216886 Henry Cohn, 2026, needs more optimization.
26 652 0.246715828308 Henry Cohn, 2026, needs more optimization.
26 653 0.246834013113 Henry Cohn, 2026, needs more optimization.
26 654 0.246958682667 Henry Cohn, 2026, needs more optimization.
26 655 0.247355255362 Henry Cohn, 2026, needs more optimization.
26 656 0.247355272134 Henry Cohn, 2026, needs more optimization.
26 657 0.247406574813 Henry Cohn, 2026, needs more optimization.
26 658 0.247450838367 Henry Cohn, 2026, needs more optimization.
26 659 0.247755290308 Henry Cohn, 2026, needs more optimization.
26 660 0.247755296940 Henry Cohn, 2026, needs more optimization.
26 661 0.247914918462 Henry Cohn, 2026, needs more optimization.
26 662 0.247964364248 Henry Cohn, 2026, needs more optimization.
26 663 0.247985431370 Henry Cohn, 2026, needs more optimization.
26 664 0.247996665283 Henry Cohn, 2026, needs more optimization.
26 665 0.248261258038 Henry Cohn, 2026, needs more optimization.
26 667 0.248261265931 Henry Cohn, 2026, needs more optimization.
26 668 0.248261269357 Henry Cohn, 2026, needs more optimization.
26 669 0.248474368446 Henry Cohn, 2026, needs more optimization.
26 670 0.248475997746 Henry Cohn, 2026, needs more optimization.
26 671 0.248551876318 Henry Cohn, 2026, needs more optimization.
26 672 0.248596801736 Henry Cohn, 2026, needs more optimization.
26 673 0.248596802960 Henry Cohn, 2026, needs more optimization.
26 674 0.248596803721 Henry Cohn, 2026, needs more optimization.
26 675 0.248596816669 Henry Cohn, 2026, needs more optimization.
26 676 0.248596817610 Henry Cohn, 2026, needs more optimization.
26 677 0.248706197120 Henry Cohn, 2026, needs more optimization.
26 678 0.248762848159 Henry Cohn, 2026, needs more optimization.
26 679 0.248788530122 Henry Cohn, 2026, needs more optimization.
26 681 0.248826671791 Henry Cohn, 2026, needs more optimization.
26 682 0.248909957394 Henry Cohn, 2026, needs more optimization.
26 683 0.248976887496 Henry Cohn, 2026, needs more optimization.
26 684 0.249063893487 Henry Cohn, 2026, needs more optimization.
26 685 0.249088203245 Henry Cohn, 2026, needs more optimization.
26 686 0.249088208651 Henry Cohn, 2026, needs more optimization.
26 687 0.249185250621 Henry Cohn, 2026, needs more optimization.
26 688 0.249191165305 Henry Cohn, 2026, needs more optimization.
26 689 0.249251034497 Henry Cohn, 2026, needs more optimization.
26 690 0.249266620163 Henry Cohn, 2026, needs more optimization.
26 691 0.249288904658 Henry Cohn, 2026, needs more optimization.
26 692 0.249288905290 Henry Cohn, 2026, needs more optimization.
26 693 0.249390240686 Henry Cohn, 2026, needs more optimization.
26 694 0.249452051847 Henry Cohn, 2026, needs more optimization.
26 695 0.249460505342 Henry Cohn, 2026, needs more optimization.
26 696 0.249460508487 Henry Cohn, 2026, needs more optimization.
26 697 0.249499175359 Henry Cohn, 2026, needs more optimization.
26 698 0.249504610474 Henry Cohn, 2026, needs more optimization.
26 699 0.249504611130 Henry Cohn, 2026, needs more optimization.
26 700 0.249504611439 Henry Cohn, 2026, needs more optimization.
26 701 0.249514451339 Henry Cohn, 2026, needs more optimization.
26 702 0.249566542813 Henry Cohn, 2026, needs more optimization.
26 703 0.249575557081 Henry Cohn, 2026, needs more optimization.
26 704 0.249584736698 Henry Cohn, 2026, needs more optimization.
26 705 0.249613458333 Henry Cohn, 2026, needs more optimization.
26 706 0.249671223631 Henry Cohn, 2026, needs more optimization.
26 707 0.249681980920 Henry Cohn, 2026, needs more optimization.
26 708 0.249718549653 Henry Cohn, 2026, needs more optimization.
26 709 0.249718549984 Henry Cohn, 2026, needs more optimization.
26 710 0.249732593377 Henry Cohn, 2026, needs more optimization.
26 712 0.249755694637 Henry Cohn, 2026, needs more optimization.
26 713 0.249758120301 Henry Cohn, 2026, needs more optimization.
26 714 0.249758120999 Henry Cohn, 2026, needs more optimization.
26 715 0.249791236672 Henry Cohn, 2026, needs more optimization.
26 716 0.249826171262 Henry Cohn, 2026, needs more optimization.
26 717 0.249826172486 Henry Cohn, 2026, needs more optimization.
26 718 0.249849018842 Henry Cohn, 2026, needs more optimization.
26 719 0.249882855977 Henry Cohn, 2026, needs more optimization.
26 720 0.249883468334 Henry Cohn, 2026, needs more optimization.
26 721 0.249907604580 Henry Cohn, 2026, needs more optimization.
26 722 0.249911176909 Henry Cohn, 2026, needs more optimization.
26 723 0.249937667796 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 0.250002537983 Henry Cohn, 2026, needs more optimization.
26 905 0.250004949384 Henry Cohn, 2026, needs more optimization.
26 906 0.250004949619 Henry Cohn, 2026, needs more optimization.
26 907 0.250004949908 Henry Cohn, 2026, needs more optimization.
26 908 0.250004951188 Henry Cohn, 2026, needs more optimization.
26 909 0.250004951275 Henry Cohn, 2026, needs more optimization.
26 910 0.250004951357 Henry Cohn, 2026, needs more optimization.
26 911 0.250004951647 Henry Cohn, 2026, needs more optimization.
26 912 0.250004952046 Henry Cohn, 2026, needs more optimization.
26 913 0.250004952095 Henry Cohn, 2026, needs more optimization.
26 915 0.250005150604 Henry Cohn, 2026, needs more optimization.
26 917 0.250008874152 Orthogonal union of 915 points in 25 dimensions and 2 points in 1 dimension.
26 919 0.250015377010 Henry Cohn, 2026, needs more optimization.
26 923 0.250015377014 Henry Cohn, 2026, needs more optimization.
26 924 0.250015377076 Henry Cohn, 2026, needs more optimization.
26 926 0.250015377086 Henry Cohn, 2026, needs more optimization.
26 927 0.250015377193 Henry Cohn, 2026, needs more optimization.
26 930 0.250015377292 Henry Cohn, 2026, needs more optimization.
26 932 0.250015377953 Henry Cohn, 2026, needs more optimization.
26 933 0.250015378083 Henry Cohn, 2026, needs more optimization.
26 934 0.250020553638 Henry Cohn, 2026, needs more optimization.
26 935 0.250048014571 Henry Cohn, 2026, needs more optimization.
26 936 0.250081086663 Henry Cohn, 2026, needs more optimization.
26 937 0.250159430586 Henry Cohn, 2026, needs more optimization.
26 938 0.250227136236 Henry Cohn, 2026, needs more optimization.
26 939 0.250322228852 Henry Cohn, 2026, needs more optimization.
26 940 0.250408047306 Henry Cohn, 2026, needs more optimization.
26 941 0.250622487463 Henry Cohn, 2026, needs more optimization.
26 942 0.250855162050 Henry Cohn, 2026, needs more optimization.
26 943 0.250997485834 Henry Cohn, 2026, needs more optimization.
26 944 0.251288808654 Henry Cohn, 2026, needs more optimization.
26 945 0.251629098658 Henry Cohn, 2026, needs more optimization.
26 946 0.252010665048 Henry Cohn, 2026, needs more optimization.
26 947 0.252267245172 Henry Cohn, 2026, needs more optimization.
26 948 0.252588383580 Henry Cohn, 2026, needs more optimization.
26 949 0.253148190284 Henry Cohn, 2026, needs more optimization.
26 950 0.253273796753 Henry Cohn, 2026, needs more optimization.
26 951 0.253532470151 Henry Cohn, 2026, needs more optimization.
26 952 0.254057978704 Henry Cohn, 2026, needs more optimization.
26 953 0.254293999373 Henry Cohn, 2026, needs more optimization.
26 954 0.254832267344 Henry Cohn, 2026, needs more optimization.
26 955 0.255196404814 Henry Cohn, 2026, needs more optimization.
26 956 0.255685089054 Henry Cohn, 2026, needs more optimization.
26 957 0.256018831027 Henry Cohn, 2026, needs more optimization.
26 958 0.256224246834 Henry Cohn, 2026, needs more optimization.
26 959 0.256644654663 Henry Cohn, 2026, needs more optimization.
26 960 0.257169273697 Henry Cohn, 2026, needs more optimization.
26 961 0.257225660544 Henry Cohn, 2026, needs more optimization.
26 962 0.257687547359 Henry Cohn, 2026, needs more optimization.
26 963 0.258249210882 Henry Cohn, 2026, needs more optimization.
26 964 0.258550566782 Henry Cohn, 2026, needs more optimization.
26 965 0.258743809323 Henry Cohn, 2026, needs more optimization.
26 966 0.258994420672 Henry Cohn, 2026, needs more optimization.
26 967 0.259474941373 Henry Cohn, 2026, needs more optimization.
26 968 0.259653298336 Henry Cohn, 2026, needs more optimization.
26 969 0.259939898530 Henry Cohn, 2026, needs more optimization.
26 970 0.260151519004 Henry Cohn, 2026, needs more optimization.
26 971 0.260714480423 Henry Cohn, 2026, needs more optimization.
26 972 0.261167685208 Henry Cohn, 2026, needs more optimization.
26 973 0.261347934444 Henry Cohn, 2026, needs more optimization.
26 974 0.261823606306 Henry Cohn, 2026, needs more optimization.
26 975 0.262199434814 Henry Cohn, 2026, needs more optimization.
26 976 0.262813918296 Henry Cohn, 2026, needs more optimization.
26 977 0.263069035058 Henry Cohn, 2026, needs more optimization.
26 978 0.263516806230 Henry Cohn, 2026, needs more optimization.
26 979 0.263663815704 Henry Cohn, 2026, needs more optimization.
26 980 0.263783061549 Henry Cohn, 2026, needs more optimization.
26 981 0.264495275805 Henry Cohn, 2026, needs more optimization.
26 982 0.265074624672 Henry Cohn, 2026, needs more optimization.
26 983 0.265459197639 Henry Cohn, 2026, needs more optimization.
26 984 0.265717408436 Henry Cohn, 2026, needs more optimization.
26 985 0.266004000008 Henry Cohn, 2026, needs more optimization.
26 986 0.266296860381 Henry Cohn, 2026, needs more optimization.
26 987 0.266357208083 Henry Cohn, 2026, needs more optimization.
26 988 0.266642858382 Henry Cohn, 2026, needs more optimization.
26 989 0.266845828645 Henry Cohn, 2026, needs more optimization.
26 990 0.267249738624 Henry Cohn, 2026, needs more optimization.
26 991 0.267331040895 Henry Cohn, 2026, needs more optimization.
26 992 0.267622580472 Henry Cohn, 2026, needs more optimization.
26 993 0.267751642129 Henry Cohn, 2026, needs more optimization.
26 994 0.268014138024 Henry Cohn, 2026, needs more optimization.
26 995 0.268103802767 Henry Cohn, 2026, needs more optimization.
26 996 0.268288714726 Henry Cohn, 2026, needs more optimization.
26 997 0.268631315043 Henry Cohn, 2026, needs more optimization.
26 998 0.268877435759 Henry Cohn, 2026, needs more optimization.
26 999 0.269300220609 Henry Cohn, 2026, needs more optimization.
26 1000 0.269506903344 Henry Cohn, 2026, needs more optimization.
26 1001 0.269870574116 Henry Cohn, 2026, needs more optimization.
26 1002 0.270003297348 Henry Cohn, 2026, needs more optimization.
26 1003 0.270413274317 Henry Cohn, 2026, needs more optimization.
26 1004 0.270535097990 Henry Cohn, 2026, needs more optimization.
26 1005 0.270737716891 Henry Cohn, 2026, needs more optimization.
26 1007 0.271164064251 Henry Cohn, 2026, needs more optimization.
26 1008 0.271296396806 Henry Cohn, 2026, needs more optimization.
26 1009 0.271569426401 Henry Cohn, 2026, needs more optimization.
26 1010 0.271824365866 Henry Cohn, 2026, needs more optimization.
26 1011 0.271997704824 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 0.056203232320 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 0.062922671881 Henry Cohn, 2026, needs more optimization.
27 71 0.064107549659 Henry Cohn, 2026, needs more optimization.
27 72 0.064938703540 Henry Cohn, 2026, needs more optimization.
27 73 0.065805531729 Henry Cohn, 2026, needs more optimization.
27 74 0.066308366331 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 0.074624795263 Henry Cohn, 2026, needs more optimization.
27 79 0.075331326633 Henry Cohn, 2026, needs more optimization.
27 80 0.076122276896 Henry Cohn, 2026, needs more optimization.
27 81 0.076640151288 Henry Cohn, 2026, needs more optimization.
27 82 0.076886312745 Henry Cohn, 2026, needs more optimization.
27 83 0.076908998835 Henry Cohn, 2026, needs more optimization.
27 84 0.077005220845 Henry Cohn, 2026, needs more optimization.
27 85 0.077375337738 Henry Cohn, 2026, needs more optimization.
27 86 0.077583325151 Henry Cohn, 2026, needs more optimization.
27 87 0.078384178560 Henry Cohn, 2026, needs more optimization.
27 88 0.078632181564 Henry Cohn, 2026, needs more optimization.
27 89 0.079086756261 Henry Cohn, 2026, needs more optimization.
27 90 0.079553023668 Henry Cohn, 2026, needs more optimization.
27 91 0.080270744374 Henry Cohn, 2026, needs more optimization.
27 92 0.080397348706 Henry Cohn, 2026, needs more optimization.
27 93 0.080671661873 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 0.084158666674 Henry Cohn, 2026, needs more optimization.
27 100 0.086593017860 Henry Cohn, 2026, needs more optimization.
27 101 0.088590539850 Henry Cohn, 2026, needs more optimization.
27 102 0.089470674911 Henry Cohn, 2026, needs more optimization.
27 103 0.089776459760 Henry Cohn, 2026, needs more optimization.
27 104 0.089999203436 Henry Cohn, 2026, needs more optimization.
27 105 0.090247516948 Henry Cohn, 2026, needs more optimization.
27 106 0.090283952777 Henry Cohn, 2026, needs more optimization.
27 107 0.090522581517 Henry Cohn, 2026, needs more optimization.
27 108 0.090586419301 Henry Cohn, 2026, needs more optimization.
27 110 0.090642434465 Henry Cohn, 2026, needs more optimization.
27 111 0.090770333671 Henry Cohn, 2026, needs more optimization.
27 112 0.090862857236 Henry Cohn, 2026, needs more optimization.
27 113 0.090892295732 Henry Cohn, 2026, needs more optimization.
27 114 0.091267459192 Henry Cohn, 2026, needs more optimization.
27 115 0.092925161070 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 0.102972750413 Henry Cohn, 2026, needs more optimization.
27 120 0.103038125850 Henry Cohn, 2026, needs more optimization.
27 121 0.103085747576 Henry Cohn, 2026, needs more optimization.
27 122 0.103118924043 Henry Cohn, 2026, needs more optimization.
27 125 0.103125332566 Henry Cohn, 2026, needs more optimization.
27 126 0.104307022419 Henry Cohn, 2026, needs more optimization.
27 127 0.105170975875 Henry Cohn, 2026, needs more optimization.
27 128 0.105903253770 Henry Cohn, 2026, needs more optimization.
27 129 0.107238353917 Henry Cohn, 2026, needs more optimization.
27 130 0.107691893750 Henry Cohn, 2026, needs more optimization.
27 131 0.108499430601 Henry Cohn, 2026, needs more optimization.
27 132 0.109607606203 Henry Cohn, 2026, needs more optimization.
27 133 0.110567852072 Henry Cohn, 2026, needs more optimization.
27 134 0.111008829150 Henry Cohn, 2026, needs more optimization.
27 135 0.111016810594 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 0.114332989846 Henry Cohn, 2026, needs more optimization.
27 139 0.114844353668 Henry Cohn, 2026, needs more optimization.
27 140 0.115273202918 Henry Cohn, 2026, needs more optimization.
27 141 0.116317506895 Henry Cohn, 2026, needs more optimization.
27 142 0.117414270965 Henry Cohn, 2026, needs more optimization.
27 143 0.119152801568 Henry Cohn, 2026, needs more optimization.
27 144 0.121001321740 Henry Cohn, 2026, needs more optimization.
27 145 0.123136128144 Henry Cohn, 2026, needs more optimization.
27 146 0.125354279892 Henry Cohn, 2026, needs more optimization.
27 147 0.127237443095 Henry Cohn, 2026, needs more optimization.
27 148 0.128556753093 Henry Cohn, 2026, needs more optimization.
27 149 0.129948575611 Henry Cohn, 2026, needs more optimization.
27 150 0.131262706091 Henry Cohn, 2026, needs more optimization.
27 151 0.131403730167 Henry Cohn, 2026, needs more optimization.
27 152 0.131615531262 Henry Cohn, 2026, needs more optimization.
27 153 0.131772785724 Henry Cohn, 2026, needs more optimization.
27 154 0.132023291682 Henry Cohn, 2026, needs more optimization.
27 155 0.132035497581 Henry Cohn, 2026, needs more optimization.
27 156 0.132209290814 Henry Cohn, 2026, needs more optimization.
27 157 0.132536431009 Henry Cohn, 2026, needs more optimization.
27 158 0.132746267108 Henry Cohn, 2026, needs more optimization.
27 159 0.133002630323 Henry Cohn, 2026, needs more optimization.
27 160 0.133268784549 Henry Cohn, 2026, needs more optimization.
27 161 0.133303030756 Henry Cohn, 2026, needs more optimization.
27 162 0.133316675319 Henry Cohn, 2026, needs more optimization.
27 163 0.133331989758 Henry Cohn, 2026, needs more optimization.
27 164 0.133483398328 Henry Cohn, 2026, needs more optimization.
27 165 0.135025550747 Henry Cohn, 2026, needs more optimization.
27 166 0.135028963645 Henry Cohn, 2026, needs more optimization.
27 167 0.135115915473 Henry Cohn, 2026, needs more optimization.
27 168 0.135132098322 Henry Cohn, 2026, needs more optimization.
27 169 0.135254176819 Henry Cohn, 2026, needs more optimization.
27 170 0.135784098276 Henry Cohn, 2026, needs more optimization.
27 171 0.136292531850 Henry Cohn, 2026, needs more optimization.
27 172 0.137281177747 Henry Cohn, 2026, needs more optimization.
27 173 0.138904481166 Henry Cohn, 2026, needs more optimization.
27 174 0.139555738541 Henry Cohn, 2026, needs more optimization.
27 175 0.140952152383 Henry Cohn, 2026, needs more optimization.
27 176 0.142253296470 Henry Cohn, 2026, needs more optimization.
27 177 0.142308512195 Henry Cohn, 2026, needs more optimization.
27 178 0.142440074880 Henry Cohn, 2026, needs more optimization.
27 179 0.142447358723 Henry Cohn, 2026, needs more optimization.
27 180 0.142511184059 Henry Cohn, 2026, needs more optimization.
27 181 0.142554217492 Henry Cohn, 2026, needs more optimization.
27 182 0.142567153173 Henry Cohn, 2026, needs more optimization.
27 183 0.142587046143 Henry Cohn, 2026, needs more optimization.
27 184 0.142692824843 Henry Cohn, 2026, needs more optimization.
27 185 0.142720229369 Henry Cohn, 2026, needs more optimization.
27 186 0.142758732304 Henry Cohn, 2026, needs more optimization.
27 187 0.142758745696 Henry Cohn, 2026, needs more optimization.
27 188 0.142764411818 Henry Cohn, 2026, needs more optimization.
27 190 0.142764414407 Henry Cohn, 2026, needs more optimization.
27 191 0.142837764909 Henry Cohn, 2026, needs more optimization.
27 192 0.142974715893 Henry Cohn, 2026, needs more optimization.
27 193 0.142979721026 Henry Cohn, 2026, needs more optimization.
27 194 0.143908234799 Henry Cohn, 2026, needs more optimization.
27 195 0.144426448550 Henry Cohn, 2026, needs more optimization.
27 196 0.145390589606 Henry Cohn, 2026, needs more optimization.
27 197 0.145413059073 Henry Cohn, 2026, needs more optimization.
27 198 0.145464787653 Henry Cohn, 2026, needs more optimization.
27 199 0.145521964302 Henry Cohn, 2026, needs more optimization.
27 200 0.145806788356 Henry Cohn, 2026, needs more optimization.
27 201 0.146107746130 Henry Cohn, 2026, needs more optimization.
27 202 0.146407778902 Henry Cohn, 2026, needs more optimization.
27 203 0.146546553847 Henry Cohn, 2026, needs more optimization.
27 204 0.146961032739 Henry Cohn, 2026, needs more optimization.
27 205 0.147172838559 Henry Cohn, 2026, needs more optimization.
27 206 0.147204669586 Henry Cohn, 2026, needs more optimization.
27 207 0.147328515081 Henry Cohn, 2026, needs more optimization.
27 208 0.147418007986 Henry Cohn, 2026, needs more optimization.
27 209 0.147419130198 Henry Cohn, 2026, needs more optimization.
27 210 0.147451677021 Henry Cohn, 2026, needs more optimization.
27 211 0.147451710708 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 0.147970911239 Henry Cohn, 2026, needs more optimization.
27 217 0.148994837323 Henry Cohn, 2026, needs more optimization.
27 218 0.149004317228 Henry Cohn, 2026, needs more optimization.
27 219 0.149322365188 Henry Cohn, 2026, needs more optimization.
27 220 0.149324490522 Henry Cohn, 2026, needs more optimization.
27 221 0.149327476738 Henry Cohn, 2026, needs more optimization.
27 222 0.149350820149 Henry Cohn, 2026, needs more optimization.
27 223 0.149351690900 Henry Cohn, 2026, needs more optimization.
27 224 0.149359040366 Henry Cohn, 2026, needs more optimization.
27 225 0.149422869994 Henry Cohn, 2026, needs more optimization.
27 226 0.149740281855 Henry Cohn, 2026, needs more optimization.
27 227 0.149780014083 Henry Cohn, 2026, needs more optimization.
27 228 0.150045098725 Henry Cohn, 2026, needs more optimization.
27 229 0.150046688508 Henry Cohn, 2026, needs more optimization.
27 230 0.150319570336 Henry Cohn, 2026, needs more optimization.
27 231 0.150371597961 Henry Cohn, 2026, needs more optimization.
27 232 0.150904429384 Henry Cohn, 2026, needs more optimization.
27 233 0.151562347679 Henry Cohn, 2026, needs more optimization.
27 234 0.152313304765 Henry Cohn, 2026, needs more optimization.
27 235 0.152397566578 Henry Cohn, 2026, needs more optimization.
27 236 0.153641786375 Henry Cohn, 2026, needs more optimization.
27 237 0.155605774450 Henry Cohn, 2026, needs more optimization.
27 238 0.157682787685 Henry Cohn, 2026, needs more optimization.
27 239 0.157708189855 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 0.160383969072 Henry Cohn, 2026, needs more optimization.
27 243 0.161434145363 Henry Cohn, 2026, needs more optimization.
27 244 0.162276896990 Henry Cohn, 2026, needs more optimization.
27 245 0.162311958263 Henry Cohn, 2026, needs more optimization.
27 246 0.162560019880 Henry Cohn, 2026, needs more optimization.
27 247 0.162684273836 Henry Cohn, 2026, needs more optimization.
27 248 0.162734601149 Henry Cohn, 2026, needs more optimization.
27 249 0.162913429939 Henry Cohn, 2026, needs more optimization.
27 250 0.163024679683 Henry Cohn, 2026, needs more optimization.
27 251 0.163648988093 Henry Cohn, 2026, needs more optimization.
27 252 0.163923859029 Henry Cohn, 2026, needs more optimization.
27 253 0.164133349256 Henry Cohn, 2026, needs more optimization.
27 254 0.164179146203 Henry Cohn, 2026, needs more optimization.
27 255 0.164518058323 Henry Cohn, 2026, needs more optimization.
27 256 0.164646670355 Henry Cohn, 2026, needs more optimization.
27 257 0.164814860193 Henry Cohn, 2026, needs more optimization.
27 258 0.165029103879 Henry Cohn, 2026, needs more optimization.
27 259 0.165140652930 Henry Cohn, 2026, needs more optimization.
27 260 0.165262198802 Henry Cohn, 2026, needs more optimization.
27 261 0.165442916694 Henry Cohn, 2026, needs more optimization.
27 262 0.165520747003 Henry Cohn, 2026, needs more optimization.
27 263 0.165609820816 Henry Cohn, 2026, needs more optimization.
27 264 0.165713162107 Henry Cohn, 2026, needs more optimization.
27 265 0.165816697164 Henry Cohn, 2026, needs more optimization.
27 266 0.165875024338 Henry Cohn, 2026, needs more optimization.
27 267 0.165911391584 Henry Cohn, 2026, needs more optimization.
27 268 0.166006190095 Henry Cohn, 2026, needs more optimization.
27 269 0.166066982679 Henry Cohn, 2026, needs more optimization.
27 270 0.166180713225 Henry Cohn, 2026, needs more optimization.
27 271 0.166288537502 Henry Cohn, 2026, needs more optimization.
27 272 0.166338167691 Henry Cohn, 2026, needs more optimization.
27 273 0.166389578488 Henry Cohn, 2026, needs more optimization.
27 274 0.166445739454 Henry Cohn, 2026, needs more optimization.
27 275 0.166484160730 Henry Cohn, 2026, needs more optimization.
27 276 0.166524099257 Henry Cohn, 2026, needs more optimization.
27 277 0.166524122914 Henry Cohn, 2026, needs more optimization.
27 278 0.166580603513 Henry Cohn, 2026, needs more optimization.
27 280 0.166618395551 Henry Cohn, 2026, needs more optimization.
27 281 0.166623497429 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 0.166666872444 Orthogonal union of 287 points in 26 dimensions and 2 points in 1 dimension.
27 291 0.166667334192 Henry Cohn, 2026, needs more optimization.
27 292 0.166667338953 Henry Cohn, 2026, needs more optimization.
27 293 0.166667403564 Henry Cohn, 2026, needs more optimization.
27 294 0.166667403656 Henry Cohn, 2026, needs more optimization.
27 295 0.166667575908 Henry Cohn, 2026, needs more optimization.
27 296 0.166667702112 Henry Cohn, 2026, needs more optimization.
27 298 0.166669535912 Henry Cohn, 2026, needs more optimization.
27 299 0.166670051886 Henry Cohn, 2026, needs more optimization.
27 302 0.166670221087 Henry Cohn, 2026, needs more optimization.
27 303 0.166670221494 Henry Cohn, 2026, needs more optimization.
27 304 0.166702439991 Henry Cohn, 2026, needs more optimization.
27 305 0.166764870695 Henry Cohn, 2026, needs more optimization.
27 306 0.166956130210 Henry Cohn, 2026, needs more optimization.
27 307 0.167321448254 Henry Cohn, 2026, needs more optimization.
27 308 0.168146829465 Henry Cohn, 2026, needs more optimization.
27 309 0.169410089551 Henry Cohn, 2026, needs more optimization.
27 310 0.170456800377 Henry Cohn, 2026, needs more optimization.
27 311 0.171699209459 Henry Cohn, 2026, needs more optimization.
27 312 0.172846745959 Henry Cohn, 2026, needs more optimization.
27 313 0.173889771999 Henry Cohn, 2026, needs more optimization.
27 314 0.174687210818 Henry Cohn, 2026, needs more optimization.
27 315 0.176010721223 Henry Cohn, 2026, needs more optimization.
27 316 0.177394432922 Henry Cohn, 2026, needs more optimization.
27 317 0.178110500915 Henry Cohn, 2026, needs more optimization.
27 318 0.179079052369 Henry Cohn, 2026, needs more optimization.
27 319 0.179758970516 Henry Cohn, 2026, needs more optimization.
27 320 0.180616457978 Henry Cohn, 2026, needs more optimization.
27 321 0.181010139724 Henry Cohn, 2026, needs more optimization.
27 322 0.181110662424 Henry Cohn, 2026, needs more optimization.
27 323 0.181198898553 Henry Cohn, 2026, needs more optimization.
27 324 0.181300207627 Henry Cohn, 2026, needs more optimization.
27 325 0.181407732378 Henry Cohn, 2026, needs more optimization.
27 326 0.181461273178 Henry Cohn, 2026, needs more optimization.
27 327 0.181517740631 Henry Cohn, 2026, needs more optimization.
27 328 0.181538084532 Henry Cohn, 2026, needs more optimization.
27 329 0.181685418667 Henry Cohn, 2026, needs more optimization.
27 330 0.181731205961 Henry Cohn, 2026, needs more optimization.
27 331 0.181754767130 Henry Cohn, 2026, needs more optimization.
27 332 0.181772743600 Henry Cohn, 2026, needs more optimization.
27 333 0.181802975573 Henry Cohn, 2026, needs more optimization.
27 334 0.181821678180 Henry Cohn, 2026, needs more optimization.
27 335 0.181821678370 Henry Cohn, 2026, needs more optimization.
27 336 0.181827116203 Henry Cohn, 2026, needs more optimization.
27 337 0.181844065435 Henry Cohn, 2026, needs more optimization.
27 338 0.181865904190 Henry Cohn, 2026, needs more optimization.
27 339 0.181989027603 Henry Cohn, 2026, needs more optimization.
27 340 0.182377515109 Henry Cohn, 2026, needs more optimization.
27 341 0.182708596117 Henry Cohn, 2026, needs more optimization.
27 342 0.183581415620 Henry Cohn, 2026, needs more optimization.
27 343 0.184180154508 Henry Cohn, 2026, needs more optimization.
27 344 0.184563627382 Henry Cohn, 2026, needs more optimization.
27 345 0.185616093099 Henry Cohn, 2026, needs more optimization.
27 346 0.186402221824 Henry Cohn, 2026, needs more optimization.
27 347 0.186714058049 Henry Cohn, 2026, needs more optimization.
27 348 0.187559100240 Henry Cohn, 2026, needs more optimization.
27 349 0.188113571200 Henry Cohn, 2026, needs more optimization.
27 350 0.188607972010 Henry Cohn, 2026, needs more optimization.
27 351 0.189343506315 Henry Cohn, 2026, needs more optimization.
27 352 0.190315590819 Henry Cohn, 2026, needs more optimization.
27 353 0.191026037582 Henry Cohn, 2026, needs more optimization.
27 354 0.191896596203 Henry Cohn, 2026, needs more optimization.
27 355 0.192706128043 Henry Cohn, 2026, needs more optimization.
27 356 0.193353329009 Henry Cohn, 2026, needs more optimization.
27 357 0.193904483644 Henry Cohn, 2026, needs more optimization.
27 358 0.193957347068 Henry Cohn, 2026, needs more optimization.
27 359 0.194036702992 Henry Cohn, 2026, needs more optimization.
27 360 0.194543668315 Henry Cohn, 2026, needs more optimization.
27 361 0.195842968835 Henry Cohn, 2026, needs more optimization.
27 362 0.195971142443 Henry Cohn, 2026, needs more optimization.
27 363 0.196064680074 Henry Cohn, 2026, needs more optimization.
27 364 0.196244975032 Henry Cohn, 2026, needs more optimization.
27 365 0.196324777059 Henry Cohn, 2026, needs more optimization.
27 366 0.196502097056 Henry Cohn, 2026, needs more optimization.
27 367 0.196528860633 Henry Cohn, 2026, needs more optimization.
27 368 0.196548972295 Henry Cohn, 2026, needs more optimization.
27 369 0.196585641254 Henry Cohn, 2026, needs more optimization.
27 370 0.196668477147 Henry Cohn, 2026, needs more optimization.
27 371 0.196762510069 Henry Cohn, 2026, needs more optimization.
27 372 0.196872234641 Henry Cohn, 2026, needs more optimization.
27 373 0.196990090514 Henry Cohn, 2026, needs more optimization.
27 374 0.197124123895 Henry Cohn, 2026, needs more optimization.
27 375 0.197159819206 Henry Cohn, 2026, needs more optimization.
27 376 0.197293061436 Henry Cohn, 2026, needs more optimization.
27 377 0.197528549993 Henry Cohn, 2026, needs more optimization.
27 378 0.197654304621 Henry Cohn, 2026, needs more optimization.
27 379 0.197752415323 Henry Cohn, 2026, needs more optimization.
27 380 0.197835413944 Henry Cohn, 2026, needs more optimization.
27 381 0.197989531118 Henry Cohn, 2026, needs more optimization.
27 382 0.198054033132 Henry Cohn, 2026, needs more optimization.
27 383 0.198149448709 Henry Cohn, 2026, needs more optimization.
27 384 0.198180506455 Henry Cohn, 2026, needs more optimization.
27 385 0.198314959673 Henry Cohn, 2026, needs more optimization.
27 386 0.198407553533 Henry Cohn, 2026, needs more optimization.
27 387 0.198490787824 Henry Cohn, 2026, needs more optimization.
27 388 0.198555204339 Henry Cohn, 2026, needs more optimization.
27 389 0.198705171815 Henry Cohn, 2026, needs more optimization.
27 390 0.198763346524 Henry Cohn, 2026, needs more optimization.
27 391 0.198800466854 Henry Cohn, 2026, needs more optimization.
27 392 0.198866580586 Henry Cohn, 2026, needs more optimization.
27 393 0.198913454682 Henry Cohn, 2026, needs more optimization.
27 394 0.199028715583 Henry Cohn, 2026, needs more optimization.
27 395 0.199104844167 Henry Cohn, 2026, needs more optimization.
27 396 0.199166817930 Henry Cohn, 2026, needs more optimization.
27 397 0.199166916106 Henry Cohn, 2026, needs more optimization.
27 398 0.199238464916 Henry Cohn, 2026, needs more optimization.
