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.
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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.
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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.
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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.
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3 299 0.977214468409 Henry Cohn, 2025.
3 300 0.977219217071 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 301 0.977392313268 Henry Cohn, 2024.
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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.
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3 387 0.982346497568 Henry Cohn, 2024.
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3 389 0.982417056387 Henry Cohn, 2026.
3 390 0.982501966288 Henry Cohn, 2026.
3 391 0.982555955538 Henry Cohn, 2024.
3 392 0.982591195901 Henry Cohn, 2024.
3 393 0.982649357699 Henry Cohn, 2024.
3 394 0.982692375827 Henry Cohn, 2024.
3 395 0.982725465540 Henry Cohn, 2024.
3 396 0.982767271242 Henry Cohn, 2024.
3 397 0.982799147942 Henry Cohn, 2024.
3 398 0.982821049056 Henry Cohn, 2024.
3 399 0.982857394032 Henry Cohn, 2024.
3 400 0.982915172693 Henry Cohn, 2024.
3 401 0.982950664530 Henry Cohn, 2024.
3 402 0.982983355551 Henry Cohn, 2024.
3 403 0.983049964328 Henry Cohn, 2024.
3 404 0.983111162319 Henry Cohn, 2024.
3 405 0.983168565133 Henry Cohn, 2024.
3 406 0.983206265163 Henry Cohn, 2024.
3 407 0.983247933087 Henry Cohn, 2024.
3 408 0.983288123210 Henry Cohn, 2024.
3 409 0.983324857501 Henry Cohn, 2024.
3 410 0.983356947085 Henry Cohn, 2024.
3 411 0.983397760620 Henry Cohn, 2024.
3 412 0.983428600189 Henry Cohn, 2024.
3 413 0.983461427167 Henry Cohn, 2024.
3 414 0.983495155996 Henry Cohn, 2024.
3 415 0.983545319874 Henry Cohn, 2024.
3 416 0.983572356049 Henry Cohn, 2024.
3 417 0.983606629507 Henry Cohn, 2024.
3 418 0.983668285529 Henry Cohn, 2024.
3 419 0.983709311243 Henry Cohn, 2024.
3 420 0.983735772266 Henry Cohn, 2024.
3 421 0.983801876824 Henry Cohn, 2024.
3 422 0.983837084033 Henry Cohn, 2024.
3 423 0.983879327689 Henry Cohn, 2024.
3 424 0.983915009758 Henry Cohn, 2024.
3 425 0.983947724258 Henry Cohn, 2024.
3 426 0.983967656850 Henry Cohn, 2024.
3 427 0.984017759902 Henry Cohn, 2024.
3 428 0.984060532882 Henry Cohn, 2024.
3 429 0.984101619024 Henry Cohn, 2024.
3 430 0.984134891966 Henry Cohn, 2024.
3 431 0.984165514392 Henry Cohn, 2024.
3 432 0.984201636678 Henry Cohn, 2024.
3 433 0.984246511178 Henry Cohn, 2024.
3 434 0.984282456244 Henry Cohn, 2024.
3 435 0.984322511170 Henry Cohn, 2024.
3 436 0.984359381087 Henry Cohn, 2024.
3 437 0.984376596212 Henry Cohn, 2024.
3 438 0.984419779873 Henry Cohn, 2024.
3 439 0.984459277522 Henry Cohn, 2024.
3 440 0.984472421765 Henry Cohn, 2024.
3 441 0.984527980944 Henry Cohn, 2024.
3 442 0.984559589051 Henry Cohn, 2024.
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 0.984813716313 Henry Cohn, 2024.
3 450 0.984846922701 Henry Cohn, 2024.
3 451 0.984872959879 Henry Cohn, 2024.
3 452 0.984911000119 Henry Cohn, 2024.
3 453 0.984942286924 Henry Cohn, 2024.
3 454 0.984966631268 Henry Cohn, 2024.
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 0.985126768610 Henry Cohn, 2024.
3 460 0.985147680864 Henry Cohn, 2026.
3 461 0.985184258024 Henry Cohn, 2026.
3 462 0.985225068423 Henry Cohn, 2024.
3 463 0.985261648362 Henry Cohn, 2024.
3 464 0.985297019485 Henry Cohn, 2024.
3 465 0.985321750708 Henry Cohn, 2024.
3 466 0.985359897849 Henry Cohn, 2024.
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 0.985527599242 Henry Cohn, 2024.
3 473 0.985558412595 Henry Cohn, 2024.
3 474 0.985607101360 Henry Cohn, 2024.
3 475 0.985630320536 Henry Cohn, 2024.
3 476 0.985635213765 Henry Cohn, 2026.
3 477 0.985650812954 Henry Cohn, 2026.
3 478 0.985679876224 Henry Cohn, 2026.
3 479 0.985721775338 Henry Cohn, 2024.
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 0.985842699690 Henry Cohn, 2024.
3 483 0.985872483761 Henry Cohn, 2024.
3 484 0.985900122939 Henry Cohn, 2024.
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 0.986063292599 Henry Cohn, 2024.
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3 492 0.986121929372 Henry Cohn, 2024.
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3 500 0.986349227234 Henry Cohn, 2024.
3 501 0.986372404028 Henry Cohn, 2024.
3 502 0.986403542281 Henry Cohn, 2024.
3 503 0.986428428291 Henry Cohn, 2024.
3 504 0.986455469484 Henry Cohn, 2024.
3 505 0.986479196655 Henry Cohn, 2024.
3 506 0.986508558172 Henry Cohn, 2024.
3 507 0.986527855040 Henry Cohn, 2024.
3 508 0.986557386755 Henry Cohn, 2026.
3 510 0.986562950498 Henry Cohn, 2025.
3 511 0.986616701042 Henry Cohn, 2026.
3 512 0.986668364004 Henry Cohn, 2024.
3 513 0.986700077118 Henry Cohn, 2024.
3 514 0.986720532797 Henry Cohn, 2024.
3 515 0.986749064827 Henry Cohn, 2024.
3 516 0.986773903019 Henry Cohn, 2024.
3 517 0.986799492641 Henry Cohn, 2024.
3 518 0.986819754209 Henry Cohn, 2024.
3 519 0.986848175284 Henry Cohn, 2024.
3 520 0.986876145782 Henry Cohn, 2024.
3 521 0.986900278325 Henry Cohn, 2024.
3 522 0.986922575232 Henry Cohn, 2024.
3 523 0.986951778704 Henry Cohn, 2024.
3 524 0.986971561505 Henry Cohn, 2024.
3 525 0.986995199336 Henry Cohn, 2024.
3 526 0.987019236077 Henry Cohn, 2024.
3 527 0.987049033347 Henry Cohn, 2024.
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 0.987234674397 Henry Cohn, 2024.
3 536 0.987259191622 Henry Cohn, 2024.
3 537 0.987271183218 Henry Cohn, 2024.
3 538 0.987304975991 Henry Cohn, 2024.
3 539 0.987336486625 Henry Cohn, 2024.
3 540 0.987351430022 Henry Cohn, 2024.
3 541 0.987374329958 Henry Cohn, 2026.
3 542 0.987388996662 Henry Cohn, 2024.
3 543 0.987425682607 Henry Cohn, 2024.
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 0.987583836919 Henry Cohn, 2024.
3 551 0.987606449640 Henry Cohn, 2024.
3 552 0.987622742921 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
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 0.987735307385 Henry Cohn, 2024.
3 558 0.987761309685 Henry Cohn, 2024.
3 559 0.987780703660 Henry Cohn, 2026.
3 560 0.987804065628 Henry Cohn, 2024.
3 561 0.987825037070 Henry Cohn, 2024.
3 562 0.987842915448 Henry Cohn, 2024.
3 563 0.987867088796 Henry Cohn, 2024.
3 564 0.987888189116 Henry Cohn, 2024.
3 565 0.987910412219 Henry Cohn, 2024.
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 0.988010035988 Henry Cohn, 2024.
3 571 0.988036994032 Henry Cohn, 2024.
3 572 0.988045143812 Henry Cohn, 2025.
3 573 0.988071465154 Henry Cohn, 2024.
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 0.988371988004 Henry Cohn, 2024.
3 589 0.988390327285 Henry Cohn, 2024.
3 590 0.988413417033 Henry Cohn, 2024.
3 591 0.988431548471 Henry Cohn, 2024.
3 592 0.988452036069 Henry Cohn, 2024.
3 593 0.988468804433 Henry Cohn, 2024.
3 594 0.988492055682 Henry Cohn, 2024.
3 595 0.988509243514 Henry Cohn, 2024.
3 596 0.988527025270 Henry Cohn, 2024.
3 597 0.988546258113 Henry Cohn, 2024.
3 598 0.988563711650 Henry Cohn, 2024.
3 599 0.988581647683 Henry Cohn, 2024.
3 600 0.988601034993 Henry Cohn, 2024.
3 601 0.988621946438 Henry Cohn, 2024.
3 602 0.988641437112 Henry Cohn, 2024.
3 603 0.988656942485 Henry Cohn, 2024.
3 604 0.988675027867 Henry Cohn, 2024.
3 605 0.988700462515 Henry Cohn, 2024.
3 606 0.988712847782 Henry Cohn, 2024.
3 607 0.988727431487 Henry Cohn, 2024.
3 608 0.988753812095 Henry Cohn, 2026.
3 609 0.988760157529 Henry Cohn, 2024.
3 610 0.988787545762 Henry Cohn, 2026.
3 611 0.988803996797 Henry Cohn, 2024.
3 612 0.988822833992 Henry Cohn, 2024.
3 613 0.988842455232 Henry Cohn, 2024.
3 614 0.988857096430 Henry Cohn, 2024.
3 615 0.988875778474 Henry Cohn, 2024.
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 0.989000876941 Henry Cohn, 2024.
3 623 0.989012818314 Henry Cohn, 2024.
3 624 0.989034528790 Henry Cohn, 2024.
3 625 0.989054157149 Henry Cohn, 2024.
3 626 0.989070144515 Henry Cohn, 2024.
3 627 0.989088135354 Henry Cohn, 2024.
3 628 0.989105386471 Henry Cohn, 2024.
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 0.989202420209 Henry Cohn, 2024.
3 635 0.989219790718 Henry Cohn, 2024.
3 636 0.989242196163 Henry Cohn, 2024.
3 637 0.989258990501 Henry Cohn, 2024.
3 638 0.989267204518 Henry Cohn, 2024.
3 639 0.989290088613 Henry Cohn, 2024.
3 640 0.989301986015 Henry Cohn, 2024.
3 641 0.989321411266 Henry Cohn, 2024.
3 642 0.989332573182 Henry Cohn, 2024.
3 643 0.989352773976 Henry Cohn, 2024.
3 644 0.989371069478 Henry Cohn, 2024.
3 645 0.989382485431 Henry Cohn, 2024.
3 646 0.989398690989 Henry Cohn, 2024.
3 647 0.989413119239 Henry Cohn, 2024.
3 648 0.989433849301 Henry Cohn, 2024.
3 649 0.989453044562 Henry Cohn, 2024.
3 650 0.989463904615 Henry Cohn, 2024.
3 651 0.989485039605 Henry Cohn, 2024.
3 652 0.989500668198 Henry Cohn, 2024.
3 653 0.989517659733 Henry Cohn, 2024.
3 654 0.989528389272 Henry Cohn, 2024.
3 655 0.989547002612 Henry Cohn, 2024.
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 0.989626363395 Henry Cohn, 2024.
3 661 0.989640005006 Henry Cohn, 2024.
3 662 0.989658469367 Henry Cohn, 2024.
3 663 0.989668542979 Henry Cohn, 2024.
3 664 0.989681374062 Henry Cohn, 2024.
3 665 0.989693744147 Henry Cohn, 2026.
3 666 0.989717535361 Henry Cohn, 2024.
3 667 0.989731743795 Henry Cohn, 2024.
3 668 0.989745751462 Henry Cohn, 2024.
3 669 0.989761473114 Henry Cohn, 2024.
3 670 0.989765777159 Henry Cohn, 2024.
3 671 0.989792890413 Henry Cohn, 2024.
3 672 0.989799643833 Henry Cohn, 2024.
3 673 0.989818330488 Henry Cohn, 2024.
3 674 0.989833722485 Henry Cohn, 2024.
3 675 0.989852452169 Henry Cohn, 2024.
3 676 0.989861529212 Henry Cohn, 2024.
3 678 0.989879779829 Henry Cohn, 2024.
3 679 0.989905728538 Henry Cohn, 2024.
3 680 0.989921085378 Henry Cohn, 2024.
3 681 0.989936920244 Henry Cohn, 2024.
3 682 0.989955559541 Henry Cohn, 2024.
3 683 0.989969934194 Henry Cohn, 2026.
3 684 0.989976827933 Henry Cohn, 2024.
3 685 0.990001449211 Henry Cohn, 2024.
3 686 0.990006418271 Henry Cohn, 2024.
3 687 0.990025982355 Henry Cohn, 2024.
3 688 0.990037853003 Henry Cohn, 2024.
3 689 0.990051064090 Henry Cohn, 2024.
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 0.990079194399 Henry Cohn, 2026.
3 694 0.990105158155 Henry Cohn, 2026.
3 695 0.990114990349 Henry Cohn, 2026.
3 696 0.990139079126 Henry Cohn, 2026.
3 697 0.990164610569 Henry Cohn, 2024.
3 698 0.990178131415 Henry Cohn, 2024.
3 699 0.990196847589 Henry Cohn, 2024.
3 700 0.990204754056 Henry Cohn, 2024.
3 702 0.990207507930 Henry Cohn, 2025.
3 703 0.990226834173 Henry Cohn, 2026.
3 704 0.990247640312 Henry Cohn, 2026.
3 705 0.990264016668 Henry Cohn, 2026.
3 706 0.990280269273 Henry Cohn, 2026.
3 707 0.990307749113 Henry Cohn, 2024.
3 708 0.990313284691 Henry Cohn, 2024.
3 709 0.990331708341 Henry Cohn, 2024.
3 711 0.990345295659 Henry Cohn, 2024.
3 712 0.990368376224 Henry Cohn, 2024.
3 713 0.990383651488 Henry Cohn, 2024.
3 714 0.990391904853 Henry Cohn, 2024.
3 715 0.990399847263 Henry Cohn, 2026.
3 716 0.990424201178 Henry Cohn, 2024.
3 717 0.990437124471 Henry Cohn, 2024.
3 718 0.990448237688 Henry Cohn, 2024.
3 719 0.990461529899 Henry Cohn, 2024.
3 720 0.990474919274 Henry Cohn, 2024.
3 721 0.990485951013 Henry Cohn, 2026.
3 722 0.990499809958 Henry Cohn, 2024.
3 723 0.990511316358 Henry Cohn, 2026.
3 724 0.990532198847 Henry Cohn, 2024.
3 725 0.990534529638 Henry Cohn, 2024.
3 726 0.990553141663 Henry Cohn, 2024.
3 727 0.990566965324 Henry Cohn, 2024.
3 728 0.990571284239 Henry Cohn, 2024.
3 729 0.990587255137 Henry Cohn, 2024.
3 730 0.990603287439 Henry Cohn, 2024.
3 731 0.990612626443 Henry Cohn, 2024.
3 732 0.990621413211 Henry Cohn, 2025.
3 733 0.990638975131 Henry Cohn, 2026.
3 734 0.990653485475 Henry Cohn, 2026.
3 735 0.990668792728 Henry Cohn, 2024.
3 736 0.990681732803 Henry Cohn, 2024.
3 737 0.990695306177 Henry Cohn, 2024.
3 738 0.990704677084 Henry Cohn, 2024.
3 739 0.990713057195 Henry Cohn, 2024.
3 740 0.990728865941 Henry Cohn, 2024.
3 741 0.990742245221 Henry Cohn, 2024.
3 742 0.990755361153 Henry Cohn, 2024.
3 743 0.990770576230 Henry Cohn, 2024.
3 744 0.990780046428 Henry Cohn, 2024.
3 745 0.990791226838 Henry Cohn, 2024.
3 746 0.990801952938 Henry Cohn, 2026.
3 747 0.990816878553 Henry Cohn, 2024.
3 748 0.990830906878 Henry Cohn, 2024.
3 749 0.990838053202 Henry Cohn, 2024.
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 0.990872395915 Henry Cohn, 2024.
3 753 0.990883514545 Henry Cohn, 2024.
3 754 0.990901296816 Henry Cohn, 2024.
3 755 0.990905033119 Henry Cohn, 2024.
3 756 0.990922227516 Henry Cohn, 2024.
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 0.990976123095 Henry Cohn, 2024.
3 762 0.990993252010 Henry Cohn, 2024.
3 763 0.991002546962 Henry Cohn, 2024.
3 764 0.991020776255 Henry Cohn, 2024.
3 765 0.991029933301 Henry Cohn, 2024.
3 766 0.991038039796 Henry Cohn, 2024.
3 767 0.991054850991 Henry Cohn, 2024.
3 768 0.991063858891 Henry Cohn, 2024.
3 769 0.991073054499 Henry Cohn, 2024.
3 770 0.991085755280 Henry Cohn, 2024.
3 771 0.991097098258 Henry Cohn, 2024.
3 772 0.991107834438 Henry Cohn, 2024.
3 773 0.991120324668 Henry Cohn, 2024.
3 774 0.991132071939 Henry Cohn, 2024.
3 775 0.991145898664 Henry Cohn, 2024.
3 776 0.991156697126 Henry Cohn, 2024.
3 777 0.991161697853 Henry Cohn, 2024.
3 778 0.991178514334 Henry Cohn, 2024.
3 779 0.991188403576 Henry Cohn, 2024.
3 780 0.991195467101 Henry Cohn, 2024.
3 781 0.991212495316 Henry Cohn, 2024.
3 782 0.991221877841 Henry Cohn, 2024.
3 783 0.991227432227 Henry Cohn, 2024.
3 784 0.991237581418 Henry Cohn, 2024.
3 785 0.991247586153 Henry Cohn, 2026.
3 786 0.991265609504 Henry Cohn, 2024.
3 787 0.991279737346 Henry Cohn, 2024.
3 788 0.991287959034 Henry Cohn, 2024.
3 789 0.991298474057 Henry Cohn, 2024.
3 790 0.991311108786 Henry Cohn, 2024.
3 791 0.991319397658 Henry Cohn, 2024.
3 792 0.991327970122 Henry Cohn, 2024.
3 793 0.991338848668 Henry Cohn, 2026.
3 794 0.991355598368 Henry Cohn, 2024.
3 795 0.991362648296 Henry Cohn, 2024.
3 796 0.991373620973 Henry Cohn, 2024.
3 797 0.991382382844 Henry Cohn, 2024.
3 798 0.991394391213 Henry Cohn, 2024.
3 799 0.991408093880 Henry Cohn, 2024.
3 800 0.991414851715 Henry Cohn, 2024.
3 801 0.991425603623 Henry Cohn, 2024.
3 802 0.991437819695 Henry Cohn, 2024.
3 803 0.991450003639 Henry Cohn, 2024.
3 804 0.991459924550 Henry Cohn, 2024.
3 805 0.991468080347 Henry Cohn, 2024.
3 806 0.991480017656 Henry Cohn, 2024.
3 807 0.991488929993 Henry Cohn, 2024.
3 808 0.991499472524 Henry Cohn, 2024.
3 809 0.991513039166 Henry Cohn, 2024.
3 810 0.991520665687 Henry Cohn, 2024.
3 811 0.991531900706 Henry Cohn, 2026.
3 812 0.991541771500 Henry Cohn, 2024.
3 813 0.991547822510 Henry Cohn, 2024.
3 814 0.991561861128 Henry Cohn, 2024.
3 815 0.991569264349 Henry Cohn, 2024.
3 816 0.991580342934 Henry Cohn, 2024.
3 817 0.991591011326 Henry Cohn, 2024.
3 818 0.991606217466 Henry Cohn, 2024.
3 819 0.991611831024 Henry Cohn, 2024.
3 820 0.991624044122 Henry Cohn, 2024.
3 821 0.991631483847 Henry Cohn, 2024.
3 822 0.991640340040 Henry Cohn, 2024.
3 823 0.991650165081 Henry Cohn, 2024.
3 824 0.991660076581 Henry Cohn, 2024.
3 825 0.991671265549 Henry Cohn, 2024.
3 826 0.991681742391 Henry Cohn, 2024.
3 827 0.991689512986 Henry Cohn, 2026.
3 828 0.991700756929 Henry Cohn, 2024.
3 829 0.991713398461 Henry Cohn, 2024.
3 830 0.991721621394 Henry Cohn, 2024.
3 831 0.991727218135 Henry Cohn, 2024.
3 832 0.991735674478 Henry Cohn, 2024.
3 833 0.991752715894 Henry Cohn, 2026.
3 834 0.991760206285 Henry Cohn, 2026.
3 835 0.991774281061 Henry Cohn, 2026.
3 836 0.991777728477 Henry Cohn, 2026.
3 837 0.991787914624 Henry Cohn, 2026.
3 838 0.991801752922 Henry Cohn, 2026.
3 840 0.991804916272 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 841 0.991814485212 Henry Cohn, 2026.
3 842 0.991823503477 Henry Cohn, 2026.
3 843 0.991831936554 Henry Cohn, 2026.
3 844 0.991855906891 Henry Cohn, 2026.
3 845 0.991858365805 Henry Cohn, 2026.
3 846 0.991862416880 Henry Cohn, 2026.
3 847 0.991870062536 Henry Cohn, 2026.
3 848 0.991877607736 Henry Cohn, 2026.
3 849 0.991885383845 Henry Cohn, 2026, needs more optimization.
3 850 0.991891394851 Henry Cohn, 2026, needs more optimization.
3 851 0.991898234568 Henry Cohn, 2026, needs more optimization.
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 0.991918219705 Henry Cohn, 2026.
3 854 0.991935712887 Henry Cohn, 2026.
3 855 0.991949565796 Henry Cohn, 2026.
3 856 0.991960761076 Henry Cohn, 2026.
3 857 0.991979003112 Henry Cohn, 2025.
3 858 0.991987713948 Henry Cohn, 2025.
3 860 0.992000324488 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 861 0.992009766000 Henry Cohn, 2026.
3 862 0.992022903669 Henry Cohn, 2025.
3 863 0.992032218857 Henry Cohn, 2026.
3 864 0.992045910827 Henry Cohn, 2025.
3 865 0.992052833787 Henry Cohn, 2025.
3 866 0.992060313002 Henry Cohn, 2026.
3 867 0.992072381754 Henry Cohn, 2025.
3 868 0.992080033785 Henry Cohn, 2025.
3 869 0.992091623959 Henry Cohn, 2025.
3 871 0.992098345459 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 0.992112147695 Henry Cohn, 2026.
3 874 0.992126269269 Henry Cohn, 2026.
3 875 0.992138836629 Henry Cohn, 2026.
3 876 0.992145742866 Henry Cohn, 2026.
3 877 0.992154329715 Henry Cohn, 2025.
3 878 0.992165376588 Henry Cohn, 2026.
3 879 0.992171243331 Henry Cohn, 2025.
3 880 0.992185909971 Henry Cohn, 2025.
3 881 0.992192486886 Henry Cohn, 2025.
3 882 0.992198371680 Henry Cohn, 2025.
3 883 0.992206322363 Henry Cohn, 2026.
3 884 0.992214559883 Henry Cohn, 2026.
3 885 0.992224887881 Henry Cohn, 2026.
3 886 0.992238913098 Henry Cohn, 2026.
3 887 0.992242382220 Henry Cohn, 2025.
3 888 0.992258876226 Henry Cohn, 2025.
3 889 0.992266590342 Henry Cohn, 2026.
3 890 0.992270692003 Henry Cohn, 2025.
3 891 0.992282908648 Henry Cohn, 2025.
3 892 0.992289973548 Henry Cohn, 2025.
3 893 0.992296614398 Henry Cohn, 2026.
3 894 0.992309459744 Henry Cohn, 2025.
3 895 0.992316358484 Henry Cohn, 2025.
3 896 0.992319789432 Henry Cohn, 2025.
3 897 0.992332110080 Henry Cohn, 2025.
3 898 0.992338696092 Henry Cohn, 2025.
3 899 0.992347170200 Henry Cohn, 2026.
3 900 0.992357664586 Henry Cohn, 2026.
3 901 0.992361149576 Henry Cohn, 2026.
3 902 0.992374954180 Henry Cohn, 2026.
3 903 0.992382061576 Henry Cohn, 2025.
3 904 0.992391535361 Henry Cohn, 2026.
3 905 0.992400631964 Henry Cohn, 2025.
3 906 0.992409191703 Henry Cohn, 2025.
3 907 0.992416883647 Henry Cohn, 2025.
3 908 0.992422545672 Henry Cohn, 2025.
3 909 0.992432062810 Henry Cohn, 2025.
3 910 0.992437123795 Henry Cohn, 2025.
3 911 0.992443166019 Henry Cohn, 2025.
3 912 0.992454600852 Henry Cohn, 2025.
3 913 0.992469933271 Henry Cohn, 2025.
3 914 0.992471207708 Henry Cohn, 2025.
3 915 0.992482565852 Henry Cohn, 2025.
3 916 0.992490047642 Henry Cohn, 2026.
3 917 0.992499945293 Henry Cohn, 2026.
3 918 0.992507205651 Henry Cohn, 2025.
3 919 0.992516908676 Henry Cohn, 2025.
3 920 0.992518345854 Henry Cohn, 2025.
3 921 0.992532122129 Henry Cohn, 2025.
3 922 0.992536144116 Henry Cohn, 2026.
3 923 0.992547647599 Henry Cohn, 2025.
3 924 0.992553990146 Henry Cohn, 2025.
3 925 0.992565731685 Henry Cohn, 2025.
3 926 0.992569938693 Henry Cohn, 2025.
3 927 0.992577590747 Henry Cohn, 2026.
3 928 0.992583930232 Henry Cohn, 2025.
3 929 0.992590355210 Henry Cohn, 2025.
3 930 0.992598510473 Henry Cohn, 2026.
3 931 0.992609528473 Henry Cohn, 2026.
3 932 0.992614241081 Henry Cohn, 2026.
3 933 0.992624602034 Henry Cohn, 2025.
3 934 0.992631107765 Henry Cohn, 2025.
3 935 0.992638889250 Henry Cohn, 2026.
3 936 0.992646759917 Henry Cohn, 2026.
3 937 0.992652545878 Henry Cohn, 2026.
3 938 0.992665682904 Henry Cohn, 2025.
3 939 0.992672947443 Henry Cohn, 2025.
3 940 0.992677739706 Henry Cohn, 2025.
3 941 0.992688089317 Henry Cohn, 2025.
3 942 0.992696579115 Henry Cohn, 2025.
3 943 0.992702546437 Henry Cohn, 2025.
3 944 0.992712884586 Henry Cohn, 2026.
3 945 0.992717631580 Henry Cohn, 2025.
3 946 0.992723034803 Henry Cohn, 2025.
3 947 0.992729250719 Henry Cohn, 2025.
3 948 0.992739976830 Henry Cohn, 2026.
3 950 0.992751947060 Henry Cohn, 2025.
3 951 0.992762286900 Henry Cohn, 2026.
3 952 0.992771438024 Henry Cohn, 2025.
3 953 0.992778114761 Henry Cohn, 2026.
3 954 0.992783154814 Henry Cohn, 2026.
3 955 0.992791162785 Henry Cohn, 2026.
3 956 0.992801093482 Henry Cohn, 2025.
3 957 0.992810004476 Henry Cohn, 2025.
3 958 0.992817667647 Henry Cohn, 2025.
3 959 0.992826125413 Henry Cohn, 2025.
3 960 0.992830967656 Henry Cohn, 2024.
3 961 0.992838773549 Henry Cohn, 2025.
3 962 0.992843794794 Henry Cohn, 2025.
3 963 0.992852425763 Henry Cohn, 2025.
3 964 0.992860398135 Henry Cohn, 2025.
3 965 0.992869292418 Henry Cohn, 2026.
3 966 0.992875386015 Henry Cohn, 2025.
3 967 0.992882714198 Henry Cohn, 2025.
3 968 0.992886923604 Henry Cohn, 2025.
3 969 0.992896341783 Henry Cohn, 2025.
3 970 0.992903243757 Henry Cohn, 2025.
3 971 0.992910234827 Henry Cohn, 2025.
3 972 0.992915598654 Henry Cohn, 2025.
3 974 0.992925603203 Henry Cohn, 2025.
3 975 0.992935839740 Henry Cohn, 2025.
3 976 0.992940838715 Henry Cohn, 2026.
3 977 0.992953433939 Henry Cohn, 2025.
3 978 0.992962810288 Henry Cohn, 2025.
3 979 0.992966796815 Henry Cohn, 2026.
3 980 0.992974636259 Henry Cohn, 2024.
3 981 0.992982747599 Henry Cohn, 2025.
3 982 0.992988090846 Henry Cohn, 2025.
3 983 0.992998353831 Henry Cohn, 2025.
3 984 0.993003417762 Henry Cohn, 2025.
3 985 0.993011691492 Henry Cohn, 2025.
3 986 0.993015554264 Henry Cohn, 2025.
3 988 0.993023719135 Henry Cohn, 2025.
3 989 0.993037184620 Henry Cohn, 2025.
3 990 0.993045751650 Henry Cohn, 2025.
3 991 0.993050187813 Henry Cohn, 2025.
3 992 0.993060823315 Henry Cohn, 2026.
3 993 0.993062803097 Henry Cohn, 2025.
3 994 0.993068407687 Henry Cohn, 2026.
3 995 0.993078560947 Henry Cohn, 2025.
3 996 0.993085360497 Henry Cohn, 2026.
3 997 0.993095368942 Henry Cohn, 2025.
3 998 0.993098230447 Henry Cohn, 2025.
3 999 0.993105196299 Henry Cohn, 2026.
3 1000 0.993111266855 Henry Cohn, 2025.
3 1001 0.993117495261 Henry Cohn, 2026.
3 1002 0.993125622347 Henry Cohn, 2025.
3 1003 0.993132170420 Henry Cohn, 2025.
3 1004 0.993137613575 Henry Cohn, 2026.
3 1005 0.993148911123 Henry Cohn, 2025.
3 1006 0.993152122720 Henry Cohn, 2025.
3 1008 0.993159005478 Henry Cohn, 2025.
3 1009 0.993168721248 Henry Cohn, 2026.
3 1010 0.993176753480 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 1011 0.993184403639 Henry Cohn, 2026.
3 1012 0.993192195263 Henry Cohn, 2026.
3 1013 0.993196528382 Henry Cohn, 2026.
3 1014 0.993203054683 Henry Cohn, 2026.
3 1015 0.993209201981 Henry Cohn, 2026.
3 1016 0.993215431799 Henry Cohn, 2026.
3 1017 0.993222604880 Henry Cohn, 2026.
3 1018 0.993230067487 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 0.993243150192 Henry Cohn, 2026.
3 1022 0.993250071050 Henry Cohn, 2026.
3 1023 0.993256367190 Henry Cohn, 2026.
3 1024 0.993263382475 Henry Cohn, 2026.
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 0.843251223216 Henry Cohn, 2025.
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 0.861336632417 Henry Cohn, 2026, needs more optimization.
4 171 0.861877205800 Henry Cohn, 2025.
4 172 0.862358805352 Henry Cohn, 2025.
4 173 0.862725307388 Henry Cohn, 2025.
4 174 0.863246308920 Henry Cohn, 2025.
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 0.868218585406 Henry Cohn, 2026, needs more optimization.
4 186 0.868518800651 Henry Cohn, 2025.
4 187 0.868835030449 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 0.872106376131 Henry Cohn, 2025.
4 196 0.872623946731 Henry Cohn, 2025.
4 197 0.873487426793 Henry Cohn, 2025.
4 198 0.874156501901 Henry Cohn, 2025.
4 199 0.875069199577 Henry Cohn, 2025.
4 200 0.875686480655 Henry Cohn, 2025.
4 201 0.876308845876 Henry Cohn, 2025.
4 202 0.876662092953 Henry Cohn, 2025.
4 203 0.876835144121 Henry Cohn, 2026, needs more optimization.
4 204 0.877235132320 Henry Cohn, 2026, needs more optimization.
4 205 0.877534211883 Henry Cohn, 2025.
4 206 0.877831247728 Henry Cohn, 2025.
4 207 0.877998486483 Henry Cohn, 2026, needs more optimization.
4 208 0.878215104089 Henry Cohn, 2025.
4 209 0.878616371731 Henry Cohn, 2025.
4 210 0.879213799752 Henry Cohn, 2025.
4 211 0.879586628106 Henry Cohn, 2025.
4 212 0.879665474531 Henry Cohn, 2025.
4 213 0.879834121318 Henry Cohn, 2025.
4 214 0.879945724274 Henry Cohn, 2025.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880905324150 Henry Cohn, 2025.
4 217 0.881535768813 Henry Cohn, 2025.
4 218 0.881833555267 Henry Cohn, 2025.
4 219 0.881957670465 Henry Cohn, 2025.
4 220 0.882547029792 Henry Cohn, 2025.
4 221 0.883034917637 Henry Cohn, 2025.
4 222 0.883456069925 Henry Cohn, 2025.
4 223 0.884138189446 Henry Cohn, 2025.
4 224 0.884684734191 Henry Cohn, 2025.
4 225 0.885129848339 Henry Cohn, 2026, needs more optimization.
4 226 0.885326282646 Henry Cohn, 2026, needs more optimization.
4 227 0.885541386047 Henry Cohn, 2025.
4 228 0.885824040293 Henry Cohn, 2025.
4 229 0.886076387066 Henry Cohn, 2026, needs more optimization.
4 230 0.886372063295 Henry Cohn, 2025.
4 231 0.886845140552 Henry Cohn, 2025.
4 232 0.887102089163 Henry Cohn, 2025.
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 0.889111473990 Henry Cohn, 2026, needs more optimization.
4 240 0.889491341544 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 0.890734551284 Henry Cohn, 2026, needs more optimization.
4 245 0.891024994652 Henry Cohn, 2025.
4 246 0.891230987587 Henry Cohn, 2025.
4 247 0.891705372760 Henry Cohn, 2026, needs more optimization.
4 248 0.891999064884 Henry Cohn, 2026, needs more optimization.
4 249 0.892301274735 Henry Cohn, 2026, needs more optimization.
4 250 0.892631521974 Henry Cohn, 2025.
4 251 0.893091527796 Henry Cohn, 2026, needs more optimization.
4 252 0.893341841396 Henry Cohn, 2025.
4 253 0.893646236229 Henry Cohn, 2025.
4 254 0.893921970145 Henry Cohn, 2025.
4 255 0.894009501823 Henry Cohn, 2025.
4 256 0.894553728947 Henry Cohn, 2026, needs more optimization.
4 257 0.894721765248 Henry Cohn, 2026, needs more optimization.
4 258 0.894984348756 Henry Cohn, 2026, needs more optimization.
4 259 0.895419741077 Henry Cohn, 2026, needs more optimization.
4 260 0.895634992808 Henry Cohn, 2026, needs more optimization.
4 261 0.896005488256 Henry Cohn, 2026, needs more optimization.
4 262 0.896210182934 Henry Cohn, 2026, needs more optimization.
4 263 0.896407402593 Henry Cohn, 2026, needs more optimization.
4 264 0.896672673016 Henry Cohn, 2026, needs more optimization.
4 265 0.896847961705 Henry Cohn, 2026, needs more optimization.
4 266 0.897013288224 Henry Cohn, 2026, needs more optimization.
4 267 0.897224396999 Henry Cohn, 2026, needs more optimization.
4 268 0.897379521992 Henry Cohn, 2026, needs more optimization.
4 269 0.897645803760 Henry Cohn, 2026, needs more optimization.
4 270 0.897837522764 Henry Cohn, 2026, needs more optimization.
4 271 0.898149362730 Ilmari Vahteristo, 2026.
4 272 0.898261745112 Henry Cohn, 2026, needs more optimization.
4 273 0.898418110924 Henry Cohn, 2026, needs more optimization.
4 274 0.898512235178 Henry Cohn, 2026, needs more optimization.
4 275 0.898744145719 Henry Cohn, 2026, needs more optimization.
4 276 0.899007356860 Henry Cohn, 2026, needs more optimization.
4 277 0.899354433069 Henry Cohn, 2026, needs more optimization.
4 278 0.899467843819 Henry Cohn, 2026, needs more optimization.
4 279 0.899602410452 Henry Cohn, 2026, needs more optimization.
4 280 0.899644628460 Henry Cohn, 2026, needs more optimization.
4 281 0.900138077748 Henry Cohn, 2026, needs more optimization.
4 282 0.900638575911 Henry Cohn, 2026, needs more optimization.
4 283 0.901094654911 Henry Cohn, 2026, needs more optimization.
4 284 0.901381062716 Ilmari Vahteristo, 2026.
4 285 0.901682529285 Henry Cohn, 2026, needs more optimization.
4 286 0.901889980685 Henry Cohn, 2026, needs more optimization.
4 287 0.902238993011 Ilmari Vahteristo, 2026.
4 288 0.902546485502 Henry Cohn, 2026, needs more optimization.
4 289 0.902745144569 Henry Cohn, 2026, needs more optimization.
4 290 0.902783857825 Henry Cohn, 2026, needs more optimization.
4 291 0.903189642641 Henry Cohn, 2026, needs more optimization.
4 292 0.903558311669 Henry Cohn, 2026, needs more optimization.
4 293 0.903828266452 Henry Cohn, 2026, needs more optimization.
4 294 0.904162262105 Henry Cohn, 2026, needs more optimization.
4 295 0.904229693511 Henry Cohn, 2026, needs more optimization.
4 296 0.904774774452 Henry Cohn, 2026, needs more optimization.
4 297 0.904792565536 Henry Cohn, 2025, needs more optimization.
4 298 0.904969620550 Henry Cohn, 2026, needs more optimization.
4 299 0.905165332857 Henry Cohn, 2026, needs more optimization.
4 300 0.905419507650 Henry Cohn, 2026, needs more optimization.