27 399 0.199238474025 Henry Cohn, 2026, needs more optimization.
27 401 0.199301977773 Henry Cohn, 2026, needs more optimization.
27 402 0.199348304838 Henry Cohn, 2026, needs more optimization.
27 403 0.199393330571 Henry Cohn, 2026, needs more optimization.
27 404 0.199427650748 Henry Cohn, 2026, needs more optimization.
27 405 0.199432201184 Henry Cohn, 2026, needs more optimization.
27 406 0.199462002958 Henry Cohn, 2026, needs more optimization.
27 407 0.199541970909 Henry Cohn, 2026, needs more optimization.
27 408 0.199570138056 Henry Cohn, 2026, needs more optimization.
27 410 0.199618614073 Henry Cohn, 2026, needs more optimization.
27 411 0.199658947761 Henry Cohn, 2026, needs more optimization.
27 412 0.199737700849 Henry Cohn, 2026, needs more optimization.
27 413 0.199749771251 Henry Cohn, 2026, needs more optimization.
27 414 0.199782244073 Henry Cohn, 2026, needs more optimization.
27 415 0.199787998787 Henry Cohn, 2026, needs more optimization.
27 416 0.199788000214 Henry Cohn, 2026, needs more optimization.
27 417 0.199826779452 Henry Cohn, 2026, needs more optimization.
27 418 0.199839151743 Henry Cohn, 2026, needs more optimization.
27 419 0.199867423465 Henry Cohn, 2026, needs more optimization.
27 420 0.199899206487 Henry Cohn, 2026, needs more optimization.
27 421 0.199923973039 Henry Cohn, 2026, needs more optimization.
27 422 0.199942082955 Henry Cohn, 2026, needs more optimization.
27 423 0.199943150481 Henry Cohn, 2026, needs more optimization.
27 424 0.199973921584 Henry Cohn, 2026, needs more optimization.
27 425 0.199990680742 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
27 563 0.200002325990 Henry Cohn, 2026, needs more optimization.
27 568 0.200002867540 Henry Cohn, 2026, needs more optimization.
27 569 0.200002987979 Henry Cohn, 2026, needs more optimization.
27 570 0.200003276382 Orthogonal union of 568 points in 26 dimensions and 2 points in 1 dimension.
27 571 0.200003588664 Henry Cohn, 2026, needs more optimization.
27 574 0.200003588990 Henry Cohn, 2026, needs more optimization.
27 575 0.200004519736 Henry Cohn, 2026, needs more optimization.
27 576 0.200041116147 Henry Cohn, 2026, needs more optimization.
27 577 0.200041118312 Henry Cohn, 2026, needs more optimization.
27 578 0.200078470672 Henry Cohn, 2026, needs more optimization.
27 579 0.200114380199 Henry Cohn, 2026, needs more optimization.
27 580 0.200182495942 Henry Cohn, 2026, needs more optimization.
27 581 0.200235754844 Henry Cohn, 2026, needs more optimization.
27 582 0.200817329600 Henry Cohn, 2026, needs more optimization.
27 583 0.201222550851 Henry Cohn, 2026, needs more optimization.
27 584 0.202609998209 Henry Cohn, 2026, needs more optimization.
27 585 0.203218005178 Henry Cohn, 2026, needs more optimization.
27 586 0.203847951068 Henry Cohn, 2026, needs more optimization.
27 587 0.205374657403 Henry Cohn, 2026, needs more optimization.
27 588 0.206507725268 Henry Cohn, 2026, needs more optimization.
27 589 0.207431710936 Henry Cohn, 2026, needs more optimization.
27 590 0.208936440786 Henry Cohn, 2026, needs more optimization.
27 591 0.209690416300 Henry Cohn, 2026, needs more optimization.
27 592 0.210703474905 Henry Cohn, 2026, needs more optimization.
27 593 0.212073225359 Henry Cohn, 2026, needs more optimization.
27 594 0.212381184616 Henry Cohn, 2026, needs more optimization.
27 595 0.213471626468 Henry Cohn, 2026, needs more optimization.
27 596 0.214002214552 Henry Cohn, 2026, needs more optimization.
27 597 0.214541089728 Henry Cohn, 2026, needs more optimization.
27 598 0.215135931451 Henry Cohn, 2026, needs more optimization.
27 604 0.238096469173 Orthogonal union of 602 points in 26 dimensions and 2 points in 1 dimension.
27 616 0.238096999325 Henry Cohn, 2026, needs more optimization.
27 619 0.238096999451 Henry Cohn, 2026, needs more optimization.
27 621 0.238096999481 Henry Cohn, 2026, needs more optimization.
27 622 0.238099174812 Henry Cohn, 2026, needs more optimization.
27 623 0.238099379102 Henry Cohn, 2026, needs more optimization.
27 628 0.238100361309 Henry Cohn, 2026, needs more optimization.
27 631 0.238100393501 Henry Cohn, 2026, needs more optimization.
27 632 0.238100397574 Henry Cohn, 2026, needs more optimization.
27 634 0.238102743589 Henry Cohn, 2026, needs more optimization.
27 636 0.238109698333 Henry Cohn, 2026, needs more optimization.
27 637 0.238109699066 Henry Cohn, 2026, needs more optimization.
27 639 0.238109699276 Henry Cohn, 2026, needs more optimization.
27 640 0.238109699318 Henry Cohn, 2026, needs more optimization.
27 641 0.238155517237 Henry Cohn, 2026, needs more optimization.
27 642 0.238172697766 Henry Cohn, 2026, needs more optimization.
27 643 0.238172756706 Henry Cohn, 2026, needs more optimization.
27 644 0.238180239734 Henry Cohn, 2026, needs more optimization.
27 645 0.238203389208 Henry Cohn, 2026, needs more optimization.
27 646 0.238215465642 Henry Cohn, 2026, needs more optimization.
27 647 0.238257120373 Henry Cohn, 2026, needs more optimization.
27 648 0.238289586416 Henry Cohn, 2026, needs more optimization.
27 649 0.238455434600 Henry Cohn, 2026, needs more optimization.
27 651 0.238455498743 Henry Cohn, 2026, needs more optimization.
27 652 0.238691763085 Henry Cohn, 2026, needs more optimization.
27 653 0.238807420332 Henry Cohn, 2026, needs more optimization.
27 654 0.238864747142 Henry Cohn, 2026, needs more optimization.
27 655 0.238982431875 Henry Cohn, 2026, needs more optimization.
27 656 0.239027996955 Henry Cohn, 2026, needs more optimization.
27 657 0.239254504737 Henry Cohn, 2026, needs more optimization.
27 658 0.239315519635 Henry Cohn, 2026, needs more optimization.
27 659 0.239324844483 Henry Cohn, 2026, needs more optimization.
27 660 0.240233905063 Henry Cohn, 2026, needs more optimization.
27 661 0.240322317928 Henry Cohn, 2026, needs more optimization.
27 662 0.240322554569 Henry Cohn, 2026, needs more optimization.
27 663 0.240323227750 Henry Cohn, 2026, needs more optimization.
27 664 0.241068642674 Henry Cohn, 2026, needs more optimization.
27 665 0.241096516422 Henry Cohn, 2026, needs more optimization.
27 666 0.241167052794 Henry Cohn, 2026, needs more optimization.
27 667 0.241245526725 Henry Cohn, 2026, needs more optimization.
27 668 0.241393448693 Henry Cohn, 2026, needs more optimization.
27 669 0.241434120326 Henry Cohn, 2026, needs more optimization.
27 670 0.241602603069 Henry Cohn, 2026, needs more optimization.
27 671 0.242299650509 Henry Cohn, 2026, needs more optimization.
27 672 0.242672279472 Henry Cohn, 2026, needs more optimization.
27 673 0.242689941292 Henry Cohn, 2026, needs more optimization.
27 674 0.242878140183 Henry Cohn, 2026, needs more optimization.
27 676 0.242978346684 Henry Cohn, 2026, needs more optimization.
27 677 0.243034885755 Henry Cohn, 2026, needs more optimization.
27 678 0.243230743118 Henry Cohn, 2026, needs more optimization.
27 679 0.243416555653 Henry Cohn, 2026, needs more optimization.
27 680 0.243499032082 Henry Cohn, 2026, needs more optimization.
27 681 0.244433607101 Henry Cohn, 2026, needs more optimization.
27 682 0.244809291656 Henry Cohn, 2026, needs more optimization.
27 683 0.244822468323 Henry Cohn, 2026, needs more optimization.
27 684 0.244822817979 Henry Cohn, 2026, needs more optimization.
27 685 0.245116867439 Henry Cohn, 2026, needs more optimization.
27 686 0.245116915081 Henry Cohn, 2026, needs more optimization.
27 687 0.245315184658 Henry Cohn, 2026, needs more optimization.
27 688 0.245389967143 Henry Cohn, 2026, needs more optimization.
27 689 0.245603979763 Henry Cohn, 2026, needs more optimization.
27 690 0.245685593875 Henry Cohn, 2026, needs more optimization.
27 691 0.245779290685 Henry Cohn, 2026, needs more optimization.
27 692 0.245946407592 Henry Cohn, 2026, needs more optimization.
27 693 0.245946423163 Henry Cohn, 2026, needs more optimization.
27 695 0.245946465835 Henry Cohn, 2026, needs more optimization.
27 696 0.245946509299 Henry Cohn, 2026, needs more optimization.
27 697 0.245986923570 Henry Cohn, 2026, needs more optimization.
27 698 0.246054170433 Henry Cohn, 2026, needs more optimization.
27 699 0.246229939900 Henry Cohn, 2026, needs more optimization.
27 700 0.246436282007 Henry Cohn, 2026, needs more optimization.
27 701 0.246616341765 Henry Cohn, 2026, needs more optimization.
27 702 0.246714876128 Henry Cohn, 2026, needs more optimization.
27 703 0.246783376729 Henry Cohn, 2026, needs more optimization.
27 704 0.246929550071 Henry Cohn, 2026, needs more optimization.
27 705 0.246966431940 Henry Cohn, 2026, needs more optimization.
27 706 0.247094687958 Henry Cohn, 2026, needs more optimization.
27 707 0.247201524154 Henry Cohn, 2026, needs more optimization.
27 708 0.247384658356 Henry Cohn, 2026, needs more optimization.
27 709 0.247468364137 Henry Cohn, 2026, needs more optimization.
27 710 0.247650614516 Henry Cohn, 2026, needs more optimization.
27 711 0.247774749244 Henry Cohn, 2026, needs more optimization.
27 712 0.247848957850 Henry Cohn, 2026, needs more optimization.
27 714 0.247848968496 Henry Cohn, 2026, needs more optimization.
27 715 0.248016731657 Henry Cohn, 2026, needs more optimization.
27 716 0.248062356282 Henry Cohn, 2026, needs more optimization.
27 717 0.248141234385 Henry Cohn, 2026, needs more optimization.
27 718 0.248160077109 Henry Cohn, 2026, needs more optimization.
27 719 0.248272286659 Henry Cohn, 2026, needs more optimization.
27 720 0.248313160796 Henry Cohn, 2026, needs more optimization.
27 721 0.248349826132 Henry Cohn, 2026, needs more optimization.
27 722 0.248349828286 Henry Cohn, 2026, needs more optimization.
27 723 0.248417023690 Henry Cohn, 2026, needs more optimization.
27 724 0.248417220056 Henry Cohn, 2026, needs more optimization.
27 725 0.248476214153 Henry Cohn, 2026, needs more optimization.
27 726 0.248584370839 Henry Cohn, 2026, needs more optimization.
27 727 0.248647090939 Henry Cohn, 2026, needs more optimization.
27 728 0.248710496846 Henry Cohn, 2026, needs more optimization.
27 729 0.248710500936 Henry Cohn, 2026, needs more optimization.
27 730 0.248801882317 Henry Cohn, 2026, needs more optimization.
27 731 0.248878258376 Henry Cohn, 2026, needs more optimization.
27 732 0.248939833119 Henry Cohn, 2026, needs more optimization.
27 733 0.248939836137 Henry Cohn, 2026, needs more optimization.
27 734 0.249063748919 Henry Cohn, 2026, needs more optimization.
27 735 0.249133768848 Henry Cohn, 2026, needs more optimization.
27 736 0.249133786777 Henry Cohn, 2026, needs more optimization.
27 737 0.249158349910 Henry Cohn, 2026, needs more optimization.
27 738 0.249243837304 Henry Cohn, 2026, needs more optimization.
27 739 0.249262686850 Henry Cohn, 2026, needs more optimization.
27 740 0.249327762667 Henry Cohn, 2026, needs more optimization.
27 741 0.249367596428 Henry Cohn, 2026, needs more optimization.
27 742 0.249405022659 Henry Cohn, 2026, needs more optimization.
27 743 0.249439637274 Henry Cohn, 2026, needs more optimization.
27 744 0.249448367063 Henry Cohn, 2026, needs more optimization.
27 745 0.249523517323 Henry Cohn, 2026, needs more optimization.
27 746 0.249523518339 Henry Cohn, 2026, needs more optimization.
27 747 0.249543142331 Henry Cohn, 2026, needs more optimization.
27 748 0.249543148741 Henry Cohn, 2026, needs more optimization.
27 749 0.249576705107 Henry Cohn, 2026, needs more optimization.
27 750 0.249597585023 Henry Cohn, 2026, needs more optimization.
27 751 0.249597605985 Henry Cohn, 2026, needs more optimization.
27 752 0.249597607311 Henry Cohn, 2026, needs more optimization.
27 753 0.249597610817 Henry Cohn, 2026, needs more optimization.
27 754 0.249641312111 Henry Cohn, 2026, needs more optimization.
27 755 0.249695296495 Henry Cohn, 2026, needs more optimization.
27 756 0.249707885003 Henry Cohn, 2026, needs more optimization.
27 757 0.249754161071 Henry Cohn, 2026, needs more optimization.
27 758 0.249759504333 Henry Cohn, 2026, needs more optimization.
27 759 0.249776582732 Henry Cohn, 2026, needs more optimization.
27 760 0.249776587794 Henry Cohn, 2026, needs more optimization.
27 761 0.249821950966 Henry Cohn, 2026, needs more optimization.
27 762 0.249827806087 Henry Cohn, 2026, needs more optimization.
27 763 0.249866771378 Henry Cohn, 2026, needs more optimization.
27 764 0.249904328085 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
27 909 0.250001204830 Henry Cohn, 2026, needs more optimization.
27 910 0.250003399479 Henry Cohn, 2026, needs more optimization.
27 914 0.250003402300 Henry Cohn, 2026, needs more optimization.
27 915 0.250003402891 Henry Cohn, 2026, needs more optimization.
27 916 0.250003408067 Henry Cohn, 2026, needs more optimization.
27 917 0.250003408886 Henry Cohn, 2026, needs more optimization.
27 918 0.250003752802 Henry Cohn, 2026, needs more optimization.
27 919 0.250003753203 Henry Cohn, 2026, needs more optimization.
27 920 0.250003753205 Henry Cohn, 2026, needs more optimization.
27 924 0.250004312796 Henry Cohn, 2026, needs more optimization.
27 930 0.250004312809 Henry Cohn, 2026, needs more optimization.
27 933 0.250004313200 Henry Cohn, 2026, needs more optimization.
27 934 0.250004313463 Henry Cohn, 2026, needs more optimization.
27 935 0.250005274550 Henry Cohn, 2026, needs more optimization.
27 936 0.250005274849 Henry Cohn, 2026, needs more optimization.
27 937 0.250005280908 Henry Cohn, 2026, needs more optimization.
27 939 0.250008421643 Henry Cohn, 2026, needs more optimization.
27 940 0.250008427507 Henry Cohn, 2026, needs more optimization.
27 943 0.250011627571 Henry Cohn, 2026, needs more optimization.
27 944 0.250015666106 Henry Cohn, 2026, needs more optimization.
27 945 0.250015667246 Henry Cohn, 2026, needs more optimization.
27 946 0.250075071740 Henry Cohn, 2026, needs more optimization.
27 947 0.250106984449 Henry Cohn, 2026, needs more optimization.
27 948 0.250139257771 Henry Cohn, 2026, needs more optimization.
27 949 0.250144476993 Henry Cohn, 2026, needs more optimization.
27 950 0.250150751452 Henry Cohn, 2026, needs more optimization.
27 951 0.250249541925 Henry Cohn, 2026, needs more optimization.
27 952 0.250293448417 Henry Cohn, 2026, needs more optimization.
27 954 0.250409435011 Henry Cohn, 2026, needs more optimization.
27 956 0.250409486313 Henry Cohn, 2026, needs more optimization.
27 959 0.250414614864 Henry Cohn, 2026, needs more optimization.
27 960 0.250506183891 Henry Cohn, 2026, needs more optimization.
27 961 0.250541975935 Henry Cohn, 2026, needs more optimization.
27 962 0.250643937911 Henry Cohn, 2026, needs more optimization.
27 963 0.250643992145 Henry Cohn, 2026, needs more optimization.
27 964 0.250644044992 Henry Cohn, 2026, needs more optimization.
27 965 0.250763703001 Henry Cohn, 2026, needs more optimization.
27 966 0.251025020507 Henry Cohn, 2026, needs more optimization.
27 967 0.251131905034 Henry Cohn, 2026, needs more optimization.
27 968 0.251615294203 Henry Cohn, 2026, needs more optimization.
27 969 0.251845881876 Henry Cohn, 2026, needs more optimization.
27 970 0.251962033372 Henry Cohn, 2026, needs more optimization.
27 971 0.252266596876 Henry Cohn, 2026, needs more optimization.
27 972 0.252683951194 Henry Cohn, 2026, needs more optimization.
27 973 0.252694717198 Henry Cohn, 2026, needs more optimization.
27 974 0.252959611667 Henry Cohn, 2026, needs more optimization.
27 975 0.252962652801 Henry Cohn, 2026, needs more optimization.
27 976 0.253285349138 Henry Cohn, 2026, needs more optimization.
27 977 0.254211861535 Henry Cohn, 2026, needs more optimization.
27 978 0.254212002303 Henry Cohn, 2026, needs more optimization.
27 979 0.254662284132 Henry Cohn, 2026, needs more optimization.
27 980 0.254847559446 Henry Cohn, 2026, needs more optimization.
27 981 0.254993204959 Henry Cohn, 2026, needs more optimization.
27 982 0.255342373690 Henry Cohn, 2026, needs more optimization.
27 983 0.255503343680 Henry Cohn, 2026, needs more optimization.
27 984 0.255609511663 Henry Cohn, 2026, needs more optimization.
27 985 0.257210842947 Henry Cohn, 2026, needs more optimization.
27 986 0.257556820976 Henry Cohn, 2026, needs more optimization.
27 987 0.257556920088 Henry Cohn, 2026, needs more optimization.
27 988 0.257837998408 Henry Cohn, 2026, needs more optimization.
27 989 0.257955927347 Henry Cohn, 2026, needs more optimization.
27 990 0.258072569141 Henry Cohn, 2026, needs more optimization.
27 991 0.259194300549 Henry Cohn, 2026, needs more optimization.
27 992 0.259484552637 Henry Cohn, 2026, needs more optimization.
27 993 0.259715836694 Henry Cohn, 2026, needs more optimization.
27 994 0.260461119690 Henry Cohn, 2026, needs more optimization.
27 995 0.260578499962 Henry Cohn, 2026, needs more optimization.
27 996 0.260647575492 Henry Cohn, 2026, needs more optimization.
27 997 0.260758876638 Henry Cohn, 2026, needs more optimization.
27 998 0.260913373030 Henry Cohn, 2026, needs more optimization.
27 999 0.261005710514 Henry Cohn, 2026, needs more optimization.
27 1000 0.261128577128 Henry Cohn, 2026, needs more optimization.
27 1001 0.262273439699 Henry Cohn, 2026, needs more optimization.
27 1002 0.262756034365 Henry Cohn, 2026, needs more optimization.
27 1003 0.263061052133 Henry Cohn, 2026, needs more optimization.
27 1004 0.263272975755 Henry Cohn, 2026, needs more optimization.
27 1005 0.263416464865 Henry Cohn, 2026, needs more optimization.
27 1006 0.263675396330 Henry Cohn, 2026, needs more optimization.
27 1007 0.263906320597 Henry Cohn, 2026, needs more optimization.
27 1008 0.264126817835 Henry Cohn, 2026, needs more optimization.
27 1009 0.264482734876 Henry Cohn, 2026, needs more optimization.
27 1010 0.264550291543 Henry Cohn, 2026, needs more optimization.
27 1011 0.264757874449 Henry Cohn, 2026, needs more optimization.
27 1012 0.264826676118 Henry Cohn, 2026, needs more optimization.
27 1013 0.265039333561 Henry Cohn, 2026, needs more optimization.
27 1014 0.265218281439 Henry Cohn, 2026, needs more optimization.
27 1015 0.265601621549 Henry Cohn, 2026, needs more optimization.
27 1016 0.265932209175 Henry Cohn, 2026, needs more optimization.
27 1017 0.266242410870 Henry Cohn, 2026, needs more optimization.
27 1018 0.266327598924 Henry Cohn, 2026, needs more optimization.
27 1019 0.266549836076 Henry Cohn, 2026, needs more optimization.
27 1020 0.266838043283 Henry Cohn, 2026, needs more optimization.
27 1021 0.267036218077 Henry Cohn, 2026, needs more optimization.
27 1022 0.267242497863 Henry Cohn, 2026, needs more optimization.
27 1023 0.267549837531 Henry Cohn, 2026, needs more optimization.
27 1024 0.267921616215 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 0.039721697123 Henry Cohn, 2026.
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 0.058160876254 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 0.063894406204 Henry Cohn, 2026, needs more optimization.
28 75 0.064460438579 Henry Cohn, 2026, needs more optimization.
28 76 0.064717246550 Henry Cohn, 2026, needs more optimization.
28 77 0.065929172371 Henry Cohn, 2026, needs more optimization.
28 78 0.067448950547 Henry Cohn, 2026, needs more optimization.
28 79 0.069484886893 Henry Cohn, 2026, needs more optimization.
28 80 0.070912616827 Henry Cohn, 2026, needs more optimization.
28 81 0.072768932730 Henry Cohn, 2026, needs more optimization.
28 82 0.074536648258 Henry Cohn, 2026, needs more optimization.
28 83 0.074851725538 Henry Cohn, 2026, needs more optimization.
28 84 0.075994545567 Henry Cohn, 2026, needs more optimization.
28 85 0.076702837875 Henry Cohn, 2026, needs more optimization.
28 86 0.076877389844 Henry Cohn, 2026, needs more optimization.
28 87 0.076913979764 Henry Cohn, 2026, needs more optimization.
28 88 0.076926800497 Henry Cohn, 2026, needs more optimization.
28 89 0.077241411223 Henry Cohn, 2026, needs more optimization.
28 90 0.077491331789 Henry Cohn, 2026, needs more optimization.
28 91 0.078294901867 Henry Cohn, 2026, needs more optimization.
28 92 0.078682972493 Henry Cohn, 2026, needs more optimization.
28 93 0.079236168053 Henry Cohn, 2026, needs more optimization.
28 94 0.079399708367 Henry Cohn, 2026, needs more optimization.
28 95 0.079800753750 Henry Cohn, 2026, needs more optimization.
28 96 0.080120720916 Henry Cohn, 2026, needs more optimization.
28 97 0.080245078014 Henry Cohn, 2026, needs more optimization.
28 98 0.080483159837 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 0.080899208948 Henry Cohn, 2026, needs more optimization.
28 103 0.083873197836 Henry Cohn, 2026, needs more optimization.
28 104 0.086348355382 Henry Cohn, 2026, needs more optimization.
28 105 0.086937092309 Henry Cohn, 2026, needs more optimization.
28 106 0.088268987224 Henry Cohn, 2026, needs more optimization.
28 107 0.088694019010 Henry Cohn, 2026, needs more optimization.
28 108 0.089296680605 Henry Cohn, 2026, needs more optimization.
28 109 0.089568787549 Henry Cohn, 2026, needs more optimization.
28 110 0.089725021628 Henry Cohn, 2026, needs more optimization.
28 111 0.089789685834 Henry Cohn, 2026, needs more optimization.
28 112 0.090107762589 Henry Cohn, 2026, needs more optimization.
28 113 0.090270049248 Henry Cohn, 2026, needs more optimization.
28 114 0.090576172949 Henry Cohn, 2026, needs more optimization.
28 115 0.090767280648 Henry Cohn, 2026, needs more optimization.
28 116 0.090841263819 Henry Cohn, 2026, needs more optimization.
28 117 0.090877261737 Henry Cohn, 2026, needs more optimization.
28 118 0.091675659471 Henry Cohn, 2026, needs more optimization.
28 119 0.093902842766 Henry Cohn, 2026, needs more optimization.
28 120 0.096032493126 Henry Cohn, 2026, needs more optimization.
28 121 0.098104131862 Henry Cohn, 2026, needs more optimization.
28 122 0.099654963974 Henry Cohn, 2026, needs more optimization.
28 123 0.101610959640 Henry Cohn, 2026, needs more optimization.
28 124 0.102467939444 Henry Cohn, 2026, needs more optimization.
28 125 0.102518396332 Henry Cohn, 2026, needs more optimization.
28 126 0.102923495228 Henry Cohn, 2026, needs more optimization.
28 127 0.102967324335 Henry Cohn, 2026, needs more optimization.
28 128 0.103052335738 Henry Cohn, 2026, needs more optimization.
28 129 0.103114193138 Henry Cohn, 2026, needs more optimization.
28 130 0.103122237523 Henry Cohn, 2026, needs more optimization.
28 131 0.104325714433 Henry Cohn, 2026, needs more optimization.
28 132 0.105408776973 Henry Cohn, 2026, needs more optimization.
28 133 0.106259650635 Henry Cohn, 2026, needs more optimization.
28 134 0.107855734217 Henry Cohn, 2026, needs more optimization.
28 135 0.108599885371 Henry Cohn, 2026, needs more optimization.
28 136 0.109062811218 Henry Cohn, 2026, needs more optimization.
28 137 0.109746829130 Henry Cohn, 2026, needs more optimization.
28 138 0.110885424178 Henry Cohn, 2026, needs more optimization.
28 139 0.110919553711 Henry Cohn, 2026, needs more optimization.
28 140 0.110993503379 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 0.119771707838 Henry Cohn, 2026, needs more optimization.
28 154 0.122975008722 Henry Cohn, 2026, needs more optimization.
28 155 0.125275324326 Henry Cohn, 2026, needs more optimization.
28 156 0.126322831783 Henry Cohn, 2026, needs more optimization.
28 157 0.127118914492 Henry Cohn, 2026, needs more optimization.
28 158 0.127742312136 Henry Cohn, 2026, needs more optimization.
28 159 0.128113945659 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 0.141622119429 Henry Cohn, 2026, needs more optimization.
28 185 0.142182127795 Henry Cohn, 2026, needs more optimization.
28 186 0.142182130340 Henry Cohn, 2026, needs more optimization.
28 187 0.142191738611 Henry Cohn, 2026, needs more optimization.
28 188 0.142223638904 Henry Cohn, 2026, needs more optimization.
28 189 0.142243849906 Henry Cohn, 2026, needs more optimization.
28 190 0.142262761781 Henry Cohn, 2026, needs more optimization.
28 191 0.142277433025 Henry Cohn, 2026, needs more optimization.
28 192 0.142446850034 Henry Cohn, 2026, needs more optimization.
28 193 0.142501460598 Henry Cohn, 2026, needs more optimization.
28 194 0.142561099238 Henry Cohn, 2026, needs more optimization.
28 195 0.142625118110 Henry Cohn, 2026, needs more optimization.
28 196 0.142713580343 Henry Cohn, 2026, needs more optimization.
28 197 0.142764827220 Henry Cohn, 2026, needs more optimization.
28 198 0.142800853568 Henry Cohn, 2026, needs more optimization.
28 199 0.142881382083 Henry Cohn, 2026, needs more optimization.
28 200 0.143371737286 Henry Cohn, 2026, needs more optimization.
28 201 0.143698799415 Henry Cohn, 2026, needs more optimization.
28 202 0.144188611855 Henry Cohn, 2026, needs more optimization.
28 203 0.145069379356 Henry Cohn, 2026, needs more optimization.
28 204 0.145915089770 Henry Cohn, 2026, needs more optimization.
28 205 0.146035591788 Henry Cohn, 2026, needs more optimization.
28 206 0.146054213877 Henry Cohn, 2026, needs more optimization.
28 207 0.146085529522 Henry Cohn, 2026, needs more optimization.
28 208 0.146085660262 Henry Cohn, 2026, needs more optimization.
28 209 0.146252742013 Henry Cohn, 2026, needs more optimization.
28 210 0.146312036769 Henry Cohn, 2026, needs more optimization.
28 211 0.146312219514 Henry Cohn, 2026, needs more optimization.
28 212 0.146481243651 Henry Cohn, 2026, needs more optimization.
28 213 0.146917977827 Henry Cohn, 2026, needs more optimization.
28 214 0.147065119078 Henry Cohn, 2026, needs more optimization.
28 215 0.147136603188 Henry Cohn, 2026, needs more optimization.
28 216 0.147136621790 Henry Cohn, 2026, needs more optimization.
28 217 0.147223895728 Henry Cohn, 2026, needs more optimization.
28 218 0.147345177798 Henry Cohn, 2026, needs more optimization.
28 219 0.147398874632 Henry Cohn, 2026, needs more optimization.
28 220 0.147497077311 Henry Cohn, 2026, needs more optimization.
28 221 0.147599696315 Henry Cohn, 2026, needs more optimization.
28 222 0.147657237255 Henry Cohn, 2026, needs more optimization.
28 223 0.147659942262 Henry Cohn, 2026, needs more optimization.
28 224 0.147660390794 Henry Cohn, 2026, needs more optimization.
28 225 0.147681938070 Henry Cohn, 2026, needs more optimization.
28 226 0.147688756777 Henry Cohn, 2026, needs more optimization.
28 227 0.147770878328 Henry Cohn, 2026, needs more optimization.
28 228 0.147903320952 Henry Cohn, 2026, needs more optimization.
28 229 0.148229106869 Henry Cohn, 2026, needs more optimization.
28 230 0.149025428496 Henry Cohn, 2026, needs more optimization.
28 231 0.149166661350 Henry Cohn, 2026, needs more optimization.
28 232 0.149231941640 Henry Cohn, 2026, needs more optimization.
28 233 0.149315399541 Henry Cohn, 2026, needs more optimization.
28 234 0.149318182081 Henry Cohn, 2026, needs more optimization.
28 235 0.149320691005 Henry Cohn, 2026, needs more optimization.
28 236 0.149334967592 Henry Cohn, 2026, needs more optimization.
28 237 0.149335019372 Henry Cohn, 2026, needs more optimization.
28 238 0.149339804546 Henry Cohn, 2026, needs more optimization.
28 239 0.149508758999 Henry Cohn, 2026, needs more optimization.
28 240 0.150192870552 Henry Cohn, 2026, needs more optimization.
28 241 0.150640574117 Henry Cohn, 2026, needs more optimization.
28 242 0.151823853483 Henry Cohn, 2026, needs more optimization.
28 243 0.152636315135 Henry Cohn, 2026, needs more optimization.
28 244 0.154128753992 Henry Cohn, 2026, needs more optimization.
28 245 0.155252424993 Henry Cohn, 2026, needs more optimization.
28 246 0.156958949703 Henry Cohn, 2026, needs more optimization.
28 247 0.157035148139 Henry Cohn, 2026, needs more optimization.
28 248 0.157636632159 Henry Cohn, 2026, needs more optimization.
28 249 0.158610062466 Henry Cohn, 2026, needs more optimization.
28 250 0.160111875571 Henry Cohn, 2026, needs more optimization.
28 251 0.161300665397 Henry Cohn, 2026, needs more optimization.
28 252 0.162037853592 Henry Cohn, 2026, needs more optimization.
28 253 0.162057107331 Henry Cohn, 2026, needs more optimization.
28 254 0.162126967823 Henry Cohn, 2026, needs more optimization.
28 255 0.162162306675 Henry Cohn, 2026, needs more optimization.
28 256 0.162423177789 Henry Cohn, 2026, needs more optimization.
28 257 0.162665552688 Henry Cohn, 2026, needs more optimization.
28 258 0.162871904187 Henry Cohn, 2026, needs more optimization.
28 259 0.163037246843 Henry Cohn, 2026, needs more optimization.
28 260 0.163404737417 Henry Cohn, 2026, needs more optimization.
28 261 0.163587789531 Henry Cohn, 2026, needs more optimization.
28 262 0.163821153780 Henry Cohn, 2026, needs more optimization.
28 263 0.163942037173 Henry Cohn, 2026, needs more optimization.
28 264 0.164132747872 Henry Cohn, 2026, needs more optimization.
28 265 0.164327894422 Henry Cohn, 2026, needs more optimization.
28 266 0.164669452945 Henry Cohn, 2026, needs more optimization.
28 267 0.164750154531 Henry Cohn, 2026, needs more optimization.
28 268 0.164862625050 Henry Cohn, 2026, needs more optimization.
28 269 0.164932791641 Henry Cohn, 2026, needs more optimization.
28 270 0.164933001493 Henry Cohn, 2026, needs more optimization.
28 271 0.164974370233 Henry Cohn, 2026, needs more optimization.
28 272 0.165073796277 Henry Cohn, 2026, needs more optimization.
28 273 0.165249438396 Henry Cohn, 2026, needs more optimization.
28 274 0.165350140865 Henry Cohn, 2026, needs more optimization.
28 275 0.165408445223 Henry Cohn, 2026, needs more optimization.
28 276 0.165459786967 Henry Cohn, 2026, needs more optimization.
28 277 0.165473738419 Henry Cohn, 2026, needs more optimization.
28 278 0.165596877931 Henry Cohn, 2026, needs more optimization.
28 279 0.165649088013 Henry Cohn, 2026, needs more optimization.
28 280 0.165679475988 Henry Cohn, 2026, needs more optimization.
28 281 0.165691571344 Henry Cohn, 2026, needs more optimization.
28 282 0.165766885736 Henry Cohn, 2026, needs more optimization.
28 283 0.165886645720 Henry Cohn, 2026, needs more optimization.
28 284 0.165898385947 Henry Cohn, 2026, needs more optimization.
28 285 0.165950432342 Henry Cohn, 2026, needs more optimization.