4 301 0.905749679486 Henry Cohn, 2025, needs more optimization.
4 302 0.905910389380 Henry Cohn, 2026, needs more optimization.
4 303 0.906127796062 Henry Cohn, 2025, needs more optimization.
4 304 0.906270018142 Henry Cohn, 2026, needs more optimization.
4 305 0.906356849962 Henry Cohn, 2026, needs more optimization.
4 306 0.906570883768 Henry Cohn, 2026, needs more optimization.
4 307 0.906882499335 Henry Cohn, 2026, needs more optimization.
4 308 0.907005361906 Henry Cohn, 2026, needs more optimization.
4 309 0.907355948835 Henry Cohn, 2025, needs more optimization.
4 310 0.907358532815 Henry Cohn, 2025, needs more optimization.
4 311 0.907546640069 Henry Cohn, 2026, needs more optimization.
4 312 0.907839838001 Henry Cohn, 2026, needs more optimization.
4 313 0.908203644484 Henry Cohn, 2026, needs more optimization.
4 314 0.908391317126 Henry Cohn, 2026, needs more optimization.
4 315 0.908572559108 Henry Cohn, 2026, needs more optimization.
4 316 0.908739365180 Henry Cohn, 2026, needs more optimization.
4 317 0.908907775062 Henry Cohn, 2026, needs more optimization.
4 318 0.909119496939 Henry Cohn, 2026, needs more optimization.
4 319 0.909208466661 Henry Cohn, 2026, needs more optimization.
4 320 0.909390987337 Henry Cohn, 2026, needs more optimization.
4 321 0.909524826028 Henry Cohn, 2026, needs more optimization.
4 322 0.909666675251 Henry Cohn, 2026, needs more optimization.
4 323 0.909755948298 Henry Cohn, 2026, needs more optimization.
4 324 0.909842149105 Henry Cohn, 2026, needs more optimization.
4 325 0.910071511705 Henry Cohn, 2026, needs more optimization.
4 326 0.910248571586 Henry Cohn, 2026, needs more optimization.
4 327 0.910330672955 Henry Cohn, 2026, needs more optimization.
4 328 0.910458949904 Henry Cohn, 2026, needs more optimization.
4 329 0.910735481835 Henry Cohn, 2026, needs more optimization.
4 330 0.910990070537 Henry Cohn, 2026, needs more optimization.
4 331 0.911187813390 Henry Cohn, 2026, needs more optimization.
4 332 0.911382095911 Henry Cohn, 2026, needs more optimization.
4 333 0.911546283710 Henry Cohn, 2026, needs more optimization.
4 334 0.911687496609 Henry Cohn, 2026, needs more optimization.
4 335 0.911955020891 Henry Cohn, 2026, needs more optimization.
4 336 0.912161399531 Henry Cohn, 2026, needs more optimization.
4 337 0.912392820444 Henry Cohn, 2025, needs more optimization.
4 338 0.912655658852 Henry Cohn, 2026, needs more optimization.
4 339 0.912870367290 Henry Cohn, 2026, needs more optimization.
4 340 0.913091478259 Henry Cohn, 2026, needs more optimization.
4 341 0.913376620602 Henry Cohn, 2025, needs more optimization.
4 342 0.913523258748 Henry Cohn, 2024, needs more optimization.
4 343 0.913763065375 Henry Cohn, 2026, needs more optimization.
4 344 0.914034198581 Henry Cohn, 2026, needs more optimization.
4 345 0.914150831785 Henry Cohn, 2026, needs more optimization.
4 346 0.914243006917 Henry Cohn, 2026, needs more optimization.
4 347 0.914430196985 Henry Cohn, 2026, needs more optimization.
4 348 0.914694036098 Henry Cohn, 2026, needs more optimization.
4 349 0.914804715376 Henry Cohn, 2026, needs more optimization.
4 350 0.914972573951 Henry Cohn, 2025, needs more optimization.
4 351 0.915014544100 Henry Cohn, 2026, needs more optimization.
4 352 0.915245920584 Henry Cohn, 2026, needs more optimization.
4 353 0.915308989155 Henry Cohn, 2026, needs more optimization.
4 354 0.915475633531 Henry Cohn, 2026, needs more optimization.
4 355 0.915538659710 Henry Cohn, 2026, needs more optimization.
4 356 0.915670324528 Henry Cohn, 2026, needs more optimization.
4 357 0.915790277691 Henry Cohn, 2026, needs more optimization.
4 358 0.915961005903 Henry Cohn, 2026, needs more optimization.
4 359 0.916108432982 Henry Cohn, 2026, needs more optimization.
4 360 0.916237301288 Henry Cohn, 2026, needs more optimization.
4 362 0.916289444191 Henry Cohn, 2026, needs more optimization.
4 363 0.916478539701 Henry Cohn, 2026, needs more optimization.
4 364 0.916585644865 Henry Cohn, 2026, needs more optimization.
4 365 0.916767663801 Henry Cohn, 2026, needs more optimization.
4 366 0.916867164782 Henry Cohn, 2026, needs more optimization.
4 367 0.917157400590 Henry Cohn, 2026, needs more optimization.
4 369 0.917274711467 Henry Cohn, 2026, needs more optimization.
4 370 0.917323335950 Henry Cohn, 2026, needs more optimization.
4 371 0.917493460397 Henry Cohn, 2026, needs more optimization.
4 372 0.917647955914 Henry Cohn, 2026, needs more optimization.
4 373 0.917916553669 Henry Cohn, 2026, needs more optimization.
4 374 0.918180255592 Henry Cohn, 2026, needs more optimization.
4 375 0.918363666181 Henry Cohn, 2026, needs more optimization.
4 376 0.918529375746 Henry Cohn, 2026, needs more optimization.
4 377 0.918659616608 Henry Cohn, 2026, needs more optimization.
4 378 0.918737538301 Henry Cohn, 2026, needs more optimization.
4 379 0.918913325442 Henry Cohn, 2026, needs more optimization.
4 380 0.919081745081 Henry Cohn, 2026, needs more optimization.
4 381 0.919163200278 Henry Cohn, 2025, needs more optimization.
4 382 0.919198683072 Henry Cohn, 2026, needs more optimization.
4 383 0.919303919971 Henry Cohn, 2026, needs more optimization.
4 385 0.919385606515 Henry Cohn, 2026, needs more optimization.
4 387 0.919487036353 Henry Cohn, 2026, needs more optimization.
4 388 0.919708660566 Henry Cohn, 2026, needs more optimization.
4 389 0.919756054809 Henry Cohn, 2026, needs more optimization.
4 390 0.919945279375 Henry Cohn, 2026, needs more optimization.
4 391 0.920150562767 Henry Cohn, 2026, needs more optimization.
4 392 0.920323648483 Henry Cohn, 2026, needs more optimization.
4 393 0.920458688366 Henry Cohn, 2026, needs more optimization.
4 394 0.920481654231 Henry Cohn, 2026, needs more optimization.
4 395 0.920580829083 Henry Cohn, 2026, needs more optimization.
4 396 0.920859602088 Henry Cohn, 2026, needs more optimization.
4 397 0.921025603330 Henry Cohn, 2026, needs more optimization.
4 398 0.921140536823 Henry Cohn, 2026, needs more optimization.
4 399 0.921206272324 Henry Cohn, 2026, needs more optimization.
4 400 0.921479230456 Henry Cohn, 2026, needs more optimization.
4 401 0.921560426099 Henry Cohn, 2025, needs more optimization.
4 402 0.921728059075 Henry Cohn, 2026, needs more optimization.
4 403 0.921822136637 Henry Cohn, 2025, needs more optimization.
4 404 0.921846716883 Henry Cohn, 2026, needs more optimization.
4 405 0.921862996211 Henry Cohn, 2026, needs more optimization.
4 406 0.921929943872 Henry Cohn, 2025, needs more optimization.
4 407 0.922032598227 Henry Cohn, 2026, needs more optimization.
4 408 0.922059915244 Henry Cohn, 2026, needs more optimization.
4 409 0.922354134070 Henry Cohn, 2026, needs more optimization.
4 410 0.922664520391 Henry Cohn, 2026, needs more optimization.
4 411 0.922708465064 Henry Cohn, 2026, needs more optimization.
4 412 0.922995574568 Henry Cohn, 2026, needs more optimization.
4 413 0.923219821260 Henry Cohn, 2026, needs more optimization.
4 414 0.923265471415 Henry Cohn, 2025, needs more optimization.
4 415 0.923452958450 Henry Cohn, 2026, needs more optimization.
4 416 0.923458302084 Henry Cohn, 2026, needs more optimization.
4 417 0.923548539344 Henry Cohn, 2026, needs more optimization.
4 418 0.923607609886 Henry Cohn, 2026, needs more optimization.
4 419 0.923732960248 Henry Cohn, 2026, needs more optimization.
4 420 0.923941519840 Henry Cohn, 2026, needs more optimization.
4 421 0.924182995846 Henry Cohn, 2026, needs more optimization.
4 422 0.924251515141 Henry Cohn, 2026, needs more optimization.
4 423 0.924318236722 Henry Cohn, 2026, needs more optimization.
4 424 0.924520687039 Henry Cohn, 2026, needs more optimization.
4 425 0.924715791316 Henry Cohn, 2026, needs more optimization.
4 426 0.924929822860 Henry Cohn, 2026, needs more optimization.
4 427 0.925140842602 Henry Cohn, 2026, needs more optimization.
4 428 0.925376567996 Henry Cohn, 2026, needs more optimization.
4 429 0.925428574645 Henry Cohn, 2026, needs more optimization.
4 430 0.925533857773 Henry Cohn, 2026, needs more optimization.
4 431 0.925727712785 Henry Cohn, 2026, needs more optimization.
4 432 0.925849797697 Henry Cohn, 2026, needs more optimization.
4 433 0.925937777261 Henry Cohn, 2026, needs more optimization.
4 434 0.926009115308 Henry Cohn, 2026, needs more optimization.
4 435 0.926208385632 Henry Cohn, 2026, needs more optimization.
4 436 0.926294787872 Henry Cohn, 2026, needs more optimization.
4 437 0.926512904192 Henry Cohn, 2026, needs more optimization.
4 438 0.926662926291 Henry Cohn, 2026, needs more optimization.
4 439 0.926766187753 Henry Cohn, 2026, needs more optimization.
4 440 0.926926352282 Henry Cohn, 2026, needs more optimization.
4 441 0.927075075822 Henry Cohn, 2026, needs more optimization.
4 442 0.927193287005 Henry Cohn, 2026, needs more optimization.
4 443 0.927362839819 Henry Cohn, 2026, needs more optimization.
4 444 0.927425982970 Henry Cohn, 2026, needs more optimization.
4 445 0.927460223824 Henry Cohn, 2026, needs more optimization.
4 446 0.927559411183 Henry Cohn, 2026, needs more optimization.
4 447 0.927654413635 Henry Cohn, 2026, needs more optimization.
4 448 0.927811513098 Henry Cohn, 2026, needs more optimization.
4 449 0.927924289302 Henry Cohn, 2026, needs more optimization.
4 450 0.928055039883 Henry Cohn, 2026, needs more optimization.
4 451 0.928097969258 Henry Cohn, 2025, needs more optimization.
4 452 0.928166063873 Henry Cohn, 2026, needs more optimization.
4 453 0.928251648680 Henry Cohn, 2026, needs more optimization.
4 454 0.928320498977 Henry Cohn, 2026, needs more optimization.
4 455 0.928381173710 Henry Cohn, 2025, needs more optimization.
4 456 0.928454925913 Henry Cohn, 2026, needs more optimization.
4 457 0.928559891923 Henry Cohn, 2025, needs more optimization.
4 458 0.928618828000 Henry Cohn, 2026, needs more optimization.
4 459 0.928701316639 Henry Cohn, 2026, needs more optimization.
4 460 0.928821803185 Henry Cohn, 2026, needs more optimization.
4 461 0.928929483225 Henry Cohn, 2026, needs more optimization.
4 462 0.929059505214 Henry Cohn, 2026, needs more optimization.
4 463 0.929136585030 Henry Cohn, 2026, needs more optimization.
4 464 0.929228421350 Henry Cohn, 2026, needs more optimization.
4 465 0.929385947577 Henry Cohn, 2026, needs more optimization.
4 466 0.929539753672 Henry Cohn, 2026, needs more optimization.
4 467 0.929668290898 Henry Cohn, 2026, needs more optimization.
4 468 0.929765230377 Henry Cohn, 2026, needs more optimization.
4 469 0.929886943176 Henry Cohn, 2026, needs more optimization.
4 470 0.929996254745 Henry Cohn, 2026, needs more optimization.
4 471 0.930129291016 Henry Cohn, 2026, needs more optimization.
4 472 0.930304679917 Henry Cohn, 2026, needs more optimization.
4 473 0.930435765053 Henry Cohn, 2026, needs more optimization.
4 474 0.930580578924 Henry Cohn, 2026, needs more optimization.
4 475 0.930685424063 Henry Cohn, 2026, needs more optimization.
4 476 0.930733622088 Henry Cohn, 2026, needs more optimization.
4 477 0.930820405012 Henry Cohn, 2025, needs more optimization.
4 478 0.930991981027 Henry Cohn, 2026, needs more optimization.
4 479 0.930997735880 Henry Cohn, 2026, needs more optimization.
4 480 0.931058589575 Henry Cohn, 2026, needs more optimization.
4 481 0.931185754306 Henry Cohn, 2026, needs more optimization.
4 482 0.931316019971 Henry Cohn, 2026, needs more optimization.
4 483 0.931424936749 Henry Cohn, 2026, needs more optimization.
4 484 0.931536467498 Henry Cohn, 2026, needs more optimization.
4 485 0.931598602760 Henry Cohn, 2025, needs more optimization.
4 486 0.931672650218 Henry Cohn, 2026, needs more optimization.
4 487 0.931748317871 Henry Cohn, 2026, needs more optimization.
4 488 0.931840218403 Henry Cohn, 2026, needs more optimization.
4 489 0.931879460145 Henry Cohn, 2025, needs more optimization.
4 490 0.931976220032 Henry Cohn, 2026, needs more optimization.
4 491 0.932073442452 Henry Cohn, 2026, needs more optimization.
4 492 0.932108274917 Henry Cohn, 2026, needs more optimization.
4 493 0.932167869065 Henry Cohn, 2026, needs more optimization.
4 494 0.932206682291 Henry Cohn, 2026, needs more optimization.
4 495 0.932323203465 Henry Cohn, 2025, needs more optimization.
4 496 0.932500272178 Henry Cohn, 2025, needs more optimization.
4 497 0.932512624213 Henry Cohn, 2025, needs more optimization.
4 498 0.932636221973 Henry Cohn, 2026, needs more optimization.
4 499 0.932641716231 Henry Cohn, 2025, needs more optimization.
4 500 0.932793878323 Henry Cohn, 2026, needs more optimization.
4 501 0.932795380893 Henry Cohn, 2025, needs more optimization.
4 502 0.932905617000 Henry Cohn, 2025, needs more optimization.
4 503 0.933005617030 Henry Cohn, 2025, needs more optimization.
4 504 0.933044432549 Henry Cohn, 2026, needs more optimization.
4 505 0.933128723647 Henry Cohn, 2025, needs more optimization.
4 506 0.933175916326 Henry Cohn, 2026, needs more optimization.
4 507 0.933399662810 Henry Cohn, 2026, needs more optimization.
4 508 0.933457715953 Henry Cohn, 2025, needs more optimization.
4 509 0.933553824747 Henry Cohn, 2025, needs more optimization.
4 510 0.933554338029 Henry Cohn, 2026, needs more optimization.
4 511 0.933747497746 Henry Cohn, 2026, needs more optimization.
4 512 0.933804302995 Henry Cohn, 2026, needs more optimization.
4 513 0.933898943863 Henry Cohn, 2026, needs more optimization.
4 514 0.933968541380 Henry Cohn, 2026, needs more optimization.
4 515 0.934045219268 Henry Cohn, 2025, needs more optimization.
4 516 0.934187930613 Henry Cohn, 2026, needs more optimization.
4 517 0.934200348230 Henry Cohn, 2026, needs more optimization.
4 518 0.934457304876 Henry Cohn, 2026, needs more optimization.
4 519 0.934540089409 Henry Cohn, 2025, needs more optimization.
4 520 0.934699248258 Henry Cohn, 2025, needs more optimization.
4 521 0.934710019106 Henry Cohn, 2025, needs more optimization.
4 522 0.934742707124 Henry Cohn, 2026, needs more optimization.
4 523 0.934852797622 Henry Cohn, 2026, needs more optimization.
4 524 0.934944371680 Henry Cohn, 2025, needs more optimization.
4 525 0.935029425094 Henry Cohn, 2026, needs more optimization.
4 526 0.935145051454 Henry Cohn, 2026, needs more optimization.
4 527 0.935256351959 Henry Cohn, 2025, needs more optimization.
4 528 0.935310315348 Henry Cohn, 2025, needs more optimization.
4 529 0.935319514565 Henry Cohn, 2026, needs more optimization.
4 530 0.935497498479 Henry Cohn, 2026, needs more optimization.
4 531 0.935510798794 Henry Cohn, 2025, needs more optimization.
4 532 0.935569232469 Henry Cohn, 2026, needs more optimization.
4 533 0.935676741118 Henry Cohn, 2025, needs more optimization.
4 534 0.935788386292 Henry Cohn, 2026, needs more optimization.
4 535 0.935811939995 Henry Cohn, 2025, needs more optimization.
4 537 0.935910089175 Henry Cohn, 2025, needs more optimization.
4 538 0.936067620630 Henry Cohn, 2026, needs more optimization.
4 539 0.936105500983 Henry Cohn, 2026, needs more optimization.
4 540 0.936187919569 Henry Cohn, 2026, needs more optimization.
4 541 0.936301405234 Henry Cohn, 2025, needs more optimization.
4 542 0.936307463358 Henry Cohn, 2025, needs more optimization.
4 543 0.936417878772 Henry Cohn, 2025, needs more optimization.
4 545 0.936558367404 Henry Cohn, 2025, needs more optimization.
4 546 0.936667874314 Henry Cohn, 2025, needs more optimization.
4 547 0.936744880456 Henry Cohn, 2026, needs more optimization.
4 548 0.936755768894 Henry Cohn, 2026, needs more optimization.
4 549 0.936916079422 Henry Cohn, 2025, needs more optimization.
4 550 0.936922956849 Henry Cohn, 2026, needs more optimization.
4 551 0.937084656947 Henry Cohn, 2026, needs more optimization.
4 552 0.937086856222 Henry Cohn, 2026, needs more optimization.
4 553 0.937240543392 Henry Cohn, 2025, needs more optimization.
4 554 0.937332328028 Henry Cohn, 2025, needs more optimization.
4 555 0.937361688429 Henry Cohn, 2025, needs more optimization.
4 556 0.937380785440 Henry Cohn, 2025, needs more optimization.
4 557 0.937468418241 Henry Cohn, 2025, needs more optimization.
4 558 0.937703346288 Henry Cohn, 2026, needs more optimization.
4 559 0.937710052202 Henry Cohn, 2025, needs more optimization.