28 286 0.166074179285 Henry Cohn, 2026, needs more optimization.
28 287 0.166134611505 Henry Cohn, 2026, needs more optimization.
28 288 0.166202101225 Henry Cohn, 2026, needs more optimization.
28 289 0.166318556002 Henry Cohn, 2026, needs more optimization.
28 290 0.166389795958 Henry Cohn, 2026, needs more optimization.
28 291 0.166414812790 Henry Cohn, 2026, needs more optimization.
28 292 0.166414983838 Henry Cohn, 2026, needs more optimization.
28 293 0.166473445896 Henry Cohn, 2026, needs more optimization.
28 294 0.166484290637 Henry Cohn, 2026, needs more optimization.
28 295 0.166505385656 Henry Cohn, 2026, needs more optimization.
28 296 0.166538539601 Henry Cohn, 2026, needs more optimization.
28 297 0.166538655365 Henry Cohn, 2026, needs more optimization.
28 298 0.166538971686 Henry Cohn, 2026, needs more optimization.
28 299 0.166586165098 Henry Cohn, 2026, needs more optimization.
28 300 0.166592329516 Henry Cohn, 2026, needs more optimization.
28 301 0.166617519910 Henry Cohn, 2026, needs more optimization.
28 302 0.166627781474 Henry Cohn, 2026, needs more optimization.
28 305 0.166665682667 Henry Cohn, 2026, needs more optimization.
28 306 0.166665768572 Henry Cohn, 2026, needs more optimization.
28 307 0.166665834668 Henry Cohn, 2026, needs more optimization.
28 309 0.166668038348 Henry Cohn, 2026, needs more optimization.
28 311 0.166683438748 Henry Cohn, 2026, needs more optimization.
28 312 0.166690655700 Henry Cohn, 2026, needs more optimization.
28 313 0.166730394153 Henry Cohn, 2026, needs more optimization.
28 314 0.167111623943 Henry Cohn, 2026, needs more optimization.
28 315 0.167177995038 Henry Cohn, 2026, needs more optimization.
28 316 0.167681928716 Henry Cohn, 2026, needs more optimization.
28 317 0.168024015381 Henry Cohn, 2026, needs more optimization.
28 318 0.168679720130 Henry Cohn, 2026, needs more optimization.
28 319 0.169505674192 Henry Cohn, 2026, needs more optimization.
28 320 0.170186639055 Henry Cohn, 2026, needs more optimization.
28 321 0.171465423748 Henry Cohn, 2026, needs more optimization.
28 322 0.171978181775 Henry Cohn, 2026, needs more optimization.
28 323 0.173003615611 Henry Cohn, 2026, needs more optimization.
28 324 0.173497462307 Henry Cohn, 2026, needs more optimization.
28 325 0.174937188893 Henry Cohn, 2026, needs more optimization.
28 326 0.175619680333 Henry Cohn, 2026, needs more optimization.
28 327 0.176215172697 Henry Cohn, 2026, needs more optimization.
28 328 0.177127478424 Henry Cohn, 2026, needs more optimization.
28 329 0.178578198183 Henry Cohn, 2026, needs more optimization.
28 330 0.178578247110 Henry Cohn, 2026, needs more optimization.
28 331 0.178583018992 Henry Cohn, 2026, needs more optimization.
28 332 0.178657052814 Henry Cohn, 2026, needs more optimization.
28 333 0.178895448445 Henry Cohn, 2026, needs more optimization.
28 334 0.178913754692 Henry Cohn, 2026, needs more optimization.
28 335 0.179529499537 Henry Cohn, 2026, needs more optimization.
28 336 0.180165191321 Henry Cohn, 2026, needs more optimization.
28 337 0.180170478153 Henry Cohn, 2026, needs more optimization.
28 338 0.180536905859 Henry Cohn, 2026, needs more optimization.
28 339 0.181453483673 Henry Cohn, 2026, needs more optimization.
28 340 0.181638821047 Henry Cohn, 2026, needs more optimization.
28 341 0.181682285734 Henry Cohn, 2026, needs more optimization.
28 342 0.181708695641 Henry Cohn, 2026, needs more optimization.
28 343 0.181724306671 Henry Cohn, 2026, needs more optimization.
28 344 0.181802894722 Henry Cohn, 2026, needs more optimization.
28 345 0.181807560117 Henry Cohn, 2026, needs more optimization.
28 346 0.181824247545 Henry Cohn, 2026, needs more optimization.
28 347 0.181831708482 Henry Cohn, 2026, needs more optimization.
28 348 0.181843245674 Henry Cohn, 2026, needs more optimization.
28 349 0.181859599505 Henry Cohn, 2026, needs more optimization.
28 350 0.181895536393 Henry Cohn, 2026, needs more optimization.
28 351 0.182149639579 Henry Cohn, 2026, needs more optimization.
28 352 0.182380303477 Henry Cohn, 2026, needs more optimization.
28 353 0.182651397621 Henry Cohn, 2026, needs more optimization.
28 354 0.183675452741 Henry Cohn, 2026, needs more optimization.
28 355 0.184399644243 Henry Cohn, 2026, needs more optimization.
28 356 0.184974402544 Henry Cohn, 2026, needs more optimization.
28 357 0.185220766878 Henry Cohn, 2026, needs more optimization.
28 358 0.185774707681 Henry Cohn, 2026, needs more optimization.
28 359 0.186365466071 Henry Cohn, 2026, needs more optimization.
28 360 0.186531212522 Henry Cohn, 2026, needs more optimization.
28 361 0.191581507198 Henry Cohn, 2026, needs more optimization.
28 362 0.191831567077 Henry Cohn, 2026, needs more optimization.
28 363 0.192284504341 Henry Cohn, 2026, needs more optimization.
28 364 0.192391346742 Henry Cohn, 2026, needs more optimization.
28 365 0.192472687473 Henry Cohn, 2026, needs more optimization.
28 366 0.192559090142 Henry Cohn, 2026, needs more optimization.
28 367 0.192843656050 Henry Cohn, 2026, needs more optimization.
28 368 0.193012005975 Henry Cohn, 2026, needs more optimization.
28 369 0.193206685480 Henry Cohn, 2026, needs more optimization.
28 370 0.193402594978 Henry Cohn, 2026, needs more optimization.
28 371 0.193741466794 Henry Cohn, 2026, needs more optimization.
28 372 0.193837147103 Henry Cohn, 2026, needs more optimization.
28 373 0.194023085965 Henry Cohn, 2026, needs more optimization.
28 374 0.194203987100 Henry Cohn, 2026, needs more optimization.
28 375 0.194404536817 Henry Cohn, 2026, needs more optimization.
28 376 0.194615947006 Henry Cohn, 2026, needs more optimization.
28 377 0.194738934214 Henry Cohn, 2026, needs more optimization.
28 378 0.194971132498 Henry Cohn, 2026, needs more optimization.
28 379 0.195114223527 Henry Cohn, 2026, needs more optimization.
28 380 0.195408522847 Henry Cohn, 2026, needs more optimization.
28 381 0.195615466757 Henry Cohn, 2026, needs more optimization.
28 382 0.195716281950 Henry Cohn, 2026, needs more optimization.
28 383 0.195914649691 Henry Cohn, 2026, needs more optimization.
28 384 0.196035051181 Henry Cohn, 2026, needs more optimization.
28 385 0.196189300100 Henry Cohn, 2026, needs more optimization.
28 386 0.196223454239 Henry Cohn, 2026, needs more optimization.
28 387 0.196385536970 Henry Cohn, 2026, needs more optimization.
28 388 0.196523881818 Henry Cohn, 2026, needs more optimization.
28 389 0.196698516546 Henry Cohn, 2026, needs more optimization.
28 390 0.196851788454 Henry Cohn, 2026, needs more optimization.
28 391 0.196866028785 Henry Cohn, 2026, needs more optimization.
28 392 0.197014258325 Henry Cohn, 2026, needs more optimization.
28 393 0.197082027464 Henry Cohn, 2026, needs more optimization.
28 394 0.197223619587 Henry Cohn, 2026, needs more optimization.
28 395 0.197395951780 Henry Cohn, 2026, needs more optimization.
28 396 0.197438461233 Henry Cohn, 2026, needs more optimization.
28 397 0.197497134088 Henry Cohn, 2026, needs more optimization.
28 398 0.197561199473 Henry Cohn, 2026, needs more optimization.
28 399 0.197655025796 Henry Cohn, 2026, needs more optimization.
28 400 0.197783051954 Henry Cohn, 2026, needs more optimization.
28 401 0.197900769319 Henry Cohn, 2026, needs more optimization.
28 402 0.197940540499 Henry Cohn, 2026, needs more optimization.
28 403 0.198133624516 Henry Cohn, 2026, needs more optimization.
28 404 0.198195233748 Henry Cohn, 2026, needs more optimization.
28 405 0.198195235745 Henry Cohn, 2026, needs more optimization.
28 406 0.198276941373 Henry Cohn, 2026, needs more optimization.
28 407 0.198292306022 Henry Cohn, 2026, needs more optimization.
28 408 0.198523625762 Henry Cohn, 2026, needs more optimization.
28 409 0.198561665841 Henry Cohn, 2026, needs more optimization.
28 410 0.198589258934 Henry Cohn, 2026, needs more optimization.
28 411 0.198647913312 Henry Cohn, 2026, needs more optimization.
28 412 0.198657392325 Henry Cohn, 2026, needs more optimization.
28 413 0.198703707347 Henry Cohn, 2026, needs more optimization.
28 414 0.198809207009 Henry Cohn, 2026, needs more optimization.
28 415 0.198810626841 Henry Cohn, 2026, needs more optimization.
28 416 0.198929227379 Henry Cohn, 2026, needs more optimization.
28 417 0.198965927597 Henry Cohn, 2026, needs more optimization.
28 418 0.199093189641 Henry Cohn, 2026, needs more optimization.
28 419 0.199093250835 Henry Cohn, 2026, needs more optimization.
28 420 0.199103089442 Henry Cohn, 2026, needs more optimization.
28 421 0.199168005369 Henry Cohn, 2026, needs more optimization.
28 422 0.199179754712 Henry Cohn, 2026, needs more optimization.
28 423 0.199280204888 Henry Cohn, 2026, needs more optimization.
28 424 0.199280216069 Henry Cohn, 2026, needs more optimization.
28 425 0.199307181681 Henry Cohn, 2026, needs more optimization.
28 426 0.199383040952 Henry Cohn, 2026, needs more optimization.
28 427 0.199383042548 Henry Cohn, 2026, needs more optimization.
28 428 0.199420696025 Henry Cohn, 2026, needs more optimization.
28 429 0.199452053319 Henry Cohn, 2026, needs more optimization.
28 430 0.199506964370 Henry Cohn, 2026, needs more optimization.
28 431 0.199547305104 Henry Cohn, 2026, needs more optimization.
28 432 0.199557092475 Henry Cohn, 2026, needs more optimization.
28 433 0.199566689685 Henry Cohn, 2026, needs more optimization.
28 434 0.199594209776 Henry Cohn, 2026, needs more optimization.
28 435 0.199598851983 Henry Cohn, 2026, needs more optimization.
28 436 0.199636449643 Henry Cohn, 2026, needs more optimization.
28 437 0.199661478980 Henry Cohn, 2026, needs more optimization.
28 438 0.199684038708 Henry Cohn, 2026, needs more optimization.
28 439 0.199711749938 Henry Cohn, 2026, needs more optimization.
28 440 0.199711817031 Henry Cohn, 2026, needs more optimization.
28 441 0.199711822336 Henry Cohn, 2026, needs more optimization.
28 442 0.199717017159 Henry Cohn, 2026, needs more optimization.
28 443 0.199760955867 Henry Cohn, 2026, needs more optimization.
28 444 0.199764339806 Henry Cohn, 2026, needs more optimization.
28 445 0.199803342072 Henry Cohn, 2026, needs more optimization.
28 446 0.199825707176 Henry Cohn, 2026, needs more optimization.
28 447 0.199868219329 Henry Cohn, 2026, needs more optimization.
28 448 0.199868455106 Henry Cohn, 2026, needs more optimization.
28 449 0.199870897325 Henry Cohn, 2026, needs more optimization.
28 450 0.199877287532 Henry Cohn, 2026, needs more optimization.
28 451 0.199882101145 Henry Cohn, 2026, needs more optimization.
28 452 0.199888983166 Henry Cohn, 2026, needs more optimization.
28 453 0.199923023735 Henry Cohn, 2026, needs more optimization.
28 455 0.199933256467 Henry Cohn, 2026, needs more optimization.
28 456 0.199933281971 Henry Cohn, 2026, needs more optimization.
28 457 0.199933298398 Henry Cohn, 2026, needs more optimization.
28 458 0.199938257850 Henry Cohn, 2026, needs more optimization.
28 459 0.199952119894 Henry Cohn, 2026, needs more optimization.
28 460 0.199966140713 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
28 569 0.200001976938 Henry Cohn, 2026, needs more optimization.
28 572 0.200002358327 Henry Cohn, 2026, needs more optimization.
28 573 0.200002358785 Henry Cohn, 2026, needs more optimization.
28 575 0.200002694290 Henry Cohn, 2026, needs more optimization.
28 577 0.200003308610 Henry Cohn, 2026, needs more optimization.
28 578 0.200005306779 Henry Cohn, 2026, needs more optimization.
28 579 0.200005889263 Henry Cohn, 2026, needs more optimization.
28 580 0.200007185950 Henry Cohn, 2026, needs more optimization.
28 582 0.200007187175 Henry Cohn, 2026, needs more optimization.
28 583 0.200009465810 Henry Cohn, 2026, needs more optimization.
28 584 0.200010296621 Henry Cohn, 2026, needs more optimization.
28 585 0.200010297375 Henry Cohn, 2026, needs more optimization.
28 586 0.200032139282 Henry Cohn, 2026, needs more optimization.
28 587 0.200072258656 Henry Cohn, 2026, needs more optimization.
28 588 0.200103150842 Henry Cohn, 2026, needs more optimization.
28 589 0.200137018769 Henry Cohn, 2026, needs more optimization.
28 590 0.200268365798 Henry Cohn, 2026, needs more optimization.
28 591 0.200435190788 Henry Cohn, 2026, needs more optimization.
28 592 0.200655731108 Henry Cohn, 2026, needs more optimization.
28 593 0.200856750912 Henry Cohn, 2026, needs more optimization.
28 594 0.200997125304 Henry Cohn, 2026, needs more optimization.
28 595 0.201759555899 Henry Cohn, 2026, needs more optimization.
28 596 0.202294060476 Henry Cohn, 2026, needs more optimization.
28 597 0.203026004944 Henry Cohn, 2026, needs more optimization.
28 598 0.203512917724 Henry Cohn, 2026, needs more optimization.
28 599 0.204094141829 Henry Cohn, 2026, needs more optimization.
28 600 0.204597482980 Henry Cohn, 2026, needs more optimization.
28 601 0.237387330681 Henry Cohn, 2026, needs more optimization.
28 602 0.237399382815 Henry Cohn, 2026, needs more optimization.
28 603 0.237500549560 Henry Cohn, 2026, needs more optimization.
28 604 0.237575554089 Henry Cohn, 2026, needs more optimization.
28 606 0.237575599439 Henry Cohn, 2026, needs more optimization.
28 608 0.237726393031 Henry Cohn, 2026, needs more optimization.
28 609 0.237733310176 Henry Cohn, 2026, needs more optimization.
28 610 0.237735293593 Henry Cohn, 2026, needs more optimization.
28 612 0.237735313936 Henry Cohn, 2026, needs more optimization.
28 613 0.237824180061 Henry Cohn, 2026, needs more optimization.
28 614 0.237904602177 Henry Cohn, 2026, needs more optimization.
28 619 0.238046357772 Henry Cohn, 2026, needs more optimization.
28 627 0.238052734419 Henry Cohn, 2026, needs more optimization.
28 629 0.238052734594 Henry Cohn, 2026, needs more optimization.
28 631 0.238052734626 Henry Cohn, 2026, needs more optimization.
28 632 0.238052734792 Henry Cohn, 2026, needs more optimization.
28 633 0.238052734892 Henry Cohn, 2026, needs more optimization.
28 636 0.238053829604 Henry Cohn, 2026, needs more optimization.
28 637 0.238053829909 Henry Cohn, 2026, needs more optimization.
28 651 0.238096094725 Henry Cohn, 2026, needs more optimization.
28 652 0.238096094767 Henry Cohn, 2026, needs more optimization.
28 653 0.238096094776 Henry Cohn, 2026, needs more optimization.
28 660 0.238098128628 Henry Cohn, 2026, needs more optimization.
28 661 0.238100029997 Henry Cohn, 2026, needs more optimization.
28 662 0.238109763277 Henry Cohn, 2026, needs more optimization.
28 665 0.238135837543 Henry Cohn, 2026, needs more optimization.
28 666 0.238135838529 Henry Cohn, 2026, needs more optimization.
28 667 0.238135840297 Henry Cohn, 2026, needs more optimization.
28 668 0.238174708941 Henry Cohn, 2026, needs more optimization.
28 669 0.238174716022 Henry Cohn, 2026, needs more optimization.
28 670 0.238185358127 Henry Cohn, 2026, needs more optimization.
28 671 0.238186221004 Henry Cohn, 2026, needs more optimization.
28 672 0.238186235895 Henry Cohn, 2026, needs more optimization.
28 673 0.238186236102 Henry Cohn, 2026, needs more optimization.
28 674 0.238225747948 Henry Cohn, 2026, needs more optimization.
28 675 0.238233036793 Henry Cohn, 2026, needs more optimization.
28 676 0.238263424275 Henry Cohn, 2026, needs more optimization.
28 677 0.238268165649 Henry Cohn, 2026, needs more optimization.
28 678 0.238268178078 Henry Cohn, 2026, needs more optimization.
28 680 0.238268185315 Henry Cohn, 2026, needs more optimization.
28 682 0.238453668582 Henry Cohn, 2026, needs more optimization.
28 683 0.238453692706 Henry Cohn, 2026, needs more optimization.
28 684 0.238662643755 Henry Cohn, 2026, needs more optimization.
28 685 0.238694084877 Henry Cohn, 2026, needs more optimization.
28 686 0.238694442689 Henry Cohn, 2026, needs more optimization.
28 687 0.238802480033 Henry Cohn, 2026, needs more optimization.
28 688 0.239046315532 Henry Cohn, 2026, needs more optimization.
28 689 0.239290699367 Henry Cohn, 2026, needs more optimization.
28 690 0.239454228246 Henry Cohn, 2026, needs more optimization.
28 691 0.239516697580 Henry Cohn, 2026, needs more optimization.
28 692 0.239582104327 Henry Cohn, 2026, needs more optimization.
28 693 0.239824390856 Henry Cohn, 2026, needs more optimization.
28 694 0.239857324088 Henry Cohn, 2026, needs more optimization.
28 695 0.239976841409 Henry Cohn, 2026, needs more optimization.
28 696 0.240513772583 Henry Cohn, 2026, needs more optimization.
28 697 0.240689399717 Henry Cohn, 2026, needs more optimization.
28 698 0.240803696401 Henry Cohn, 2026, needs more optimization.
28 699 0.240912354936 Henry Cohn, 2026, needs more optimization.
28 700 0.241336515758 Henry Cohn, 2026, needs more optimization.
28 701 0.241380006534 Henry Cohn, 2026, needs more optimization.
28 702 0.241495846082 Henry Cohn, 2026, needs more optimization.
28 703 0.241535943609 Henry Cohn, 2026, needs more optimization.
28 704 0.241603625909 Henry Cohn, 2026, needs more optimization.
28 705 0.241658578090 Henry Cohn, 2026, needs more optimization.
28 707 0.241763882995 Henry Cohn, 2026, needs more optimization.
28 708 0.242110283373 Henry Cohn, 2026, needs more optimization.
28 709 0.242292240440 Henry Cohn, 2026, needs more optimization.
28 710 0.242402591442 Henry Cohn, 2026, needs more optimization.
28 711 0.242804027789 Henry Cohn, 2026, needs more optimization.
28 712 0.242898652134 Henry Cohn, 2026, needs more optimization.
28 713 0.242980112846 Henry Cohn, 2026, needs more optimization.
28 714 0.243100568087 Henry Cohn, 2026, needs more optimization.
28 715 0.243364263510 Henry Cohn, 2026, needs more optimization.
28 716 0.243364273550 Henry Cohn, 2026, needs more optimization.
28 717 0.243983665343 Henry Cohn, 2026, needs more optimization.
28 718 0.247541288190 Henry Cohn, 2026, needs more optimization.
28 719 0.247566550377 Henry Cohn, 2026, needs more optimization.
28 720 0.247576670694 Henry Cohn, 2026, needs more optimization.
28 721 0.247646013925 Henry Cohn, 2026, needs more optimization.
28 722 0.247678322504 Henry Cohn, 2026, needs more optimization.
28 723 0.247678335931 Henry Cohn, 2026, needs more optimization.
28 724 0.247690636150 Henry Cohn, 2026, needs more optimization.
28 725 0.247690642086 Henry Cohn, 2026, needs more optimization.
28 726 0.247761661649 Henry Cohn, 2026, needs more optimization.
28 727 0.247761673550 Henry Cohn, 2026, needs more optimization.
28 728 0.247920133688 Henry Cohn, 2026, needs more optimization.
28 730 0.247925429544 Henry Cohn, 2026, needs more optimization.
28 731 0.247937719111 Henry Cohn, 2026, needs more optimization.
28 732 0.247937719571 Henry Cohn, 2026, needs more optimization.
28 733 0.247998835533 Henry Cohn, 2026, needs more optimization.
28 734 0.248006717472 Henry Cohn, 2026, needs more optimization.
28 735 0.248039504851 Henry Cohn, 2026, needs more optimization.
28 736 0.248063229599 Henry Cohn, 2026, needs more optimization.
28 737 0.248124329475 Henry Cohn, 2026, needs more optimization.
28 738 0.248162618244 Henry Cohn, 2026, needs more optimization.
28 739 0.248187880530 Henry Cohn, 2026, needs more optimization.
28 740 0.248221658760 Henry Cohn, 2026, needs more optimization.
28 741 0.248245779742 Henry Cohn, 2026, needs more optimization.
28 742 0.248321400688 Henry Cohn, 2026, needs more optimization.
28 743 0.248361102921 Henry Cohn, 2026, needs more optimization.
28 744 0.248409130949 Henry Cohn, 2026, needs more optimization.
28 746 0.248409133745 Henry Cohn, 2026, needs more optimization.
28 747 0.248462506550 Henry Cohn, 2026, needs more optimization.
28 748 0.248498291833 Henry Cohn, 2026, needs more optimization.
28 749 0.248514587202 Henry Cohn, 2026, needs more optimization.
28 750 0.248593283772 Henry Cohn, 2026, needs more optimization.
28 751 0.248634016265 Henry Cohn, 2026, needs more optimization.
28 752 0.248668618511 Henry Cohn, 2026, needs more optimization.
28 753 0.248720462693 Henry Cohn, 2026, needs more optimization.
28 754 0.248773022915 Henry Cohn, 2026, needs more optimization.
28 755 0.248816015518 Henry Cohn, 2026, needs more optimization.
28 756 0.248844710642 Henry Cohn, 2026, needs more optimization.
28 757 0.248897337844 Henry Cohn, 2026, needs more optimization.
28 759 0.248938993326 Henry Cohn, 2026, needs more optimization.
28 760 0.248949536900 Henry Cohn, 2026, needs more optimization.
28 761 0.249011012669 Henry Cohn, 2026, needs more optimization.
28 762 0.249030995614 Henry Cohn, 2026, needs more optimization.
28 763 0.249067199876 Henry Cohn, 2026, needs more optimization.
28 764 0.249067203241 Henry Cohn, 2026, needs more optimization.
28 765 0.249078602975 Henry Cohn, 2026, needs more optimization.
28 766 0.249133404626 Henry Cohn, 2026, needs more optimization.
28 767 0.249149742285 Henry Cohn, 2026, needs more optimization.
28 768 0.249188508624 Henry Cohn, 2026, needs more optimization.
28 769 0.249208653272 Henry Cohn, 2026, needs more optimization.
28 770 0.249250003584 Henry Cohn, 2026, needs more optimization.
28 771 0.249260443435 Henry Cohn, 2026, needs more optimization.
28 772 0.249286840076 Henry Cohn, 2026, needs more optimization.
28 773 0.249317417388 Henry Cohn, 2026, needs more optimization.
28 774 0.249346654666 Henry Cohn, 2026, needs more optimization.
28 775 0.249366824152 Henry Cohn, 2026, needs more optimization.
28 776 0.249375505146 Henry Cohn, 2026, needs more optimization.
28 777 0.249414942966 Henry Cohn, 2026, needs more optimization.
28 778 0.249414943040 Henry Cohn, 2026, needs more optimization.
28 779 0.249429809345 Henry Cohn, 2026, needs more optimization.
28 780 0.249463215319 Henry Cohn, 2026, needs more optimization.
28 781 0.249463217504 Henry Cohn, 2026, needs more optimization.
28 782 0.249465021109 Henry Cohn, 2026, needs more optimization.
28 783 0.249511287071 Henry Cohn, 2026, needs more optimization.
28 784 0.249511289248 Henry Cohn, 2026, needs more optimization.
28 785 0.249555325978 Henry Cohn, 2026, needs more optimization.
28 786 0.249559707130 Henry Cohn, 2026, needs more optimization.
28 787 0.249559709724 Henry Cohn, 2026, needs more optimization.
28 788 0.249569692162 Henry Cohn, 2026, needs more optimization.
28 789 0.249569692441 Henry Cohn, 2026, needs more optimization.
28 790 0.249595630778 Henry Cohn, 2026, needs more optimization.
28 791 0.249603041522 Henry Cohn, 2026, needs more optimization.
28 792 0.249603042695 Henry Cohn, 2026, needs more optimization.
28 793 0.249618927776 Henry Cohn, 2026, needs more optimization.
28 794 0.249620102365 Henry Cohn, 2026, needs more optimization.
28 795 0.249640633759 Henry Cohn, 2026, needs more optimization.
28 796 0.249640640962 Henry Cohn, 2026, needs more optimization.
28 797 0.249659456946 Henry Cohn, 2026, needs more optimization.
28 798 0.249659457230 Henry Cohn, 2026, needs more optimization.
28 799 0.249672313117 Henry Cohn, 2026, needs more optimization.
28 801 0.249702833231 Henry Cohn, 2026, needs more optimization.
28 802 0.249702833548 Henry Cohn, 2026, needs more optimization.
28 803 0.249716292365 Henry Cohn, 2026, needs more optimization.
28 804 0.249718829264 Henry Cohn, 2026, needs more optimization.
28 805 0.249730309125 Henry Cohn, 2026, needs more optimization.
28 806 0.249749933700 Henry Cohn, 2026, needs more optimization.
28 807 0.249749933873 Henry Cohn, 2026, needs more optimization.
28 808 0.249749935167 Henry Cohn, 2026, needs more optimization.
28 809 0.249764534304 Henry Cohn, 2026, needs more optimization.
28 810 0.249768658546 Henry Cohn, 2026, needs more optimization.
28 811 0.249782724787 Henry Cohn, 2026, needs more optimization.
28 814 0.249818139738 Henry Cohn, 2026, needs more optimization.
28 815 0.249833069524 Henry Cohn, 2026, needs more optimization.
28 816 0.249838449307 Henry Cohn, 2026, needs more optimization.
28 817 0.249864022103 Henry Cohn, 2026, needs more optimization.
28 818 0.249879696115 Henry Cohn, 2026, needs more optimization.
28 819 0.249881597939 Henry Cohn, 2026, needs more optimization.
28 820 0.249881598192 Henry Cohn, 2026, needs more optimization.
28 821 0.249896719890 Henry Cohn, 2026, needs more optimization.
28 822 0.249908823396 Henry Cohn, 2026, needs more optimization.
28 823 0.249908823507 Henry Cohn, 2026, needs more optimization.
28 825 0.249917164726 Henry Cohn, 2026, needs more optimization.
28 976 0.25 Henry Cohn, 2026.
4⁢x−1
28 977 0.250003692685 Henry Cohn, 2026, needs more optimization.
28 979 0.250008784882 Henry Cohn, 2026, needs more optimization.
28 981 0.250011985130 Henry Cohn, 2026, needs more optimization.
28 982 0.250017038337 Henry Cohn, 2026, needs more optimization.
28 986 0.250018012942 Henry Cohn, 2026, needs more optimization.
28 987 0.250018015169 Henry Cohn, 2026, needs more optimization.
28 989 0.250018015651 Henry Cohn, 2026, needs more optimization.
28 993 0.250018055865 Henry Cohn, 2026, needs more optimization.
28 994 0.250027227439 Henry Cohn, 2026, needs more optimization.
28 995 0.250027235693 Henry Cohn, 2026, needs more optimization.
28 997 0.250048161414 Henry Cohn, 2026, needs more optimization.
28 998 0.250048200865 Henry Cohn, 2026, needs more optimization.
28 1002 0.250048273475 Henry Cohn, 2026, needs more optimization.
28 1004 0.250081311588 Henry Cohn, 2026, needs more optimization.
28 1005 0.250116794581 Henry Cohn, 2026, needs more optimization.
28 1006 0.250160712365 Henry Cohn, 2026, needs more optimization.
28 1009 0.250325100462 Henry Cohn, 2026, needs more optimization.
28 1010 0.250505047916 Henry Cohn, 2026, needs more optimization.
28 1011 0.250690448939 Henry Cohn, 2026, needs more optimization.
28 1012 0.250746534256 Henry Cohn, 2026, needs more optimization.
28 1013 0.251095728815 Henry Cohn, 2026, needs more optimization.
28 1014 0.251322013056 Henry Cohn, 2026, needs more optimization.
28 1015 0.251381668235 Henry Cohn, 2026, needs more optimization.
28 1016 0.251714949793 Henry Cohn, 2026, needs more optimization.
28 1017 0.252039383218 Henry Cohn, 2026, needs more optimization.
28 1018 0.252317426100 Henry Cohn, 2026, needs more optimization.
28 1019 0.252582216610 Henry Cohn, 2026, needs more optimization.
28 1020 0.252852232619 Henry Cohn, 2026, needs more optimization.
28 1021 0.253009773268 Henry Cohn, 2026, needs more optimization.
28 1022 0.253134950838 Henry Cohn, 2026, needs more optimization.
28 1023 0.253457532063 Henry Cohn, 2026, needs more optimization.
28 1024 0.253815867864 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 0.044634959618 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 0.054294848297 Henry Cohn, 2026, needs more optimization.
29 72 0.056102523445 Henry Cohn, 2026, needs more optimization.
29 73 0.057724695253 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 0.062593921311 Henry Cohn, 2026, needs more optimization.
29 77 0.063110090192 Henry Cohn, 2026, needs more optimization.
29 78 0.063579419232 Henry Cohn, 2026, needs more optimization.
29 79 0.064149508491 Henry Cohn, 2026, needs more optimization.
29 80 0.065731223905 Henry Cohn, 2026, needs more optimization.
29 81 0.066916771097 Henry Cohn, 2026, needs more optimization.
29 82 0.068551140992 Henry Cohn, 2026, needs more optimization.
29 83 0.070359470510 Henry Cohn, 2026, needs more optimization.
29 84 0.072177323531 Henry Cohn, 2026, needs more optimization.
29 85 0.073571723199 Henry Cohn, 2026, needs more optimization.
29 86 0.074839660480 Henry Cohn, 2026, needs more optimization.
29 87 0.075744746089 Henry Cohn, 2026, needs more optimization.
29 88 0.075920843886 Henry Cohn, 2026, needs more optimization.
29 89 0.076455846839 Henry Cohn, 2026, needs more optimization.
29 90 0.076780766933 Henry Cohn, 2026, needs more optimization.
29 91 0.076985849380 Henry Cohn, 2026, needs more optimization.
29 92 0.077170908446 Henry Cohn, 2026, needs more optimization.
29 93 0.077370861774 Henry Cohn, 2026, needs more optimization.
29 94 0.077819997175 Henry Cohn, 2026, needs more optimization.
29 95 0.078080044551 Henry Cohn, 2026, needs more optimization.
29 96 0.078171349901 Henry Cohn, 2026, needs more optimization.
29 97 0.078819535289 Henry Cohn, 2026, needs more optimization.
29 98 0.078878823083 Henry Cohn, 2026, needs more optimization.
29 99 0.079120877407 Henry Cohn, 2026, needs more optimization.
29 100 0.079421796784 Henry Cohn, 2026, needs more optimization.
29 101 0.080120946698 Henry Cohn, 2026, needs more optimization.
29 102 0.080261661364 Henry Cohn, 2026, needs more optimization.
29 103 0.080658815687 Henry Cohn, 2026, needs more optimization.
29 104 0.080673075170 Henry Cohn, 2026, needs more optimization.
29 105 0.080717042485 Henry Cohn, 2026, needs more optimization.
29 106 0.081984613771 Henry Cohn, 2026, needs more optimization.
29 107 0.082807667521 Henry Cohn, 2026, needs more optimization.
29 108 0.084753845663 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 0.089548687616 Henry Cohn, 2026, needs more optimization.
29 114 0.089828549794 Henry Cohn, 2026, needs more optimization.
29 115 0.089913158057 Henry Cohn, 2026, needs more optimization.
29 116 0.090013372974 Henry Cohn, 2026, needs more optimization.
29 117 0.090304309247 Henry Cohn, 2026, needs more optimization.
29 118 0.090556266778 Henry Cohn, 2026, needs more optimization.
29 119 0.090618007126 Henry Cohn, 2026, needs more optimization.
29 120 0.090744307083 Henry Cohn, 2026, needs more optimization.
29 121 0.091123623593 Henry Cohn, 2026, needs more optimization.
29 122 0.091825082020 Henry Cohn, 2026, needs more optimization.
29 123 0.093254360064 Henry Cohn, 2026, needs more optimization.
29 124 0.094254719919 Henry Cohn, 2026, needs more optimization.
29 125 0.096614678389 Henry Cohn, 2026, needs more optimization.
29 126 0.098256838980 Henry Cohn, 2026, needs more optimization.
29 127 0.099853019653 Henry Cohn, 2026, needs more optimization.
29 128 0.101514436638 Henry Cohn, 2026, needs more optimization.
29 129 0.102416996666 Henry Cohn, 2026, needs more optimization.
29 130 0.102457215282 Henry Cohn, 2026, needs more optimization.
29 131 0.102540925618 Henry Cohn, 2026, needs more optimization.
29 132 0.102568617327 Henry Cohn, 2026, needs more optimization.
29 133 0.102597544195 Henry Cohn, 2026, needs more optimization.
29 134 0.102726784826 Henry Cohn, 2026, needs more optimization.
29 135 0.103128797998 Henry Cohn, 2026, needs more optimization.
29 136 0.103823445421 Henry Cohn, 2026, needs more optimization.
29 137 0.105088867755 Henry Cohn, 2026, needs more optimization.
29 138 0.106293172532 Henry Cohn, 2026, needs more optimization.
29 139 0.107443060452 Henry Cohn, 2026, needs more optimization.
29 140 0.108105107626 Henry Cohn, 2026, needs more optimization.
29 141 0.108724944469 Henry Cohn, 2026, needs more optimization.
29 142 0.109463750440 Henry Cohn, 2026, needs more optimization.
29 143 0.110254027513 Henry Cohn, 2026, needs more optimization.
29 144 0.110691892505 Henry Cohn, 2026, needs more optimization.
29 145 0.110906903086 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 0.111111750190 Henry Cohn, 2026, needs more optimization.
29 154 0.111111882650 Henry Cohn, 2026, needs more optimization.
29 155 0.112126665179 Henry Cohn, 2026, needs more optimization.
29 156 0.113942539203 Henry Cohn, 2026, needs more optimization.
29 157 0.117885649182 Henry Cohn, 2026, needs more optimization.
29 158 0.119126440608 Henry Cohn, 2026, needs more optimization.
29 159 0.121144792532 Henry Cohn, 2026, needs more optimization.
29 160 0.121317516397 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 0.125681873484 Henry Cohn, 2026, needs more optimization.
29 164 0.126056794387 Henry Cohn, 2026, needs more optimization.
29 165 0.126268343754 Henry Cohn, 2026, needs more optimization.
29 166 0.128059393784 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 0.128239587753 Henry Cohn, 2026, needs more optimization.
29 186 0.129332814720 Henry Cohn, 2026, needs more optimization.
29 187 0.131049515929 Henry Cohn, 2026, needs more optimization.
29 188 0.131507084628 Henry Cohn, 2026, needs more optimization.
29 189 0.131507963507 Henry Cohn, 2026, needs more optimization.
29 190 0.138804154115 Henry Cohn, 2026, needs more optimization.
29 191 0.139947916613 Henry Cohn, 2026, needs more optimization.
29 192 0.140859553993 Henry Cohn, 2026, needs more optimization.
29 193 0.141734339954 Henry Cohn, 2026, needs more optimization.
29 194 0.141865292305 Henry Cohn, 2026, needs more optimization.
29 195 0.141872752403 Henry Cohn, 2026, needs more optimization.
29 196 0.142055176543 Henry Cohn, 2026, needs more optimization.
29 197 0.142093470938 Henry Cohn, 2026, needs more optimization.
29 198 0.142157094766 Henry Cohn, 2026, needs more optimization.
29 199 0.142202563317 Henry Cohn, 2026, needs more optimization.
29 200 0.142284537381 Henry Cohn, 2026, needs more optimization.
29 201 0.142341586325 Henry Cohn, 2026, needs more optimization.
29 202 0.142387513090 Henry Cohn, 2026, needs more optimization.
29 203 0.142414005572 Henry Cohn, 2026, needs more optimization.
29 204 0.142448498114 Henry Cohn, 2026, needs more optimization.
29 205 0.142549231032 Henry Cohn, 2026, needs more optimization.
29 206 0.142700850402 Henry Cohn, 2026, needs more optimization.
29 207 0.142865526879 Henry Cohn, 2026, needs more optimization.
29 208 0.142994666733 Henry Cohn, 2026, needs more optimization.
29 209 0.143548836595 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 0.144978931600 Henry Cohn, 2026, needs more optimization.
29 213 0.145546804335 Henry Cohn, 2026, needs more optimization.
29 214 0.145808128597 Henry Cohn, 2026, needs more optimization.
29 215 0.145808479905 Henry Cohn, 2026, needs more optimization.
29 216 0.145808593007 Henry Cohn, 2026, needs more optimization.
29 217 0.145820633490 Henry Cohn, 2026, needs more optimization.
29 218 0.145989538380 Henry Cohn, 2026, needs more optimization.
29 219 0.146215138769 Henry Cohn, 2026, needs more optimization.
29 220 0.146403603827 Henry Cohn, 2026, needs more optimization.
29 221 0.146511582396 Henry Cohn, 2026, needs more optimization.
29 222 0.146615496281 Henry Cohn, 2026, needs more optimization.
29 223 0.146732633004 Henry Cohn, 2026, needs more optimization.
29 224 0.146924253984 Henry Cohn, 2026, needs more optimization.
29 225 0.146924288875 Henry Cohn, 2026, needs more optimization.
29 235 0.147102976680 Henry Cohn, 2026.
87⁢x2−6⁢x−1
29 236 0.147883834935 Henry Cohn, 2026, needs more optimization.
29 237 0.147928792271 Henry Cohn, 2026, needs more optimization.
29 238 0.147937619953 Henry Cohn, 2026, needs more optimization.
29 239 0.147982610080 Henry Cohn, 2026.
29 240 0.148016671450 Henry Cohn, 2026, needs more optimization.
29 241 0.148222721045 Henry Cohn, 2026, needs more optimization.
29 242 0.148380081089 Henry Cohn, 2026, needs more optimization.
29 243 0.148718686403 Henry Cohn, 2026, needs more optimization.
29 244 0.148931743178 Henry Cohn, 2026, needs more optimization.
29 245 0.149388341309 Henry Cohn, 2026, needs more optimization.
29 246 0.149972704765 Henry Cohn, 2026, needs more optimization.
29 247 0.150247780667 Henry Cohn, 2026, needs more optimization.
29 248 0.150634963723 Henry Cohn, 2026, needs more optimization.
29 249 0.151084780300 Henry Cohn, 2026, needs more optimization.
29 250 0.151763346317 Henry Cohn, 2026, needs more optimization.
29 251 0.152199660361 Henry Cohn, 2026, needs more optimization.
29 252 0.153234841177 Henry Cohn, 2026, needs more optimization.
29 253 0.153816864714 Henry Cohn, 2026, needs more optimization.
29 254 0.155257980603 Henry Cohn, 2026, needs more optimization.
29 255 0.156029272722 Henry Cohn, 2026, needs more optimization.
29 256 0.156636016265 Henry Cohn, 2026, needs more optimization.
29 257 0.157586989050 Henry Cohn, 2026, needs more optimization.
29 258 0.158319184140 Henry Cohn, 2026, needs more optimization.
29 259 0.159057371484 Henry Cohn, 2026, needs more optimization.
29 260 0.159345306886 Henry Cohn, 2026, needs more optimization.
29 261 0.159994118648 Henry Cohn, 2026, needs more optimization.
29 262 0.160795074179 Henry Cohn, 2026, needs more optimization.
29 263 0.161860757472 Henry Cohn, 2026, needs more optimization.
29 264 0.162304870421 Henry Cohn, 2026, needs more optimization.
29 265 0.162329570262 Henry Cohn, 2026, needs more optimization.
29 266 0.162364595828 Henry Cohn, 2026, needs more optimization.
29 267 0.162366905462 Henry Cohn, 2026, needs more optimization.
29 268 0.162426734540 Henry Cohn, 2026, needs more optimization.
29 269 0.162826776704 Henry Cohn, 2026, needs more optimization.
29 270 0.162827436566 Henry Cohn, 2026, needs more optimization.
29 271 0.162872519919 Henry Cohn, 2026, needs more optimization.
29 272 0.162959377940 Henry Cohn, 2026, needs more optimization.
29 273 0.163378071903 Henry Cohn, 2026, needs more optimization.
29 274 0.163438716678 Henry Cohn, 2026, needs more optimization.
29 275 0.163519952936 Henry Cohn, 2026, needs more optimization.
29 276 0.163583762385 Henry Cohn, 2026, needs more optimization.
29 277 0.163665937624 Henry Cohn, 2026, needs more optimization.
29 278 0.163814020336 Henry Cohn, 2026, needs more optimization.
29 279 0.163888531585 Henry Cohn, 2026, needs more optimization.
29 280 0.163968290675 Henry Cohn, 2026, needs more optimization.
29 281 0.164149278310 Henry Cohn, 2026, needs more optimization.
29 282 0.164312376433 Henry Cohn, 2026, needs more optimization.
29 283 0.164462024774 Henry Cohn, 2026, needs more optimization.
29 284 0.164572132230 Henry Cohn, 2026, needs more optimization.
29 285 0.164661295051 Henry Cohn, 2026, needs more optimization.
29 286 0.164700632918 Henry Cohn, 2026, needs more optimization.
29 287 0.164813427480 Henry Cohn, 2026, needs more optimization.
29 288 0.164973116157 Henry Cohn, 2026, needs more optimization.
29 289 0.165051391115 Henry Cohn, 2026, needs more optimization.
29 290 0.165086268995 Henry Cohn, 2026, needs more optimization.
29 291 0.165134192173 Henry Cohn, 2026, needs more optimization.
29 292 0.165146419222 Henry Cohn, 2026, needs more optimization.
29 293 0.165184693031 Henry Cohn, 2026, needs more optimization.
29 294 0.165241868431 Henry Cohn, 2026, needs more optimization.
29 295 0.165265385924 Henry Cohn, 2026, needs more optimization.
29 296 0.165285750099 Henry Cohn, 2026, needs more optimization.
29 297 0.165344067080 Henry Cohn, 2026, needs more optimization.
29 298 0.165388469448 Henry Cohn, 2026, needs more optimization.
29 299 0.165485537456 Henry Cohn, 2026, needs more optimization.
29 300 0.165559377603 Henry Cohn, 2026, needs more optimization.
29 301 0.165607348252 Henry Cohn, 2026, needs more optimization.
29 302 0.165739238029 Henry Cohn, 2026, needs more optimization.
29 303 0.165768717532 Henry Cohn, 2026, needs more optimization.
29 304 0.165824850705 Henry Cohn, 2026, needs more optimization.
29 305 0.165883504984 Henry Cohn, 2026, needs more optimization.
29 306 0.166001129466 Henry Cohn, 2026, needs more optimization.
29 307 0.166027257785 Henry Cohn, 2026, needs more optimization.
29 308 0.166168101356 Henry Cohn, 2026, needs more optimization.
29 309 0.166210597329 Henry Cohn, 2026, needs more optimization.
29 310 0.166378549577 Henry Cohn, 2026, needs more optimization.
29 311 0.166421938795 Henry Cohn, 2026, needs more optimization.
29 312 0.166531560876 Henry Cohn, 2026, needs more optimization.
29 314 0.166562554107 Henry Cohn, 2026, needs more optimization.
29 315 0.166642931272 Henry Cohn, 2026, needs more optimization.
29 316 0.166664845086 Henry Cohn, 2026, needs more optimization.
29 317 0.166666259336 Henry Cohn, 2026, needs more optimization.
29 318 0.166667405370 Henry Cohn, 2026, needs more optimization.
29 319 0.166669075765 Henry Cohn, 2026, needs more optimization.
29 320 0.166676813544 Henry Cohn, 2026, needs more optimization.
29 321 0.166693601901 Henry Cohn, 2026, needs more optimization.
29 322 0.166700890978 Henry Cohn, 2026, needs more optimization.
29 323 0.166915726497 Henry Cohn, 2026, needs more optimization.
29 324 0.166963286430 Henry Cohn, 2026, needs more optimization.
29 325 0.167117464268 Henry Cohn, 2026, needs more optimization.
29 326 0.167203232120 Henry Cohn, 2026, needs more optimization.
29 327 0.167437243750 Henry Cohn, 2026, needs more optimization.
29 328 0.167860519537 Henry Cohn, 2026, needs more optimization.
29 329 0.168255959471 Henry Cohn, 2026, needs more optimization.
29 330 0.168906317607 Henry Cohn, 2026, needs more optimization.
29 331 0.169512107527 Henry Cohn, 2026, needs more optimization.
29 332 0.170984578458 Henry Cohn, 2026, needs more optimization.
29 333 0.171177852844 Henry Cohn, 2026, needs more optimization.
29 334 0.172423155148 Henry Cohn, 2026, needs more optimization.
29 335 0.172796881072 Henry Cohn, 2026, needs more optimization.
29 336 0.173866172483 Henry Cohn, 2026, needs more optimization.
29 337 0.174603944131 Henry Cohn, 2026, needs more optimization.
29 338 0.175327682370 Henry Cohn, 2026, needs more optimization.
29 339 0.175824302625 Henry Cohn, 2026, needs more optimization.
29 340 0.176282500198 Henry Cohn, 2026, needs more optimization.
29 341 0.177212424386 Henry Cohn, 2026, needs more optimization.
29 342 0.177791615417 Henry Cohn, 2026, needs more optimization.
29 343 0.178584707360 Henry Cohn, 2026, needs more optimization.
29 344 0.178627980687 Henry Cohn, 2026, needs more optimization.
29 345 0.178658691945 Henry Cohn, 2026, needs more optimization.
29 346 0.178949782446 Henry Cohn, 2026, needs more optimization.
29 347 0.179178394450 Henry Cohn, 2026, needs more optimization.
29 348 0.179967885363 Henry Cohn, 2026, needs more optimization.
29 349 0.180016774139 Henry Cohn, 2026, needs more optimization.
29 350 0.180415384414 Henry Cohn, 2026, needs more optimization.
29 351 0.180510401284 Henry Cohn, 2026, needs more optimization.
29 352 0.180510746663 Henry Cohn, 2026, needs more optimization.
29 353 0.180555214694 Henry Cohn, 2026, needs more optimization.
29 354 0.181061468066 Henry Cohn, 2026, needs more optimization.
29 355 0.181066680526 Henry Cohn, 2026, needs more optimization.
29 356 0.181197052935 Henry Cohn, 2026, needs more optimization.
29 357 0.181350366400 Henry Cohn, 2026, needs more optimization.
29 358 0.181496025098 Henry Cohn, 2026, needs more optimization.
29 359 0.181627568229 Henry Cohn, 2026, needs more optimization.
29 360 0.181682924545 Henry Cohn, 2026, needs more optimization.
29 361 0.184792074489 Henry Cohn, 2026, needs more optimization.
29 362 0.185294114281 Henry Cohn, 2026, needs more optimization.
29 363 0.185897133630 Henry Cohn, 2026, needs more optimization.
29 364 0.186086296839 Henry Cohn, 2026, needs more optimization.
29 365 0.186256244044 Henry Cohn, 2026, needs more optimization.
29 366 0.186798460257 Henry Cohn, 2026, needs more optimization.
29 367 0.187163282216 Henry Cohn, 2026, needs more optimization.
29 368 0.187296469065 Henry Cohn, 2026, needs more optimization.
29 369 0.187697411134 Henry Cohn, 2026, needs more optimization.
29 370 0.187986246543 Henry Cohn, 2026, needs more optimization.
29 371 0.188374165775 Henry Cohn, 2026, needs more optimization.
29 372 0.188583641748 Henry Cohn, 2026, needs more optimization.
29 373 0.188979812310 Henry Cohn, 2026, needs more optimization.
29 374 0.189345633123 Henry Cohn, 2026, needs more optimization.
29 375 0.189546598891 Henry Cohn, 2026, needs more optimization.
29 376 0.189663718625 Henry Cohn, 2026, needs more optimization.
29 377 0.189983535039 Henry Cohn, 2026, needs more optimization.
29 378 0.190280081473 Henry Cohn, 2026, needs more optimization.
29 379 0.190387725249 Henry Cohn, 2026, needs more optimization.
29 380 0.190820052971 Henry Cohn, 2026, needs more optimization.
29 381 0.191164328933 Henry Cohn, 2026, needs more optimization.
29 382 0.191194355323 Henry Cohn, 2026, needs more optimization.
29 383 0.191439742726 Henry Cohn, 2026, needs more optimization.
29 384 0.191577568119 Henry Cohn, 2026, needs more optimization.
29 385 0.191846475170 Henry Cohn, 2026, needs more optimization.
29 386 0.192009072705 Henry Cohn, 2026, needs more optimization.
29 387 0.192197834377 Henry Cohn, 2026, needs more optimization.
29 388 0.192294982603 Henry Cohn, 2026, needs more optimization.
29 389 0.192780596809 Henry Cohn, 2026, needs more optimization.
29 390 0.192937863287 Henry Cohn, 2026, needs more optimization.
29 391 0.193259339430 Henry Cohn, 2026, needs more optimization.
29 392 0.193571118124 Henry Cohn, 2026, needs more optimization.
29 393 0.193908828450 Henry Cohn, 2026, needs more optimization.
29 394 0.194064192335 Henry Cohn, 2026, needs more optimization.
29 395 0.194315077668 Henry Cohn, 2026, needs more optimization.
29 396 0.194398816680 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.
29 454 0.199401525529 Henry Cohn, 2026, needs more optimization.
29 455 0.199401587721 Henry Cohn, 2026, needs more optimization.
29 456 0.199401638843 Henry Cohn, 2026, needs more optimization.
29 457 0.199401652077 Henry Cohn, 2026, needs more optimization.
29 458 0.199433772074 Henry Cohn, 2026, needs more optimization.
29 459 0.199457718361 Henry Cohn, 2026, needs more optimization.
29 460 0.199500694560 Henry Cohn, 2026, needs more optimization.
29 461 0.199525945029 Henry Cohn, 2026, needs more optimization.
29 462 0.199525946752 Henry Cohn, 2026, needs more optimization.
29 463 0.199525947615 Henry Cohn, 2026, needs more optimization.
29 464 0.199563529449 Henry Cohn, 2026, needs more optimization.
29 465 0.199586191561 Henry Cohn, 2026, needs more optimization.
29 466 0.199586200383 Henry Cohn, 2026, needs more optimization.
29 467 0.199677972679 Henry Cohn, 2026, needs more optimization.
29 468 0.199683425971 Henry Cohn, 2026, needs more optimization.
29 469 0.199686239814 Henry Cohn, 2026, needs more optimization.
29 470 0.199692885066 Henry Cohn, 2026, needs more optimization.
29 471 0.199696387389 Henry Cohn, 2026, needs more optimization.
29 472 0.199696441113 Henry Cohn, 2026, needs more optimization.
29 473 0.199696443848 Henry Cohn, 2026, needs more optimization.
29 474 0.199720466750 Henry Cohn, 2026, needs more optimization.
29 475 0.199727259138 Henry Cohn, 2026, needs more optimization.
29 476 0.199727260384 Henry Cohn, 2026, needs more optimization.
29 477 0.199740525493 Henry Cohn, 2026, needs more optimization.
29 478 0.199745992863 Henry Cohn, 2026, needs more optimization.
29 479 0.199767959301 Henry Cohn, 2026, needs more optimization.
29 480 0.199767960310 Henry Cohn, 2026, needs more optimization.
29 481 0.199782709395 Henry Cohn, 2026, needs more optimization.
29 482 0.199782731004 Henry Cohn, 2026, needs more optimization.
29 483 0.199794185529 Henry Cohn, 2026, needs more optimization.
29 484 0.199794195566 Henry Cohn, 2026, needs more optimization.
29 485 0.199821749388 Henry Cohn, 2026, needs more optimization.
29 486 0.199864927016 Henry Cohn, 2026, needs more optimization.
29 487 0.199890064565 Henry Cohn, 2026, needs more optimization.
29 488 0.199890068630 Henry Cohn, 2026, needs more optimization.
29 489 0.199890069985 Henry Cohn, 2026, needs more optimization.
29 490 0.199892374130 Henry Cohn, 2026, needs more optimization.
29 491 0.199892376454 Henry Cohn, 2026, needs more optimization.
29 492 0.199916959582 Henry Cohn, 2026, needs more optimization.
29 493 0.199936187648 Henry Cohn, 2026, needs more optimization.
29 494 0.199936201889 Henry Cohn, 2026, needs more optimization.
29 495 0.199943595783 Henry Cohn, 2026, needs more optimization.
29 496 0.199960797210 Henry Cohn, 2026, needs more optimization.
29 576 0.2 Henry Cohn, 2026.
5⁢x−1
29 580 0.200002355916 Henry Cohn, 2026, needs more optimization.
29 582 0.200002356031 Henry Cohn, 2026, needs more optimization.
29 583 0.200002891365 Henry Cohn, 2026, needs more optimization.
29 587 0.200002891782 Henry Cohn, 2026, needs more optimization.
29 588 0.200006509315 Henry Cohn, 2026, needs more optimization.
29 589 0.200006545180 Henry Cohn, 2026, needs more optimization.
29 592 0.200006549202 Henry Cohn, 2026, needs more optimization.
29 593 0.200006551673 Henry Cohn, 2026, needs more optimization.
29 594 0.200006553803 Henry Cohn, 2026, needs more optimization.
29 596 0.200014279258 Henry Cohn, 2026, needs more optimization.
29 597 0.200014282296 Henry Cohn, 2026, needs more optimization.
29 599 0.200028900145 Henry Cohn, 2026, needs more optimization.
29 600 0.200037140658 Henry Cohn, 2026, needs more optimization.
29 601 0.200049854814 Henry Cohn, 2026, needs more optimization.
29 602 0.200066305851 Henry Cohn, 2026, needs more optimization.
29 603 0.200427696882 Henry Cohn, 2026, needs more optimization.
29 604 0.235482428107 Henry Cohn, 2026, needs more optimization.
29 605 0.235495895127 Henry Cohn, 2026, needs more optimization.
29 606 0.235547989937 Henry Cohn, 2026, needs more optimization.
29 607 0.235572901504 Henry Cohn, 2026, needs more optimization.
29 609 0.235590388043 Henry Cohn, 2026, needs more optimization.
29 610 0.235663968046 Henry Cohn, 2026, needs more optimization.
29 611 0.235669030020 Henry Cohn, 2026, needs more optimization.
29 612 0.236051050699 Henry Cohn, 2026, needs more optimization.
29 613 0.236051072244 Henry Cohn, 2026, needs more optimization.
29 617 0.236094042991 Henry Cohn, 2026, needs more optimization.
29 620 0.236094152245 Henry Cohn, 2026, needs more optimization.
29 621 0.236094245877 Henry Cohn, 2026, needs more optimization.
29 622 0.236094247132 Henry Cohn, 2026, needs more optimization.
29 623 0.236109649275 Henry Cohn, 2026, needs more optimization.
29 624 0.236755444336 Henry Cohn, 2026, needs more optimization.
29 627 0.236803707659 Henry Cohn, 2026, needs more optimization.
29 628 0.236803879912 Henry Cohn, 2026, needs more optimization.
29 629 0.236804079803 Henry Cohn, 2026, needs more optimization.
29 630 0.236865931457 Henry Cohn, 2026, needs more optimization.
29 631 0.236865944094 Henry Cohn, 2026, needs more optimization.
29 633 0.236907411734 Henry Cohn, 2026, needs more optimization.
29 634 0.237450188190 Henry Cohn, 2026, needs more optimization.
29 636 0.237522465365 Henry Cohn, 2026, needs more optimization.
29 637 0.237587184115 Henry Cohn, 2026, needs more optimization.
29 639 0.237587221207 Henry Cohn, 2026, needs more optimization.
29 640 0.237587264998 Henry Cohn, 2026, needs more optimization.
29 641 0.237587318414 Henry Cohn, 2026, needs more optimization.
29 646 0.237645574447 Henry Cohn, 2026, needs more optimization.
29 647 0.237645598605 Henry Cohn, 2026, needs more optimization.
29 652 0.237696203765 Henry Cohn, 2026, needs more optimization.
29 653 0.237696216699 Henry Cohn, 2026, needs more optimization.
29 655 0.237704011765 Henry Cohn, 2026, needs more optimization.
29 657 0.237743334391 Henry Cohn, 2026, needs more optimization.
29 658 0.237748750995 Henry Cohn, 2026, needs more optimization.
29 660 0.238010017455 Henry Cohn, 2026, needs more optimization.
29 661 0.238010017515 Henry Cohn, 2026, needs more optimization.
29 662 0.238010017528 Henry Cohn, 2026, needs more optimization.
29 663 0.238010017562 Henry Cohn, 2026, needs more optimization.
29 669 0.238010017587 Henry Cohn, 2026, needs more optimization.
29 673 0.238010017614 Henry Cohn, 2026, needs more optimization.
29 677 0.238010017764 Henry Cohn, 2026, needs more optimization.
29 678 0.238010017885 Henry Cohn, 2026, needs more optimization.
29 679 0.238031569531 Henry Cohn, 2026, needs more optimization.
29 681 0.238038464692 Henry Cohn, 2026, needs more optimization.
29 682 0.238038464790 Henry Cohn, 2026, needs more optimization.
29 683 0.238038464923 Henry Cohn, 2026, needs more optimization.
29 684 0.238038464943 Henry Cohn, 2026, needs more optimization.
29 685 0.238056676031 Henry Cohn, 2026, needs more optimization.
29 687 0.238058517619 Henry Cohn, 2026, needs more optimization.
29 688 0.238058517621 Henry Cohn, 2026, needs more optimization.
29 689 0.238058517909 Henry Cohn, 2026, needs more optimization.
29 690 0.238058518011 Henry Cohn, 2026, needs more optimization.
29 691 0.238058518049 Henry Cohn, 2026, needs more optimization.
29 692 0.238076879599 Henry Cohn, 2026, needs more optimization.
29 699 0.238088466890 Henry Cohn, 2026, needs more optimization.
29 700 0.238096934933 Henry Cohn, 2026, needs more optimization.
29 702 0.238098258810 Henry Cohn, 2026, needs more optimization.
29 705 0.238109968258 Henry Cohn, 2026, needs more optimization.
29 707 0.238109968782 Henry Cohn, 2026, needs more optimization.
29 710 0.238122451130 Henry Cohn, 2026, needs more optimization.
29 711 0.238122476255 Henry Cohn, 2026, needs more optimization.
29 712 0.238133282991 Henry Cohn, 2026, needs more optimization.
29 713 0.238249563052 Henry Cohn, 2026, needs more optimization.
29 715 0.238290056493 Henry Cohn, 2026, needs more optimization.
29 716 0.238325205339 Henry Cohn, 2026, needs more optimization.
29 717 0.238325412545 Henry Cohn, 2026, needs more optimization.
29 718 0.238407504370 Henry Cohn, 2026, needs more optimization.
29 719 0.241556164539 Henry Cohn, 2026, needs more optimization.
29 720 0.241564325231 Henry Cohn, 2026, needs more optimization.
29 721 0.241690630103 Henry Cohn, 2026, needs more optimization.
29 722 0.241734373737 Henry Cohn, 2026, needs more optimization.
29 723 0.241981954482 Henry Cohn, 2026, needs more optimization.
29 724 0.242015008522 Henry Cohn, 2026, needs more optimization.
29 728 0.242015130705 Henry Cohn, 2026, needs more optimization.
29 729 0.242304622741 Henry Cohn, 2026, needs more optimization.
29 730 0.242338573341 Henry Cohn, 2026, needs more optimization.
29 731 0.242343662836 Henry Cohn, 2026, needs more optimization.
29 733 0.242413171063 Henry Cohn, 2026, needs more optimization.
29 735 0.242413174548 Henry Cohn, 2026, needs more optimization.
29 736 0.242693158231 Henry Cohn, 2026, needs more optimization.
29 737 0.242808597302 Henry Cohn, 2026, needs more optimization.
29 738 0.242886978371 Henry Cohn, 2026, needs more optimization.
29 739 0.242972420164 Henry Cohn, 2026, needs more optimization.
29 740 0.243039780041 Henry Cohn, 2026, needs more optimization.
29 741 0.243048591380 Henry Cohn, 2026, needs more optimization.
29 742 0.243174172965 Henry Cohn, 2026, needs more optimization.
29 743 0.243174224645 Henry Cohn, 2026, needs more optimization.
29 744 0.243204530088 Henry Cohn, 2026, needs more optimization.
29 745 0.243309285437 Henry Cohn, 2026, needs more optimization.
29 746 0.243394024561 Henry Cohn, 2026, needs more optimization.
29 747 0.243397309431 Henry Cohn, 2026, needs more optimization.
29 748 0.243486148713 Henry Cohn, 2026, needs more optimization.
29 749 0.243686337379 Henry Cohn, 2026, needs more optimization.
29 750 0.243839959161 Henry Cohn, 2026, needs more optimization.
29 751 0.243897613878 Henry Cohn, 2026, needs more optimization.
29 752 0.244066347574 Henry Cohn, 2026, needs more optimization.
29 753 0.244066410074 Henry Cohn, 2026, needs more optimization.
29 755 0.244277997152 Henry Cohn, 2026, needs more optimization.
29 756 0.244357635236 Henry Cohn, 2026, needs more optimization.
29 760 0.244521753903 Henry Cohn, 2026, needs more optimization.
29 761 0.244521933066 Henry Cohn, 2026, needs more optimization.
29 762 0.244635566286 Henry Cohn, 2026, needs more optimization.
29 763 0.244771511443 Henry Cohn, 2026, needs more optimization.
29 764 0.244817974664 Henry Cohn, 2026, needs more optimization.
29 765 0.244966704706 Henry Cohn, 2026, needs more optimization.
29 766 0.245085954605 Henry Cohn, 2026, needs more optimization.
29 767 0.245222349920 Henry Cohn, 2026, needs more optimization.
29 769 0.245237109578 Henry Cohn, 2026, needs more optimization.
29 770 0.245309422354 Henry Cohn, 2026, needs more optimization.
29 771 0.245378265743 Henry Cohn, 2026, needs more optimization.
29 772 0.245565558488 Henry Cohn, 2026, needs more optimization.
29 773 0.245685702346 Henry Cohn, 2026, needs more optimization.
29 774 0.245857405709 Henry Cohn, 2026, needs more optimization.
29 775 0.245903751948 Henry Cohn, 2026, needs more optimization.
29 776 0.245955606615 Henry Cohn, 2026, needs more optimization.
29 778 0.246028950421 Henry Cohn, 2026, needs more optimization.
29 779 0.246163844457 Henry Cohn, 2026, needs more optimization.
29 780 0.246287593876 Henry Cohn, 2026, needs more optimization.
29 781 0.246327006553 Henry Cohn, 2026, needs more optimization.
29 782 0.246418336785 Henry Cohn, 2026, needs more optimization.
29 783 0.246464360430 Henry Cohn, 2026, needs more optimization.
29 784 0.246577180965 Henry Cohn, 2026, needs more optimization.
29 785 0.246614457038 Henry Cohn, 2026, needs more optimization.
29 786 0.246647338741 Henry Cohn, 2026, needs more optimization.
29 787 0.246671083995 Henry Cohn, 2026, needs more optimization.
29 788 0.246671106445 Henry Cohn, 2026, needs more optimization.
29 790 0.246783434486 Henry Cohn, 2026, needs more optimization.
29 791 0.246826579605 Henry Cohn, 2026, needs more optimization.
29 792 0.246907461417 Henry Cohn, 2026, needs more optimization.
29 793 0.247038962284 Henry Cohn, 2026, needs more optimization.
29 794 0.247144451649 Henry Cohn, 2026, needs more optimization.
29 795 0.247212997014 Henry Cohn, 2026, needs more optimization.
29 796 0.247220104111 Henry Cohn, 2026, needs more optimization.
29 797 0.247312218485 Henry Cohn, 2026, needs more optimization.
29 798 0.247342215761 Henry Cohn, 2026, needs more optimization.
29 799 0.247342290472 Henry Cohn, 2026, needs more optimization.
29 800 0.247433797616 Henry Cohn, 2026, needs more optimization.
29 801 0.247484771429 Henry Cohn, 2026, needs more optimization.
29 802 0.247566025767 Henry Cohn, 2026, needs more optimization.
29 803 0.247617079079 Henry Cohn, 2026, needs more optimization.
29 804 0.247700668501 Henry Cohn, 2026, needs more optimization.
29 805 0.247700669474 Henry Cohn, 2026, needs more optimization.
29 806 0.247819400944 Henry Cohn, 2026, needs more optimization.
29 807 0.247973194938 Henry Cohn, 2026, needs more optimization.
29 808 0.247973203570 Henry Cohn, 2026, needs more optimization.
29 809 0.247973230237 Henry Cohn, 2026, needs more optimization.
29 811 0.248066212605 Henry Cohn, 2026, needs more optimization.
29 812 0.248066513225 Henry Cohn, 2026, needs more optimization.
29 813 0.248141174327 Henry Cohn, 2026, needs more optimization.
29 814 0.248237211741 Henry Cohn, 2026, needs more optimization.
29 815 0.248280310306 Henry Cohn, 2026, needs more optimization.
29 816 0.248356668399 Henry Cohn, 2026, needs more optimization.
29 817 0.248419966180 Henry Cohn, 2026, needs more optimization.
29 818 0.248446324091 Henry Cohn, 2026, needs more optimization.
29 819 0.248483800100 Henry Cohn, 2026, needs more optimization.
29 820 0.248483803143 Henry Cohn, 2026, needs more optimization.
29 822 0.248508514759 Henry Cohn, 2026, needs more optimization.
29 824 0.248508601366 Henry Cohn, 2026, needs more optimization.
29 825 0.248581145764 Henry Cohn, 2026, needs more optimization.
29 826 0.248589997685 Henry Cohn, 2026, needs more optimization.
29 827 0.248639713543 Henry Cohn, 2026, needs more optimization.
29 829 0.248639738076 Henry Cohn, 2026, needs more optimization.
29 830 0.248693869206 Henry Cohn, 2026, needs more optimization.
29 832 0.248728810144 Henry Cohn, 2026, needs more optimization.
29 833 0.248846831063 Henry Cohn, 2026, needs more optimization.
29 834 0.248867942583 Henry Cohn, 2026, needs more optimization.
29 835 0.248871436403 Henry Cohn, 2026, needs more optimization.
29 836 0.248871437359 Henry Cohn, 2026, needs more optimization.
29 837 0.248871438118 Henry Cohn, 2026, needs more optimization.
29 840 0.248957578495 Henry Cohn, 2026, needs more optimization.