4 560 0.937735092692 Henry Cohn, 2026, needs more optimization.
4 561 0.937829919092 Henry Cohn, 2026, needs more optimization.
4 562 0.937832503268 Henry Cohn, 2025, needs more optimization.
4 563 0.937955041395 Henry Cohn, 2025, needs more optimization.
4 564 0.937956581160 Henry Cohn, 2025, needs more optimization.
4 565 0.938152651024 Henry Cohn, 2025, needs more optimization.
4 566 0.938193533043 Henry Cohn, 2026, needs more optimization.
4 567 0.938202567350 Henry Cohn, 2025, needs more optimization.
4 568 0.938330431684 Henry Cohn, 2025, needs more optimization.
4 569 0.938356329917 Henry Cohn, 2026, needs more optimization.
4 570 0.938496721966 Henry Cohn, 2025, needs more optimization.
4 571 0.938513797968 Henry Cohn, 2025, needs more optimization.
4 572 0.938564289842 Henry Cohn, 2025, needs more optimization.
4 573 0.938764076152 Henry Cohn, 2025, needs more optimization.
4 574 0.938926625054 Henry Cohn, 2025, needs more optimization.
4 575 0.938934741529 Henry Cohn, 2025, needs more optimization.
4 576 0.939022786047 Henry Cohn, 2025, needs more optimization.
4 577 0.939023197122 Henry Cohn, 2025, needs more optimization.
4 578 0.939061344245 Henry Cohn, 2026, needs more optimization.
4 579 0.939148002539 Henry Cohn, 2025, needs more optimization.
4 580 0.939201274675 Henry Cohn, 2026, needs more optimization.
4 581 0.939214925124 Henry Cohn, 2026, needs more optimization.
4 582 0.939302950715 Henry Cohn, 2026, needs more optimization.
4 583 0.939358108278 Henry Cohn, 2025, needs more optimization.
4 584 0.939443313373 Henry Cohn, 2025, needs more optimization.
4 585 0.939460812797 Henry Cohn, 2025, needs more optimization.
4 586 0.939571319618 Henry Cohn, 2026, needs more optimization.
4 587 0.939573167768 Henry Cohn, 2026, needs more optimization.
4 588 0.939585867764 Henry Cohn, 2026, needs more optimization.
4 590 0.939702708834 Henry Cohn, 2025, needs more optimization.
4 592 0.939866827831 Henry Cohn, 2026, needs more optimization.
4 593 0.939871636807 Henry Cohn, 2026, needs more optimization.
4 594 0.939873198645 Henry Cohn, 2026, needs more optimization.
4 595 0.939983098032 Henry Cohn, 2026, needs more optimization.
4 596 0.939986602888 Henry Cohn, 2026, needs more optimization.
4 597 0.940099681249 Henry Cohn, 2025, needs more optimization.
4 598 0.940191207503 Henry Cohn, 2025, needs more optimization.
4 600 0.940371740470 Henry Cohn, 2025, needs more optimization.
4 601 0.940462666331 Henry Cohn, 2025, needs more optimization.
4 602 0.940522289962 Henry Cohn, 2026, needs more optimization.
4 603 0.940525601449 Henry Cohn, 2025, needs more optimization.
4 604 0.940582967501 Henry Cohn, 2026, needs more optimization.
4 605 0.940660094668 Henry Cohn, 2025, needs more optimization.
4 606 0.940661806135 Henry Cohn, 2026, needs more optimization.
4 607 0.940742759433 Henry Cohn, 2025, needs more optimization.
4 608 0.940825165665 Henry Cohn, 2026, needs more optimization.
4 609 0.940963167178 Henry Cohn, 2025, needs more optimization.
4 610 0.940978080401 Henry Cohn, 2026, needs more optimization.
4 611 0.941051663092 Henry Cohn, 2025, needs more optimization.
4 612 0.941115211625 Henry Cohn, 2025, needs more optimization.
4 613 0.941175083386 Henry Cohn, 2025, needs more optimization.
4 614 0.941194775682 Henry Cohn, 2026, needs more optimization.
4 615 0.941274274186 Henry Cohn, 2026, needs more optimization.
4 616 0.941285182477 Henry Cohn, 2025, needs more optimization.
4 618 0.941531802932 Henry Cohn, 2026, needs more optimization.
4 619 0.941542102122 Henry Cohn, 2025, needs more optimization.
4 620 0.941642267240 Henry Cohn, 2025, needs more optimization.
4 621 0.941645219406 Henry Cohn, 2025, needs more optimization.
4 622 0.941698195844 Henry Cohn, 2025, needs more optimization.
4 623 0.941737504146 Henry Cohn, 2026, needs more optimization.
4 624 0.941798551676 Henry Cohn, 2026, needs more optimization.
4 625 0.941981654285 Henry Cohn, 2025, needs more optimization.
4 626 0.942000937392 Henry Cohn, 2025, needs more optimization.
4 627 0.942024040458 Henry Cohn, 2025, needs more optimization.
4 628 0.942134996678 Henry Cohn, 2025, needs more optimization.
4 629 0.942192328200 Henry Cohn, 2025, needs more optimization.
4 630 0.942346216379 Henry Cohn, 2026, needs more optimization.
4 631 0.942363907789 Henry Cohn, 2025, needs more optimization.
4 632 0.942374827195 Henry Cohn, 2026, needs more optimization.
4 633 0.942473650646 Henry Cohn, 2025, needs more optimization.
4 634 0.942729029929 Henry Cohn, 2026, needs more optimization.
4 636 0.942737019308 Henry Cohn, 2025, needs more optimization.
4 637 0.942739881086 Henry Cohn, 2025, needs more optimization.
4 638 0.942776833443 Henry Cohn, 2026, needs more optimization.
4 639 0.942840895043 Henry Cohn, 2025, needs more optimization.
4 640 0.942921344577 Henry Cohn, 2026, needs more optimization.
4 641 0.943053199796 Henry Cohn, 2025, needs more optimization.
4 642 0.943076996937 Henry Cohn, 2026, needs more optimization.
4 643 0.943078020099 Henry Cohn, 2025, needs more optimization.
4 644 0.943180934082 Henry Cohn, 2025, needs more optimization.
4 645 0.943263346821 Henry Cohn, 2025, needs more optimization.
4 646 0.943264536655 Henry Cohn, 2025, needs more optimization.
4 647 0.943280433531 Henry Cohn, 2025, needs more optimization.
4 648 0.943291031540 Henry Cohn, 2025, needs more optimization.
4 649 0.943391411174 Henry Cohn, 2026, needs more optimization.
4 650 0.943396727354 Henry Cohn, 2026, needs more optimization.
4 651 0.943398346882 Henry Cohn, 2025, needs more optimization.
4 652 0.943420599120 Henry Cohn, 2026, needs more optimization.
4 653 0.943464499018 Henry Cohn, 2025, needs more optimization.
4 654 0.943468290411 Henry Cohn, 2026, needs more optimization.
4 655 0.943571235187 Henry Cohn, 2025, needs more optimization.
4 656 0.943573032589 Henry Cohn, 2026, needs more optimization.
4 657 0.943574218096 Henry Cohn, 2025, needs more optimization.
4 658 0.943601414683 Henry Cohn, 2025, needs more optimization.
4 659 0.943721696295 Henry Cohn, 2025, needs more optimization.
4 660 0.943757169743 Henry Cohn, 2026, needs more optimization.
4 661 0.943761106881 Henry Cohn, 2026, needs more optimization.
4 662 0.943765195886 Henry Cohn, 2025, needs more optimization.
4 664 0.943843773518 Henry Cohn, 2026, needs more optimization.
4 665 0.943851005572 Henry Cohn, 2025, needs more optimization.
4 666 0.943921780861 Henry Cohn, 2025, needs more optimization.
4 667 0.943923348839 Henry Cohn, 2025, needs more optimization.
4 668 0.943926024634 Henry Cohn, 2025, needs more optimization.
4 669 0.944000307055 Henry Cohn, 2025, needs more optimization.
4 670 0.944106517091 Henry Cohn, 2025, needs more optimization.
4 671 0.944118208019 Henry Cohn, 2025, needs more optimization.
4 672 0.944256472700 Henry Cohn, 2026, needs more optimization.
4 673 0.944357960966 Henry Cohn, 2025, needs more optimization.
4 674 0.944368205369 Henry Cohn, 2025, needs more optimization.
4 675 0.944537997000 Henry Cohn, 2025, needs more optimization.
4 676 0.944653424057 Henry Cohn, 2025, needs more optimization.
4 677 0.944654159692 Henry Cohn, 2026, needs more optimization.
4 679 0.944725392304 Henry Cohn, 2025, needs more optimization.
4 680 0.944745136087 Henry Cohn, 2025, needs more optimization.
4 681 0.944749674631 Henry Cohn, 2026, needs more optimization.
4 682 0.944859053848 Henry Cohn, 2026, needs more optimization.
4 683 0.944864452596 Henry Cohn, 2026, needs more optimization.
4 684 0.944933518727 Henry Cohn, 2025, needs more optimization.
4 685 0.944991182167 Henry Cohn, 2026, needs more optimization.
4 686 0.945085693951 Henry Cohn, 2025, needs more optimization.
4 687 0.945446050038 Henry Cohn, 2026, needs more optimization.
4 688 0.945446825922 Henry Cohn, 2026, needs more optimization.
4 689 0.945721674323 Henry Cohn, 2025, needs more optimization.
4 690 0.945777629919 Henry Cohn, 2026, needs more optimization.
4 691 0.945834751690 Henry Cohn, 2025, needs more optimization.
4 692 0.945892174743 Henry Cohn, 2026, needs more optimization.
4 693 0.945961558591 Henry Cohn, 2025, needs more optimization.
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4 695 0.946062307104 Henry Cohn, 2025, needs more optimization.
4 696 0.946064301813 Henry Cohn, 2026, needs more optimization.
4 697 0.946179220827 Henry Cohn, 2025, needs more optimization.
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4 700 0.946242389787 Henry Cohn, 2026, needs more optimization.
4 701 0.946299327617 Henry Cohn, 2026, needs more optimization.
4 702 0.946360743623 Henry Cohn, 2026, needs more optimization.
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4 704 0.946441318944 Henry Cohn, 2026, needs more optimization.
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4 706 0.946610192676 Henry Cohn, 2026, needs more optimization.
4 707 0.946622017817 Henry Cohn, 2026, needs more optimization.
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4 711 0.946797578469 Henry Cohn, 2025, needs more optimization.
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4 715 0.946865146098 Henry Cohn, 2026, needs more optimization.
4 716 0.946892530953 Henry Cohn, 2026, needs more optimization.
4 717 0.946943565916 Henry Cohn, 2026, needs more optimization.
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4 723 0.947165493995 Henry Cohn, 2026, needs more optimization.
4 724 0.947240345492 Henry Cohn, 2026, needs more optimization.
4 726 0.947247520945 Henry Cohn, 2025, needs more optimization.
4 727 0.947355354591 Henry Cohn, 2026, needs more optimization.
4 728 0.947430437257 Henry Cohn, 2026, needs more optimization.
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4 731 0.947552842569 Henry Cohn, 2026, needs more optimization.
4 732 0.947578648263 Henry Cohn, 2025, needs more optimization.
4 733 0.947580880680 Henry Cohn, 2025, needs more optimization.
4 734 0.947587098177 Henry Cohn, 2025, needs more optimization.
4 735 0.947679801418 Henry Cohn, 2026, needs more optimization.
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4 737 0.947797653156 Henry Cohn, 2026, needs more optimization.
4 738 0.947819269951 Henry Cohn, 2026, needs more optimization.
4 739 0.947981830405 Henry Cohn, 2026, needs more optimization.
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4 741 0.948078273286 Henry Cohn, 2026, needs more optimization.
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4 743 0.948093353662 Henry Cohn, 2026, needs more optimization.
4 744 0.948106489674 Henry Cohn, 2026, needs more optimization.
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4 746 0.948222072640 Henry Cohn, 2025, needs more optimization.
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4 748 0.948396609258 Henry Cohn, 2026, needs more optimization.
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4 750 0.948404264588 Henry Cohn, 2026, needs more optimization.
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4 754 0.948560623374 Henry Cohn, 2026, needs more optimization.
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4 758 0.948792950573 Henry Cohn, 2025, needs more optimization.
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4 760 0.948840430339 Henry Cohn, 2026, needs more optimization.
4 761 0.948846590102 Henry Cohn, 2026, needs more optimization.
4 762 0.948949691720 Henry Cohn, 2025, needs more optimization.
4 763 0.948951196392 Henry Cohn, 2025, needs more optimization.
4 764 0.948995346035 Henry Cohn, 2025, needs more optimization.
4 765 0.949001397228 Henry Cohn, 2025, needs more optimization.
4 766 0.949174288632 Henry Cohn, 2026, needs more optimization.
4 767 0.949180216694 Henry Cohn, 2026, needs more optimization.
4 768 0.949199812706 Henry Cohn, 2026, needs more optimization.
4 769 0.949245336819 Henry Cohn, 2025, needs more optimization.
4 770 0.949400655861 Henry Cohn, 2026, needs more optimization.
4 771 0.949407103985 Henry Cohn, 2026, needs more optimization.
4 772 0.949430772935 Henry Cohn, 2026, needs more optimization.
4 773 0.949433529396 Henry Cohn, 2026, needs more optimization.
4 774 0.949455425705 Henry Cohn, 2026, needs more optimization.
4 775 0.949488997959 Henry Cohn, 2026, needs more optimization.
4 776 0.949519384499 Henry Cohn, 2026, needs more optimization.
4 777 0.949685957377 Henry Cohn, 2026, needs more optimization.
4 778 0.949703143437 Henry Cohn, 2026, needs more optimization.
4 779 0.949716535062 Henry Cohn, 2026, needs more optimization.
4 780 0.949732425293 Henry Cohn, 2026, needs more optimization.
4 781 0.949987000772 Henry Cohn, 2025, needs more optimization.
4 782 0.949988721320 Henry Cohn, 2025, needs more optimization.
4 788 0.949998985865 Henry Cohn, 2025, needs more optimization.
4 789 0.950008069781 Henry Cohn, 2025, needs more optimization.
4 790 0.950206068340 Henry Cohn, 2026, needs more optimization.
4 791 0.950219265567 Henry Cohn, 2026, needs more optimization.
4 792 0.950243741902 Henry Cohn, 2026, needs more optimization.
4 806 0.950425128955 Henry Cohn, 2026, needs more optimization.
4 807 0.950447888812 Henry Cohn, 2026, needs more optimization.
4 808 0.950450816999 Henry Cohn, 2026, needs more optimization.
4 809 0.950463806899 Henry Cohn, 2026, needs more optimization.
4 810 0.950470505906 Henry Cohn, 2026, needs more optimization.
4 811 0.950491346887 Henry Cohn, 2026, needs more optimization.
4 812 0.950498096535 Henry Cohn, 2026, needs more optimization.
4 813 0.950524145027 Henry Cohn, 2026, needs more optimization.
4 814 0.950537274111 Henry Cohn, 2026, needs more optimization.
4 815 0.950566527955 Henry Cohn, 2026, needs more optimization.
4 816 0.950596492661 Henry Cohn, 2026, needs more optimization.
4 817 0.950615899528 Henry Cohn, 2026, needs more optimization.
4 818 0.950633486569 Henry Cohn, 2026, needs more optimization.
4 819 0.950646411677 Henry Cohn, 2026, needs more optimization.
4 820 0.950655675218 Henry Cohn, 2026, needs more optimization.
4 821 0.950682983311 Henry Cohn, 2026, needs more optimization.
4 822 0.950739138085 Henry Cohn, 2026, needs more optimization.
4 823 0.950785182187 Henry Cohn, 2026, needs more optimization.
4 840 0.950797547280 Henry Cohn, 2025, needs more optimization.
4 841 0.951624701851 Henry Cohn, 2026, needs more optimization.
4 842 0.951932284894 Henry Cohn, 2026, needs more optimization.
4 843 0.951950022478 Henry Cohn, 2026, needs more optimization.
4 844 0.951961649164 Henry Cohn, 2026, needs more optimization.
4 845 0.952192208755 Henry Cohn, 2025, needs more optimization.
4 847 0.952217603021 Henry Cohn, 2025, needs more optimization.
4 848 0.952218987686 Henry Cohn, 2025, needs more optimization.
4 849 0.952222127536 Henry Cohn, 2025, needs more optimization.
4 850 0.952239784851 Henry Cohn, 2025, needs more optimization.
4 851 0.952274634721 Henry Cohn, 2026, needs more optimization.
4 852 0.952284747198 Henry Cohn, 2026, needs more optimization.
4 853 0.952300651380 Henry Cohn, 2026, needs more optimization.
4 854 0.952385981186 Henry Cohn, 2026, needs more optimization.
4 856 0.952469970909 Henry Cohn, 2025, needs more optimization.
4 857 0.952471686698 Henry Cohn, 2025, needs more optimization.
4 858 0.952695248097 Henry Cohn, 2025, needs more optimization.
4 859 0.952698737895 Henry Cohn, 2026, needs more optimization.
4 860 0.952700137997 Henry Cohn, 2026, needs more optimization.
4 861 0.952757307626 Henry Cohn, 2026, needs more optimization.
4 862 0.952859748402 Henry Cohn, 2026, needs more optimization.
4 863 0.952869680563 Henry Cohn, 2026, needs more optimization.
4 865 0.952875917661 Henry Cohn, 2026, needs more optimization.
4 866 0.952882242899 Henry Cohn, 2025, needs more optimization.
4 867 0.952902665462 Henry Cohn, 2025, needs more optimization.
4 868 0.952906611806 Henry Cohn, 2025, needs more optimization.
4 869 0.952912284416 Henry Cohn, 2026, needs more optimization.
4 872 0.953067626897 Henry Cohn, 2025, needs more optimization.
4 875 0.953104992009 Henry Cohn, 2025, needs more optimization.
4 876 0.953108610967 Henry Cohn, 2025, needs more optimization.
4 877 0.953110513304 Henry Cohn, 2025, needs more optimization.
4 878 0.953201275044 Henry Cohn, 2026, needs more optimization.
4 880 0.953473362023 Henry Cohn, 2025, needs more optimization.
4 881 0.953498792528 Henry Cohn, 2025, needs more optimization.
4 882 0.953511928838 Henry Cohn, 2026, needs more optimization.
4 883 0.953513789505 Henry Cohn, 2026, needs more optimization.
4 884 0.953525074998 Henry Cohn, 2025, needs more optimization.
4 885 0.953660979356 Henry Cohn, 2025, needs more optimization.
4 886 0.953669586269 Henry Cohn, 2025, needs more optimization.
4 887 0.953692518734 Henry Cohn, 2026, needs more optimization.
4 888 0.953700645565 Henry Cohn, 2026, needs more optimization.
4 889 0.953706262664 Henry Cohn, 2025, needs more optimization.
4 890 0.953717464100 Henry Cohn, 2025, needs more optimization.
4 891 0.953856705201 Henry Cohn, 2025, needs more optimization.
4 893 0.953864479437 Henry Cohn, 2025, needs more optimization.