29 841 0.248987456001 Henry Cohn, 2026, needs more optimization.
29 842 0.249053635300 Henry Cohn, 2026, needs more optimization.
29 843 0.249124309914 Henry Cohn, 2026, needs more optimization.
29 844 0.249124310055 Henry Cohn, 2026, needs more optimization.
29 847 0.249136839134 Henry Cohn, 2026, needs more optimization.
29 850 0.249136903403 Henry Cohn, 2026, needs more optimization.
29 851 0.249136914478 Henry Cohn, 2026, needs more optimization.
29 852 0.249165475166 Henry Cohn, 2026, needs more optimization.
29 853 0.249187580098 Henry Cohn, 2026, needs more optimization.
29 854 0.249220519503 Henry Cohn, 2026, needs more optimization.
29 855 0.249229844768 Henry Cohn, 2026, needs more optimization.
29 860 0.249262822053 Henry Cohn, 2026, needs more optimization.
29 861 0.249262828576 Henry Cohn, 2026, needs more optimization.
29 862 0.249353126959 Henry Cohn, 2026, needs more optimization.
29 863 0.249354903796 Henry Cohn, 2026, needs more optimization.
29 868 0.249408532062 Henry Cohn, 2026, needs more optimization.
29 869 0.249415145291 Henry Cohn, 2026, needs more optimization.
29 873 0.249519358866 Henry Cohn, 2026, needs more optimization.
29 877 0.249545175893 Henry Cohn, 2026, needs more optimization.
29 878 0.249577763963 Henry Cohn, 2026, needs more optimization.
29 880 0.249603978496 Henry Cohn, 2026, needs more optimization.
29 881 0.249607840395 Henry Cohn, 2026, needs more optimization.
29 882 0.249645906583 Henry Cohn, 2026, needs more optimization.
29 884 0.249645908597 Henry Cohn, 2026, needs more optimization.
29 889 0.249645910569 Henry Cohn, 2026, needs more optimization.
29 890 0.249670292107 Henry Cohn, 2026, needs more optimization.
29 891 0.249683608537 Henry Cohn, 2026, needs more optimization.
29 893 0.249690491576 Henry Cohn, 2026, needs more optimization.
29 894 0.249690496757 Henry Cohn, 2026, needs more optimization.
29 895 0.249709162006 Henry Cohn, 2026, needs more optimization.
29 897 0.249709162890 Henry Cohn, 2026, needs more optimization.
29 898 0.249735143290 Henry Cohn, 2026, needs more optimization.
29 899 0.249735145723 Henry Cohn, 2026, needs more optimization.
29 900 0.249749858919 Henry Cohn, 2026, needs more optimization.
29 901 0.249778346618 Henry Cohn, 2026, needs more optimization.
29 902 0.249778346660 Henry Cohn, 2026, needs more optimization.
29 903 0.249789326865 Henry Cohn, 2026, needs more optimization.
29 904 0.249821240695 Henry Cohn, 2026, needs more optimization.
29 905 0.249837949030 Henry Cohn, 2026, needs more optimization.
29 978 0.25 Orthogonal union of 976 points in 28 dimensions and 2 points in 1 dimension.
4⁢x−1
29 979 0.250000000109 Henry Cohn, 2026, needs more optimization.
29 980 0.250000000149 Henry Cohn, 2026, needs more optimization.
29 982 0.250000621829 Henry Cohn, 2026, needs more optimization.
29 984 0.250000639619 Henry Cohn, 2026, needs more optimization.
29 988 0.250000724827 Henry Cohn, 2026, needs more optimization.
29 991 0.250000894516 Henry Cohn, 2026, needs more optimization.
29 993 0.250001547245 Henry Cohn, 2026, needs more optimization.
29 995 0.250001735201 Henry Cohn, 2026, needs more optimization.
29 999 0.250001754626 Henry Cohn, 2026, needs more optimization.
29 1000 0.250001979762 Henry Cohn, 2026, needs more optimization.
29 1006 0.250002293839 Henry Cohn, 2026, needs more optimization.
29 1010 0.250012002111 Henry Cohn, 2026, needs more optimization.
29 1011 0.250012003170 Henry Cohn, 2026, needs more optimization.
29 1013 0.250019221049 Henry Cohn, 2026, needs more optimization.
29 1015 0.250035687631 Henry Cohn, 2026, needs more optimization.
29 1016 0.250035687913 Henry Cohn, 2026, needs more optimization.
29 1018 0.250035688006 Henry Cohn, 2026, needs more optimization.
29 1019 0.250047448683 Henry Cohn, 2026, needs more optimization.
29 1022 0.250052940722 Henry Cohn, 2026, needs more optimization.
29 1023 0.250052940725 Henry Cohn, 2026, needs more optimization.
29 1024 0.250052949751 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 0.042449229616 Henry Cohn, 2026, needs more optimization.
30 67 0.043919519972 Henry Cohn, 2026, needs more optimization.
30 68 0.044556632067 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 0.051259526087 Henry Cohn, 2026, needs more optimization.
30 73 0.052421740293 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 0.059053175487 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 0.062598281088 Henry Cohn, 2026, needs more optimization.
30 81 0.062840662714 Henry Cohn, 2026, needs more optimization.
30 82 0.064290492948 Henry Cohn, 2026, needs more optimization.
30 83 0.065112988237 Henry Cohn, 2026, needs more optimization.
30 84 0.066460260059 Henry Cohn, 2026, needs more optimization.
30 85 0.068029477489 Henry Cohn, 2026, needs more optimization.
30 86 0.069489198711 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 0.074431580844 Henry Cohn, 2026, needs more optimization.
30 91 0.075429099944 Henry Cohn, 2026, needs more optimization.
30 92 0.076276608691 Henry Cohn, 2026, needs more optimization.
30 93 0.076899157753 Henry Cohn, 2026, needs more optimization.
30 94 0.076904630711 Henry Cohn, 2026, needs more optimization.
30 95 0.076937528311 Henry Cohn, 2026, needs more optimization.
30 96 0.077028792235 Henry Cohn, 2026, needs more optimization.
30 97 0.077180799396 Henry Cohn, 2026, needs more optimization.
30 98 0.077277068549 Henry Cohn, 2026, needs more optimization.
30 99 0.077386846264 Henry Cohn, 2026, needs more optimization.
30 100 0.077770052790 Henry Cohn, 2026, needs more optimization.
30 101 0.077932023961 Henry Cohn, 2026, needs more optimization.
30 102 0.078190094211 Henry Cohn, 2026, needs more optimization.
30 103 0.078816993119 Henry Cohn, 2026, needs more optimization.
30 104 0.079148117726 Henry Cohn, 2026, needs more optimization.
30 105 0.079626581404 Henry Cohn, 2026, needs more optimization.
30 106 0.080491310066 Henry Cohn, 2026, needs more optimization.
30 107 0.080667019057 Henry Cohn, 2026, needs more optimization.
30 108 0.080814373233 Henry Cohn, 2026, needs more optimization.
30 109 0.081524428652 Henry Cohn, 2026, needs more optimization.
30 110 0.082137976220 Henry Cohn, 2026, needs more optimization.
30 111 0.082309248752 Henry Cohn, 2026, needs more optimization.
30 112 0.083254192309 Henry Cohn, 2026, needs more optimization.
30 113 0.085104782273 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 0.087985528516 Henry Cohn, 2026, needs more optimization.
30 116 0.088188744897 Henry Cohn, 2026, needs more optimization.
30 117 0.088552613702 Henry Cohn, 2026, needs more optimization.
30 118 0.089022485365 Henry Cohn, 2026, needs more optimization.
30 119 0.089356232364 Henry Cohn, 2026, needs more optimization.
30 120 0.089668039937 Henry Cohn, 2026, needs more optimization.
30 121 0.090005545434 Henry Cohn, 2026, needs more optimization.
30 122 0.090225927344 Henry Cohn, 2026, needs more optimization.
30 123 0.090523748833 Henry Cohn, 2026, needs more optimization.
30 124 0.090790490683 Henry Cohn, 2026, needs more optimization.
30 125 0.090956360885 Henry Cohn, 2026, needs more optimization.
30 126 0.091624817005 Henry Cohn, 2026, needs more optimization.
30 127 0.092702729313 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 0.098512387987 Henry Cohn, 2026, needs more optimization.
30 132 0.099549074965 Henry Cohn, 2026, needs more optimization.
30 133 0.100627373644 Henry Cohn, 2026, needs more optimization.
30 134 0.102005780605 Henry Cohn, 2026, needs more optimization.
30 135 0.102474515392 Henry Cohn, 2026, needs more optimization.
30 136 0.102554222719 Henry Cohn, 2026, needs more optimization.
30 137 0.102576170150 Henry Cohn, 2026, needs more optimization.
30 138 0.102582646337 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 0.102673058295 Henry Cohn, 2026, needs more optimization.
30 142 0.103624116798 Henry Cohn, 2026, needs more optimization.
30 143 0.105325607457 Henry Cohn, 2026, needs more optimization.
30 144 0.106166452708 Henry Cohn, 2026, needs more optimization.
30 145 0.107203591453 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 0.109650972631 Henry Cohn, 2026, needs more optimization.
30 150 0.110161927471 Henry Cohn, 2026, needs more optimization.
30 151 0.110744160769 Henry Cohn, 2026, needs more optimization.
30 152 0.111074171735 Henry Cohn, 2026, needs more optimization.
30 153 0.111087776823 Henry Cohn, 2026, needs more optimization.
30 154 0.111092292250 Henry Cohn, 2026, needs more optimization.
30 155 0.111100541073 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 0.111117292251 Henry Cohn, 2026, needs more optimization.
30 159 0.112283545696 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 0.118961066607 Henry Cohn, 2026, needs more optimization.
30 164 0.120040444741 Henry Cohn, 2026, needs more optimization.
30 165 0.120969842673 Henry Cohn, 2026, needs more optimization.
30 166 0.121727486976 Henry Cohn, 2026, needs more optimization.
30 167 0.121977498008 Henry Cohn, 2026, needs more optimization.
30 168 0.122829734605 Henry Cohn, 2026, needs more optimization.
30 169 0.123550450680 Henry Cohn, 2026, needs more optimization.
30 170 0.124639117941 Henry Cohn, 2026, needs more optimization.
30 171 0.126576867802 Henry Cohn, 2026, needs more optimization.
30 172 0.127612427241 Henry Cohn, 2026, needs more optimization.
30 173 0.128234743889 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 0.128239365370 Henry Cohn, 2026, needs more optimization.
30 188 0.128252766845 Henry Cohn, 2026, needs more optimization.
30 189 0.128435237543 Henry Cohn, 2026, needs more optimization.
30 190 0.129252161322 Henry Cohn, 2026, needs more optimization.
30 191 0.130283139643 Henry Cohn, 2026, needs more optimization.
30 192 0.131445579794 Henry Cohn, 2026, needs more optimization.
30 193 0.131447922516 Henry Cohn, 2026, needs more optimization.
30 194 0.131449694514 Henry Cohn, 2026, needs more optimization.
30 195 0.131462171329 Henry Cohn, 2026, needs more optimization.
30 196 0.131462571223 Henry Cohn, 2026, needs more optimization.
30 197 0.137965894920 Henry Cohn, 2026, needs more optimization.
30 198 0.138517739496 Henry Cohn, 2026, needs more optimization.
30 199 0.139406147390 Henry Cohn, 2026, needs more optimization.
30 200 0.140310314368 Henry Cohn, 2026, needs more optimization.
30 201 0.141156791789 Henry Cohn, 2026, needs more optimization.
30 202 0.141184157837 Henry Cohn, 2026, needs more optimization.
30 203 0.141278239653 Henry Cohn, 2026, needs more optimization.
30 204 0.141306214613 Henry Cohn, 2026, needs more optimization.
30 205 0.141407257951 Henry Cohn, 2026, needs more optimization.
30 206 0.141520871444 Henry Cohn, 2026, needs more optimization.
30 207 0.141569458483 Henry Cohn, 2026, needs more optimization.
30 208 0.141645551347 Henry Cohn, 2026, needs more optimization.
30 209 0.141837620569 Henry Cohn, 2026, needs more optimization.
30 210 0.141991854053 Henry Cohn, 2026, needs more optimization.
30 211 0.142188607308 Henry Cohn, 2026, needs more optimization.
30 212 0.142295987510 Henry Cohn, 2026, needs more optimization.
30 213 0.142299118485 Henry Cohn, 2026, needs more optimization.
30 214 0.142363040440 Henry Cohn, 2026, needs more optimization.
30 215 0.142512399636 Henry Cohn, 2026, needs more optimization.
30 216 0.142827783915 Henry Cohn, 2026, needs more optimization.
30 217 0.142871420662 Henry Cohn, 2026, needs more optimization.
30 218 0.143128476635 Henry Cohn, 2026, needs more optimization.
30 219 0.143711246788 Henry Cohn, 2026, needs more optimization.
30 220 0.143960995079 Henry Cohn, 2026, needs more optimization.
30 221 0.144389951345 Henry Cohn, 2026, needs more optimization.
30 222 0.144505706413 Henry Cohn, 2026, needs more optimization.
30 223 0.144850357694 Henry Cohn, 2026, needs more optimization.
30 224 0.144985225202 Henry Cohn, 2026, needs more optimization.
30 225 0.145227411028 Henry Cohn, 2026, needs more optimization.
30 226 0.145355355267 Henry Cohn, 2026, needs more optimization.
30 227 0.145544450138 Henry Cohn, 2026, needs more optimization.
30 228 0.145901998489 Henry Cohn, 2026, needs more optimization.
30 229 0.146419729386 Henry Cohn, 2026, needs more optimization.
30 230 0.146498165214 Henry Cohn, 2026, needs more optimization.
30 231 0.146623104438 Henry Cohn, 2026, needs more optimization.
30 232 0.146740016148 Henry Cohn, 2026, needs more optimization.
30 233 0.146909261071 Henry Cohn, 2026, needs more optimization.
30 234 0.146939445172 Henry Cohn, 2026, needs more optimization.
30 235 0.147046314138 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 0.147104068966 Henry Cohn, 2026, needs more optimization.
30 239 0.147105191481 Henry Cohn, 2026, needs more optimization.
30 240 0.147130110331 Henry Cohn, 2026, needs more optimization.
30 241 0.147151802244 Henry Cohn, 2026, needs more optimization.
30 242 0.147841371884 Henry Cohn, 2026, needs more optimization.
30 243 0.147842653274 Henry Cohn, 2026, needs more optimization.
30 244 0.147880869492 Henry Cohn, 2026, needs more optimization.
30 245 0.147881534607 Henry Cohn, 2026, needs more optimization.
30 246 0.147940409011 Henry Cohn, 2026, needs more optimization.
30 247 0.147941387512 Henry Cohn, 2026, needs more optimization.
30 248 0.147981540391 Henry Cohn, 2026, needs more optimization.
30 249 0.147987348572 Henry Cohn, 2026, needs more optimization.
30 250 0.148006334524 Henry Cohn, 2026, needs more optimization.
30 251 0.148080552679 Henry Cohn, 2026, needs more optimization.
30 252 0.148331748593 Henry Cohn, 2026, needs more optimization.
30 253 0.148490770792 Henry Cohn, 2026, needs more optimization.
30 254 0.148953320479 Henry Cohn, 2026, needs more optimization.
30 255 0.149533041754 Henry Cohn, 2026, needs more optimization.
30 256 0.149899778985 Henry Cohn, 2026, needs more optimization.
30 257 0.150633619236 Henry Cohn, 2026, needs more optimization.
30 258 0.150840153470 Henry Cohn, 2026, needs more optimization.
30 259 0.151550472481 Henry Cohn, 2026, needs more optimization.
30 260 0.152184389077 Henry Cohn, 2026, needs more optimization.
30 261 0.153137095978 Henry Cohn, 2026, needs more optimization.
30 262 0.153640654266 Henry Cohn, 2026, needs more optimization.
30 263 0.154188827021 Henry Cohn, 2026, needs more optimization.
30 264 0.154839085985 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 0.157446120899 Henry Cohn, 2026, needs more optimization.
30 269 0.158216861487 Henry Cohn, 2026, needs more optimization.
30 270 0.158917559432 Henry Cohn, 2026, needs more optimization.
30 271 0.159531857453 Henry Cohn, 2026, needs more optimization.
30 272 0.160092996355 Henry Cohn, 2026, needs more optimization.
30 273 0.160711847691 Henry Cohn, 2026, needs more optimization.
30 274 0.161452473599 Henry Cohn, 2026, needs more optimization.
30 275 0.161788333286 Henry Cohn, 2026, needs more optimization.
30 276 0.161830241912 Henry Cohn, 2026, needs more optimization.
30 277 0.161847422407 Henry Cohn, 2026, needs more optimization.
30 278 0.161891410958 Henry Cohn, 2026, needs more optimization.
30 279 0.161897647919 Henry Cohn, 2026, needs more optimization.
30 280 0.161916774399 Henry Cohn, 2026, needs more optimization.
30 281 0.161983470116 Henry Cohn, 2026, needs more optimization.
30 282 0.162019622306 Henry Cohn, 2026, needs more optimization.
30 283 0.162125275201 Henry Cohn, 2026, needs more optimization.
30 284 0.162285179078 Henry Cohn, 2026, needs more optimization.
30 285 0.162391868564 Henry Cohn, 2026, needs more optimization.
30 286 0.162531985507 Henry Cohn, 2026, needs more optimization.
30 287 0.162787179522 Henry Cohn, 2026, needs more optimization.
30 288 0.162893388345 Henry Cohn, 2026, needs more optimization.
30 289 0.163010874894 Henry Cohn, 2026, needs more optimization.
30 290 0.163071981481 Henry Cohn, 2026, needs more optimization.
30 291 0.163199810832 Henry Cohn, 2026, needs more optimization.
30 292 0.163350525086 Henry Cohn, 2026, needs more optimization.
30 293 0.163368501201 Henry Cohn, 2026, needs more optimization.
30 294 0.163456518155 Henry Cohn, 2026, needs more optimization.
30 295 0.163580646627 Henry Cohn, 2026, needs more optimization.
30 296 0.163636848813 Henry Cohn, 2026, needs more optimization.
30 297 0.163703612643 Henry Cohn, 2026, needs more optimization.
30 298 0.163759994536 Henry Cohn, 2026, needs more optimization.
30 299 0.163852724585 Henry Cohn, 2026, needs more optimization.
30 300 0.163943252483 Henry Cohn, 2026, needs more optimization.
30 301 0.164055531551 Henry Cohn, 2026, needs more optimization.
30 302 0.164152222186 Henry Cohn, 2026, needs more optimization.
30 303 0.164402522515 Henry Cohn, 2026, needs more optimization.
30 304 0.164558054878 Henry Cohn, 2026, needs more optimization.
30 305 0.164655872354 Henry Cohn, 2026, needs more optimization.
30 306 0.164734265382 Henry Cohn, 2026, needs more optimization.
30 307 0.164825463859 Henry Cohn, 2026, needs more optimization.
30 308 0.164972144258 Henry Cohn, 2026, needs more optimization.
30 309 0.165070231290 Henry Cohn, 2026, needs more optimization.
30 310 0.165102921572 Henry Cohn, 2026, needs more optimization.
30 311 0.165228906369 Henry Cohn, 2026, needs more optimization.
30 312 0.165250049283 Henry Cohn, 2026, needs more optimization.
30 313 0.165293267967 Henry Cohn, 2026, needs more optimization.
30 314 0.165398100599 Henry Cohn, 2026, needs more optimization.
30 315 0.165472323437 Henry Cohn, 2026, needs more optimization.
30 316 0.165585250165 Henry Cohn, 2026, needs more optimization.
30 317 0.165665637301 Henry Cohn, 2026, needs more optimization.
30 318 0.165700057697 Henry Cohn, 2026, needs more optimization.
30 319 0.165755789342 Henry Cohn, 2026, needs more optimization.
30 320 0.165890347676 Henry Cohn, 2026, needs more optimization.
30 321 0.165892702947 Henry Cohn, 2026, needs more optimization.
30 322 0.166104687656 Henry Cohn, 2026, needs more optimization.
30 323 0.166187408788 Henry Cohn, 2026, needs more optimization.
30 324 0.166273774072 Henry Cohn, 2026, needs more optimization.
30 325 0.166386481426 Henry Cohn, 2026, needs more optimization.
30 326 0.166552303649 Henry Cohn, 2026, needs more optimization.
30 327 0.166584496400 Henry Cohn, 2026, needs more optimization.
30 329 0.166617241614 Henry Cohn, 2026, needs more optimization.
30 330 0.166632065104 Henry Cohn, 2026, needs more optimization.
30 331 0.166662155309 Henry Cohn, 2026, needs more optimization.
30 332 0.166685695499 Henry Cohn, 2026, needs more optimization.
30 333 0.166697882030 Henry Cohn, 2026, needs more optimization.
30 334 0.166768075552 Henry Cohn, 2026, needs more optimization.
30 335 0.166863650608 Henry Cohn, 2026, needs more optimization.
30 336 0.167035290595 Henry Cohn, 2026, needs more optimization.
30 337 0.167186585659 Henry Cohn, 2026, needs more optimization.
30 338 0.167268834199 Henry Cohn, 2026, needs more optimization.
30 339 0.167380591966 Henry Cohn, 2026, needs more optimization.
30 340 0.167767148385 Henry Cohn, 2026, needs more optimization.
30 341 0.168088633041 Henry Cohn, 2026, needs more optimization.
30 342 0.168372380568 Henry Cohn, 2026, needs more optimization.
30 343 0.169681561917 Henry Cohn, 2026, needs more optimization.
30 344 0.170187800554 Henry Cohn, 2026, needs more optimization.
30 345 0.171269146334 Henry Cohn, 2026, needs more optimization.
30 346 0.171722362850 Henry Cohn, 2026, needs more optimization.
30 347 0.172549921466 Henry Cohn, 2026, needs more optimization.
30 348 0.172783709749 Henry Cohn, 2026, needs more optimization.
30 349 0.173924233596 Henry Cohn, 2026, needs more optimization.
30 350 0.174549762337 Henry Cohn, 2026, needs more optimization.
30 351 0.174836620105 Henry Cohn, 2026, needs more optimization.
30 352 0.175793905319 Henry Cohn, 2026, needs more optimization.
30 353 0.176393540377 Henry Cohn, 2026, needs more optimization.
30 354 0.177016306506 Henry Cohn, 2026, needs more optimization.
30 355 0.177453731214 Henry Cohn, 2026, needs more optimization.
30 356 0.178197131216 Henry Cohn, 2026, needs more optimization.
30 357 0.178692449132 Henry Cohn, 2026, needs more optimization.
30 358 0.179186707270 Henry Cohn, 2026, needs more optimization.
30 359 0.179807235695 Henry Cohn, 2026, needs more optimization.
30 360 0.180424944455 Henry Cohn, 2026, needs more optimization.
30 361 0.180705392259 Henry Cohn, 2026, needs more optimization.
30 362 0.181144391150 Henry Cohn, 2026, needs more optimization.
30 363 0.181436185123 Henry Cohn, 2026, needs more optimization.
30 364 0.181882804077 Henry Cohn, 2026, needs more optimization.
30 365 0.182236182181 Henry Cohn, 2026, needs more optimization.
30 366 0.182804627266 Henry Cohn, 2026, needs more optimization.
30 367 0.183035481567 Henry Cohn, 2026, needs more optimization.
30 368 0.183271751636 Henry Cohn, 2026, needs more optimization.
30 369 0.183491792365 Henry Cohn, 2026, needs more optimization.
30 370 0.184949879727 Henry Cohn, 2026, needs more optimization.
30 371 0.185107067014 Henry Cohn, 2026, needs more optimization.
30 372 0.185435320478 Henry Cohn, 2026, needs more optimization.
30 373 0.185555308569 Henry Cohn, 2026, needs more optimization.
30 374 0.185599490855 Henry Cohn, 2026, needs more optimization.
30 375 0.186729303158 Henry Cohn, 2026, needs more optimization.
30 376 0.186925709983 Henry Cohn, 2026, needs more optimization.
30 377 0.187086677782 Henry Cohn, 2026, needs more optimization.
30 378 0.187134905333 Henry Cohn, 2026, needs more optimization.
30 379 0.187289678813 Henry Cohn, 2026, needs more optimization.
30 380 0.187349951700 Henry Cohn, 2026, needs more optimization.
30 381 0.187357523037 Henry Cohn, 2026, needs more optimization.
30 382 0.187376162745 Henry Cohn, 2026, needs more optimization.
30 383 0.187531962601 Henry Cohn, 2026, needs more optimization.
30 384 0.187819917581 Henry Cohn, 2026, needs more optimization.
30 385 0.187869637145 Henry Cohn, 2026, needs more optimization.
30 386 0.187899647992 Henry Cohn, 2026, needs more optimization.
30 387 0.187991131143 Henry Cohn, 2026, needs more optimization.
30 388 0.188541393103 Henry Cohn, 2026, needs more optimization.
30 389 0.188603069230 Henry Cohn, 2026, needs more optimization.
30 390 0.188615423499 Henry Cohn, 2026, needs more optimization.
30 391 0.189086993326 Henry Cohn, 2026, needs more optimization.
30 392 0.189144775816 Henry Cohn, 2026, needs more optimization.
30 393 0.189254766271 Henry Cohn, 2026, needs more optimization.
30 394 0.189282932083 Henry Cohn, 2026, needs more optimization.
30 395 0.189845877348 Henry Cohn, 2026, needs more optimization.
30 396 0.190032566439 Henry Cohn, 2026, needs more optimization.
30 397 0.190092666921 Henry Cohn, 2026, needs more optimization.
30 398 0.190660179542 Henry Cohn, 2026, needs more optimization.
30 399 0.190734254576 Henry Cohn, 2026, needs more optimization.
30 400 0.191123331624 Henry Cohn, 2026, needs more optimization.
30 401 0.191452690531 Henry Cohn, 2026, needs more optimization.
30 402 0.191658690053 Henry Cohn, 2026, needs more optimization.
30 403 0.192197336832 Henry Cohn, 2026, needs more optimization.
30 404 0.192304815239 Henry Cohn, 2026, needs more optimization.
30 405 0.192511053370 Henry Cohn, 2026, needs more optimization.
30 406 0.192822429239 Henry Cohn, 2026, needs more optimization.
30 407 0.193026675812 Henry Cohn, 2026, needs more optimization.
30 408 0.193167253880 Henry Cohn, 2026, needs more optimization.
30 409 0.193565307324 Henry Cohn, 2026, needs more optimization.
30 410 0.193866620342 Henry Cohn, 2026, needs more optimization.
30 411 0.194090996809 Henry Cohn, 2026, needs more optimization.
30 412 0.194367091423 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 0.197993733657 Henry Cohn, 2026, needs more optimization.
30 456 0.198018734322 Henry Cohn, 2026, needs more optimization.
30 457 0.198049012402 Henry Cohn, 2026, needs more optimization.
30 458 0.198101119107 Henry Cohn, 2026, needs more optimization.
30 459 0.198108672787 Henry Cohn, 2026, needs more optimization.
30 460 0.198191782430 Henry Cohn, 2026, needs more optimization.
30 461 0.198201319691 Henry Cohn, 2026, needs more optimization.
30 462 0.198349863297 Henry Cohn, 2026, needs more optimization.
30 463 0.198439180405 Henry Cohn, 2026, needs more optimization.
30 464 0.198490379221 Henry Cohn, 2026, needs more optimization.
30 465 0.198528062111 Henry Cohn, 2026, needs more optimization.
30 466 0.198537982968 Henry Cohn, 2026, needs more optimization.
30 467 0.198597425556 Henry Cohn, 2026, needs more optimization.
30 468 0.198621795158 Henry Cohn, 2026, needs more optimization.
30 469 0.198658748723 Henry Cohn, 2026, needs more optimization.
30 470 0.198741532219 Henry Cohn, 2026, needs more optimization.
30 471 0.198780420545 Henry Cohn, 2026, needs more optimization.
30 472 0.198868837976 Henry Cohn, 2026, needs more optimization.
30 473 0.198890125093 Henry Cohn, 2026, needs more optimization.
30 474 0.198966986996 Henry Cohn, 2026, needs more optimization.
30 475 0.199014791564 Henry Cohn, 2026, needs more optimization.
30 476 0.199035026667 Henry Cohn, 2026, needs more optimization.
30 477 0.199120577311 Henry Cohn, 2026, needs more optimization.
30 478 0.199136904912 Henry Cohn, 2026, needs more optimization.
30 479 0.199163819603 Henry Cohn, 2026, needs more optimization.
30 480 0.199230704555 Henry Cohn, 2026, needs more optimization.
30 481 0.199230722527 Henry Cohn, 2026, needs more optimization.
30 482 0.199246754900 Henry Cohn, 2026, needs more optimization.
30 483 0.199298726895 Henry Cohn, 2026, needs more optimization.
30 484 0.199303478975 Henry Cohn, 2026, needs more optimization.
30 485 0.199340732564 Henry Cohn, 2026, needs more optimization.
30 486 0.199345054947 Henry Cohn, 2026, needs more optimization.
30 487 0.199360210698 Henry Cohn, 2026, needs more optimization.
30 488 0.199393506678 Henry Cohn, 2026, needs more optimization.
30 489 0.199429282707 Henry Cohn, 2026, needs more optimization.
30 490 0.199429289753 Henry Cohn, 2026, needs more optimization.
30 491 0.199434255401 Henry Cohn, 2026, needs more optimization.
30 492 0.199461660928 Henry Cohn, 2026, needs more optimization.
30 493 0.199471096873 Henry Cohn, 2026, needs more optimization.
30 494 0.199481520984 Henry Cohn, 2026, needs more optimization.
30 495 0.199481528592 Henry Cohn, 2026, needs more optimization.
30 496 0.199481529691 Henry Cohn, 2026, needs more optimization.
30 497 0.199496155342 Henry Cohn, 2026, needs more optimization.
30 498 0.199496162513 Henry Cohn, 2026, needs more optimization.
30 499 0.199496168430 Henry Cohn, 2026, needs more optimization.
30 500 0.199524518234 Henry Cohn, 2026, needs more optimization.
30 501 0.199526596364 Henry Cohn, 2026, needs more optimization.
30 502 0.199574682692 Henry Cohn, 2026, needs more optimization.
30 503 0.199588078281 Henry Cohn, 2026, needs more optimization.
30 504 0.199607704177 Henry Cohn, 2026, needs more optimization.
30 505 0.199607704354 Henry Cohn, 2026, needs more optimization.
30 506 0.199610822547 Henry Cohn, 2026, needs more optimization.
30 507 0.199625121393 Henry Cohn, 2026, needs more optimization.
30 508 0.199687342050 Henry Cohn, 2026, needs more optimization.
30 509 0.199693389883 Henry Cohn, 2026, needs more optimization.
30 510 0.199726646462 Henry Cohn, 2026, needs more optimization.
30 511 0.199733422863 Henry Cohn, 2026, needs more optimization.
30 512 0.199756857713 Henry Cohn, 2026, needs more optimization.
30 513 0.199779749369 Henry Cohn, 2026, needs more optimization.
30 514 0.199779751578 Henry Cohn, 2026, needs more optimization.
30 515 0.199797341656 Henry Cohn, 2026, needs more optimization.
30 516 0.199797343534 Henry Cohn, 2026, needs more optimization.
30 517 0.199797356820 Henry Cohn, 2026, needs more optimization.
30 518 0.199808658905 Henry Cohn, 2026, needs more optimization.
30 519 0.199834256865 Henry Cohn, 2026, needs more optimization.
30 520 0.199834260405 Henry Cohn, 2026, needs more optimization.
30 521 0.199846918337 Henry Cohn, 2026, needs more optimization.
30 522 0.199858633778 Henry Cohn, 2026, needs more optimization.
30 523 0.199858647813 Henry Cohn, 2026, needs more optimization.
30 524 0.199872329531 Henry Cohn, 2026, needs more optimization.
30 525 0.199882695157 Henry Cohn, 2026, needs more optimization.
30 526 0.199908693942 Henry Cohn, 2026, needs more optimization.
30 528 0.199908704874 Henry Cohn, 2026, needs more optimization.
30 529 0.199913208104 Henry Cohn, 2026, needs more optimization.
30 530 0.199939142537 Henry Cohn, 2026, needs more optimization.
30 531 0.199939173856 Henry Cohn, 2026, needs more optimization.
30 532 0.199939176645 Henry Cohn, 2026, needs more optimization.
30 533 0.199940014961 Henry Cohn, 2026, needs more optimization.
30 534 0.199960018139 Henry Cohn, 2026, needs more optimization.
30 536 0.199960024113 Henry Cohn, 2026, needs more optimization.
30 537 0.199960029792 Henry Cohn, 2026, needs more optimization.
30 538 0.199968031463 Henry Cohn, 2026, needs more optimization.
30 539 0.199980751645 Henry Cohn, 2026, needs more optimization.
30 540 0.199995767795 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 0.236734115898 Henry Cohn, 2026, needs more optimization.
30 668 0.236768769230 Henry Cohn, 2026, needs more optimization.
30 669 0.236768955224 Henry Cohn, 2026, needs more optimization.
30 670 0.236860031073 Henry Cohn, 2026, needs more optimization.
30 671 0.236860185920 Henry Cohn, 2026, needs more optimization.
30 672 0.236884506021 Henry Cohn, 2026, needs more optimization.
30 673 0.237116049462 Henry Cohn, 2026, needs more optimization.
30 674 0.237140764860 Henry Cohn, 2026, needs more optimization.
30 676 0.237140787641 Henry Cohn, 2026, needs more optimization.
30 677 0.237140817125 Henry Cohn, 2026, needs more optimization.
30 678 0.237140835086 Henry Cohn, 2026, needs more optimization.
30 681 0.237140873581 Henry Cohn, 2026, needs more optimization.
30 682 0.237195545817 Henry Cohn, 2026, needs more optimization.
30 683 0.237195663375 Henry Cohn, 2026, needs more optimization.
30 684 0.237208977609 Henry Cohn, 2026, needs more optimization.
30 685 0.237231406862 Henry Cohn, 2026, needs more optimization.
30 686 0.237231412636 Henry Cohn, 2026, needs more optimization.
30 687 0.237283236714 Henry Cohn, 2026, needs more optimization.
30 691 0.237298845030 Henry Cohn, 2026, needs more optimization.