4 894 0.953875593353 Henry Cohn, 2026, needs more optimization.
4 895 0.953876489808 Henry Cohn, 2025, needs more optimization.
4 896 0.953887694041 Henry Cohn, 2026, needs more optimization.
4 897 0.953928577875 Henry Cohn, 2026, needs more optimization.
4 898 0.953936780784 Henry Cohn, 2026, needs more optimization.
4 899 0.954061867925 Henry Cohn, 2026, needs more optimization.
4 900 0.954062876830 Henry Cohn, 2026, needs more optimization.
4 901 0.954065787352 Henry Cohn, 2026, needs more optimization.
4 902 0.954068349973 Henry Cohn, 2025, needs more optimization.
4 904 0.954139878150 Henry Cohn, 2025, needs more optimization.
4 905 0.954145649734 Henry Cohn, 2025, needs more optimization.
4 906 0.954152636902 Henry Cohn, 2025, needs more optimization.
4 907 0.954159588073 Henry Cohn, 2026, needs more optimization.
4 908 0.954165607366 Henry Cohn, 2025, needs more optimization.
4 909 0.954182216184 Henry Cohn, 2026, needs more optimization.
4 910 0.954196017446 Henry Cohn, 2026, needs more optimization.
4 911 0.954215213612 Henry Cohn, 2026, needs more optimization.
4 912 0.954332283926 Henry Cohn, 2026, needs more optimization.
4 913 0.954332978380 Henry Cohn, 2025, needs more optimization.
4 914 0.954361550477 Henry Cohn, 2026, needs more optimization.
4 915 0.954371201370 Henry Cohn, 2025, needs more optimization.
4 916 0.954372638011 Henry Cohn, 2025, needs more optimization.
4 917 0.954373815292 Henry Cohn, 2025, needs more optimization.
4 918 0.954377733468 Henry Cohn, 2025, needs more optimization.
4 919 0.954486263001 Henry Cohn, 2026, needs more optimization.
4 920 0.954544086173 Henry Cohn, 2026, needs more optimization.
4 921 0.954548289830 Henry Cohn, 2026, needs more optimization.
4 922 0.954633358317 Henry Cohn, 2026, needs more optimization.
4 923 0.954633838585 Henry Cohn, 2026, needs more optimization.
4 924 0.954806246462 Henry Cohn, 2025, needs more optimization.
4 925 0.954808607347 Henry Cohn, 2025, needs more optimization.
4 926 0.954811686442 Henry Cohn, 2025, needs more optimization.
4 927 0.954936284612 Henry Cohn, 2025, needs more optimization.
4 928 0.954936964671 Henry Cohn, 2026, needs more optimization.
4 929 0.954953403066 Henry Cohn, 2026, needs more optimization.
4 930 0.954992520001 Henry Cohn, 2025, needs more optimization.
4 931 0.955012597814 Henry Cohn, 2026, needs more optimization.
4 932 0.955021331426 Henry Cohn, 2025, needs more optimization.
4 933 0.955042300106 Henry Cohn, 2026, needs more optimization.
4 934 0.955113964488 Henry Cohn, 2026, needs more optimization.
4 935 0.955250315669 Henry Cohn, 2026, needs more optimization.
4 937 0.955255579061 Henry Cohn, 2026, needs more optimization.
4 938 0.955261977602 Henry Cohn, 2026, needs more optimization.
4 940 0.955356743070 Henry Cohn, 2025, needs more optimization.
4 942 0.955384752051 Henry Cohn, 2026, needs more optimization.
4 943 0.955410528628 Henry Cohn, 2026, needs more optimization.
4 944 0.955626784466 Henry Cohn, 2026, needs more optimization.
4 945 0.955651274771 Henry Cohn, 2026, needs more optimization.
4 946 0.955663730596 Henry Cohn, 2026, needs more optimization.
4 947 0.955734221450 Henry Cohn, 2026, needs more optimization.
4 948 0.955814638725 Henry Cohn, 2026, needs more optimization.
4 949 0.955816098291 Henry Cohn, 2026, needs more optimization.
4 950 0.955818526127 Henry Cohn, 2026, needs more optimization.
4 951 0.955823780266 Henry Cohn, 2026, needs more optimization.
4 952 0.955901860381 Henry Cohn, 2026, needs more optimization.
4 953 0.955904599015 Henry Cohn, 2026, needs more optimization.
4 954 0.955908026022 Henry Cohn, 2026, needs more optimization.
4 955 0.955912557426 Henry Cohn, 2026, needs more optimization.
4 956 0.955914956613 Henry Cohn, 2026, needs more optimization.
4 957 0.955916742199 Henry Cohn, 2026, needs more optimization.
4 958 0.955931778657 Henry Cohn, 2026, needs more optimization.
4 959 0.955934470120 Henry Cohn, 2026, needs more optimization.
4 960 0.955934538885 Henry Cohn, 2025, needs more optimization.
4 961 0.956011466695 Henry Cohn, 2026, needs more optimization.
4 962 0.956015541503 Henry Cohn, 2026, needs more optimization.
4 964 0.956100925104 Henry Cohn, 2026, needs more optimization.
4 965 0.956103673391 Henry Cohn, 2026, needs more optimization.
4 966 0.956104990579 Henry Cohn, 2026, needs more optimization.
4 967 0.956150085065 Henry Cohn, 2026, needs more optimization.
4 969 0.956152349556 Henry Cohn, 2026, needs more optimization.
4 970 0.956162959522 Henry Cohn, 2026, needs more optimization.
4 971 0.956180010786 Henry Cohn, 2026, needs more optimization.
4 972 0.956232654010 Henry Cohn, 2026, needs more optimization.
4 973 0.956331648598 Henry Cohn, 2025, needs more optimization.
4 974 0.956332591997 Henry Cohn, 2025, needs more optimization.
4 975 0.956336720773 Henry Cohn, 2026, needs more optimization.
4 976 0.956436399700 Henry Cohn, 2026, needs more optimization.
4 977 0.956436615854 Henry Cohn, 2025, needs more optimization.
4 978 0.956451283150 Henry Cohn, 2026, needs more optimization.
4 979 0.956490512655 Henry Cohn, 2025, needs more optimization.
4 980 0.956507243147 Henry Cohn, 2025, needs more optimization.
4 981 0.956577480898 Henry Cohn, 2026, needs more optimization.
4 982 0.956584248453 Henry Cohn, 2026, needs more optimization.
4 983 0.956655794511 Henry Cohn, 2025, needs more optimization.
4 984 0.956677294066 Henry Cohn, 2026, needs more optimization.
4 985 0.956682587765 Henry Cohn, 2026, needs more optimization.
4 986 0.956684377189 Henry Cohn, 2026, needs more optimization.
4 987 0.956727897983 Henry Cohn, 2026, needs more optimization.
4 988 0.956859819250 Henry Cohn, 2026, needs more optimization.
4 989 0.956957088473 Henry Cohn, 2026, needs more optimization.
4 990 0.957090467119 Henry Cohn, 2026, needs more optimization.
4 991 0.957174013613 Henry Cohn, 2026, needs more optimization.
4 992 0.957233711366 Henry Cohn, 2026, needs more optimization.
4 994 0.957330300484 Henry Cohn, 2026, needs more optimization.
4 995 0.957468615157 Henry Cohn, 2026, needs more optimization.
4 997 0.957469247295 Henry Cohn, 2025, needs more optimization.
4 998 0.957621777801 Henry Cohn, 2025, needs more optimization.
4 999 0.957624065661 Henry Cohn, 2025, needs more optimization.
4 1000 0.957724044528 Henry Cohn, 2026, needs more optimization.
4 1001 0.957725490244 Henry Cohn, 2026, needs more optimization.
4 1002 0.957879169599 Henry Cohn, 2025, needs more optimization.
4 1003 0.957879722807 Henry Cohn, 2025, needs more optimization.
4 1004 0.957932175239 Henry Cohn, 2026, needs more optimization.
4 1005 0.957932661703 Henry Cohn, 2026, needs more optimization.
4 1006 0.958015395640 Henry Cohn, 2026, needs more optimization.
4 1007 0.958017179892 Henry Cohn, 2026, needs more optimization.
4 1008 0.958025392605 Henry Cohn, 2025, needs more optimization.
4 1009 0.958106117370 Henry Cohn, 2026, needs more optimization.
4 1010 0.958106563311 Henry Cohn, 2026, needs more optimization.
4 1011 0.958226110686 Henry Cohn, 2026, needs more optimization.
4 1012 0.958235111952 Henry Cohn, 2025, needs more optimization.
4 1013 0.958243797980 Henry Cohn, 2025, needs more optimization.
4 1014 0.958252619948 Henry Cohn, 2026, needs more optimization.
4 1015 0.958307571281 Henry Cohn, 2025, needs more optimization.
4 1016 0.958323656469 Henry Cohn, 2026, needs more optimization.
4 1017 0.958432858016 Henry Cohn, 2026, needs more optimization.
4 1018 0.958438216138 Henry Cohn, 2026, needs more optimization.
4 1019 0.958443399717 Henry Cohn, 2026, needs more optimization.
4 1020 0.958491952684 Henry Cohn, 2026, needs more optimization.
4 1021 0.958497702940 Henry Cohn, 2026, needs more optimization.
4 1023 0.958667893556 Henry Cohn, 2025, needs more optimization.
4 1024 0.958676090349 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 0.673830986224 Henry Cohn, 2025.
5 94 0.675154811372 Henry Cohn, 2025.
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 0.715099002544 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
5 125 0.716589774161 Henry Cohn, 2025.
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 0.724187141022 Henry Cohn, 2026, needs more optimization.
5 133 0.725096024568 Henry Cohn, 2026, needs more optimization.
5 134 0.726667487692 Henry Cohn, 2026, needs more optimization.
5 135 0.727819930944 Henry Cohn, 2025.
5 136 0.728641959070 Henry Cohn, 2026.
5 137 0.730011100633 Henry Cohn, 2025.
5 138 0.730143082796 Henry Cohn, 2025.
5 139 0.731013425800 Henry Cohn, 2026, needs more optimization.
5 140 0.731880138963 Henry Cohn, 2025.
5 141 0.732960070489 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 0.739521406019 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 0.743500742995 Henry Cohn, 2025.
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 0.758619562940 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 0.762581523757 Henry Cohn, 2026, needs more optimization.
5 178 0.763315108223 Henry Cohn, 2025.
5 179 0.763757298175 Henry Cohn, 2026, needs more optimization.
5 180 0.763981428591 Henry Cohn, 2026, needs more optimization.
5 181 0.764793757607 Henry Cohn, 2026, needs more optimization.
5 182 0.765131874610 Henry Cohn, 2026, needs more optimization.
5 183 0.765682100282 Henry Cohn, 2026, needs more optimization.
5 184 0.766389332741 Henry Cohn, 2026, needs more optimization.
5 185 0.766837211808 Henry Cohn, 2026, needs more optimization.
5 186 0.767281859923 Henry Cohn, 2026, needs more optimization.
5 187 0.767838929503 Henry Cohn, 2026, needs more optimization.
5 188 0.768546384654 Henry Cohn, 2026, needs more optimization.
5 189 0.769621056776 Henry Cohn, 2026, needs more optimization.
5 190 0.770220241203 Henry Cohn, 2025.
5 191 0.770477151449 Henry Cohn, 2025.
5 192 0.771139501692 Henry Cohn, 2026, needs more optimization.
5 193 0.771332727721 Henry Cohn, 2026, needs more optimization.
5 194 0.772357310102 Henry Cohn, 2025.
5 195 0.772914025091 Henry Cohn, 2025.
5 196 0.773820141713 Henry Cohn, 2025.
5 197 0.774290878773 Henry Cohn, 2025.
5 198 0.774933378717 Henry Cohn, 2026, needs more optimization.
5 199 0.775242540360 Henry Cohn, 2025.
5 200 0.775814258853 Henry Cohn, 2025.
5 201 0.776374604752 Henry Cohn, 2026, needs more optimization.
5 202 0.777028127031 Henry Cohn, 2026, needs more optimization.
5 203 0.777810844710 Henry Cohn, 2026, needs more optimization.
5 204 0.778262339953 Henry Cohn, 2025.
5 205 0.779048071982 Henry Cohn, 2025.
5 206 0.779364771310 Henry Cohn, 2026, needs more optimization.
5 207 0.780063470637 Henry Cohn, 2026, needs more optimization.
5 208 0.780741024052 Henry Cohn, 2026, needs more optimization.
5 209 0.781330258270 Henry Cohn, 2026, needs more optimization.
5 210 0.782169856126 Henry Cohn, 2026, needs more optimization.
5 211 0.782800982838 Henry Cohn, 2026, needs more optimization.
5 212 0.783016654957 Henry Cohn, 2025.
5 213 0.783587855604 Henry Cohn, 2026, needs more optimization.
5 214 0.784221920412 Henry Cohn, 2025.
5 215 0.784440391336 Henry Cohn, 2025.
5 216 0.785136183086 Henry Cohn, 2026, needs more optimization.
5 217 0.785510050827 Henry Cohn, 2025.
5 218 0.785996484357 Henry Cohn, 2025.
5 219 0.786676988085 Henry Cohn, 2026, needs more optimization.
5 220 0.787295059910 Henry Cohn, 2025.
5 221 0.787561403335 Henry Cohn, 2025.
5 222 0.788126323248 Henry Cohn, 2025.
5 223 0.788437486442 Henry Cohn, 2025.
5 224 0.788866206268 Henry Cohn, 2025.
5 225 0.789325624436 Henry Cohn, 2025.
5 226 0.789487643417 Henry Cohn, 2026, needs more optimization.
5 227 0.789764435439 Henry Cohn, 2026, needs more optimization.
5 228 0.790389220467 Henry Cohn, 2026, needs more optimization.
5 229 0.790656107169 Henry Cohn, 2026, needs more optimization.
5 230 0.791410552263 Henry Cohn, 2026, needs more optimization.
5 231 0.791681381153 Henry Cohn, 2026, needs more optimization.
5 232 0.792366664976 Henry Cohn, 2026, needs more optimization.
5 233 0.792635775713 Henry Cohn, 2026, needs more optimization.
5 234 0.792936161090 Henry Cohn, 2026, needs more optimization.
5 235 0.793374220825 Henry Cohn, 2026, needs more optimization.
5 236 0.794002574311 Henry Cohn, 2026, needs more optimization.
5 237 0.794579922950 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 0.796790771833 Henry Cohn, 2026, needs more optimization.
5 243 0.797091538228 Henry Cohn, 2026, needs more optimization.
5 244 0.797576344095 Henry Cohn, 2026, needs more optimization.
5 245 0.797636988343 Henry Cohn, 2026, needs more optimization.
5 246 0.797900463165 Henry Cohn, 2026, needs more optimization.
5 247 0.797961693690 Henry Cohn, 2026, needs more optimization.
5 248 0.798580940805 Henry Cohn, 2026, needs more optimization.
5 249 0.798819600939 Henry Cohn, 2026, needs more optimization.
5 250 0.799102103951 Henry Cohn, 2026, needs more optimization.
5 251 0.799463632907 Henry Cohn, 2026, needs more optimization.
5 252 0.799785430587 Henry Cohn, 2026, needs more optimization.
5 253 0.800204692658 Henry Cohn, 2026, needs more optimization.
5 254 0.800362627172 Henry Cohn, 2026, needs more optimization.
5 255 0.800684050064 Henry Cohn, 2026, needs more optimization.
5 256 0.801157632990 Henry Cohn, 2026, needs more optimization.
5 257 0.801509983310 Henry Cohn, 2026, needs more optimization.
5 258 0.802272849424 Henry Cohn, 2026, needs more optimization.
5 259 0.802472388888 Henry Cohn, 2026, needs more optimization.
5 260 0.802955540642 Henry Cohn, 2026, needs more optimization.
5 261 0.803389071665 Henry Cohn, 2026, needs more optimization.
5 262 0.803753543401 Henry Cohn, 2026, needs more optimization.
5 263 0.803971629049 Henry Cohn, 2026, needs more optimization.
5 264 0.804313740782 Henry Cohn, 2026, needs more optimization.
5 265 0.804474671698 Henry Cohn, 2026, needs more optimization.
5 266 0.804634142894 Henry Cohn, 2026, needs more optimization.
5 267 0.804989975129 Henry Cohn, 2026, needs more optimization.
5 268 0.805324711335 Henry Cohn, 2026, needs more optimization.
5 269 0.805464810769 Henry Cohn, 2026, needs more optimization.
5 270 0.805596754447 Henry Cohn, 2026, needs more optimization.
5 271 0.805929380100 Henry Cohn, 2026, needs more optimization.
5 272 0.806276531765 Henry Cohn, 2026, needs more optimization.
5 273 0.806363181856 Henry Cohn, 2026, needs more optimization.
5 274 0.806401832709 Henry Cohn, 2026, needs more optimization.
5 275 0.806536381064 Henry Cohn, 2026, needs more optimization.
5 277 0.806554230123 Henry Cohn, 2026, needs more optimization.
5 278 0.806727308582 Henry Cohn, 2026, needs more optimization.
5 279 0.806888910396 Henry Cohn, 2026, needs more optimization.
5 282 0.807198164900 Henry Cohn, 2026, needs more optimization.
5 283 0.807833150762 Henry Cohn, 2026, needs more optimization.
5 284 0.808253548978 Henry Cohn, 2026, needs more optimization.
5 285 0.808660074599 Henry Cohn, 2026, needs more optimization.
5 286 0.809216550393 Henry Cohn, 2026, needs more optimization.
5 287 0.809600405797 Henry Cohn, 2026, needs more optimization.
5 288 0.810250884750 Henry Cohn, 2026, needs more optimization.
5 289 0.810478057953 Henry Cohn, 2026, needs more optimization.
5 290 0.811175808254 Henry Cohn, 2026, needs more optimization.
5 291 0.811819311420 Henry Cohn, 2026, needs more optimization.
5 292 0.812315403741 Henry Cohn, 2026, needs more optimization.
5 293 0.812721102542 Henry Cohn, 2026, needs more optimization.
5 294 0.813143628184 Henry Cohn, 2026, needs more optimization.
5 295 0.813744198452 Henry Cohn, 2026, needs more optimization.
5 296 0.813999789538 Henry Cohn, 2026, needs more optimization.
5 297 0.814703809102 Henry Cohn, 2026, needs more optimization.
5 298 0.815109799991 Henry Cohn, 2026, needs more optimization.
5 299 0.815466870898 Henry Cohn, 2026, needs more optimization.
5 300 0.816073676287 Henry Cohn, 2026, needs more optimization.
5 301 0.816814516969 Henry Cohn, 2026, needs more optimization.
5 302 0.817416382715 Henry Cohn, 2026, needs more optimization.
5 303 0.817678249405 Henry Cohn, 2025, needs more optimization.
5 304 0.818236802717 Henry Cohn, 2026, needs more optimization.
5 305 0.818530915024 Henry Cohn, 2025, needs more optimization.
5 306 0.818846725648 Henry Cohn, 2026, needs more optimization.
5 307 0.819649993393 Ilmari Vahteristo, 2026.
5 308 0.819704042350 Henry Cohn, 2025, needs more optimization.
5 309 0.820136258550 Henry Cohn, 2025, needs more optimization.
5 310 0.820291870315 Henry Cohn, 2025, needs more optimization.
5 311 0.820683934305 Henry Cohn, 2025, needs more optimization.
5 312 0.820907477416 Henry Cohn, 2025, needs more optimization.
5 313 0.821238678583 Henry Cohn, 2025, needs more optimization.
5 314 0.821842718616 Henry Cohn, 2025, needs more optimization.
5 315 0.822166006099 Henry Cohn, 2025, needs more optimization.
5 316 0.822348273561 Henry Cohn, 2026, needs more optimization.
5 317 0.822600119096 Henry Cohn, 2025, needs more optimization.
5 318 0.822851367310 Henry Cohn, 2025, needs more optimization.
5 319 0.823386083659 Henry Cohn, 2026, needs more optimization.
5 321 0.823945293516 Henry Cohn, 2025, needs more optimization.
5 322 0.824227974650 Henry Cohn, 2026, needs more optimization.
5 323 0.824521620521 Henry Cohn, 2025, needs more optimization.
5 324 0.824672784814 Ilmari Vahteristo, 2026.
5 325 0.825136817529 Henry Cohn, 2026, needs more optimization.
5 326 0.825464785143 Henry Cohn, 2026, needs more optimization.
5 327 0.825636523896 Henry Cohn, 2026, needs more optimization.
5 328 0.826102388552 Henry Cohn, 2025, needs more optimization.
5 329 0.826424481057 Ilmari Vahteristo, 2026.
5 330 0.826545411548 Henry Cohn, 2026, needs more optimization.
5 331 0.826573216614 Ilmari Vahteristo, 2026.
5 332 0.827012207972 Ilmari Vahteristo, 2026.
5 333 0.827486994092 Ilmari Vahteristo, 2026.
5 334 0.827773996545 Ilmari Vahteristo, 2026.
5 335 0.828006262238 Henry Cohn, 2026, needs more optimization.
5 336 0.828034033820 Ilmari Vahteristo, 2026.
5 337 0.828501751462 Ilmari Vahteristo, 2026.
5 338 0.828711070437 Henry Cohn, 2026, needs more optimization.
5 339 0.828788082318 Ilmari Vahteristo, 2026.
5 340 0.829152368222 Henry Cohn, 2025, needs more optimization.
5 341 0.829388117676 Henry Cohn, 2026, needs more optimization.
5 342 0.829748545697 Henry Cohn, 2026, needs more optimization.
5 343 0.829988638760 Ilmari Vahteristo, 2026.
5 344 0.830288948112 Henry Cohn, 2025, needs more optimization.
5 345 0.830334873964 Ilmari Vahteristo, 2026.
5 346 0.830743543200 Henry Cohn, 2025, needs more optimization.
5 347 0.830944830997 Ilmari Vahteristo, 2026.
5 348 0.831093213465 Ilmari Vahteristo, 2026.
5 349 0.831549947592 Henry Cohn, 2026, needs more optimization.
5 350 0.831603555680 Henry Cohn, 2026, needs more optimization.
5 351 0.831919598187 Henry Cohn, 2025, needs more optimization.
5 352 0.831978050097 Ilmari Vahteristo, 2026.
5 353 0.832359675560 Ilmari Vahteristo, 2026.
5 354 0.832781308439 Ilmari Vahteristo, 2026.
5 355 0.832820133321 Ilmari Vahteristo, 2026.
5 356 0.833098647880 Ilmari Vahteristo, 2026.
5 357 0.833368449930 Henry Cohn, 2025, needs more optimization.
5 358 0.833445277288 Henry Cohn, 2026, needs more optimization.
5 359 0.833777259172 Ilmari Vahteristo, 2026.
5 360 0.833869567239 Henry Cohn, 2026, needs more optimization.
5 361 0.834182975616 Henry Cohn, 2025, needs more optimization.
5 362 0.834256973601 Henry Cohn, 2026, needs more optimization.
5 363 0.834618950083 Henry Cohn, 2025, needs more optimization.
5 364 0.834837068276 Henry Cohn, 2026, needs more optimization.
5 365 0.835048430244 Henry Cohn, 2026, needs more optimization.
5 366 0.835378855985 Henry Cohn, 2026, needs more optimization.
5 367 0.835389435183 Henry Cohn, 2025, needs more optimization.
5 368 0.835712494152 Henry Cohn, 2026, needs more optimization.
5 369 0.835765894972 Henry Cohn, 2025, needs more optimization.
5 370 0.836140292070 Henry Cohn, 2026, needs more optimization.
5 371 0.836473545501 Henry Cohn, 2025, needs more optimization.
5 372 0.836679323230 Henry Cohn, 2026, needs more optimization.
5 373 0.836702413007 Henry Cohn, 2026, needs more optimization.
5 374 0.836999067577 Henry Cohn, 2026, needs more optimization.
5 375 0.837271070757 Henry Cohn, 2025, needs more optimization.
5 376 0.837539201868 Henry Cohn, 2025, needs more optimization.
5 377 0.837708951550 Henry Cohn, 2025, needs more optimization.
5 378 0.838003296452 Henry Cohn, 2025, needs more optimization.
5 379 0.838083866651 Henry Cohn, 2026, needs more optimization.
5 380 0.838327924680 Henry Cohn, 2025, needs more optimization.
5 381 0.838354217251 Henry Cohn, 2025, needs more optimization.
5 382 0.838798152226 Henry Cohn, 2025, needs more optimization.
5 383 0.838881488627 Henry Cohn, 2025, needs more optimization.
5 384 0.839339620040 Henry Cohn, 2025, needs more optimization.
5 385 0.839355829121 Henry Cohn, 2025, needs more optimization.
5 386 0.839622713054 Henry Cohn, 2026, needs more optimization.
5 387 0.839804191321 Henry Cohn, 2026, needs more optimization.
5 388 0.839991024596 Henry Cohn, 2025, needs more optimization.
5 389 0.840516182174 Henry Cohn, 2026, needs more optimization.
5 390 0.840803815311 Henry Cohn, 2025, needs more optimization.
5 391 0.840904105112 Henry Cohn, 2026, needs more optimization.
5 392 0.840920101150 Henry Cohn, 2026, needs more optimization.
5 393 0.841234032091 Henry Cohn, 2025, needs more optimization.
5 394 0.841517571002 Henry Cohn, 2025, needs more optimization.
5 395 0.841518430864 Henry Cohn, 2025, needs more optimization.
5 396 0.841721666351 Henry Cohn, 2026, needs more optimization.
5 397 0.841929833352 Henry Cohn, 2026, needs more optimization.
5 398 0.842017901054 Henry Cohn, 2026, needs more optimization.
5 399 0.842351224361 Henry Cohn, 2025, needs more optimization.
5 400 0.842667381746 Henry Cohn, 2026, needs more optimization.
5 401 0.842755099804 Henry Cohn, 2025, needs more optimization.
5 402 0.843046815328 Henry Cohn, 2026, needs more optimization.
5 403 0.843178483011 Henry Cohn, 2025, needs more optimization.
5 404 0.843229111918 Henry Cohn, 2026, needs more optimization.
5 405 0.843596031205 Henry Cohn, 2025, needs more optimization.
5 406 0.843634464056 Henry Cohn, 2026, needs more optimization.
5 407 0.843834979070 Henry Cohn, 2025, needs more optimization.
5 408 0.843903654365 Henry Cohn, 2026, needs more optimization.
5 409 0.843990630575 Henry Cohn, 2025, needs more optimization.
5 410 0.844138429797 Henry Cohn, 2025, needs more optimization.
5 411 0.844505725469 Henry Cohn, 2026, needs more optimization.
5 412 0.844673191519 Henry Cohn, 2026, needs more optimization.
5 413 0.844824973155 Henry Cohn, 2025, needs more optimization.
5 414 0.844870169871 Henry Cohn, 2025, needs more optimization.
5 415 0.845396059797 Henry Cohn, 2025, needs more optimization.
5 416 0.845502920468 Henry Cohn, 2025, needs more optimization.
5 417 0.845632826733 Henry Cohn, 2025, needs more optimization.
5 418 0.845740891849 Henry Cohn, 2026, needs more optimization.
5 419 0.845818752271 Henry Cohn, 2025, needs more optimization.
5 420 0.845998590783 Henry Cohn, 2026, needs more optimization.
5 421 0.846210387692 Henry Cohn, 2026, needs more optimization.
5 422 0.846488117361 Henry Cohn, 2025, needs more optimization.
5 423 0.846740415916 Henry Cohn, 2025, needs more optimization.
5 424 0.846828782623 Henry Cohn, 2026, needs more optimization.
5 425 0.847111917510 Henry Cohn, 2026, needs more optimization.
5 426 0.847141264817 Henry Cohn, 2025, needs more optimization.
5 427 0.847356510265 Henry Cohn, 2026, needs more optimization.
5 428 0.847780543164 Henry Cohn, 2026, needs more optimization.
5 429 0.847871831387 Henry Cohn, 2026, needs more optimization.
5 430 0.848148846253 Henry Cohn, 2025, needs more optimization.
5 431 0.848182648352 Henry Cohn, 2026, needs more optimization.
5 432 0.848428081817 Henry Cohn, 2025, needs more optimization.
5 433 0.848473227014 Henry Cohn, 2025, needs more optimization.
5 434 0.848750844911 Henry Cohn, 2026, needs more optimization.
5 435 0.848935967498 Henry Cohn, 2025, needs more optimization.
5 436 0.849091145842 Henry Cohn, 2026, needs more optimization.
5 437 0.849166823783 Henry Cohn, 2025, needs more optimization.
5 438 0.849457353237 Henry Cohn, 2026, needs more optimization.
5 439 0.849665555849 Henry Cohn, 2026, needs more optimization.
5 440 0.849761491108 Henry Cohn, 2026, needs more optimization.
5 441 0.849905344307 Henry Cohn, 2026, needs more optimization.
5 442 0.850005854540 Henry Cohn, 2026, needs more optimization.
5 443 0.850173997001 Henry Cohn, 2026, needs more optimization.
5 444 0.850591420205 Henry Cohn, 2025, needs more optimization.
5 445 0.850688858705 Henry Cohn, 2025, needs more optimization.
5 446 0.850872757151 Henry Cohn, 2026, needs more optimization.
5 447 0.851046882825 Henry Cohn, 2025, needs more optimization.
5 448 0.851136609114 Henry Cohn, 2026, needs more optimization.
5 449 0.851144183240 Henry Cohn, 2025, needs more optimization.
5 450 0.851519869513 Henry Cohn, 2025, needs more optimization.
5 451 0.851797504621 Henry Cohn, 2025, needs more optimization.
5 452 0.851801424273 Henry Cohn, 2026, needs more optimization.
5 453 0.852169963403 Henry Cohn, 2026, needs more optimization.
5 454 0.852178960242 Henry Cohn, 2026, needs more optimization.
5 455 0.852341044858 Henry Cohn, 2026, needs more optimization.
5 456 0.852509268186 Henry Cohn, 2026, needs more optimization.
5 457 0.852749067895 Henry Cohn, 2025, needs more optimization.
5 458 0.852753611237 Henry Cohn, 2026, needs more optimization.
5 459 0.852826843904 Henry Cohn, 2026, needs more optimization.
5 460 0.853097261023 Henry Cohn, 2026, needs more optimization.
5 461 0.853282800509 Henry Cohn, 2026, needs more optimization.
5 462 0.853612151025 Henry Cohn, 2026, needs more optimization.
5 463 0.853616344570 Henry Cohn, 2025, needs more optimization.
5 464 0.853696327126 Henry Cohn, 2026, needs more optimization.
5 465 0.853910231679 Henry Cohn, 2025, needs more optimization.
5 466 0.854125175508 Henry Cohn, 2025, needs more optimization.
5 467 0.854126192783 Henry Cohn, 2026, needs more optimization.
5 468 0.854465241932 Henry Cohn, 2025, needs more optimization.
5 469 0.854481278069 Henry Cohn, 2026, needs more optimization.
5 470 0.854680276390 Henry Cohn, 2026, needs more optimization.
5 471 0.854796588645 Henry Cohn, 2026, needs more optimization.
5 472 0.854963819384 Henry Cohn, 2025, needs more optimization.
5 473 0.855271668132 Henry Cohn, 2025, needs more optimization.
5 474 0.855274943930 Henry Cohn, 2025, needs more optimization.
5 475 0.855315364840 Henry Cohn, 2025, needs more optimization.
5 476 0.855484878935 Henry Cohn, 2026, needs more optimization.
5 477 0.855695759041 Henry Cohn, 2025, needs more optimization.
5 478 0.855841719507 Henry Cohn, 2026, needs more optimization.
5 479 0.856359033178 Henry Cohn, 2026, needs more optimization.
5 481 0.856438290668 Henry Cohn, 2025, needs more optimization.
5 482 0.856474710540 Henry Cohn, 2026, needs more optimization.
5 483 0.856712971651 Henry Cohn, 2025, needs more optimization.
5 484 0.856722994352 Henry Cohn, 2025, needs more optimization.
5 485 0.856820007940 Henry Cohn, 2025, needs more optimization.
5 486 0.857094821423 Henry Cohn, 2025, needs more optimization.
5 487 0.857117989588 Henry Cohn, 2025, needs more optimization.
5 488 0.857287179940 Henry Cohn, 2025, needs more optimization.
5 489 0.857435857392 Henry Cohn, 2025, needs more optimization.
5 490 0.857565211369 Henry Cohn, 2025, needs more optimization.
5 491 0.857620435328 Henry Cohn, 2025, needs more optimization.
5 492 0.857846614823 Henry Cohn, 2025, needs more optimization.
5 493 0.857887587311 Henry Cohn, 2026, needs more optimization.
5 494 0.857978095786 Henry Cohn, 2026, needs more optimization.
5 495 0.858367120376 Henry Cohn, 2025, needs more optimization.
5 496 0.858507150778 Henry Cohn, 2025, needs more optimization.
5 497 0.858685307857 Henry Cohn, 2025, needs more optimization.
5 498 0.858833192245 Henry Cohn, 2025, needs more optimization.
5 499 0.858944591166 Henry Cohn, 2026, needs more optimization.
5 500 0.859136977171 Henry Cohn, 2025, needs more optimization.
5 501 0.859512033864 Henry Cohn, 2025, needs more optimization.
5 502 0.859555607488 Henry Cohn, 2026, needs more optimization.
5 503 0.859590934115 Henry Cohn, 2025, needs more optimization.
5 504 0.859701419249 Henry Cohn, 2026, needs more optimization.
5 505 0.859778505009 Henry Cohn, 2025, needs more optimization.
5 506 0.859876844867 Henry Cohn, 2025, needs more optimization.
5 507 0.860054961546 Henry Cohn, 2026, needs more optimization.
5 508 0.860267863182 Henry Cohn, 2026, needs more optimization.
5 509 0.860322505942 Henry Cohn, 2025, needs more optimization.
5 510 0.860625685298 Henry Cohn, 2026, needs more optimization.
5 511 0.860697231201 Henry Cohn, 2025, needs more optimization.
5 512 0.860725260477 Henry Cohn, 2025, needs more optimization.
5 513 0.860797749661 Henry Cohn, 2026, needs more optimization.
5 515 0.861143775119 Henry Cohn, 2026, needs more optimization.
5 516 0.861368957008 Henry Cohn, 2025, needs more optimization.
5 517 0.861388637378 Henry Cohn, 2026, needs more optimization.
5 518 0.861543720608 Henry Cohn, 2025, needs more optimization.
5 519 0.861749444634 Henry Cohn, 2026, needs more optimization.
5 520 0.861749994508 Henry Cohn, 2026, needs more optimization.
5 521 0.861795267361 Henry Cohn, 2025, needs more optimization.
5 522 0.862086743829 Henry Cohn, 2026, needs more optimization.
5 523 0.862318412803 Henry Cohn, 2025, needs more optimization.
5 524 0.862466887973 Henry Cohn, 2026, needs more optimization.
5 525 0.862470664059 Henry Cohn, 2025, needs more optimization.
5 526 0.862683702407 Henry Cohn, 2025, needs more optimization.
5 527 0.862707887103 Henry Cohn, 2026, needs more optimization.
5 528 0.862884014457 Henry Cohn, 2026, needs more optimization.
5 529 0.863035952578 Henry Cohn, 2025, needs more optimization.
5 530 0.863104542022 Henry Cohn, 2026, needs more optimization.
5 531 0.863240337579 Henry Cohn, 2025, needs more optimization.
5 532 0.863458712182 Henry Cohn, 2026, needs more optimization.
5 533 0.863618313032 Henry Cohn, 2026, needs more optimization.
5 534 0.863839677112 Henry Cohn, 2026, needs more optimization.
5 535 0.863880240397 Henry Cohn, 2025, needs more optimization.
5 536 0.863923777463 Henry Cohn, 2025, needs more optimization.
5 537 0.864152691676 Henry Cohn, 2026, needs more optimization.
5 538 0.864154701351 Henry Cohn, 2025, needs more optimization.
5 540 0.864395058631 Henry Cohn, 2025, needs more optimization.
5 542 0.864745296806 Henry Cohn, 2025, needs more optimization.
5 543 0.864969144430 Henry Cohn, 2026, needs more optimization.
5 544 0.864997867521 Henry Cohn, 2025, needs more optimization.
5 545 0.865069847868 Henry Cohn, 2025, needs more optimization.
5 546 0.865281323991 Henry Cohn, 2026, needs more optimization.
5 547 0.865434209594 Henry Cohn, 2026, needs more optimization.
5 548 0.865438315541 Henry Cohn, 2026, needs more optimization.
5 549 0.865712585376 Henry Cohn, 2025, needs more optimization.
5 550 0.865823955936 Henry Cohn, 2026, needs more optimization.
5 551 0.865842695323 Henry Cohn, 2026, needs more optimization.
5 552 0.865879307122 Henry Cohn, 2025, needs more optimization.
5 553 0.866159324412 Henry Cohn, 2025, needs more optimization.
5 554 0.866190255715 Henry Cohn, 2026, needs more optimization.
5 555 0.866352525315 Henry Cohn, 2025, needs more optimization.
5 556 0.866362800622 Henry Cohn, 2025, needs more optimization.
5 557 0.866758622688 Henry Cohn, 2026, needs more optimization.
5 558 0.866872959031 Henry Cohn, 2025, needs more optimization.
5 559 0.866900685443 Henry Cohn, 2025, needs more optimization.
5 560 0.867099425536 Henry Cohn, 2025, needs more optimization.
5 561 0.867325322385 Henry Cohn, 2025, needs more optimization.
5 562 0.867343447361 Henry Cohn, 2025, needs more optimization.
5 563 0.867436150282 Henry Cohn, 2025, needs more optimization.
5 564 0.867447737084 Henry Cohn, 2026, needs more optimization.
5 565 0.867452395939 Henry Cohn, 2025, needs more optimization.
5 566 0.867640678237 Henry Cohn, 2026, needs more optimization.
5 567 0.867784283396 Henry Cohn, 2026, needs more optimization.