30 693 0.237430313346 Henry Cohn, 2026, needs more optimization.
30 696 0.237430450501 Henry Cohn, 2026, needs more optimization.
30 697 0.237432775008 Henry Cohn, 2026, needs more optimization.
30 700 0.237432791594 Henry Cohn, 2026, needs more optimization.
30 701 0.237432891495 Henry Cohn, 2026, needs more optimization.
30 702 0.237544040444 Henry Cohn, 2026, needs more optimization.
30 703 0.237583956670 Henry Cohn, 2026, needs more optimization.
30 705 0.237583966225 Henry Cohn, 2026, needs more optimization.
30 706 0.237596352904 Henry Cohn, 2026, needs more optimization.
30 708 0.237926679374 Henry Cohn, 2026, needs more optimization.
30 710 0.237926680834 Henry Cohn, 2026, needs more optimization.
30 711 0.237932486022 Henry Cohn, 2026, needs more optimization.
30 712 0.237932486200 Henry Cohn, 2026, needs more optimization.
30 713 0.237932486303 Henry Cohn, 2026, needs more optimization.
30 714 0.237932487523 Henry Cohn, 2026, needs more optimization.
30 716 0.237932488442 Henry Cohn, 2026, needs more optimization.
30 717 0.237932488658 Henry Cohn, 2026, needs more optimization.
30 719 0.237932489262 Henry Cohn, 2026, needs more optimization.
30 720 0.238088593458 Henry Cohn, 2026, needs more optimization.
30 721 0.238874725236 Henry Cohn, 2026, needs more optimization.
30 722 0.238874729688 Henry Cohn, 2026, needs more optimization.
30 723 0.238926113750 Henry Cohn, 2026, needs more optimization.
30 724 0.238956104259 Henry Cohn, 2026, needs more optimization.
30 726 0.239188235403 Henry Cohn, 2026, needs more optimization.
30 727 0.239188330942 Henry Cohn, 2026, needs more optimization.
30 728 0.239227159855 Henry Cohn, 2026, needs more optimization.
30 730 0.239271974780 Henry Cohn, 2026, needs more optimization.
30 731 0.239298012638 Henry Cohn, 2026, needs more optimization.
30 732 0.239361337993 Henry Cohn, 2026, needs more optimization.
30 733 0.239627260747 Henry Cohn, 2026, needs more optimization.
30 734 0.239629322461 Henry Cohn, 2026, needs more optimization.
30 735 0.239637841659 Henry Cohn, 2026, needs more optimization.
30 736 0.239711235817 Henry Cohn, 2026, needs more optimization.
30 737 0.239747769986 Henry Cohn, 2026, needs more optimization.
30 738 0.239873162179 Henry Cohn, 2026, needs more optimization.
30 739 0.240038356329 Henry Cohn, 2026, needs more optimization.
30 740 0.240039535828 Henry Cohn, 2026, needs more optimization.
30 741 0.240152571614 Henry Cohn, 2026, needs more optimization.
30 742 0.240166571084 Henry Cohn, 2026, needs more optimization.
30 743 0.240243102376 Henry Cohn, 2026, needs more optimization.
30 744 0.240243175799 Henry Cohn, 2026, needs more optimization.
30 745 0.240466419362 Henry Cohn, 2026, needs more optimization.
30 746 0.240530645194 Henry Cohn, 2026, needs more optimization.
30 747 0.240571366115 Henry Cohn, 2026, needs more optimization.
30 748 0.240598884632 Henry Cohn, 2026, needs more optimization.
30 749 0.240624567602 Henry Cohn, 2026, needs more optimization.
30 750 0.240906436073 Henry Cohn, 2026, needs more optimization.
30 751 0.241006156626 Henry Cohn, 2026, needs more optimization.
30 752 0.241107906832 Henry Cohn, 2026, needs more optimization.
30 753 0.241189565498 Henry Cohn, 2026, needs more optimization.
30 756 0.241354630815 Henry Cohn, 2026, needs more optimization.
30 757 0.241421240627 Henry Cohn, 2026, needs more optimization.
30 759 0.241526459799 Henry Cohn, 2026, needs more optimization.
30 760 0.241526481328 Henry Cohn, 2026, needs more optimization.
30 761 0.241526516740 Henry Cohn, 2026, needs more optimization.
30 762 0.241663670683 Henry Cohn, 2026, needs more optimization.
30 763 0.241782027124 Henry Cohn, 2026, needs more optimization.
30 770 0.241782137160 Henry Cohn, 2026, needs more optimization.
30 773 0.241782306743 Henry Cohn, 2026, needs more optimization.
30 776 0.242107041580 Henry Cohn, 2026, needs more optimization.
30 777 0.242221301561 Henry Cohn, 2026, needs more optimization.
30 778 0.242389024586 Henry Cohn, 2026, needs more optimization.
30 779 0.242501910000 Henry Cohn, 2026, needs more optimization.
30 780 0.242544212497 Henry Cohn, 2026, needs more optimization.
30 781 0.242638115421 Henry Cohn, 2026, needs more optimization.
30 782 0.242796824989 Henry Cohn, 2026, needs more optimization.
30 783 0.242835100946 Henry Cohn, 2026, needs more optimization.
30 784 0.242871263592 Henry Cohn, 2026, needs more optimization.
30 785 0.242916232627 Henry Cohn, 2026, needs more optimization.
30 786 0.242916255694 Henry Cohn, 2026, needs more optimization.
30 787 0.243016967554 Henry Cohn, 2026, needs more optimization.
30 788 0.243102156550 Henry Cohn, 2026, needs more optimization.
30 789 0.243190527590 Henry Cohn, 2026, needs more optimization.
30 790 0.243228474137 Henry Cohn, 2026, needs more optimization.
30 791 0.243310725339 Henry Cohn, 2026, needs more optimization.
30 792 0.243421066993 Henry Cohn, 2026, needs more optimization.
30 793 0.243421078494 Henry Cohn, 2026, needs more optimization.
30 794 0.243421082474 Henry Cohn, 2026, needs more optimization.
30 795 0.243588678289 Henry Cohn, 2026, needs more optimization.
30 796 0.243588698295 Henry Cohn, 2026, needs more optimization.
30 797 0.243690624632 Henry Cohn, 2026, needs more optimization.
30 798 0.243861996065 Henry Cohn, 2026, needs more optimization.
30 799 0.244017969742 Henry Cohn, 2026, needs more optimization.
30 801 0.244050951225 Henry Cohn, 2026, needs more optimization.
30 802 0.244050974010 Henry Cohn, 2026, needs more optimization.
30 803 0.244187650223 Henry Cohn, 2026, needs more optimization.
30 804 0.244348850028 Henry Cohn, 2026, needs more optimization.
30 805 0.244485341458 Henry Cohn, 2026, needs more optimization.
30 806 0.244611806260 Henry Cohn, 2026, needs more optimization.
30 808 0.244729111053 Henry Cohn, 2026, needs more optimization.
30 809 0.244816659920 Henry Cohn, 2026, needs more optimization.
30 810 0.244977137151 Henry Cohn, 2026, needs more optimization.
30 811 0.245053341864 Henry Cohn, 2026, needs more optimization.
30 812 0.245085122585 Henry Cohn, 2026, needs more optimization.
30 813 0.245194960034 Henry Cohn, 2026, needs more optimization.
30 814 0.245233006823 Henry Cohn, 2026, needs more optimization.
30 815 0.245295035517 Henry Cohn, 2026, needs more optimization.
30 816 0.245403979460 Henry Cohn, 2026, needs more optimization.
30 817 0.245432053849 Henry Cohn, 2026, needs more optimization.
30 820 0.245580693344 Henry Cohn, 2026, needs more optimization.
30 821 0.245720622124 Henry Cohn, 2026, needs more optimization.
30 822 0.245850010221 Henry Cohn, 2026, needs more optimization.
30 823 0.245934237835 Henry Cohn, 2026, needs more optimization.
30 824 0.245957922044 Henry Cohn, 2026, needs more optimization.
30 825 0.245975708177 Henry Cohn, 2026, needs more optimization.
30 826 0.245975746340 Henry Cohn, 2026, needs more optimization.
30 827 0.246101471658 Henry Cohn, 2026, needs more optimization.
30 828 0.246173688077 Henry Cohn, 2026, needs more optimization.
30 829 0.246241181345 Henry Cohn, 2026, needs more optimization.
30 831 0.246264708552 Henry Cohn, 2026, needs more optimization.
30 832 0.246410717206 Henry Cohn, 2026, needs more optimization.
30 833 0.246447722305 Henry Cohn, 2026, needs more optimization.
30 834 0.246449849020 Henry Cohn, 2026, needs more optimization.
30 835 0.246493147516 Henry Cohn, 2026, needs more optimization.
30 836 0.246515246295 Henry Cohn, 2026, needs more optimization.
30 837 0.246593859817 Henry Cohn, 2026, needs more optimization.
30 838 0.246675140070 Henry Cohn, 2026, needs more optimization.
30 839 0.246677509269 Henry Cohn, 2026, needs more optimization.
30 840 0.246800848304 Henry Cohn, 2026, needs more optimization.
30 841 0.246843450388 Henry Cohn, 2026, needs more optimization.
30 842 0.246914749531 Henry Cohn, 2026, needs more optimization.
30 843 0.246914752299 Henry Cohn, 2026, needs more optimization.
30 844 0.246914754815 Henry Cohn, 2026, needs more optimization.
30 845 0.247075601353 Henry Cohn, 2026, needs more optimization.
30 846 0.247172860820 Henry Cohn, 2026, needs more optimization.
30 847 0.247244306058 Henry Cohn, 2026, needs more optimization.
30 848 0.247318527032 Henry Cohn, 2026, needs more optimization.
30 849 0.247408306759 Henry Cohn, 2026, needs more optimization.
30 850 0.247408355094 Henry Cohn, 2026, needs more optimization.
30 851 0.247465257790 Henry Cohn, 2026, needs more optimization.
30 852 0.247472866431 Henry Cohn, 2026, needs more optimization.
30 853 0.247554675693 Henry Cohn, 2026, needs more optimization.
30 855 0.247576825539 Henry Cohn, 2026, needs more optimization.
30 856 0.247606034198 Henry Cohn, 2026, needs more optimization.
30 857 0.247656687143 Henry Cohn, 2026, needs more optimization.
30 858 0.247657710479 Henry Cohn, 2026, needs more optimization.
30 861 0.247703528313 Henry Cohn, 2026, needs more optimization.
30 862 0.247818118938 Henry Cohn, 2026, needs more optimization.
30 863 0.247818137983 Henry Cohn, 2026, needs more optimization.
30 864 0.247843735768 Henry Cohn, 2026, needs more optimization.
30 865 0.247928723758 Henry Cohn, 2026, needs more optimization.
30 866 0.247997142769 Henry Cohn, 2026, needs more optimization.
30 867 0.248002037464 Henry Cohn, 2026, needs more optimization.
30 868 0.248003117868 Henry Cohn, 2026, needs more optimization.
30 869 0.248045672036 Henry Cohn, 2026, needs more optimization.
30 870 0.248045681943 Henry Cohn, 2026, needs more optimization.
30 871 0.248128030069 Henry Cohn, 2026, needs more optimization.
30 872 0.248162312124 Henry Cohn, 2026, needs more optimization.
30 873 0.248188704122 Henry Cohn, 2026, needs more optimization.
30 874 0.248190226417 Henry Cohn, 2026, needs more optimization.
30 876 0.248279030174 Henry Cohn, 2026, needs more optimization.
30 877 0.248281334218 Henry Cohn, 2026, needs more optimization.
30 878 0.248281346167 Henry Cohn, 2026, needs more optimization.
30 879 0.248342530899 Henry Cohn, 2026, needs more optimization.
30 880 0.248418278058 Henry Cohn, 2026, needs more optimization.
30 881 0.248467345596 Henry Cohn, 2026, needs more optimization.
30 883 0.248467348070 Henry Cohn, 2026, needs more optimization.
30 884 0.248467350695 Henry Cohn, 2026, needs more optimization.
30 886 0.248494112722 Henry Cohn, 2026, needs more optimization.
30 887 0.248550759152 Henry Cohn, 2026, needs more optimization.
30 888 0.248574762612 Henry Cohn, 2026, needs more optimization.
30 889 0.248614163891 Henry Cohn, 2026, needs more optimization.
30 890 0.248649755102 Henry Cohn, 2026, needs more optimization.
30 891 0.248689329895 Henry Cohn, 2026, needs more optimization.
30 892 0.248699339153 Henry Cohn, 2026, needs more optimization.
30 893 0.248699339155 Henry Cohn, 2026, needs more optimization.
30 894 0.248740213563 Henry Cohn, 2026, needs more optimization.
30 896 0.248740292966 Henry Cohn, 2026, needs more optimization.
30 897 0.248763593177 Henry Cohn, 2026, needs more optimization.
30 898 0.248780995627 Henry Cohn, 2026, needs more optimization.
30 899 0.248780995862 Henry Cohn, 2026, needs more optimization.
30 900 0.248822494958 Henry Cohn, 2026, needs more optimization.
30 901 0.248844006787 Henry Cohn, 2026, needs more optimization.
30 902 0.248898383605 Henry Cohn, 2026, needs more optimization.
30 904 0.248914489229 Henry Cohn, 2026, needs more optimization.
30 905 0.248949907518 Henry Cohn, 2026, needs more optimization.
30 906 0.248979831622 Henry Cohn, 2026, needs more optimization.
30 907 0.249013582961 Henry Cohn, 2026, needs more optimization.
30 908 0.249021464022 Henry Cohn, 2026, needs more optimization.
30 909 0.249021507141 Henry Cohn, 2026, needs more optimization.
30 910 0.249048850062 Henry Cohn, 2026, needs more optimization.
30 911 0.249053929115 Henry Cohn, 2026, needs more optimization.
30 915 0.249091757211 Henry Cohn, 2026, needs more optimization.
30 916 0.249091757391 Henry Cohn, 2026, needs more optimization.
30 917 0.249091765261 Henry Cohn, 2026, needs more optimization.
30 918 0.249100185251 Henry Cohn, 2026, needs more optimization.
30 922 0.249174147637 Henry Cohn, 2026, needs more optimization.
30 923 0.249217279065 Henry Cohn, 2026, needs more optimization.
30 926 0.249229131032 Henry Cohn, 2026, needs more optimization.
30 927 0.249241918427 Henry Cohn, 2026, needs more optimization.
30 928 0.249241977113 Henry Cohn, 2026, needs more optimization.
30 929 0.249291794165 Henry Cohn, 2026, needs more optimization.
30 930 0.249318252147 Henry Cohn, 2026, needs more optimization.
30 931 0.249320873170 Henry Cohn, 2026, needs more optimization.
30 932 0.249320873757 Henry Cohn, 2026, needs more optimization.
30 933 0.249352682060 Henry Cohn, 2026, needs more optimization.
30 934 0.249363833535 Henry Cohn, 2026, needs more optimization.
30 935 0.249377457148 Henry Cohn, 2026, needs more optimization.
30 939 0.249394308743 Henry Cohn, 2026, needs more optimization.
30 940 0.249394329804 Henry Cohn, 2026, needs more optimization.
30 942 0.249394362094 Henry Cohn, 2026, needs more optimization.
30 945 0.249394400258 Henry Cohn, 2026, needs more optimization.
30 946 0.249429707256 Henry Cohn, 2026, needs more optimization.
30 947 0.249458784832 Henry Cohn, 2026, needs more optimization.
30 951 0.249485075479 Henry Cohn, 2026, needs more optimization.
30 952 0.249485075483 Henry Cohn, 2026, needs more optimization.
30 953 0.249485075491 Henry Cohn, 2026, needs more optimization.
30 954 0.249486932282 Henry Cohn, 2026, needs more optimization.
30 958 0.249511694720 Henry Cohn, 2026, needs more optimization.
30 972 0.249590140367 Henry Cohn, 2026, needs more optimization.
30 973 0.249599282582 Henry Cohn, 2026, needs more optimization.
30 977 0.249619355684 Henry Cohn, 2026, needs more optimization.
30 978 0.249628625322 Henry Cohn, 2026, needs more optimization.
30 980 0.249659887678 Henry Cohn, 2026, needs more optimization.
30 981 0.249659887683 Henry Cohn, 2026, needs more optimization.
30 982 0.249659887686 Henry Cohn, 2026, needs more optimization.
30 983 0.249659887735 Henry Cohn, 2026, needs more optimization.
30 984 0.249696157772 Henry Cohn, 2026, needs more optimization.
30 985 0.249709961146 Henry Cohn, 2026, needs more optimization.
30 986 0.249710052554 Henry Cohn, 2026, needs more optimization.
30 987 0.249716539125 Henry Cohn, 2026, needs more optimization.
30 988 0.249727372890 Henry Cohn, 2026, needs more optimization.
30 993 0.249797973813 Henry Cohn, 2026, needs more optimization.
30 996 0.249816433099 Henry Cohn, 2026, needs more optimization.
30 997 0.249852906278 Henry Cohn, 2026, needs more optimization.
30 998 0.249876560407 Henry Cohn, 2026, needs more optimization.
30 1001 0.249876561856 Henry Cohn, 2026, needs more optimization.
30 1024 0.249939028962 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 0.038112340475 Henry Cohn, 2026, needs more optimization.
31 68 0.041220604868 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 0.044034146773 Henry Cohn, 2026, needs more optimization.
31 72 0.044583881513 Henry Cohn, 2026, needs more optimization.
31 73 0.048631532114 Henry Cohn, 2026, needs more optimization.
31 74 0.050068906633 Henry Cohn, 2026, needs more optimization.
31 75 0.051024214945 Henry Cohn, 2026, needs more optimization.
31 76 0.052578474476 Henry Cohn, 2026, needs more optimization.
31 77 0.054427328684 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 0.061360497540 Henry Cohn, 2026, needs more optimization.
31 83 0.061682454668 Henry Cohn, 2026, needs more optimization.
31 84 0.062332555905 Henry Cohn, 2026, needs more optimization.
31 85 0.063452446643 Henry Cohn, 2026, needs more optimization.
31 86 0.064362380190 Henry Cohn, 2026, needs more optimization.
31 87 0.065619149576 Henry Cohn, 2026, needs more optimization.
31 88 0.067040280394 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 0.072712278803 Henry Cohn, 2026, needs more optimization.
31 93 0.074056359375 Henry Cohn, 2026, needs more optimization.
31 94 0.074944641928 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 0.076162266039 Henry Cohn, 2026, needs more optimization.
31 98 0.076822090727 Henry Cohn, 2026, needs more optimization.
31 99 0.076874283367 Henry Cohn, 2026, needs more optimization.
31 100 0.076928779485 Henry Cohn, 2026, needs more optimization.
31 101 0.076991668133 Henry Cohn, 2026, needs more optimization.
31 102 0.077154916117 Henry Cohn, 2026, needs more optimization.
31 103 0.077295634472 Henry Cohn, 2026, needs more optimization.
31 104 0.077401066139 Henry Cohn, 2026, needs more optimization.
31 105 0.077815101299 Henry Cohn, 2026, needs more optimization.
31 106 0.078227925532 Henry Cohn, 2026, needs more optimization.
31 107 0.078676677442 Henry Cohn, 2026, needs more optimization.
31 108 0.079523974217 Henry Cohn, 2026, needs more optimization.
31 109 0.079852304347 Henry Cohn, 2026, needs more optimization.
31 110 0.080318497739 Henry Cohn, 2026, needs more optimization.
31 111 0.080626698823 Henry Cohn, 2026, needs more optimization.
31 112 0.080739352359 Henry Cohn, 2026, needs more optimization.
31 113 0.081339754371 Henry Cohn, 2026, needs more optimization.
31 114 0.081694453685 Henry Cohn, 2026, needs more optimization.
31 115 0.082456612902 Henry Cohn, 2026, needs more optimization.
31 116 0.083371330447 Henry Cohn, 2026, needs more optimization.
31 117 0.084483653628 Henry Cohn, 2026, needs more optimization.
31 120 0.084959387951 Henry Cohn, 2026.
115⁢x2+2⁢x−1
31 121 0.088322589893 Henry Cohn, 2026, needs more optimization.
31 122 0.088708879532 Henry Cohn, 2026, needs more optimization.
31 123 0.088854833985 Henry Cohn, 2026, needs more optimization.
31 124 0.089184858058 Henry Cohn, 2026, needs more optimization.
31 125 0.089588508607 Henry Cohn, 2026, needs more optimization.
31 126 0.089920694216 Henry Cohn, 2026, needs more optimization.
31 127 0.090306649965 Henry Cohn, 2026, needs more optimization.
31 128 0.090379506720 Henry Cohn, 2026, needs more optimization.
31 129 0.090757783511 Henry Cohn, 2026, needs more optimization.
31 130 0.091274921879 Henry Cohn, 2026, needs more optimization.
31 131 0.092149237851 Henry Cohn, 2026, needs more optimization.
31 132 0.093190738514 Henry Cohn, 2026, needs more optimization.
31 133 0.094606477357 Henry Cohn, 2026, needs more optimization.
31 134 0.095448357669 Henry Cohn, 2026, needs more optimization.
31 135 0.096348341664 Henry Cohn, 2026, needs more optimization.
31 136 0.097760269792 Henry Cohn, 2026, needs more optimization.
31 137 0.098801227519 Henry Cohn, 2026, needs more optimization.
31 138 0.099762218836 Henry Cohn, 2026, needs more optimization.
31 139 0.100442420662 Henry Cohn, 2026, needs more optimization.
31 140 0.101617334460 Henry Cohn, 2026, needs more optimization.
31 141 0.102424294010 Henry Cohn, 2026, needs more optimization.
31 142 0.102449892044 Henry Cohn, 2026, needs more optimization.
31 143 0.102507590801 Henry Cohn, 2026, needs more optimization.
31 145 0.102556345363 Henry Cohn, 2026, needs more optimization.
31 146 0.102850444229 Henry Cohn, 2026, needs more optimization.
31 147 0.103822486488 Henry Cohn, 2026, needs more optimization.
31 148 0.104757375478 Henry Cohn, 2026, needs more optimization.
31 149 0.105241075816 Henry Cohn, 2026, needs more optimization.
31 150 0.106275030708 Henry Cohn, 2026, needs more optimization.
31 151 0.106990228860 Henry Cohn, 2026, needs more optimization.
31 152 0.107773739180 Henry Cohn, 2026, needs more optimization.
31 153 0.108598479797 Henry Cohn, 2026, needs more optimization.
31 154 0.109343190427 Henry Cohn, 2026, needs more optimization.
31 155 0.109958583863 Henry Cohn, 2026, needs more optimization.
31 156 0.110152838352 Henry Cohn, 2026, needs more optimization.
31 157 0.110355939103 Henry Cohn, 2026, needs more optimization.
31 158 0.110465962135 Henry Cohn, 2026, needs more optimization.
31 159 0.110683803185 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 0.113823417172 Henry Cohn, 2026, needs more optimization.
31 165 0.114366610289 Henry Cohn, 2026, needs more optimization.
31 166 0.115477090885 Henry Cohn, 2026, needs more optimization.
31 167 0.116373350389 Henry Cohn, 2026, needs more optimization.
31 168 0.117342446013 Henry Cohn, 2026, needs more optimization.
31 169 0.118281888469 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 0.124763897966 Henry Cohn, 2026, needs more optimization.
31 176 0.125712115766 Henry Cohn, 2026, needs more optimization.
31 177 0.126364877108 Henry Cohn, 2026, needs more optimization.
31 178 0.127056451651 Henry Cohn, 2026, needs more optimization.
31 179 0.127668293745 Henry Cohn, 2026, needs more optimization.
31 180 0.127825206316 Henry Cohn, 2026, needs more optimization.
31 181 0.128021243933 Henry Cohn, 2026, needs more optimization.
31 182 0.128102244608 Henry Cohn, 2026, needs more optimization.
31 183 0.128116052639 Henry Cohn, 2026, needs more optimization.
31 184 0.128188550403 Henry Cohn, 2026, needs more optimization.
31 188 0.128237513434 Henry Cohn, 2026, needs more optimization.
31 189 0.128239365370 Orthogonal union of 187 points in 30 dimensions and 2 points in 1 dimension.
31 190 0.128240710799 Henry Cohn, 2026, needs more optimization.
31 191 0.128241696206 Henry Cohn, 2026, needs more optimization.
31 192 0.128243744691 Henry Cohn, 2026, needs more optimization.
31 193 0.128279657934 Henry Cohn, 2026, needs more optimization.
31 194 0.128493392190 Henry Cohn, 2026, needs more optimization.
31 195 0.128968657722 Henry Cohn, 2026, needs more optimization.
31 196 0.129779038459 Henry Cohn, 2026, needs more optimization.
31 197 0.131112785207 Henry Cohn, 2026, needs more optimization.
31 198 0.131120719479 Henry Cohn, 2026, needs more optimization.
31 199 0.131430075321 Henry Cohn, 2026, needs more optimization.
31 200 0.131451220397 Henry Cohn, 2026, needs more optimization.
31 201 0.135039657114 Henry Cohn, 2026, needs more optimization.
31 202 0.135900340420 Henry Cohn, 2026, needs more optimization.
31 203 0.136750801301 Henry Cohn, 2026, needs more optimization.
31 204 0.137364167601 Henry Cohn, 2026, needs more optimization.
31 205 0.137534137818 Henry Cohn, 2026, needs more optimization.
31 206 0.138237068994 Henry Cohn, 2026, needs more optimization.
31 207 0.138689633302 Henry Cohn, 2026, needs more optimization.
31 208 0.138976346016 Henry Cohn, 2026, needs more optimization.
31 209 0.139731913220 Henry Cohn, 2026, needs more optimization.
31 210 0.140527763760 Henry Cohn, 2026, needs more optimization.
31 211 0.140544387314 Henry Cohn, 2026, needs more optimization.
31 212 0.140686441907 Henry Cohn, 2026, needs more optimization.
31 213 0.140714090009 Henry Cohn, 2026, needs more optimization.
31 214 0.140917366000 Henry Cohn, 2026, needs more optimization.
31 215 0.141024572807 Henry Cohn, 2026, needs more optimization.
31 216 0.141062799056 Henry Cohn, 2026, needs more optimization.
31 217 0.141222969151 Henry Cohn, 2026, needs more optimization.
31 218 0.141309510531 Henry Cohn, 2026, needs more optimization.
31 219 0.141544148362 Henry Cohn, 2026, needs more optimization.
31 220 0.141908372450 Henry Cohn, 2026, needs more optimization.
31 221 0.141978284764 Henry Cohn, 2026, needs more optimization.
31 222 0.142055223077 Henry Cohn, 2026, needs more optimization.
31 223 0.142106362266 Henry Cohn, 2026, needs more optimization.
31 224 0.142164380232 Henry Cohn, 2026, needs more optimization.
31 225 0.142428790175 Henry Cohn, 2026, needs more optimization.
31 226 0.142820242868 Henry Cohn, 2026, needs more optimization.
31 227 0.142972400095 Henry Cohn, 2026, needs more optimization.
31 228 0.143198539609 Henry Cohn, 2026, needs more optimization.
31 229 0.143790628677 Henry Cohn, 2026, needs more optimization.
31 230 0.144364147698 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 0.145133712392 Henry Cohn, 2026, needs more optimization.
31 234 0.145344420864 Henry Cohn, 2026, needs more optimization.
31 235 0.145413607573 Henry Cohn, 2026, needs more optimization.
31 236 0.145518131245 Henry Cohn, 2026, needs more optimization.
31 237 0.145638889790 Henry Cohn, 2026, needs more optimization.
31 238 0.145806503411 Henry Cohn, 2026, needs more optimization.
31 239 0.145909626950 Henry Cohn, 2026, needs more optimization.
31 240 0.146045135702 Henry Cohn, 2026, needs more optimization.
31 241 0.146084770868 Henry Cohn, 2026, needs more optimization.
31 242 0.146219082497 Henry Cohn, 2026, needs more optimization.
31 243 0.146421809774 Henry Cohn, 2026, needs more optimization.
31 244 0.146542879306 Henry Cohn, 2026, needs more optimization.
31 245 0.146641451115 Henry Cohn, 2026, needs more optimization.
31 246 0.146743136841 Henry Cohn, 2026, needs more optimization.
31 247 0.146854692649 Henry Cohn, 2026, needs more optimization.
31 248 0.146921542148 Henry Cohn, 2026, needs more optimization.
31 249 0.147165067412 Henry Cohn, 2026, needs more optimization.
31 250 0.147214046432 Henry Cohn, 2026, needs more optimization.
31 251 0.147290507675 Henry Cohn, 2026, needs more optimization.
31 252 0.147351892540 Henry Cohn, 2026, needs more optimization.
31 253 0.147524535575 Henry Cohn, 2026, needs more optimization.
31 254 0.147593830133 Henry Cohn, 2026, needs more optimization.
31 255 0.147689612171 Henry Cohn, 2026, needs more optimization.
31 256 0.147846856893 Henry Cohn, 2026, needs more optimization.
31 257 0.147997075602 Henry Cohn, 2026, needs more optimization.
31 258 0.148284040868 Henry Cohn, 2026, needs more optimization.
31 259 0.148601520866 Henry Cohn, 2026, needs more optimization.
31 260 0.148618681391 Henry Cohn, 2026, needs more optimization.
31 261 0.148661457393 Henry Cohn, 2026, needs more optimization.
31 262 0.149117514884 Henry Cohn, 2026, needs more optimization.
31 263 0.149306864987 Henry Cohn, 2026, needs more optimization.
31 264 0.149745411812 Henry Cohn, 2026, needs more optimization.
31 265 0.150253531831 Henry Cohn, 2026, needs more optimization.
31 266 0.150589766450 Henry Cohn, 2026, needs more optimization.
31 267 0.150844849753 Henry Cohn, 2026, needs more optimization.
31 268 0.151041962608 Henry Cohn, 2026, needs more optimization.
31 269 0.151401893695 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 0.154358950905 Henry Cohn, 2026, needs more optimization.
31 274 0.154522248938 Henry Cohn, 2026, needs more optimization.
31 275 0.154697628107 Henry Cohn, 2026, needs more optimization.
31 276 0.155442250408 Henry Cohn, 2026, needs more optimization.
31 277 0.156137942880 Henry Cohn, 2026, needs more optimization.
31 278 0.156483433603 Henry Cohn, 2026, needs more optimization.
31 279 0.156902833872 Henry Cohn, 2026, needs more optimization.
31 280 0.157544910845 Henry Cohn, 2026, needs more optimization.
31 281 0.158314442486 Henry Cohn, 2026, needs more optimization.
31 282 0.158895586941 Henry Cohn, 2026, needs more optimization.
31 283 0.159191984914 Henry Cohn, 2026, needs more optimization.
31 284 0.159689821654 Henry Cohn, 2026, needs more optimization.
31 285 0.160185341465 Henry Cohn, 2026, needs more optimization.
31 286 0.160565265510 Henry Cohn, 2026, needs more optimization.
31 287 0.161083134853 Henry Cohn, 2026, needs more optimization.
31 288 0.161664330228 Henry Cohn, 2026, needs more optimization.
31 289 0.161700581382 Henry Cohn, 2026, needs more optimization.
31 290 0.161742053144 Henry Cohn, 2026, needs more optimization.
31 291 0.161742054700 Henry Cohn, 2026, needs more optimization.
31 292 0.161797003395 Henry Cohn, 2026, needs more optimization.
31 293 0.161810315708 Henry Cohn, 2026, needs more optimization.
31 294 0.161822492768 Henry Cohn, 2026, needs more optimization.
31 295 0.161837826869 Henry Cohn, 2026, needs more optimization.
31 296 0.161864731132 Henry Cohn, 2026, needs more optimization.
31 297 0.161914060965 Henry Cohn, 2026, needs more optimization.
31 298 0.161953105470 Henry Cohn, 2026, needs more optimization.
31 299 0.162073171692 Henry Cohn, 2026, needs more optimization.
31 300 0.162158966896 Henry Cohn, 2026, needs more optimization.
31 301 0.162210095106 Henry Cohn, 2026, needs more optimization.
31 302 0.162378403393 Henry Cohn, 2026, needs more optimization.
31 303 0.162488314380 Henry Cohn, 2026, needs more optimization.
31 304 0.162511510366 Henry Cohn, 2026, needs more optimization.
31 305 0.162848352102 Henry Cohn, 2026, needs more optimization.
31 306 0.162988996671 Henry Cohn, 2026, needs more optimization.
31 307 0.163149419757 Henry Cohn, 2026, needs more optimization.
31 308 0.163251673767 Henry Cohn, 2026, needs more optimization.
31 309 0.163342589986 Henry Cohn, 2026, needs more optimization.
31 310 0.163548538457 Henry Cohn, 2026, needs more optimization.
31 311 0.163734835048 Henry Cohn, 2026, needs more optimization.
31 312 0.163856052163 Henry Cohn, 2026, needs more optimization.
31 313 0.163958376368 Henry Cohn, 2026, needs more optimization.
31 314 0.163958388484 Henry Cohn, 2026, needs more optimization.
31 315 0.164019754422 Henry Cohn, 2026, needs more optimization.
31 316 0.164151306779 Henry Cohn, 2026, needs more optimization.
31 317 0.164248318828 Henry Cohn, 2026, needs more optimization.
31 318 0.164274458601 Henry Cohn, 2026, needs more optimization.
31 319 0.164395380875 Henry Cohn, 2026, needs more optimization.
31 320 0.164519952724 Henry Cohn, 2026, needs more optimization.
31 321 0.164565566642 Henry Cohn, 2026, needs more optimization.
31 322 0.164632833363 Henry Cohn, 2026, needs more optimization.
31 323 0.164654357876 Henry Cohn, 2026, needs more optimization.
31 324 0.164740265975 Henry Cohn, 2026, needs more optimization.
31 325 0.164818192456 Henry Cohn, 2026, needs more optimization.
31 326 0.164906253377 Henry Cohn, 2026, needs more optimization.
31 327 0.164984075321 Henry Cohn, 2026, needs more optimization.
31 328 0.165106374736 Henry Cohn, 2026, needs more optimization.
31 329 0.165232292674 Henry Cohn, 2026, needs more optimization.
31 330 0.165252626658 Henry Cohn, 2026, needs more optimization.
31 331 0.165409204465 Henry Cohn, 2026, needs more optimization.
31 332 0.165431746348 Henry Cohn, 2026, needs more optimization.
31 333 0.165576141177 Henry Cohn, 2026, needs more optimization.
31 334 0.165591926303 Henry Cohn, 2026, needs more optimization.
31 335 0.165725767289 Henry Cohn, 2026, needs more optimization.
31 336 0.165751867677 Henry Cohn, 2026, needs more optimization.
31 337 0.165908039999 Henry Cohn, 2026, needs more optimization.
31 338 0.165979167921 Henry Cohn, 2026, needs more optimization.
31 339 0.166174217409 Henry Cohn, 2026, needs more optimization.
31 340 0.166295974607 Henry Cohn, 2026, needs more optimization.
31 341 0.166493298171 Henry Cohn, 2026, needs more optimization.
31 342 0.166547393499 Henry Cohn, 2026, needs more optimization.
31 343 0.166615417098 Henry Cohn, 2026, needs more optimization.
31 344 0.166670116054 Henry Cohn, 2026, needs more optimization.
31 345 0.166738755304 Henry Cohn, 2026, needs more optimization.
31 346 0.166791783774 Henry Cohn, 2026, needs more optimization.
31 347 0.166830400342 Henry Cohn, 2026, needs more optimization.
31 348 0.166932548235 Henry Cohn, 2026, needs more optimization.
31 349 0.167008628160 Henry Cohn, 2026, needs more optimization.
31 350 0.167112530297 Henry Cohn, 2026, needs more optimization.
31 351 0.167481615618 Henry Cohn, 2026, needs more optimization.
31 352 0.168451209620 Henry Cohn, 2026, needs more optimization.
31 353 0.168666572018 Henry Cohn, 2026, needs more optimization.
31 354 0.168937836749 Henry Cohn, 2026, needs more optimization.
31 355 0.169156255773 Henry Cohn, 2026, needs more optimization.
31 356 0.170053550809 Henry Cohn, 2026, needs more optimization.
31 357 0.170389437225 Henry Cohn, 2026, needs more optimization.
31 358 0.171060468809 Henry Cohn, 2026, needs more optimization.
31 359 0.171421536499 Henry Cohn, 2026, needs more optimization.
31 360 0.171775858393 Henry Cohn, 2026, needs more optimization.
31 361 0.178349342935 Henry Cohn, 2026, needs more optimization.
31 362 0.178349346370 Henry Cohn, 2026, needs more optimization.
31 363 0.178415559713 Henry Cohn, 2026, needs more optimization.
31 364 0.178447315538 Henry Cohn, 2026, needs more optimization.
31 365 0.178447316115 Henry Cohn, 2026, needs more optimization.
31 366 0.178605615094 Henry Cohn, 2026, needs more optimization.
31 367 0.178639500712 Henry Cohn, 2026, needs more optimization.
31 368 0.178661724152 Henry Cohn, 2026, needs more optimization.
31 369 0.178736876912 Henry Cohn, 2026, needs more optimization.
31 370 0.178906496764 Henry Cohn, 2026, needs more optimization.
31 371 0.179065788722 Henry Cohn, 2026, needs more optimization.
31 372 0.179416701790 Henry Cohn, 2026, needs more optimization.
31 373 0.179474896048 Henry Cohn, 2026, needs more optimization.
31 374 0.180118469875 Henry Cohn, 2026, needs more optimization.
31 375 0.180431776832 Henry Cohn, 2026, needs more optimization.
31 376 0.180599243995 Henry Cohn, 2026, needs more optimization.
31 377 0.180988545505 Henry Cohn, 2026, needs more optimization.
31 378 0.181592626396 Henry Cohn, 2026, needs more optimization.
31 379 0.181688971019 Henry Cohn, 2026, needs more optimization.
31 380 0.181732973529 Henry Cohn, 2026, needs more optimization.
31 381 0.181738308114 Henry Cohn, 2026, needs more optimization.
31 382 0.181977894639 Henry Cohn, 2026, needs more optimization.
31 383 0.182020722499 Henry Cohn, 2026, needs more optimization.
31 384 0.182093628868 Henry Cohn, 2026, needs more optimization.
31 385 0.182282801967 Henry Cohn, 2026, needs more optimization.
31 386 0.182283752145 Henry Cohn, 2026, needs more optimization.
31 387 0.182299409443 Henry Cohn, 2026, needs more optimization.
31 388 0.182569717873 Henry Cohn, 2026, needs more optimization.
31 389 0.182718944766 Henry Cohn, 2026, needs more optimization.
31 390 0.182835328170 Henry Cohn, 2026, needs more optimization.
31 391 0.183001314909 Henry Cohn, 2026, needs more optimization.
31 392 0.183434548652 Henry Cohn, 2026, needs more optimization.
31 393 0.183598298834 Henry Cohn, 2026, needs more optimization.
31 394 0.183826741000 Henry Cohn, 2026, needs more optimization.
31 395 0.183982652229 Henry Cohn, 2026, needs more optimization.
31 396 0.184441151678 Henry Cohn, 2026, needs more optimization.
31 397 0.184700350544 Henry Cohn, 2026, needs more optimization.
31 398 0.184921205504 Henry Cohn, 2026, needs more optimization.
31 399 0.185378464015 Henry Cohn, 2026, needs more optimization.
31 400 0.185904956464 Henry Cohn, 2026, needs more optimization.
31 401 0.186012231210 Henry Cohn, 2026, needs more optimization.
31 402 0.186087472409 Henry Cohn, 2026, needs more optimization.
31 403 0.186309903824 Henry Cohn, 2026, needs more optimization.
31 404 0.186529882464 Henry Cohn, 2026, needs more optimization.
31 405 0.186940865562 Henry Cohn, 2026, needs more optimization.
31 406 0.187182293751 Henry Cohn, 2026, needs more optimization.
31 407 0.187365207503 Henry Cohn, 2026, needs more optimization.
31 408 0.187633822684 Henry Cohn, 2026, needs more optimization.
31 409 0.187728858672 Henry Cohn, 2026, needs more optimization.
31 410 0.187932454105 Henry Cohn, 2026, needs more optimization.
31 411 0.188199105443 Henry Cohn, 2026, needs more optimization.
31 412 0.188499694573 Henry Cohn, 2026, needs more optimization.
31 413 0.188721316030 Henry Cohn, 2026, needs more optimization.
31 414 0.189014149572 Henry Cohn, 2026, needs more optimization.
31 415 0.189172211367 Henry Cohn, 2026, needs more optimization.
31 416 0.189310328366 Henry Cohn, 2026, needs more optimization.
31 417 0.189600373643 Henry Cohn, 2026, needs more optimization.
31 418 0.189718610957 Henry Cohn, 2026, needs more optimization.
31 419 0.190046691790 Henry Cohn, 2026, needs more optimization.
31 420 0.190209878238 Henry Cohn, 2026, needs more optimization.
31 421 0.190414402143 Henry Cohn, 2026, needs more optimization.
31 422 0.190620877255 Henry Cohn, 2026, needs more optimization.
31 423 0.190859752791 Henry Cohn, 2026, needs more optimization.
31 424 0.191130913929 Henry Cohn, 2026, needs more optimization.
31 425 0.191337098866 Henry Cohn, 2026, needs more optimization.
31 426 0.191628017745 Henry Cohn, 2026, needs more optimization.
31 427 0.191802031317 Henry Cohn, 2026, needs more optimization.
31 428 0.191847290164 Henry Cohn, 2026, needs more optimization.
31 429 0.192037059519 Henry Cohn, 2026, needs more optimization.
31 430 0.192139163119 Henry Cohn, 2026, needs more optimization.
31 431 0.192444996992 Henry Cohn, 2026, needs more optimization.
31 432 0.192675283497 Henry Cohn, 2026, needs more optimization.
31 433 0.192972603015 Henry Cohn, 2026, needs more optimization.
31 434 0.193172022779 Henry Cohn, 2026, needs more optimization.
31 435 0.193288826644 Henry Cohn, 2026, needs more optimization.
31 436 0.193453823479 Henry Cohn, 2026, needs more optimization.
31 437 0.193713829267 Henry Cohn, 2026, needs more optimization.
31 438 0.193815541761 Henry Cohn, 2026, needs more optimization.
31 439 0.194026065771 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 0.194632496974 Henry Cohn, 2026, needs more optimization.
31 457 0.195844916143 Henry Cohn, 2026, needs more optimization.
31 458 0.195938496744 Henry Cohn, 2026, needs more optimization.
31 459 0.195988082611 Henry Cohn, 2026, needs more optimization.
31 460 0.196207019154 Henry Cohn, 2026, needs more optimization.
31 461 0.196413216621 Henry Cohn, 2026, needs more optimization.
31 462 0.196494835204 Henry Cohn, 2026, needs more optimization.
31 463 0.196668295747 Henry Cohn, 2026, needs more optimization.
31 464 0.196783172664 Henry Cohn, 2026, needs more optimization.
31 465 0.196913422372 Henry Cohn, 2026, needs more optimization.
31 466 0.196988309403 Henry Cohn, 2026, needs more optimization.
31 467 0.197146745452 Henry Cohn, 2026, needs more optimization.
31 468 0.197301862428 Henry Cohn, 2026, needs more optimization.
31 469 0.197384632264 Henry Cohn, 2026, needs more optimization.
31 470 0.197455250511 Henry Cohn, 2026, needs more optimization.
31 471 0.197525619657 Henry Cohn, 2026, needs more optimization.
31 472 0.197594813060 Henry Cohn, 2026, needs more optimization.
31 473 0.197621045822 Henry Cohn, 2026, needs more optimization.
31 474 0.197645839016 Henry Cohn, 2026, needs more optimization.
31 475 0.197749637756 Henry Cohn, 2026, needs more optimization.
31 476 0.197817859215 Henry Cohn, 2026, needs more optimization.
31 477 0.197901675698 Henry Cohn, 2026, needs more optimization.
31 478 0.197923803920 Henry Cohn, 2026, needs more optimization.
31 479 0.198064591185 Henry Cohn, 2026, needs more optimization.
31 480 0.198095691201 Henry Cohn, 2026, needs more optimization.
31 481 0.198176400059 Henry Cohn, 2026, needs more optimization.
31 482 0.198259228553 Henry Cohn, 2026, needs more optimization.
31 484 0.198259278872 Henry Cohn, 2026, needs more optimization.
31 485 0.198259320250 Henry Cohn, 2026, needs more optimization.
31 486 0.198259465676 Henry Cohn, 2026, needs more optimization.
31 487 0.198411769115 Henry Cohn, 2026, needs more optimization.
31 488 0.198411771685 Henry Cohn, 2026, needs more optimization.
31 489 0.198515446893 Henry Cohn, 2026, needs more optimization.
31 490 0.198526002409 Henry Cohn, 2026, needs more optimization.
31 491 0.198578136893 Henry Cohn, 2026, needs more optimization.
31 492 0.198637113875 Henry Cohn, 2026, needs more optimization.
31 493 0.198680329044 Henry Cohn, 2026, needs more optimization.
31 494 0.198713531094 Henry Cohn, 2026, needs more optimization.
31 495 0.198829953501 Henry Cohn, 2026, needs more optimization.
31 496 0.198865600890 Henry Cohn, 2026, needs more optimization.
31 498 0.198871069962 Henry Cohn, 2026, needs more optimization.
31 499 0.198871093948 Henry Cohn, 2026, needs more optimization.
31 500 0.198879152610 Henry Cohn, 2026, needs more optimization.
31 501 0.198935744230 Henry Cohn, 2026, needs more optimization.
31 502 0.198994332908 Henry Cohn, 2026, needs more optimization.
31 503 0.199013076542 Henry Cohn, 2026, needs more optimization.
31 504 0.199049700994 Henry Cohn, 2026, needs more optimization.
31 505 0.199056131573 Henry Cohn, 2026, needs more optimization.
31 506 0.199083884741 Henry Cohn, 2026, needs more optimization.
31 507 0.199093962173 Henry Cohn, 2026, needs more optimization.
31 509 0.199132120716 Henry Cohn, 2026, needs more optimization.
31 510 0.199132127020 Henry Cohn, 2026, needs more optimization.
31 511 0.199167282257 Henry Cohn, 2026, needs more optimization.
31 512 0.199173666312 Henry Cohn, 2026, needs more optimization.
31 513 0.199224562284 Henry Cohn, 2026, needs more optimization.
31 514 0.199253620381 Henry Cohn, 2026, needs more optimization.
31 515 0.199314783487 Henry Cohn, 2026, needs more optimization.
31 516 0.199314787873 Henry Cohn, 2026, needs more optimization.
31 517 0.199346219585 Henry Cohn, 2026, needs more optimization.
31 518 0.199392210473 Henry Cohn, 2026, needs more optimization.
31 520 0.199401612547 Henry Cohn, 2026, needs more optimization.
31 521 0.199442021264 Henry Cohn, 2026, needs more optimization.
31 522 0.199460670400 Henry Cohn, 2026, needs more optimization.
31 523 0.199476422036 Henry Cohn, 2026, needs more optimization.
31 524 0.199496331384 Henry Cohn, 2026, needs more optimization.
31 525 0.199534208592 Henry Cohn, 2026, needs more optimization.
31 527 0.199534209832 Henry Cohn, 2026, needs more optimization.
31 529 0.199545123842 Henry Cohn, 2026, needs more optimization.
31 530 0.199569020940 Henry Cohn, 2026, needs more optimization.
31 531 0.199590754049 Henry Cohn, 2026, needs more optimization.
31 532 0.199599186124 Henry Cohn, 2026, needs more optimization.
31 533 0.199599194003 Henry Cohn, 2026, needs more optimization.
31 534 0.199617756860 Henry Cohn, 2026, needs more optimization.
31 537 0.199627583442 Henry Cohn, 2026, needs more optimization.
31 538 0.199627590985 Henry Cohn, 2026, needs more optimization.
31 539 0.199652592860 Henry Cohn, 2026, needs more optimization.
31 540 0.199652596116 Henry Cohn, 2026, needs more optimization.
31 541 0.199662935041 Henry Cohn, 2026, needs more optimization.
31 542 0.199662942122 Henry Cohn, 2026, needs more optimization.
31 543 0.199691098978 Henry Cohn, 2026, needs more optimization.
31 544 0.199702364247 Henry Cohn, 2026, needs more optimization.
31 545 0.199702378574 Henry Cohn, 2026, needs more optimization.
31 547 0.199702379254 Henry Cohn, 2026, needs more optimization.
31 548 0.199737893846 Henry Cohn, 2026, needs more optimization.
31 549 0.199737909466 Henry Cohn, 2026, needs more optimization.
31 550 0.199737917264 Henry Cohn, 2026, needs more optimization.
31 551 0.199737918830 Henry Cohn, 2026, needs more optimization.
31 552 0.199751855574 Henry Cohn, 2026, needs more optimization.
31 554 0.199785126710 Henry Cohn, 2026, needs more optimization.
31 555 0.199785136334 Henry Cohn, 2026, needs more optimization.
31 557 0.199800228925 Henry Cohn, 2026, needs more optimization.
31 559 0.199825351522 Henry Cohn, 2026, needs more optimization.
31 561 0.199825353372 Henry Cohn, 2026, needs more optimization.
31 562 0.199857412595 Henry Cohn, 2026, needs more optimization.
31 563 0.199858735520 Henry Cohn, 2026, needs more optimization.
31 564 0.199866660269 Henry Cohn, 2026, needs more optimization.
31 565 0.199867999275 Henry Cohn, 2026, needs more optimization.
31 566 0.199896063392 Henry Cohn, 2026, needs more optimization.
31 568 0.199901011969 Henry Cohn, 2026, needs more optimization.
31 569 0.199918636511 Henry Cohn, 2026, needs more optimization.
31 570 0.199924097147 Henry Cohn, 2026, needs more optimization.
31 571 0.199939486569 Henry Cohn, 2026, needs more optimization.
31 572 0.199941355846 Henry Cohn, 2026, needs more optimization.
31 573 0.199943464295 Henry Cohn, 2026, needs more optimization.
31 574 0.199945349412 Henry Cohn, 2026, needs more optimization.
31 575 0.199946366779 Henry Cohn, 2026, needs more optimization.
31 576 0.199950671721 Henry Cohn, 2026, needs more optimization.
31 577 0.199953049100 Henry Cohn, 2026, needs more optimization.
31 578 0.199955801382 Henry Cohn, 2026, needs more optimization.
31 579 0.199958126309 Henry Cohn, 2026, needs more optimization.
31 580 0.199960725379 Henry Cohn, 2026, needs more optimization.
31 581 0.199963497552 Henry Cohn, 2026, needs more optimization.
31 582 0.199965841825 Henry Cohn, 2026, needs more optimization.
31 583 0.199967949434 Henry Cohn, 2026, needs more optimization.
31 584 0.199970459449 Henry Cohn, 2026, needs more optimization.
31 585 0.199989646017 Henry Cohn, 2026, needs more optimization.
31 688 0.2 Henry Cohn, 2026.
5⁢x−1
31 689 0.206391434129 Henry Cohn, 2026, needs more optimization.
31 690 0.216338176812 Henry Cohn, 2026, needs more optimization.
31 691 0.216590345403 Henry Cohn, 2026, needs more optimization.
31 692 0.217009528022 Henry Cohn, 2026, needs more optimization.
31 693 0.217312962303 Henry Cohn, 2026, needs more optimization.
31 694 0.217688205885 Henry Cohn, 2026, needs more optimization.
31 695 0.217922012025 Henry Cohn, 2026, needs more optimization.
31 696 0.218108040765 Henry Cohn, 2026, needs more optimization.
31 697 0.218329132811 Henry Cohn, 2026, needs more optimization.
31 698 0.218575056428 Henry Cohn, 2026, needs more optimization.
31 699 0.218824881811 Henry Cohn, 2026, needs more optimization.
31 700 0.219088911384 Henry Cohn, 2026, needs more optimization.
31 701 0.219319303755 Henry Cohn, 2026, needs more optimization.
31 702 0.219637702849 Henry Cohn, 2026, needs more optimization.
31 703 0.219949437920 Henry Cohn, 2026, needs more optimization.
31 704 0.220228930159 Henry Cohn, 2026, needs more optimization.
31 705 0.220514148946 Henry Cohn, 2026, needs more optimization.
31 706 0.220678514400 Henry Cohn, 2026, needs more optimization.
31 707 0.220925803888 Henry Cohn, 2026, needs more optimization.
31 708 0.221176902224 Henry Cohn, 2026, needs more optimization.
31 709 0.221463718727 Henry Cohn, 2026, needs more optimization.
31 710 0.221768358129 Henry Cohn, 2026, needs more optimization.
31 711 0.222045225414 Henry Cohn, 2026, needs more optimization.
31 712 0.222260865608 Henry Cohn, 2026, needs more optimization.
31 713 0.222544620891 Henry Cohn, 2026, needs more optimization.
31 714 0.222748789700 Henry Cohn, 2026, needs more optimization.
31 715 0.223040660226 Henry Cohn, 2026, needs more optimization.
31 716 0.223296000004 Henry Cohn, 2026, needs more optimization.
31 717 0.223588290853 Henry Cohn, 2026, needs more optimization.
31 718 0.223884036197 Henry Cohn, 2026, needs more optimization.
31 719 0.224147250281 Henry Cohn, 2026, needs more optimization.
31 720 0.224417022403 Henry Cohn, 2026, needs more optimization.
31 721 0.224603196171 Henry Cohn, 2026, needs more optimization.
31 722 0.224883689210 Henry Cohn, 2026, needs more optimization.
31 723 0.225122445942 Henry Cohn, 2026, needs more optimization.
31 724 0.225399306466 Henry Cohn, 2026, needs more optimization.
31 725 0.225502491257 Henry Cohn, 2026, needs more optimization.
31 726 0.225828435538 Henry Cohn, 2026, needs more optimization.
31 727 0.226041191777 Henry Cohn, 2026, needs more optimization.
31 728 0.226234187424 Henry Cohn, 2026, needs more optimization.
31 729 0.226558345786 Henry Cohn, 2026, needs more optimization.
31 730 0.226669306614 Henry Cohn, 2026, needs more optimization.
31 731 0.226944160022 Henry Cohn, 2026, needs more optimization.
31 732 0.227196762025 Henry Cohn, 2026, needs more optimization.
31 733 0.227363110942 Henry Cohn, 2026, needs more optimization.
31 734 0.227664547903 Henry Cohn, 2026, needs more optimization.
31 735 0.227802980533 Henry Cohn, 2026, needs more optimization.
31 736 0.228091972799 Henry Cohn, 2026, needs more optimization.
31 737 0.228310537048 Henry Cohn, 2026, needs more optimization.
31 738 0.228623586888 Henry Cohn, 2026, needs more optimization.
31 739 0.228823921917 Henry Cohn, 2026, needs more optimization.
31 740 0.229058524181 Henry Cohn, 2026, needs more optimization.
31 741 0.229255573373 Henry Cohn, 2026, needs more optimization.
31 742 0.229437158850 Henry Cohn, 2026, needs more optimization.
31 743 0.229747171550 Henry Cohn, 2026, needs more optimization.
31 744 0.230002661000 Henry Cohn, 2026, needs more optimization.
31 745 0.230225334840 Henry Cohn, 2026, needs more optimization.
31 746 0.230448144474 Henry Cohn, 2026, needs more optimization.
31 747 0.230701151389 Henry Cohn, 2026, needs more optimization.
31 748 0.230902709354 Henry Cohn, 2026, needs more optimization.
31 749 0.231042179035 Henry Cohn, 2026, needs more optimization.
31 750 0.231291497268 Henry Cohn, 2026, needs more optimization.
31 751 0.231526555980 Henry Cohn, 2026, needs more optimization.
31 752 0.231757930590 Henry Cohn, 2026, needs more optimization.
31 753 0.231960049164 Henry Cohn, 2026, needs more optimization.
31 754 0.232135308094 Henry Cohn, 2026, needs more optimization.
31 755 0.232301063440 Henry Cohn, 2026, needs more optimization.
31 756 0.232468717492 Henry Cohn, 2026, needs more optimization.
31 757 0.232583207798 Henry Cohn, 2026, needs more optimization.
31 758 0.232801852541 Henry Cohn, 2026, needs more optimization.
31 759 0.233078455256 Henry Cohn, 2026, needs more optimization.
31 760 0.233241838766 Henry Cohn, 2026, needs more optimization.
31 761 0.233482210802 Henry Cohn, 2026, needs more optimization.
31 762 0.233582508809 Henry Cohn, 2026, needs more optimization.
31 763 0.233882281066 Henry Cohn, 2026, needs more optimization.
31 764 0.234041216240 Henry Cohn, 2026, needs more optimization.
31 765 0.234194199435 Henry Cohn, 2026, needs more optimization.
31 766 0.234379326589 Henry Cohn, 2026, needs more optimization.
31 767 0.234580064313 Henry Cohn, 2026, needs more optimization.
31 768 0.234752368010 Henry Cohn, 2026, needs more optimization.
31 769 0.234897542000 Henry Cohn, 2026, needs more optimization.
31 770 0.235034634122 Henry Cohn, 2026, needs more optimization.
31 771 0.235208795460 Henry Cohn, 2026, needs more optimization.
31 772 0.235444411158 Henry Cohn, 2026, needs more optimization.
31 773 0.235660778828 Henry Cohn, 2026, needs more optimization.
31 774 0.235807317199 Henry Cohn, 2026, needs more optimization.
31 775 0.236044806004 Henry Cohn, 2026, needs more optimization.
31 776 0.236173384752 Henry Cohn, 2026, needs more optimization.
31 777 0.236349792869 Henry Cohn, 2026, needs more optimization.
31 778 0.236585209918 Henry Cohn, 2026, needs more optimization.
31 779 0.236754963826 Henry Cohn, 2026, needs more optimization.
31 780 0.236975829107 Henry Cohn, 2026, needs more optimization.
31 781 0.237144560870 Henry Cohn, 2026, needs more optimization.
31 782 0.237367637127 Henry Cohn, 2026, needs more optimization.
31 783 0.237539863483 Henry Cohn, 2026, needs more optimization.
31 784 0.237776766401 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 0.036061152313 Henry Cohn, 2026, needs more optimization.
32 68 0.036921898559 Henry Cohn, 2026.
32 69 0.037652090605 Henry Cohn, 2026.
32 70 0.040286937964 Henry Cohn, 2026, needs more optimization.
32 71 0.043042345588 Henry Cohn, 2026, needs more optimization.
32 72 0.043340506635 Henry Cohn, 2026, needs more optimization.
32 73 0.043649527601 Henry Cohn, 2026, needs more optimization.
32 74 0.044312064799 Henry Cohn, 2026, needs more optimization.
32 75 0.046983087351 Henry Cohn, 2026, needs more optimization.
32 76 0.048916158880 Henry Cohn, 2026, needs more optimization.
32 77 0.049882260350 Henry Cohn, 2026, needs more optimization.
32 78 0.051358756718 Henry Cohn, 2026, needs more optimization.
32 79 0.053166694893 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 0.058225444672 Henry Cohn, 2026, needs more optimization.
32 84 0.059657784392 Henry Cohn, 2026, needs more optimization.
32 85 0.060925480895 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 0.064359806694 Henry Cohn, 2026, needs more optimization.
32 89 0.065582105025 Henry Cohn, 2026, needs more optimization.
32 90 0.066403448391 Henry Cohn, 2026, needs more optimization.
32 91 0.067775431578 Henry Cohn, 2026, needs more optimization.
32 92 0.068708894786 Henry Cohn, 2026, needs more optimization.
32 93 0.069830639940 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 0.072860781694 Henry Cohn, 2026, needs more optimization.
32 97 0.073898376460 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 0.075940923611 Henry Cohn, 2026, needs more optimization.
32 102 0.076146477049 Henry Cohn, 2026, needs more optimization.
32 103 0.076788415496 Henry Cohn, 2026, needs more optimization.
32 104 0.076963158807 Henry Cohn, 2026, needs more optimization.
32 105 0.077085242698 Henry Cohn, 2026, needs more optimization.
32 106 0.077296229610 Henry Cohn, 2026, needs more optimization.
32 107 0.077429832695 Henry Cohn, 2026, needs more optimization.
32 108 0.077645580351 Henry Cohn, 2026, needs more optimization.
32 109 0.077719579583 Henry Cohn, 2026, needs more optimization.
32 110 0.078037359868 Henry Cohn, 2026, needs more optimization.
32 111 0.078890319865 Henry Cohn, 2026, needs more optimization.
32 112 0.079498079455 Henry Cohn, 2026, needs more optimization.
32 113 0.079894749350 Henry Cohn, 2026, needs more optimization.
32 114 0.080452963809 Henry Cohn, 2026, needs more optimization.
32 115 0.080601475173 Henry Cohn, 2026, needs more optimization.
32 116 0.080914990317 Henry Cohn, 2026, needs more optimization.
32 117 0.080994875491 Henry Cohn, 2026, needs more optimization.
32 118 0.081659658551 Henry Cohn, 2026, needs more optimization.
32 119 0.082502674851 Henry Cohn, 2026, needs more optimization.
32 120 0.083465319900 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 0.085680288649 Henry Cohn, 2026, needs more optimization.
32 124 0.086119637915 Henry Cohn, 2026, needs more optimization.
32 125 0.086493345699 Henry Cohn, 2026, needs more optimization.
32 126 0.086721062536 Henry Cohn, 2026, needs more optimization.
32 127 0.088536772434 Henry Cohn, 2026, needs more optimization.
32 128 0.088888373712 Henry Cohn, 2026, needs more optimization.
32 129 0.089213253860 Henry Cohn, 2026, needs more optimization.
32 130 0.089584420213 Henry Cohn, 2026, needs more optimization.
32 131 0.089746228529 Henry Cohn, 2026, needs more optimization.
32 132 0.089801873848 Henry Cohn, 2026, needs more optimization.
32 133 0.090008967229 Henry Cohn, 2026, needs more optimization.
32 134 0.090084545577 Henry Cohn, 2026, needs more optimization.
32 135 0.090191820007 Henry Cohn, 2026, needs more optimization.
32 136 0.090741726049 Henry Cohn, 2026, needs more optimization.
32 137 0.091859633383 Henry Cohn, 2026, needs more optimization.
32 138 0.092898105084 Henry Cohn, 2026, needs more optimization.
32 139 0.093783657395 Henry Cohn, 2026, needs more optimization.
32 140 0.094496703573 Henry Cohn, 2026, needs more optimization.
32 141 0.095596744202 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 0.100379529121 Henry Cohn, 2026, needs more optimization.
32 147 0.101198657582 Henry Cohn, 2026, needs more optimization.
32 148 0.101934590215 Henry Cohn, 2026, needs more optimization.
32 150 0.102443523026 Henry Cohn, 2026, needs more optimization.
32 151 0.102501132502 Henry Cohn, 2026, needs more optimization.
32 152 0.102599994417 Henry Cohn, 2026, needs more optimization.
32 153 0.103097449276 Henry Cohn, 2026, needs more optimization.
32 154 0.103775244423 Henry Cohn, 2026, needs more optimization.
32 155 0.104815744565 Henry Cohn, 2026, needs more optimization.
32 156 0.105837798789 Henry Cohn, 2026, needs more optimization.
32 157 0.106398508784 Henry Cohn, 2026, needs more optimization.
32 158 0.106942418727 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 0.107901730598 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 0.109509351667 Henry Cohn, 2026, needs more optimization.
32 165 0.110129418768 Henry Cohn, 2026, needs more optimization.
32 166 0.110631224937 Henry Cohn, 2026, needs more optimization.
32 167 0.111438960617 Henry Cohn, 2026, needs more optimization.
32 168 0.112094438635 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 0.118177394537 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 0.120418872556 Henry Cohn, 2026, needs more optimization.
32 179 0.121440619030 Henry Cohn, 2026, needs more optimization.
32 180 0.121966363186 Henry Cohn, 2026, needs more optimization.
32 181 0.122754483680 Henry Cohn, 2026, needs more optimization.
32 182 0.123469211836 Henry Cohn, 2026, needs more optimization.
32 183 0.124137146124 Henry Cohn, 2026, needs more optimization.
32 184 0.125019992123 Henry Cohn, 2026, needs more optimization.
32 185 0.125751758172 Henry Cohn, 2026, needs more optimization.
32 186 0.126202970908 Henry Cohn, 2026, needs more optimization.
32 187 0.126981387371 Henry Cohn, 2026, needs more optimization.
32 188 0.127638593883 Henry Cohn, 2026, needs more optimization.
32 190 0.128172541156 Henry Cohn, 2026, needs more optimization.
32 191 0.128226958730 Henry Cohn, 2026, needs more optimization.
32 192 0.128228415628 Henry Cohn, 2026, needs more optimization.
32 194 0.128233231624 Henry Cohn, 2026, needs more optimization.
32 195 0.128236254494 Henry Cohn, 2026, needs more optimization.
32 196 0.128248198248 Henry Cohn, 2026, needs more optimization.
32 197 0.128250132101 Henry Cohn, 2026, needs more optimization.
32 198 0.128295477495 Henry Cohn, 2026, needs more optimization.
32 199 0.128662325021 Henry Cohn, 2026, needs more optimization.
32 200 0.128838437401 Henry Cohn, 2026, needs more optimization.
32 201 0.129268974861 Henry Cohn, 2026, needs more optimization.
32 202 0.129939667090 Henry Cohn, 2026, needs more optimization.
32 203 0.130459321444 Henry Cohn, 2026, needs more optimization.
32 204 0.130630595726 Henry Cohn, 2026, needs more optimization.
32 205 0.130942251325 Henry Cohn, 2026, needs more optimization.
32 206 0.131130963107 Henry Cohn, 2026, needs more optimization.
32 207 0.131237058023 Henry Cohn, 2026, needs more optimization.
32 208 0.131402565471 Henry Cohn, 2026, needs more optimization.
32 209 0.134560054280 Henry Cohn, 2026, needs more optimization.
32 210 0.134993085245 Henry Cohn, 2026, needs more optimization.
32 211 0.135574181636 Henry Cohn, 2026, needs more optimization.
32 212 0.135902304507 Henry Cohn, 2026, needs more optimization.
32 213 0.136448417876 Henry Cohn, 2026, needs more optimization.
32 214 0.136793581058 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 0.138573313858 Henry Cohn, 2026, needs more optimization.
32 218 0.138899808519 Henry Cohn, 2026, needs more optimization.
32 219 0.139255310598 Henry Cohn, 2026, needs more optimization.
32 220 0.139857416233 Henry Cohn, 2026, needs more optimization.
32 221 0.140299646025 Henry Cohn, 2026, needs more optimization.
32 222 0.140459441029 Henry Cohn, 2026, needs more optimization.
32 223 0.140540812005 Henry Cohn, 2026, needs more optimization.
32 224 0.140682048694 Henry Cohn, 2026, needs more optimization.
32 225 0.140757069527 Henry Cohn, 2026, needs more optimization.
32 226 0.140896404705 Henry Cohn, 2026, needs more optimization.
32 227 0.141141531231 Henry Cohn, 2026, needs more optimization.
32 228 0.141248060595 Henry Cohn, 2026, needs more optimization.
32 229 0.141420570263 Henry Cohn, 2026, needs more optimization.
32 230 0.141503615857 Henry Cohn, 2026, needs more optimization.
32 231 0.141750646608 Henry Cohn, 2026, needs more optimization.
32 232 0.141908487656 Henry Cohn, 2026, needs more optimization.
32 233 0.142036355402 Henry Cohn, 2026, needs more optimization.
32 234 0.142131438503 Henry Cohn, 2026, needs more optimization.
32 235 0.142442640134 Henry Cohn, 2026, needs more optimization.
32 236 0.142699837335 Henry Cohn, 2026, needs more optimization.
32 237 0.142777469639 Henry Cohn, 2026, needs more optimization.
32 238 0.142903038419 Henry Cohn, 2026, needs more optimization.
32 239 0.143079482003 Henry Cohn, 2026, needs more optimization.
32 240 0.143627436472 Henry Cohn, 2026, needs more optimization.
32 241 0.143698079386 Henry Cohn, 2026, needs more optimization.
32 242 0.143935552130 Henry Cohn, 2026, needs more optimization.
32 243 0.144095714524 Henry Cohn, 2026, needs more optimization.