5 568 0.867887760645 Henry Cohn, 2025, needs more optimization.
5 569 0.868077290034 Henry Cohn, 2025, needs more optimization.
5 570 0.868211021279 Henry Cohn, 2026, needs more optimization.
5 572 0.868451973652 Henry Cohn, 2026, needs more optimization.
5 573 0.868654373375 Henry Cohn, 2025, needs more optimization.
5 574 0.868673755205 Henry Cohn, 2025, needs more optimization.
5 575 0.868676712166 Henry Cohn, 2026, needs more optimization.
5 577 0.868935335122 Henry Cohn, 2025, needs more optimization.
5 578 0.868979873983 Henry Cohn, 2026, needs more optimization.
5 579 0.869153575403 Henry Cohn, 2026, needs more optimization.
5 580 0.869345631288 Henry Cohn, 2025, needs more optimization.
5 581 0.869468305984 Henry Cohn, 2025, needs more optimization.
5 582 0.869553483878 Henry Cohn, 2026, needs more optimization.
5 583 0.869749722833 Henry Cohn, 2026, needs more optimization.
5 584 0.869920874945 Henry Cohn, 2026, needs more optimization.
5 585 0.869929165808 Henry Cohn, 2026, needs more optimization.
5 586 0.870175585547 Henry Cohn, 2025, needs more optimization.
5 587 0.870179294621 Henry Cohn, 2025, needs more optimization.
5 588 0.870186408492 Henry Cohn, 2026, needs more optimization.
5 589 0.870249803628 Henry Cohn, 2025, needs more optimization.
5 590 0.870385377115 Henry Cohn, 2025, needs more optimization.
5 591 0.870414929971 Henry Cohn, 2025, needs more optimization.
5 592 0.870655172327 Henry Cohn, 2026, needs more optimization.
5 593 0.870691681545 Henry Cohn, 2026, needs more optimization.
5 594 0.870805809384 Henry Cohn, 2026, needs more optimization.
5 595 0.871066955540 Henry Cohn, 2025, needs more optimization.
5 596 0.871070914052 Henry Cohn, 2026, needs more optimization.
5 597 0.871105033160 Henry Cohn, 2025, needs more optimization.
5 598 0.871326407700 Henry Cohn, 2025, needs more optimization.
5 599 0.871327354638 Henry Cohn, 2026, needs more optimization.
5 600 0.871382362457 Henry Cohn, 2026, needs more optimization.
5 601 0.871604091828 Henry Cohn, 2026, needs more optimization.
5 602 0.871605806855 Henry Cohn, 2026, needs more optimization.
5 603 0.871665796035 Henry Cohn, 2026, needs more optimization.
5 604 0.871805838747 Henry Cohn, 2026, needs more optimization.
5 605 0.871824322660 Henry Cohn, 2025, needs more optimization.
5 606 0.871896707478 Henry Cohn, 2026, needs more optimization.
5 607 0.872081555797 Henry Cohn, 2026, needs more optimization.
5 608 0.872084141228 Henry Cohn, 2026, needs more optimization.
5 609 0.872517588599 Henry Cohn, 2026, needs more optimization.
5 610 0.872521651154 Henry Cohn, 2026, needs more optimization.
5 611 0.872670113057 Henry Cohn, 2025, needs more optimization.
5 612 0.872701370708 Henry Cohn, 2026, needs more optimization.
5 613 0.872895228619 Henry Cohn, 2026, needs more optimization.
5 614 0.872896331494 Henry Cohn, 2026, needs more optimization.
5 615 0.873090713168 Henry Cohn, 2025, needs more optimization.
5 616 0.873103833019 Henry Cohn, 2026, needs more optimization.
5 617 0.873301059105 Henry Cohn, 2025, needs more optimization.
5 618 0.873377831234 Henry Cohn, 2026, needs more optimization.
5 619 0.873472760121 Henry Cohn, 2026, needs more optimization.
5 620 0.873605610177 Henry Cohn, 2026, needs more optimization.
5 621 0.873622039759 Henry Cohn, 2025, needs more optimization.
5 622 0.873753446890 Henry Cohn, 2025, needs more optimization.
5 623 0.873905770256 Henry Cohn, 2025, needs more optimization.
5 624 0.873949410115 Henry Cohn, 2026, needs more optimization.
5 625 0.874124521820 Henry Cohn, 2026, needs more optimization.
5 626 0.874138805817 Henry Cohn, 2025, needs more optimization.
5 627 0.874162709567 Henry Cohn, 2025, needs more optimization.
5 628 0.874359782501 Henry Cohn, 2026, needs more optimization.
5 629 0.874485297919 Henry Cohn, 2025, needs more optimization.
5 630 0.874703509407 Henry Cohn, 2025, needs more optimization.
5 631 0.874836646897 Henry Cohn, 2026, needs more optimization.
5 633 0.874969572156 Henry Cohn, 2025, needs more optimization.
5 634 0.874987432232 Henry Cohn, 2026, needs more optimization.
5 635 0.875121083724 Henry Cohn, 2026, needs more optimization.
5 636 0.875300468091 Henry Cohn, 2025, needs more optimization.
5 637 0.875307252400 Henry Cohn, 2025, needs more optimization.
5 638 0.875377336976 Henry Cohn, 2026, needs more optimization.
5 639 0.875463236969 Henry Cohn, 2025, needs more optimization.
5 640 0.875640540653 Henry Cohn, 2026, needs more optimization.
5 641 0.875645428560 Henry Cohn, 2026, needs more optimization.
5 642 0.875662658082 Henry Cohn, 2026, needs more optimization.
5 643 0.875835676045 Henry Cohn, 2025, needs more optimization.
5 644 0.876028785170 Henry Cohn, 2026, needs more optimization.
5 645 0.876115945893 Henry Cohn, 2026, needs more optimization.
5 646 0.876190173583 Henry Cohn, 2026, needs more optimization.
5 647 0.876317790109 Henry Cohn, 2026, needs more optimization.
5 648 0.876321229584 Henry Cohn, 2025, needs more optimization.
5 649 0.876512730152 Henry Cohn, 2026, needs more optimization.
5 650 0.876533376542 Henry Cohn, 2026, needs more optimization.
5 651 0.876643344064 Henry Cohn, 2026, needs more optimization.
5 652 0.876649196799 Henry Cohn, 2025, needs more optimization.
5 653 0.876891012640 Henry Cohn, 2025, needs more optimization.
5 654 0.876994791383 Henry Cohn, 2026, needs more optimization.
5 655 0.877194944627 Henry Cohn, 2025, needs more optimization.
5 656 0.877250936425 Henry Cohn, 2026, needs more optimization.
5 657 0.877335064927 Henry Cohn, 2026, needs more optimization.
5 658 0.877416859395 Henry Cohn, 2026, needs more optimization.
5 659 0.877422215326 Henry Cohn, 2025, needs more optimization.
5 660 0.877460598524 Henry Cohn, 2026, needs more optimization.
5 661 0.877492961756 Henry Cohn, 2025, needs more optimization.
5 662 0.877622878303 Henry Cohn, 2025, needs more optimization.
5 663 0.877665604940 Henry Cohn, 2025, needs more optimization.
5 664 0.877808986150 Henry Cohn, 2025, needs more optimization.
5 665 0.877818204583 Henry Cohn, 2025, needs more optimization.
5 666 0.877882963051 Henry Cohn, 2025, needs more optimization.
5 667 0.878015154801 Henry Cohn, 2025, needs more optimization.
5 668 0.878121319924 Henry Cohn, 2026, needs more optimization.
5 669 0.878257366556 Henry Cohn, 2026, needs more optimization.
5 670 0.878394096821 Henry Cohn, 2025, needs more optimization.
5 671 0.878396868361 Henry Cohn, 2026, needs more optimization.
5 672 0.878555950413 Henry Cohn, 2026, needs more optimization.
5 673 0.878568357345 Henry Cohn, 2025, needs more optimization.
5 674 0.878675826146 Henry Cohn, 2026, needs more optimization.
5 675 0.878691240621 Henry Cohn, 2026, needs more optimization.
5 676 0.878895335529 Henry Cohn, 2025, needs more optimization.
5 677 0.879051400128 Henry Cohn, 2026, needs more optimization.
5 678 0.879056198237 Henry Cohn, 2025, needs more optimization.
5 680 0.879254843264 Henry Cohn, 2025, needs more optimization.
5 681 0.879266797921 Henry Cohn, 2025, needs more optimization.
5 683 0.879420942902 Henry Cohn, 2026, needs more optimization.
5 685 0.879604768234 Henry Cohn, 2025, needs more optimization.
5 686 0.879615298504 Henry Cohn, 2025, needs more optimization.
5 687 0.879927224792 Henry Cohn, 2025, needs more optimization.
5 688 0.879940879306 Henry Cohn, 2025, needs more optimization.
5 689 0.880050272700 Henry Cohn, 2025, needs more optimization.
5 690 0.880076920142 Henry Cohn, 2026, needs more optimization.
5 691 0.880186913631 Henry Cohn, 2025, needs more optimization.
5 692 0.880342004990 Henry Cohn, 2026, needs more optimization.
5 693 0.880342482614 Henry Cohn, 2026, needs more optimization.
5 694 0.880434990743 Henry Cohn, 2026, needs more optimization.
5 695 0.880560210580 Henry Cohn, 2025, needs more optimization.
5 696 0.880565807461 Henry Cohn, 2026, needs more optimization.
5 697 0.880726173156 Henry Cohn, 2026, needs more optimization.
5 698 0.880748341053 Henry Cohn, 2026, needs more optimization.
5 699 0.880831552541 Henry Cohn, 2025, needs more optimization.
5 700 0.880840937215 Henry Cohn, 2026, needs more optimization.
5 701 0.881073608246 Henry Cohn, 2026, needs more optimization.
5 702 0.881075411709 Henry Cohn, 2026, needs more optimization.
5 703 0.881076952719 Henry Cohn, 2026, needs more optimization.
5 704 0.881254031900 Henry Cohn, 2026, needs more optimization.
5 705 0.881266162475 Henry Cohn, 2025, needs more optimization.
5 706 0.881503126136 Henry Cohn, 2026, needs more optimization.
5 707 0.881504079243 Henry Cohn, 2026, needs more optimization.
5 708 0.881611839007 Henry Cohn, 2026, needs more optimization.
5 709 0.881738346869 Henry Cohn, 2026, needs more optimization.
5 710 0.881746195595 Henry Cohn, 2025, needs more optimization.
5 711 0.881848780380 Henry Cohn, 2026, needs more optimization.
5 712 0.881972602373 Henry Cohn, 2026, needs more optimization.
5 713 0.882002322005 Henry Cohn, 2026, needs more optimization.
5 714 0.882161638275 Henry Cohn, 2025, needs more optimization.
5 715 0.882179073366 Henry Cohn, 2026, needs more optimization.
5 716 0.882320732625 Henry Cohn, 2025, needs more optimization.
5 717 0.882323465849 Henry Cohn, 2026, needs more optimization.
5 718 0.882448099525 Henry Cohn, 2026, needs more optimization.
5 719 0.882451993509 Henry Cohn, 2026, needs more optimization.
5 720 0.882579799033 Henry Cohn, 2026, needs more optimization.
5 721 0.882847707400 Henry Cohn, 2026, needs more optimization.
5 722 0.882852390341 Henry Cohn, 2026, needs more optimization.
5 723 0.882955687290 Henry Cohn, 2025, needs more optimization.
5 724 0.882977268110 Henry Cohn, 2026, needs more optimization.
5 725 0.882978206211 Henry Cohn, 2026, needs more optimization.
5 726 0.883106952536 Henry Cohn, 2025, needs more optimization.
5 727 0.883131612758 Henry Cohn, 2025, needs more optimization.
5 728 0.883292687410 Henry Cohn, 2026, needs more optimization.
5 729 0.883320153712 Henry Cohn, 2026, needs more optimization.
5 730 0.883442618904 Henry Cohn, 2026, needs more optimization.
5 731 0.883524469603 Henry Cohn, 2026, needs more optimization.
5 732 0.883524699608 Henry Cohn, 2025, needs more optimization.
5 733 0.883673589741 Henry Cohn, 2026, needs more optimization.
5 734 0.883710902643 Henry Cohn, 2026, needs more optimization.
5 735 0.883860058056 Henry Cohn, 2026, needs more optimization.
5 736 0.883894566369 Henry Cohn, 2026, needs more optimization.
5 737 0.883896428072 Henry Cohn, 2026, needs more optimization.
5 738 0.883986347823 Henry Cohn, 2025, needs more optimization.
5 739 0.884167589206 Henry Cohn, 2025, needs more optimization.
5 740 0.884196725787 Henry Cohn, 2026, needs more optimization.
5 741 0.884315138410 Henry Cohn, 2026, needs more optimization.
5 742 0.884402016745 Henry Cohn, 2026, needs more optimization.
5 743 0.884526608919 Henry Cohn, 2025, needs more optimization.
5 744 0.884643952628 Henry Cohn, 2026, needs more optimization.
5 745 0.884681580162 Henry Cohn, 2026, needs more optimization.
5 746 0.884791620398 Henry Cohn, 2026, needs more optimization.
5 747 0.884901229453 Henry Cohn, 2026, needs more optimization.
5 748 0.885005159387 Henry Cohn, 2025, needs more optimization.
5 749 0.885008274623 Henry Cohn, 2026, needs more optimization.
5 750 0.885064693816 Henry Cohn, 2026, needs more optimization.
5 751 0.885132825074 Henry Cohn, 2026, needs more optimization.
5 752 0.885244724931 Henry Cohn, 2025, needs more optimization.
5 753 0.885246223059 Henry Cohn, 2026, needs more optimization.
5 754 0.885355810051 Henry Cohn, 2025, needs more optimization.
5 755 0.885389819977 Henry Cohn, 2025, needs more optimization.
5 756 0.885486686725 Henry Cohn, 2026, needs more optimization.
5 757 0.885576627751 Henry Cohn, 2025, needs more optimization.
5 758 0.885608708664 Henry Cohn, 2026, needs more optimization.
5 759 0.885788496516 Henry Cohn, 2025, needs more optimization.
5 760 0.885791735831 Henry Cohn, 2025, needs more optimization.
5 761 0.885915712593 Henry Cohn, 2025, needs more optimization.
5 762 0.885947010386 Henry Cohn, 2026, needs more optimization.
5 763 0.886054211065 Henry Cohn, 2026, needs more optimization.
5 764 0.886068745964 Henry Cohn, 2026, needs more optimization.
5 765 0.886195389172 Henry Cohn, 2025, needs more optimization.
5 766 0.886239507362 Henry Cohn, 2025, needs more optimization.
5 767 0.886280392515 Henry Cohn, 2026, needs more optimization.
5 768 0.886313548380 Henry Cohn, 2026, needs more optimization.
5 769 0.886332511139 Henry Cohn, 2026, needs more optimization.
5 771 0.886566932341 Henry Cohn, 2025, needs more optimization.
5 772 0.886580171023 Henry Cohn, 2026, needs more optimization.
5 773 0.886810630619 Henry Cohn, 2026, needs more optimization.
5 774 0.886818199717 Henry Cohn, 2026, needs more optimization.
5 775 0.886853249770 Henry Cohn, 2026, needs more optimization.
5 776 0.886976946131 Henry Cohn, 2026, needs more optimization.
5 777 0.886985397660 Henry Cohn, 2026, needs more optimization.
5 778 0.887166152141 Henry Cohn, 2025, needs more optimization.
5 779 0.887173242230 Henry Cohn, 2026, needs more optimization.
5 780 0.887282002983 Henry Cohn, 2026, needs more optimization.
5 781 0.887293711372 Henry Cohn, 2026, needs more optimization.
5 782 0.887318221044 Henry Cohn, 2026, needs more optimization.
5 783 0.887387168253 Henry Cohn, 2026, needs more optimization.
5 784 0.887486537415 Henry Cohn, 2026, needs more optimization.
5 785 0.887487426156 Henry Cohn, 2025, needs more optimization.
5 786 0.887548227422 Henry Cohn, 2025, needs more optimization.
5 787 0.887727286658 Henry Cohn, 2025, needs more optimization.
5 788 0.887728284656 Henry Cohn, 2026, needs more optimization.
5 789 0.887822163350 Henry Cohn, 2026, needs more optimization.
5 790 0.887929616199 Henry Cohn, 2025, needs more optimization.
5 791 0.887936822195 Henry Cohn, 2025, needs more optimization.
5 792 0.888004025348 Henry Cohn, 2026, needs more optimization.
5 793 0.888116581586 Henry Cohn, 2025, needs more optimization.
5 794 0.888134980619 Henry Cohn, 2026, needs more optimization.
5 795 0.888214561367 Henry Cohn, 2026, needs more optimization.
5 796 0.888241437301 Henry Cohn, 2026, needs more optimization.
5 797 0.888445319206 Henry Cohn, 2025, needs more optimization.
5 798 0.888463671895 Henry Cohn, 2026, needs more optimization.
5 799 0.888486462856 Henry Cohn, 2025, needs more optimization.
5 800 0.888530875178 Henry Cohn, 2026, needs more optimization.
5 801 0.888651958404 Henry Cohn, 2025, needs more optimization.
5 802 0.888655481864 Henry Cohn, 2025, needs more optimization.
5 803 0.888896550093 Henry Cohn, 2025, needs more optimization.
5 804 0.888903636362 Henry Cohn, 2026, needs more optimization.
5 805 0.888947331540 Henry Cohn, 2026, needs more optimization.
5 806 0.888961995804 Henry Cohn, 2025, needs more optimization.
5 807 0.889157983995 Henry Cohn, 2025, needs more optimization.
5 808 0.889232054009 Henry Cohn, 2026, needs more optimization.
5 809 0.889293843886 Henry Cohn, 2025, needs more optimization.
5 810 0.889368730713 Henry Cohn, 2026, needs more optimization.
5 811 0.889450629631 Henry Cohn, 2026, needs more optimization.
5 812 0.889465251480 Henry Cohn, 2026, needs more optimization.
5 813 0.889599428123 Henry Cohn, 2026, needs more optimization.
5 814 0.889708667362 Henry Cohn, 2025, needs more optimization.
5 815 0.889709777622 Henry Cohn, 2026, needs more optimization.
5 816 0.889735671604 Henry Cohn, 2026, needs more optimization.
5 817 0.889771290214 Henry Cohn, 2025, needs more optimization.
5 818 0.889876459009 Henry Cohn, 2026, needs more optimization.
5 819 0.889885890089 Henry Cohn, 2025, needs more optimization.
5 820 0.889896735801 Henry Cohn, 2026, needs more optimization.
5 821 0.890121941524 Henry Cohn, 2026, needs more optimization.
5 822 0.890124860445 Henry Cohn, 2026, needs more optimization.
5 823 0.890283993163 Henry Cohn, 2026, needs more optimization.
5 824 0.890287123138 Henry Cohn, 2026, needs more optimization.
5 825 0.890421726452 Henry Cohn, 2026, needs more optimization.
5 826 0.890422086940 Henry Cohn, 2026, needs more optimization.
5 827 0.890443189481 Henry Cohn, 2025, needs more optimization.