32 244 0.144503533098 Henry Cohn, 2026, needs more optimization.
32 245 0.144878213450 Henry Cohn, 2026, needs more optimization.
32 246 0.144958594557 Henry Cohn, 2026, needs more optimization.
32 247 0.145090335821 Henry Cohn, 2026, needs more optimization.
32 248 0.145394704302 Henry Cohn, 2026, needs more optimization.
32 249 0.145592198201 Henry Cohn, 2026, needs more optimization.
32 250 0.145794247680 Henry Cohn, 2026, needs more optimization.
32 251 0.146020443465 Henry Cohn, 2026, needs more optimization.
32 252 0.146061573012 Henry Cohn, 2026, needs more optimization.
32 253 0.146263223355 Henry Cohn, 2026, needs more optimization.
32 254 0.146396195407 Henry Cohn, 2026, needs more optimization.
32 255 0.146486267216 Henry Cohn, 2026, needs more optimization.
32 256 0.146625483128 Henry Cohn, 2026, needs more optimization.
32 257 0.146626601304 Henry Cohn, 2026, needs more optimization.
32 258 0.146743380612 Henry Cohn, 2026, needs more optimization.
32 259 0.146916659768 Henry Cohn, 2026, needs more optimization.
32 260 0.147243432040 Henry Cohn, 2026, needs more optimization.
32 261 0.147519439851 Henry Cohn, 2026, needs more optimization.
32 262 0.147614611608 Henry Cohn, 2026, needs more optimization.
32 263 0.147943904504 Henry Cohn, 2026, needs more optimization.
32 264 0.148069647375 Henry Cohn, 2026, needs more optimization.
32 265 0.148210528605 Henry Cohn, 2026, needs more optimization.
32 266 0.148412357769 Henry Cohn, 2026, needs more optimization.
32 267 0.148498649486 Henry Cohn, 2026, needs more optimization.
32 268 0.148669195514 Henry Cohn, 2026, needs more optimization.
32 269 0.148964324371 Henry Cohn, 2026, needs more optimization.
32 270 0.149162647677 Henry Cohn, 2026, needs more optimization.
32 271 0.149384855569 Henry Cohn, 2026, needs more optimization.
32 272 0.149877327614 Henry Cohn, 2026, needs more optimization.
32 273 0.150478981175 Henry Cohn, 2026, needs more optimization.
32 274 0.150825120472 Henry Cohn, 2026, needs more optimization.
32 275 0.151464121882 Henry Cohn, 2026, needs more optimization.
32 276 0.151954210298 Henry Cohn, 2026, needs more optimization.
32 277 0.152558570525 Henry Cohn, 2026, needs more optimization.
32 278 0.152878973845 Henry Cohn, 2026, needs more optimization.
32 279 0.153141562275 Henry Cohn, 2026, needs more optimization.
32 280 0.153266955526 Henry Cohn, 2026, needs more optimization.
32 281 0.153734089257 Henry Cohn, 2026, needs more optimization.
32 282 0.154007710812 Henry Cohn, 2026, needs more optimization.
32 283 0.154427841265 Henry Cohn, 2026, needs more optimization.
32 284 0.155003692002 Henry Cohn, 2026, needs more optimization.
32 285 0.155424110231 Henry Cohn, 2026, needs more optimization.
32 286 0.155892296885 Henry Cohn, 2026, needs more optimization.
32 287 0.156441813780 Henry Cohn, 2026, needs more optimization.
32 288 0.156727613101 Henry Cohn, 2026, needs more optimization.
32 289 0.157137461560 Henry Cohn, 2026, needs more optimization.
32 290 0.157559149746 Henry Cohn, 2026, needs more optimization.
32 291 0.157719395956 Henry Cohn, 2026, needs more optimization.
32 292 0.158325396065 Henry Cohn, 2026, needs more optimization.
32 293 0.158595847882 Henry Cohn, 2026, needs more optimization.
32 294 0.159046681568 Henry Cohn, 2026, needs more optimization.
32 295 0.159377634900 Henry Cohn, 2026, needs more optimization.
32 296 0.159901421961 Henry Cohn, 2026, needs more optimization.
32 297 0.160138815737 Henry Cohn, 2026, needs more optimization.
32 298 0.160657374775 Henry Cohn, 2026, needs more optimization.
32 299 0.160992657048 Henry Cohn, 2026, needs more optimization.
32 300 0.161008612839 Henry Cohn, 2026, needs more optimization.
32 301 0.161040246722 Henry Cohn, 2026, needs more optimization.
32 302 0.161163650313 Henry Cohn, 2026, needs more optimization.
32 303 0.161338995495 Henry Cohn, 2026, needs more optimization.
32 304 0.161460241596 Henry Cohn, 2026, needs more optimization.
32 305 0.161541276300 Henry Cohn, 2026, needs more optimization.
32 306 0.161542939734 Henry Cohn, 2026, needs more optimization.
32 307 0.161658054040 Henry Cohn, 2026, needs more optimization.
32 308 0.161716581721 Henry Cohn, 2026, needs more optimization.
32 309 0.161799099595 Henry Cohn, 2026, needs more optimization.
32 310 0.161841119368 Henry Cohn, 2026, needs more optimization.
32 311 0.161895934103 Henry Cohn, 2026, needs more optimization.
32 312 0.161954776444 Henry Cohn, 2026, needs more optimization.
32 313 0.162006445326 Henry Cohn, 2026, needs more optimization.
32 314 0.162059519519 Henry Cohn, 2026, needs more optimization.
32 315 0.162103069491 Henry Cohn, 2026, needs more optimization.
32 316 0.162202044060 Henry Cohn, 2026, needs more optimization.
32 317 0.162276667807 Henry Cohn, 2026, needs more optimization.
32 318 0.162349021112 Henry Cohn, 2026, needs more optimization.
32 319 0.162420858941 Henry Cohn, 2026, needs more optimization.
32 320 0.162495503112 Henry Cohn, 2026, needs more optimization.
32 321 0.162556291261 Henry Cohn, 2026, needs more optimization.
32 322 0.162638508318 Henry Cohn, 2026, needs more optimization.
32 323 0.162727110823 Henry Cohn, 2026, needs more optimization.
32 324 0.162836269165 Henry Cohn, 2026, needs more optimization.
32 325 0.163004207308 Henry Cohn, 2026, needs more optimization.
32 326 0.163092839156 Henry Cohn, 2026, needs more optimization.
32 327 0.163190943037 Henry Cohn, 2026, needs more optimization.
32 328 0.163243093763 Henry Cohn, 2026, needs more optimization.
32 329 0.163334202294 Henry Cohn, 2026, needs more optimization.
32 330 0.163406811351 Henry Cohn, 2026, needs more optimization.
32 331 0.163500076598 Henry Cohn, 2026, needs more optimization.
32 332 0.163601724033 Henry Cohn, 2026, needs more optimization.
32 333 0.163751843739 Henry Cohn, 2026, needs more optimization.
32 334 0.163836901445 Henry Cohn, 2026, needs more optimization.
32 335 0.163906235335 Henry Cohn, 2026, needs more optimization.
32 336 0.164033493223 Henry Cohn, 2026, needs more optimization.
32 337 0.164175961415 Henry Cohn, 2026, needs more optimization.
32 338 0.164275480899 Henry Cohn, 2026, needs more optimization.
32 339 0.164476051090 Henry Cohn, 2026, needs more optimization.
32 340 0.164560174652 Henry Cohn, 2026, needs more optimization.
32 341 0.164665064286 Henry Cohn, 2026, needs more optimization.
32 342 0.164725895555 Henry Cohn, 2026, needs more optimization.
32 343 0.164856893713 Henry Cohn, 2026, needs more optimization.
32 344 0.164936491278 Henry Cohn, 2026, needs more optimization.
32 345 0.165006093056 Henry Cohn, 2026, needs more optimization.
32 346 0.165107859734 Henry Cohn, 2026, needs more optimization.
32 347 0.165264700385 Henry Cohn, 2026, needs more optimization.
32 348 0.165379902808 Henry Cohn, 2026, needs more optimization.
32 349 0.165533079999 Henry Cohn, 2026, needs more optimization.
32 350 0.165647137468 Henry Cohn, 2026, needs more optimization.
32 351 0.165775346469 Henry Cohn, 2026, needs more optimization.
32 352 0.165897670947 Henry Cohn, 2026, needs more optimization.
32 353 0.166023816687 Henry Cohn, 2026, needs more optimization.
32 354 0.166211589834 Henry Cohn, 2026, needs more optimization.
32 355 0.166430973509 Henry Cohn, 2026, needs more optimization.
32 356 0.166710512701 Henry Cohn, 2026, needs more optimization.
32 357 0.166726709482 Henry Cohn, 2026, needs more optimization.
32 358 0.166749749008 Henry Cohn, 2026, needs more optimization.
32 359 0.166815149507 Henry Cohn, 2026, needs more optimization.
32 360 0.167081884362 Henry Cohn, 2026, needs more optimization.
32 361 0.167426200291 Henry Cohn, 2026, needs more optimization.
32 362 0.167461622803 Henry Cohn, 2026, needs more optimization.
32 363 0.177296449063 Henry Cohn, 2026, needs more optimization.
32 364 0.177331859708 Henry Cohn, 2026, needs more optimization.
32 365 0.177349678259 Henry Cohn, 2026, needs more optimization.
32 366 0.177376369193 Henry Cohn, 2026, needs more optimization.
32 367 0.177401796186 Henry Cohn, 2026, needs more optimization.
32 368 0.177890691739 Henry Cohn, 2026, needs more optimization.
32 369 0.177899346459 Henry Cohn, 2026, needs more optimization.
32 370 0.177927279868 Henry Cohn, 2026, needs more optimization.
32 371 0.177952853060 Henry Cohn, 2026, needs more optimization.
32 372 0.177976083201 Henry Cohn, 2026, needs more optimization.
32 373 0.178094760840 Henry Cohn, 2026, needs more optimization.
32 374 0.178146392112 Henry Cohn, 2026, needs more optimization.
32 375 0.178193941661 Henry Cohn, 2026, needs more optimization.
32 376 0.178232251818 Henry Cohn, 2026, needs more optimization.
32 377 0.178262505554 Henry Cohn, 2026, needs more optimization.
32 378 0.178283369943 Henry Cohn, 2026, needs more optimization.
32 379 0.178327409939 Henry Cohn, 2026, needs more optimization.
32 380 0.178544975070 Henry Cohn, 2026, needs more optimization.
32 381 0.178544983165 Henry Cohn, 2026, needs more optimization.
32 382 0.178544985887 Henry Cohn, 2026, needs more optimization.
32 383 0.178576512671 Henry Cohn, 2026, needs more optimization.
32 384 0.178579522409 Henry Cohn, 2026, needs more optimization.
32 385 0.178604661512 Henry Cohn, 2026, needs more optimization.
32 386 0.178608724559 Henry Cohn, 2026, needs more optimization.
32 387 0.178633000205 Henry Cohn, 2026, needs more optimization.
32 388 0.178652482845 Henry Cohn, 2026, needs more optimization.
32 389 0.178655646890 Henry Cohn, 2026, needs more optimization.
32 390 0.178681916177 Henry Cohn, 2026, needs more optimization.
32 391 0.178735393965 Henry Cohn, 2026, needs more optimization.
32 392 0.178769740902 Henry Cohn, 2026, needs more optimization.
32 393 0.178846547716 Henry Cohn, 2026, needs more optimization.
32 394 0.178863537251 Henry Cohn, 2026, needs more optimization.
32 395 0.178878126736 Henry Cohn, 2026, needs more optimization.
32 396 0.178958671457 Henry Cohn, 2026, needs more optimization.
32 397 0.179072504799 Henry Cohn, 2026, needs more optimization.
32 398 0.179491348858 Henry Cohn, 2026, needs more optimization.
32 399 0.179620431519 Henry Cohn, 2026, needs more optimization.
32 400 0.180086453635 Henry Cohn, 2026, needs more optimization.
32 401 0.180215201462 Henry Cohn, 2026, needs more optimization.
32 402 0.180456871445 Henry Cohn, 2026, needs more optimization.
32 403 0.180907696744 Henry Cohn, 2026, needs more optimization.
32 404 0.180969230784 Henry Cohn, 2026, needs more optimization.
32 405 0.181337184567 Henry Cohn, 2026, needs more optimization.
32 406 0.181477897908 Henry Cohn, 2026, needs more optimization.
32 407 0.181625553630 Henry Cohn, 2026, needs more optimization.
32 408 0.182314828811 Henry Cohn, 2026, needs more optimization.
32 409 0.182427467766 Henry Cohn, 2026, needs more optimization.
32 410 0.182626083739 Henry Cohn, 2026, needs more optimization.
32 411 0.182929760491 Henry Cohn, 2026, needs more optimization.
32 412 0.183014772829 Henry Cohn, 2026, needs more optimization.
32 413 0.183188430150 Henry Cohn, 2026, needs more optimization.
32 414 0.183307524017 Henry Cohn, 2026, needs more optimization.
32 415 0.183596303240 Henry Cohn, 2026, needs more optimization.
32 416 0.183988723259 Henry Cohn, 2026, needs more optimization.
32 417 0.184159731821 Henry Cohn, 2026, needs more optimization.
32 418 0.184675915951 Henry Cohn, 2026, needs more optimization.
32 419 0.184994357367 Henry Cohn, 2026, needs more optimization.
32 420 0.185154113389 Henry Cohn, 2026, needs more optimization.
32 421 0.185699941430 Henry Cohn, 2026, needs more optimization.
32 422 0.185944770407 Henry Cohn, 2026, needs more optimization.
32 423 0.186177730732 Henry Cohn, 2026, needs more optimization.
32 424 0.186233094151 Henry Cohn, 2026, needs more optimization.
32 425 0.186304116182 Henry Cohn, 2026, needs more optimization.
32 426 0.186381304463 Henry Cohn, 2026, needs more optimization.
32 427 0.186649350661 Henry Cohn, 2026, needs more optimization.
32 428 0.187156364274 Henry Cohn, 2026, needs more optimization.
32 429 0.187449291253 Henry Cohn, 2026, needs more optimization.
32 430 0.187603838433 Henry Cohn, 2026, needs more optimization.
32 431 0.187756849313 Henry Cohn, 2026, needs more optimization.
32 432 0.188235115104 Henry Cohn, 2026, needs more optimization.
32 433 0.188412936944 Henry Cohn, 2026, needs more optimization.
32 434 0.188533277590 Henry Cohn, 2026, needs more optimization.
32 435 0.188639103914 Henry Cohn, 2026, needs more optimization.
32 436 0.188959678276 Henry Cohn, 2026, needs more optimization.
32 437 0.188982492285 Henry Cohn, 2026, needs more optimization.
32 438 0.189124076490 Henry Cohn, 2026, needs more optimization.
32 439 0.189324231523 Henry Cohn, 2026, needs more optimization.
32 440 0.189532395250 Henry Cohn, 2026, needs more optimization.
32 441 0.189672258883 Henry Cohn, 2026, needs more optimization.
32 442 0.189900822841 Henry Cohn, 2026, needs more optimization.
32 443 0.189987915327 Henry Cohn, 2026, needs more optimization.
32 444 0.189997392507 Henry Cohn, 2026, needs more optimization.
32 445 0.190078725039 Henry Cohn, 2026, needs more optimization.
32 446 0.190201296336 Henry Cohn, 2026, needs more optimization.
32 447 0.190463819200 Henry Cohn, 2026, needs more optimization.
32 448 0.190683313031 Henry Cohn, 2026, needs more optimization.
32 449 0.191155918450 Henry Cohn, 2026, needs more optimization.
32 450 0.191282100701 Henry Cohn, 2026, needs more optimization.
32 451 0.191495074441 Henry Cohn, 2026, needs more optimization.
32 452 0.191576874046 Henry Cohn, 2026, needs more optimization.
32 453 0.191659509363 Henry Cohn, 2026, needs more optimization.
32 454 0.191704845876 Henry Cohn, 2026, needs more optimization.
32 455 0.191861009476 Henry Cohn, 2026, needs more optimization.
32 456 0.192091257315 Henry Cohn, 2026, needs more optimization.
32 457 0.192171979647 Henry Cohn, 2026, needs more optimization.
32 458 0.192211983176 Henry Cohn, 2026, needs more optimization.
32 459 0.192489231936 Henry Cohn, 2026, needs more optimization.
32 460 0.192629755920 Henry Cohn, 2026, needs more optimization.
32 461 0.192696328602 Henry Cohn, 2026, needs more optimization.
32 462 0.192915274987 Henry Cohn, 2026, needs more optimization.
32 463 0.193033415145 Henry Cohn, 2026, needs more optimization.
32 464 0.193220004382 Henry Cohn, 2026, needs more optimization.
32 465 0.193270114332 Henry Cohn, 2026, needs more optimization.
32 466 0.193533482901 Henry Cohn, 2026, needs more optimization.
32 467 0.193687131965 Henry Cohn, 2026, needs more optimization.
32 468 0.193776743824 Henry Cohn, 2026, needs more optimization.
32 469 0.194046629409 Henry Cohn, 2026, needs more optimization.
32 470 0.194121139486 Henry Cohn, 2026, needs more optimization.
32 471 0.194171426391 Henry Cohn, 2026, needs more optimization.
32 472 0.194193295816 Henry Cohn, 2026, needs more optimization.
32 473 0.194392808262 Henry Cohn, 2026, needs more optimization.
32 474 0.194463204140 Henry Cohn, 2026, needs more optimization.
32 475 0.194505407736 Henry Cohn, 2026, needs more optimization.
32 476 0.194555464974 Henry Cohn, 2026, needs more optimization.
32 477 0.194738904849 Henry Cohn, 2026, needs more optimization.
32 478 0.194840092443 Henry Cohn, 2026, needs more optimization.
32 479 0.194948223692 Henry Cohn, 2026, needs more optimization.
32 528 0.195121951220 Henry Cohn, 2026.
41⁢x−8
32 529 0.199431859062 Henry Cohn, 2026, needs more optimization.
32 530 0.199436751407 Henry Cohn, 2026, needs more optimization.
32 531 0.199447344544 Henry Cohn, 2026, needs more optimization.
32 532 0.199449515476 Henry Cohn, 2026, needs more optimization.
32 533 0.199451414322 Henry Cohn, 2026, needs more optimization.
32 534 0.199454132896 Henry Cohn, 2026, needs more optimization.
32 535 0.199458156343 Henry Cohn, 2026, needs more optimization.
32 536 0.199461831874 Henry Cohn, 2026, needs more optimization.
32 537 0.199479527259 Henry Cohn, 2026, needs more optimization.
32 538 0.199484920454 Henry Cohn, 2026, needs more optimization.
32 539 0.199514389083 Henry Cohn, 2026, needs more optimization.
32 540 0.199517716943 Henry Cohn, 2026, needs more optimization.
32 541 0.199521620135 Henry Cohn, 2026, needs more optimization.
32 542 0.199618068302 Henry Cohn, 2026, needs more optimization.
32 543 0.199624969938 Henry Cohn, 2026, needs more optimization.
32 544 0.199653799310 Henry Cohn, 2026, needs more optimization.
32 545 0.199656135176 Henry Cohn, 2026, needs more optimization.
32 546 0.199659740871 Henry Cohn, 2026, needs more optimization.
32 547 0.199662268004 Henry Cohn, 2026, needs more optimization.
32 548 0.199670692982 Henry Cohn, 2026, needs more optimization.
32 549 0.199681097163 Henry Cohn, 2026, needs more optimization.
32 550 0.199684046406 Henry Cohn, 2026, needs more optimization.
32 551 0.199687699077 Henry Cohn, 2026, needs more optimization.
32 552 0.199690659694 Henry Cohn, 2026, needs more optimization.
32 553 0.199692729875 Henry Cohn, 2026, needs more optimization.
32 554 0.199696355898 Henry Cohn, 2026, needs more optimization.
32 555 0.199706455516 Henry Cohn, 2026, needs more optimization.
32 556 0.199709937456 Henry Cohn, 2026, needs more optimization.
32 557 0.199718303651 Henry Cohn, 2026, needs more optimization.
32 558 0.199721777800 Henry Cohn, 2026, needs more optimization.
32 559 0.199726383870 Henry Cohn, 2026, needs more optimization.
32 560 0.199729776685 Henry Cohn, 2026, needs more optimization.
32 561 0.199732600370 Henry Cohn, 2026, needs more optimization.
32 562 0.199736348253 Henry Cohn, 2026, needs more optimization.
32 563 0.199740383628 Henry Cohn, 2026, needs more optimization.
32 564 0.199745819261 Henry Cohn, 2026, needs more optimization.
32 565 0.199754080500 Henry Cohn, 2026, needs more optimization.
32 566 0.199756691506 Henry Cohn, 2026, needs more optimization.
32 567 0.199758509809 Henry Cohn, 2026, needs more optimization.
32 568 0.199759999442 Henry Cohn, 2026, needs more optimization.
32 569 0.199762412290 Henry Cohn, 2026, needs more optimization.
32 570 0.199765878061 Henry Cohn, 2026, needs more optimization.
32 571 0.199770590957 Henry Cohn, 2026, needs more optimization.
32 572 0.199773657912 Henry Cohn, 2026, needs more optimization.
32 573 0.199777070714 Henry Cohn, 2026, needs more optimization.
32 574 0.199803357082 Henry Cohn, 2026, needs more optimization.
32 575 0.199807689003 Henry Cohn, 2026, needs more optimization.
32 576 0.199813697357 Henry Cohn, 2026, needs more optimization.
32 577 0.199817684777 Henry Cohn, 2026, needs more optimization.
32 578 0.199824624122 Henry Cohn, 2026, needs more optimization.
32 579 0.199827165677 Henry Cohn, 2026, needs more optimization.
32 580 0.199831514521 Henry Cohn, 2026, needs more optimization.
32 581 0.199834217332 Henry Cohn, 2026, needs more optimization.
32 582 0.199839798743 Henry Cohn, 2026, needs more optimization.
32 583 0.199860232759 Henry Cohn, 2026, needs more optimization.
32 584 0.199862379697 Henry Cohn, 2026, needs more optimization.
32 585 0.199864297432 Henry Cohn, 2026, needs more optimization.
32 586 0.199867460461 Henry Cohn, 2026, needs more optimization.
32 587 0.199869694003 Henry Cohn, 2026, needs more optimization.
32 588 0.199872222796 Henry Cohn, 2026, needs more optimization.
32 589 0.199874264211 Henry Cohn, 2026, needs more optimization.
32 590 0.199877923205 Henry Cohn, 2026, needs more optimization.
32 591 0.199897320322 Henry Cohn, 2026, needs more optimization.
32 592 0.199901134588 Henry Cohn, 2026, needs more optimization.
32 593 0.199903897587 Henry Cohn, 2026, needs more optimization.
32 594 0.199905484174 Henry Cohn, 2026, needs more optimization.
32 595 0.199909006440 Henry Cohn, 2026, needs more optimization.
32 596 0.199925706924 Henry Cohn, 2026, needs more optimization.
32 597 0.199977842161 Henry Cohn, 2026, needs more optimization.
32 598 0.199978339022 Henry Cohn, 2026, needs more optimization.
32 599 0.199978706126 Henry Cohn, 2026, needs more optimization.
32 601 0.199978724722 Henry Cohn, 2026, needs more optimization.
32 602 0.199980744190 Henry Cohn, 2026, needs more optimization.
32 603 0.199981675661 Henry Cohn, 2026, needs more optimization.
32 604 0.199982564176 Henry Cohn, 2026, needs more optimization.
32 605 0.199982864227 Henry Cohn, 2026, needs more optimization.
32 607 0.199983232760 Henry Cohn, 2026, needs more optimization.
32 608 0.199985289871 Henry Cohn, 2026, needs more optimization.
32 609 0.199986441542 Henry Cohn, 2026, needs more optimization.
32 610 0.199986700999 Henry Cohn, 2026, needs more optimization.
32 611 0.199988008718 Henry Cohn, 2026, needs more optimization.
32 612 0.199989656041 Henry Cohn, 2026, needs more optimization.
32 613 0.199989875093 Henry Cohn, 2026, needs more optimization.
32 614 0.199990825107 Henry Cohn, 2026, needs more optimization.
32 615 0.199991368944 Henry Cohn, 2026, needs more optimization.
32 616 0.199993104067 Henry Cohn, 2026, needs more optimization.
32 617 0.199996443438 Henry Cohn, 2026, needs more optimization.
32 618 0.199997074498 Henry Cohn, 2026, needs more optimization.
32 619 0.199997545555 Henry Cohn, 2026, needs more optimization.
32 620 0.199998191059 Henry Cohn, 2026, needs more optimization.
32 704 0.2 Henry Cohn, 2026.
5⁢x−1
32 705 0.209423885673 Henry Cohn, 2026, needs more optimization.
32 706 0.212811478400 Henry Cohn, 2026, needs more optimization.
32 707 0.212885087047 Henry Cohn, 2026, needs more optimization.
32 708 0.213156030882 Henry Cohn, 2026, needs more optimization.
32 709 0.213267931456 Henry Cohn, 2026, needs more optimization.
32 710 0.214374261015 Henry Cohn, 2026, needs more optimization.
32 711 0.214611956197 Henry Cohn, 2026, needs more optimization.
32 712 0.214687762422 Henry Cohn, 2026, needs more optimization.
32 713 0.214811424730 Henry Cohn, 2026, needs more optimization.
32 714 0.214978416692 Henry Cohn, 2026, needs more optimization.
32 715 0.215010987654 Henry Cohn, 2026, needs more optimization.
32 716 0.215261969909 Henry Cohn, 2026, needs more optimization.
32 717 0.215350046951 Henry Cohn, 2026, needs more optimization.
32 718 0.216550659862 Henry Cohn, 2026, needs more optimization.
32 719 0.216604579288 Henry Cohn, 2026, needs more optimization.
32 720 0.216776306813 Henry Cohn, 2026, needs more optimization.
32 721 0.216825373108 Henry Cohn, 2026, needs more optimization.
32 722 0.217195437270 Henry Cohn, 2026, needs more optimization.
32 723 0.217281605368 Henry Cohn, 2026, needs more optimization.
32 724 0.217746970844 Henry Cohn, 2026, needs more optimization.
32 725 0.217795858888 Henry Cohn, 2026, needs more optimization.
32 726 0.218145803870 Henry Cohn, 2026, needs more optimization.
32 727 0.218200707650 Henry Cohn, 2026, needs more optimization.
32 728 0.218222674715 Henry Cohn, 2026, needs more optimization.
32 729 0.218302463568 Henry Cohn, 2026, needs more optimization.
32 730 0.218351989295 Henry Cohn, 2026, needs more optimization.
32 731 0.219225775519 Henry Cohn, 2026, needs more optimization.
32 732 0.219419712269 Henry Cohn, 2026, needs more optimization.
32 733 0.219511767072 Henry Cohn, 2026, needs more optimization.
32 734 0.219764051022 Henry Cohn, 2026, needs more optimization.
32 735 0.219794551782 Henry Cohn, 2026, needs more optimization.
32 736 0.220189206177 Henry Cohn, 2026, needs more optimization.
32 737 0.220285978350 Henry Cohn, 2026, needs more optimization.
32 738 0.220500622438 Henry Cohn, 2026, needs more optimization.
32 739 0.220625221021 Henry Cohn, 2026, needs more optimization.
32 740 0.220698823057 Henry Cohn, 2026, needs more optimization.
32 741 0.221558178515 Henry Cohn, 2026, needs more optimization.
32 742 0.221661186966 Henry Cohn, 2026, needs more optimization.
32 743 0.221778956520 Henry Cohn, 2026, needs more optimization.
32 744 0.221824893755 Henry Cohn, 2026, needs more optimization.
32 745 0.221987034674 Henry Cohn, 2026, needs more optimization.
32 746 0.222032173289 Henry Cohn, 2026, needs more optimization.
32 747 0.222191906995 Henry Cohn, 2026, needs more optimization.
32 748 0.222238774500 Henry Cohn, 2026, needs more optimization.
32 749 0.222304762835 Henry Cohn, 2026, needs more optimization.
32 750 0.223439547683 Henry Cohn, 2026, needs more optimization.
32 751 0.223500514519 Henry Cohn, 2026, needs more optimization.
32 752 0.223615546793 Henry Cohn, 2026, needs more optimization.
32 753 0.223747072909 Henry Cohn, 2026, needs more optimization.
32 754 0.223795922628 Henry Cohn, 2026, needs more optimization.
32 755 0.223965788081 Henry Cohn, 2026, needs more optimization.
32 756 0.224029882037 Henry Cohn, 2026, needs more optimization.
32 757 0.224192082467 Henry Cohn, 2026, needs more optimization.
32 758 0.224419431216 Henry Cohn, 2026, needs more optimization.
32 759 0.225229437702 Henry Cohn, 2026, needs more optimization.
32 760 0.225298685933 Henry Cohn, 2026, needs more optimization.
32 761 0.225459625532 Henry Cohn, 2026, needs more optimization.
32 762 0.225475678240 Henry Cohn, 2026, needs more optimization.
32 763 0.225640798778 Henry Cohn, 2026, needs more optimization.
32 764 0.225693332294 Henry Cohn, 2026, needs more optimization.
32 765 0.225735478101 Henry Cohn, 2026, needs more optimization.
32 766 0.226375287841 Henry Cohn, 2026, needs more optimization.
32 767 0.226492504458 Henry Cohn, 2026, needs more optimization.
32 768 0.226554473579 Henry Cohn, 2026, needs more optimization.
32 769 0.226743043792 Henry Cohn, 2026, needs more optimization.
32 770 0.226797330657 Henry Cohn, 2026, needs more optimization.
32 771 0.227791055671 Henry Cohn, 2026, needs more optimization.
32 772 0.227813728598 Henry Cohn, 2026, needs more optimization.
32 773 0.227944376818 Henry Cohn, 2026, needs more optimization.
32 774 0.227986485454 Henry Cohn, 2026, needs more optimization.
32 775 0.227996873237 Henry Cohn, 2026, needs more optimization.
32 776 0.228186804408 Henry Cohn, 2026, needs more optimization.
32 777 0.228394002716 Henry Cohn, 2026, needs more optimization.
32 778 0.228416326323 Henry Cohn, 2026, needs more optimization.
32 779 0.228671785648 Henry Cohn, 2026, needs more optimization.
32 780 0.228813406441 Henry Cohn, 2026, needs more optimization.
32 781 0.228895054916 Henry Cohn, 2026, needs more optimization.
32 782 0.228962007445 Henry Cohn, 2026, needs more optimization.
32 783 0.228999071869 Henry Cohn, 2026, needs more optimization.
32 784 0.229103741653 Henry Cohn, 2026, needs more optimization.
32 785 0.229258858667 Henry Cohn, 2026, needs more optimization.
32 786 0.231579457109 Henry Cohn, 2026, needs more optimization.
32 787 0.231659503878 Henry Cohn, 2026, needs more optimization.
32 788 0.231659608767 Henry Cohn, 2026, needs more optimization.
32 789 0.231844901661 Henry Cohn, 2026, needs more optimization.
32 790 0.231876966804 Henry Cohn, 2026, needs more optimization.
32 791 0.232004500694 Henry Cohn, 2026, needs more optimization.
32 792 0.232079510424 Henry Cohn, 2026, needs more optimization.
32 793 0.232122197420 Henry Cohn, 2026, needs more optimization.
32 794 0.232176331714 Henry Cohn, 2026, needs more optimization.
32 795 0.232303306135 Henry Cohn, 2026, needs more optimization.
32 796 0.232410543105 Henry Cohn, 2026, needs more optimization.
32 797 0.232462187932 Henry Cohn, 2026, needs more optimization.
32 798 0.232620659902 Henry Cohn, 2026, needs more optimization.
32 799 0.232733733989 Henry Cohn, 2026, needs more optimization.
32 800 0.232891775062 Henry Cohn, 2026, needs more optimization.
32 801 0.232994675353 Henry Cohn, 2026, needs more optimization.
32 802 0.233196684116 Henry Cohn, 2026, needs more optimization.
32 803 0.233312253648 Henry Cohn, 2026, needs more optimization.
32 804 0.233475205810 Henry Cohn, 2026, needs more optimization.
32 805 0.233615625511 Henry Cohn, 2026, needs more optimization.
32 806 0.233767048781 Henry Cohn, 2026, needs more optimization.
32 807 0.233914963922 Henry Cohn, 2026, needs more optimization.
32 808 0.234138879665 Henry Cohn, 2026, needs more optimization.
32 809 0.234267057416 Henry Cohn, 2026, needs more optimization.
32 810 0.234478622471 Henry Cohn, 2026, needs more optimization.
32 811 0.234639870498 Henry Cohn, 2026, needs more optimization.
32 812 0.234784246116 Henry Cohn, 2026, needs more optimization.
32 813 0.234882545086 Henry Cohn, 2026, needs more optimization.
32 814 0.235059737939 Henry Cohn, 2026, needs more optimization.
32 815 0.235230260608 Henry Cohn, 2026, needs more optimization.
32 816 0.235347549633 Henry Cohn, 2026, needs more optimization.
32 817 0.235587043851 Henry Cohn, 2026, needs more optimization.
32 818 0.235717562561 Henry Cohn, 2026, needs more optimization.
32 819 0.235852132358 Henry Cohn, 2026, needs more optimization.
32 820 0.235978368281 Henry Cohn, 2026, needs more optimization.
32 821 0.236125009874 Henry Cohn, 2026, needs more optimization.
32 822 0.236297277418 Henry Cohn, 2026, needs more optimization.
32 823 0.236420209173 Henry Cohn, 2026, needs more optimization.
32 824 0.236533430232 Henry Cohn, 2026, needs more optimization.
32 825 0.236735283022 Henry Cohn, 2026, needs more optimization.
32 826 0.236880670701 Henry Cohn, 2026, needs more optimization.
32 827 0.237018616814 Henry Cohn, 2026, needs more optimization.
32 828 0.237214433497 Henry Cohn, 2026, needs more optimization.
32 829 0.237429748990 Henry Cohn, 2026, needs more optimization.
32 830 0.237550694320 Henry Cohn, 2026, needs more optimization.
32 831 0.237712270202 Henry Cohn, 2026, needs more optimization.
32 832 0.237776898053 Henry Cohn, 2026, needs more optimization.
32 833 0.237981391417 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