5 828 0.890565574880 Henry Cohn, 2026, needs more optimization.
5 829 0.890603650063 Henry Cohn, 2026, needs more optimization.
5 830 0.890713303532 Henry Cohn, 2026, needs more optimization.
5 831 0.890729720533 Henry Cohn, 2026, needs more optimization.
5 832 0.890754211876 Henry Cohn, 2026, needs more optimization.
5 833 0.890774541388 Henry Cohn, 2026, needs more optimization.
5 834 0.890799815802 Henry Cohn, 2026, needs more optimization.
5 835 0.891029814074 Henry Cohn, 2026, needs more optimization.
5 836 0.891033531559 Henry Cohn, 2026, needs more optimization.
5 837 0.891258500023 Henry Cohn, 2026, needs more optimization.
5 838 0.891262029631 Henry Cohn, 2026, needs more optimization.
5 839 0.891295870406 Henry Cohn, 2025, needs more optimization.
5 840 0.891307991324 Henry Cohn, 2026, needs more optimization.
5 841 0.891426470359 Henry Cohn, 2025, needs more optimization.
5 842 0.891451579999 Henry Cohn, 2026, needs more optimization.
5 843 0.891563208434 Henry Cohn, 2025, needs more optimization.
5 844 0.891565320583 Henry Cohn, 2026, needs more optimization.
5 845 0.891706512207 Henry Cohn, 2025, needs more optimization.
5 846 0.891719866224 Henry Cohn, 2026, needs more optimization.
5 847 0.891744285824 Henry Cohn, 2026, needs more optimization.
5 848 0.891879939732 Henry Cohn, 2026, needs more optimization.
5 849 0.891890847202 Henry Cohn, 2026, needs more optimization.
5 850 0.891961059961 Henry Cohn, 2026, needs more optimization.
5 851 0.891972040917 Henry Cohn, 2025, needs more optimization.
5 852 0.892114758060 Henry Cohn, 2025, needs more optimization.
5 853 0.892116266712 Henry Cohn, 2025, needs more optimization.
5 854 0.892203056941 Henry Cohn, 2026, needs more optimization.
5 855 0.892308835936 Henry Cohn, 2026, needs more optimization.
5 856 0.892364658170 Henry Cohn, 2026, needs more optimization.
5 857 0.892371050019 Henry Cohn, 2026, needs more optimization.
5 858 0.892427569330 Henry Cohn, 2026, needs more optimization.
5 859 0.892628479638 Henry Cohn, 2026, needs more optimization.
5 860 0.892629264993 Henry Cohn, 2026, needs more optimization.
5 861 0.892631422338 Henry Cohn, 2026, needs more optimization.
5 862 0.892636630150 Henry Cohn, 2025, needs more optimization.
5 863 0.892800318127 Henry Cohn, 2026, needs more optimization.
5 864 0.892813781513 Henry Cohn, 2026, needs more optimization.
5 865 0.892903895898 Henry Cohn, 2026, needs more optimization.
5 866 0.892931703932 Henry Cohn, 2026, needs more optimization.
5 867 0.893064841036 Henry Cohn, 2026, needs more optimization.
5 869 0.893092115983 Henry Cohn, 2025, needs more optimization.
5 870 0.893249121722 Henry Cohn, 2026, needs more optimization.
5 871 0.893283299030 Henry Cohn, 2026, needs more optimization.
5 872 0.893349843187 Henry Cohn, 2026, needs more optimization.
5 873 0.893401125154 Henry Cohn, 2025, needs more optimization.
5 874 0.893405519716 Henry Cohn, 2026, needs more optimization.
5 875 0.893537264211 Henry Cohn, 2026, needs more optimization.
5 876 0.893548204171 Henry Cohn, 2026, needs more optimization.
5 877 0.893672010170 Henry Cohn, 2026, needs more optimization.
5 878 0.893675401364 Henry Cohn, 2026, needs more optimization.
5 879 0.893830168591 Henry Cohn, 2025, needs more optimization.
5 880 0.893831729413 Henry Cohn, 2025, needs more optimization.
5 881 0.893862019107 Henry Cohn, 2026, needs more optimization.
5 882 0.893870916377 Henry Cohn, 2026, needs more optimization.
5 883 0.893949232568 Henry Cohn, 2026, needs more optimization.
5 884 0.894089862035 Henry Cohn, 2025, needs more optimization.
5 885 0.894100882712 Henry Cohn, 2026, needs more optimization.
5 886 0.894271519384 Henry Cohn, 2026, needs more optimization.
5 887 0.894275947139 Henry Cohn, 2026, needs more optimization.
5 888 0.894376187680 Henry Cohn, 2026, needs more optimization.
5 889 0.894397153171 Henry Cohn, 2025, needs more optimization.
5 890 0.894515998427 Henry Cohn, 2026, needs more optimization.
5 891 0.894527491923 Henry Cohn, 2026, needs more optimization.
5 892 0.894550995136 Henry Cohn, 2026, needs more optimization.
5 893 0.894619921474 Henry Cohn, 2026, needs more optimization.
5 894 0.894665448614 Henry Cohn, 2026, needs more optimization.
5 895 0.894667517151 Henry Cohn, 2025, needs more optimization.
5 896 0.894750896742 Henry Cohn, 2025, needs more optimization.
5 897 0.894838699596 Henry Cohn, 2025, needs more optimization.
5 898 0.894839527562 Henry Cohn, 2025, needs more optimization.
5 899 0.894961663289 Henry Cohn, 2026, needs more optimization.
5 900 0.894963952553 Henry Cohn, 2026, needs more optimization.
5 901 0.895053554088 Henry Cohn, 2026, needs more optimization.
5 902 0.895056901178 Henry Cohn, 2025, needs more optimization.
5 903 0.895266108241 Henry Cohn, 2025, needs more optimization.
5 904 0.895275689100 Henry Cohn, 2025, needs more optimization.
5 905 0.895302120772 Henry Cohn, 2026, needs more optimization.
5 906 0.895398566320 Henry Cohn, 2025, needs more optimization.
5 907 0.895399183332 Henry Cohn, 2025, needs more optimization.
5 908 0.895486681607 Henry Cohn, 2026, needs more optimization.
5 909 0.895528356750 Henry Cohn, 2026, needs more optimization.
5 910 0.895634459369 Henry Cohn, 2026, needs more optimization.
5 911 0.895718454547 Henry Cohn, 2026, needs more optimization.
5 912 0.895721235146 Henry Cohn, 2026, needs more optimization.
5 913 0.895831413756 Henry Cohn, 2026, needs more optimization.
5 914 0.895864388648 Henry Cohn, 2026, needs more optimization.
5 915 0.895865427116 Henry Cohn, 2026, needs more optimization.
5 916 0.896008207188 Henry Cohn, 2026, needs more optimization.
5 917 0.896010138422 Henry Cohn, 2026, needs more optimization.
5 918 0.896128589466 Henry Cohn, 2026, needs more optimization.
5 919 0.896157599104 Henry Cohn, 2025, needs more optimization.
5 920 0.896279397003 Henry Cohn, 2026, needs more optimization.
5 921 0.896297467584 Henry Cohn, 2026, needs more optimization.
5 922 0.896299418572 Henry Cohn, 2026, needs more optimization.
5 923 0.896387283905 Henry Cohn, 2026, needs more optimization.
5 924 0.896388483329 Henry Cohn, 2026, needs more optimization.
5 925 0.896425434670 Henry Cohn, 2026, needs more optimization.
5 926 0.896481322352 Henry Cohn, 2026, needs more optimization.
5 927 0.896566089205 Henry Cohn, 2026, needs more optimization.
5 928 0.896570399324 Henry Cohn, 2026, needs more optimization.
5 929 0.896663763757 Henry Cohn, 2026, needs more optimization.
5 931 0.896785863752 Henry Cohn, 2026, needs more optimization.
5 932 0.896898653164 Henry Cohn, 2026, needs more optimization.
5 933 0.896900601306 Henry Cohn, 2026, needs more optimization.
5 934 0.897005323952 Henry Cohn, 2026, needs more optimization.
5 935 0.897007731039 Henry Cohn, 2025, needs more optimization.
5 936 0.897038468539 Henry Cohn, 2026, needs more optimization.
5 937 0.897156379733 Henry Cohn, 2026, needs more optimization.
5 938 0.897159993258 Henry Cohn, 2025, needs more optimization.
5 939 0.897261248058 Henry Cohn, 2026, needs more optimization.
5 940 0.897301498985 Henry Cohn, 2026, needs more optimization.
5 941 0.897423600886 Henry Cohn, 2026, needs more optimization.
5 942 0.897428392170 Henry Cohn, 2026, needs more optimization.
5 943 0.897435822418 Henry Cohn, 2025, needs more optimization.
5 944 0.897512142346 Henry Cohn, 2026, needs more optimization.
5 945 0.897673470977 Henry Cohn, 2026, needs more optimization.
5 946 0.897711366435 Henry Cohn, 2026, needs more optimization.
5 947 0.897799373036 Henry Cohn, 2026, needs more optimization.
5 948 0.897802739305 Henry Cohn, 2026, needs more optimization.
5 949 0.897825980378 Henry Cohn, 2026, needs more optimization.
5 950 0.897931543882 Henry Cohn, 2026, needs more optimization.
5 952 0.897962728304 Henry Cohn, 2026, needs more optimization.
5 953 0.898026166430 Henry Cohn, 2026, needs more optimization.
5 954 0.898039568578 Henry Cohn, 2026, needs more optimization.
5 955 0.898060512435 Henry Cohn, 2026, needs more optimization.
5 956 0.898075128638 Henry Cohn, 2025, needs more optimization.
5 957 0.898237898688 Henry Cohn, 2026, needs more optimization.
5 958 0.898247608210 Henry Cohn, 2026, needs more optimization.
5 959 0.898260200473 Henry Cohn, 2026, needs more optimization.
5 960 0.898312398441 Henry Cohn, 2026, needs more optimization.
5 961 0.898393471322 Henry Cohn, 2026, needs more optimization.
5 962 0.898408422618 Henry Cohn, 2026, needs more optimization.
5 963 0.898419458972 Henry Cohn, 2026, needs more optimization.
5 964 0.898521213325 Henry Cohn, 2026, needs more optimization.
5 965 0.898534843820 Henry Cohn, 2025, needs more optimization.
5 966 0.898735260894 Henry Cohn, 2026, needs more optimization.
5 967 0.898736339900 Henry Cohn, 2026, needs more optimization.
5 968 0.898831647675 Henry Cohn, 2026, needs more optimization.
5 969 0.898833436753 Henry Cohn, 2026, needs more optimization.
5 970 0.898855023817 Henry Cohn, 2026, needs more optimization.
5 971 0.898934578212 Henry Cohn, 2026, needs more optimization.
5 972 0.898939223336 Henry Cohn, 2025, needs more optimization.
5 973 0.899008765823 Henry Cohn, 2026, needs more optimization.
5 974 0.899113176274 Henry Cohn, 2026, needs more optimization.
5 975 0.899118129317 Henry Cohn, 2026, needs more optimization.
5 976 0.899130526227 Henry Cohn, 2025, needs more optimization.
5 977 0.899240395585 Henry Cohn, 2026, needs more optimization.
5 978 0.899359638664 Henry Cohn, 2026, needs more optimization.
5 979 0.899370405114 Henry Cohn, 2026, needs more optimization.
5 980 0.899385690646 Henry Cohn, 2026, needs more optimization.
5 981 0.899409604665 Henry Cohn, 2026, needs more optimization.
5 982 0.899488303056 Henry Cohn, 2026, needs more optimization.
5 983 0.899611274544 Henry Cohn, 2026, needs more optimization.
5 984 0.899630531156 Henry Cohn, 2026, needs more optimization.
5 985 0.899632280944 Henry Cohn, 2026, needs more optimization.
5 986 0.899708088763 Henry Cohn, 2025, needs more optimization.
5 987 0.899728049908 Henry Cohn, 2026, needs more optimization.
5 988 0.899890869229 Henry Cohn, 2026, needs more optimization.
5 989 0.899894750397 Henry Cohn, 2026, needs more optimization.
5 990 0.899896298443 Henry Cohn, 2026, needs more optimization.
5 991 0.899929613953 Henry Cohn, 2025, needs more optimization.
5 992 0.899964158387 Henry Cohn, 2026, needs more optimization.
5 993 0.900076650655 Henry Cohn, 2026, needs more optimization.
5 994 0.900135221354 Henry Cohn, 2026, needs more optimization.
5 995 0.900257343491 Henry Cohn, 2026, needs more optimization.
5 996 0.900271407903 Henry Cohn, 2026, needs more optimization.
5 997 0.900353938698 Henry Cohn, 2026, needs more optimization.
5 998 0.900423137276 Henry Cohn, 2026, needs more optimization.
5 999 0.900427166892 Henry Cohn, 2026, needs more optimization.
5 1000 0.900448613272 Henry Cohn, 2026, needs more optimization.
5 1001 0.900507533899 Henry Cohn, 2026, needs more optimization.
5 1002 0.900539735076 Henry Cohn, 2026, needs more optimization.
5 1003 0.900571881483 Henry Cohn, 2026, needs more optimization.
5 1004 0.900586582336 Henry Cohn, 2026, needs more optimization.
5 1005 0.900825579321 Henry Cohn, 2026, needs more optimization.
5 1006 0.900828745221 Henry Cohn, 2026, needs more optimization.
5 1007 0.900848354252 Henry Cohn, 2026, needs more optimization.
5 1008 0.900860790028 Henry Cohn, 2026, needs more optimization.
5 1009 0.900977221912 Henry Cohn, 2026, needs more optimization.
5 1010 0.900982202691 Henry Cohn, 2026, needs more optimization.
5 1011 0.900984766740 Henry Cohn, 2026, needs more optimization.
5 1012 0.901010944206 Henry Cohn, 2026, needs more optimization.
5 1013 0.901097951835 Henry Cohn, 2026, needs more optimization.
5 1014 0.901116747645 Henry Cohn, 2026, needs more optimization.
5 1015 0.901119985764 Henry Cohn, 2026, needs more optimization.
5 1016 0.901144980530 Henry Cohn, 2026, needs more optimization.
5 1017 0.901212921648 Henry Cohn, 2026, needs more optimization.
5 1018 0.901218963043 Henry Cohn, 2026, needs more optimization.
5 1019 0.901325787568 Henry Cohn, 2025, needs more optimization.
5 1020 0.901329213303 Henry Cohn, 2026, needs more optimization.
5 1021 0.901442156851 Henry Cohn, 2025, needs more optimization.
5 1022 0.901561636441 Henry Cohn, 2026, needs more optimization.
5 1023 0.901637057621 Henry Cohn, 2026, needs more optimization.
5 1024 0.901697490054 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 0.441277260126 Henry Cohn, 2023.
24⁢x3+16⁢x2−14⁢x+1
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 0.486119746833 Henry Cohn, 2023.
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 0.525662331586 Henry Cohn, 2026.
6 76 0.526754953537 Henry Cohn, 2025.
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 0.539006300696 Henry Cohn, 2025.
6 82 0.541487958459 Henry Cohn, 2025.
6 83 0.543866459696 Henry Cohn, 2025.
6 84 0.546018230582 Henry Cohn, 2025.
6 85 0.546038397748 Henry Cohn, 2026.
6 86 0.550011129820 Henry Cohn, 2025.
6 87 0.551714767476 Henry Cohn, 2023.
6 88 0.552456735670 Henry Cohn, 2025.
6 89 0.555561660912 Henry Cohn, 2025, needs more optimization.
6 91 0.557603429720 Henry Cohn, 2024.
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 0.571167178278 Henry Cohn, 2025.
6 99 0.573881665753 Henry Cohn, 2023.
6 100 0.574916276575 Henry Cohn, 2024.
6 101 0.578331393550 Henry Cohn, 2023.
6 102 0.580736682189 Henry Cohn, 2023, needs more optimization.
6 103 0.583220131624 Henry Cohn, 2024.
6 106 0.583371498649 Henry Cohn, 2026.
6 107 0.583372432432 Henry Cohn, 2026.
6 108 0.584811059741 Henry Cohn, 2026.
6 109 0.585348750770 Henry Cohn, 2026.
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 0.596006832892 Henry Cohn, 2025, needs more optimization.
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 0.599174837096 Henry Cohn, 2026.
6 121 0.604468330433 Henry Cohn, 2026, needs more optimization.
6 122 0.606495869812 Henry Cohn, 2026, needs more optimization.
6 123 0.607115797651 Henry Cohn, 2025.
6 124 0.607974063056 Henry Cohn, 2025, needs more optimization.
6 125 0.607974063065 Henry Cohn, 2024, needs more optimization.
6 126 0.610387312456 Henry Cohn, 2026, needs more optimization.
6 127 0.616514741171 Henry Cohn, 2026, needs more optimization.
6 128 0.619107420038 Henry Cohn, 2025.
6 129 0.620224367829 Henry Cohn, 2025.
6 130 0.623555028154 Henry Cohn, 2026, needs more optimization.
6 132 0.624698587774 Henry Cohn, 2026, needs more optimization.
6 133 0.626200566214 Henry Cohn, 2026, needs more optimization.
6 134 0.628625331128 Henry Cohn, 2026, needs more optimization.
6 135 0.630741016800 Henry Cohn, 2026, needs more optimization.
6 136 0.631780124977 Henry Cohn, 2026, needs more optimization.
6 137 0.633402294823 Henry Cohn, 2025.
6 138 0.634581559739 Henry Cohn, 2026, needs more optimization.
6 139 0.636180232032 Henry Cohn, 2026, needs more optimization.
6 140 0.637396216664 Henry Cohn, 2026, needs more optimization.
6 141 0.639558404219 Henry Cohn, 2026, needs more optimization.
6 142 0.639920042691 Henry Cohn, 2026, needs more optimization.
6 143 0.641459805982 Henry Cohn, 2026, needs more optimization.
6 144 0.642197637303 Henry Cohn, 2026, needs more optimization.
6 145 0.643736984203 Henry Cohn, 2026, needs more optimization.
6 146 0.644837388208 Henry Cohn, 2026, needs more optimization.
6 147 0.645794059330 Henry Cohn, 2026, needs more optimization.
6 148 0.646695015426 Henry Cohn, 2026, needs more optimization.
6 149 0.648310953648 Henry Cohn, 2026, needs more optimization.
6 150 0.649239191212 Henry Cohn, 2026, needs more optimization.
6 151 0.649913058330 Henry Cohn, 2026, needs more optimization.
6 152 0.651391785770 Henry Cohn, 2026, needs more optimization.
6 153 0.652205289705 Henry Cohn, 2026, needs more optimization.
6 154 0.652618605342 Henry Cohn, 2026, needs more optimization.
6 155 0.652683071764 Henry Cohn, 2026, needs more optimization.
6 156 0.653218986491 Henry Cohn, 2026, needs more optimization.
6 157 0.653907785712 Henry Cohn, 2026, needs more optimization.
6 158 0.654508318001 Henry Cohn, 2026, needs more optimization.
6 159 0.654917507675 Henry Cohn, 2026, needs more optimization.
6 160 0.655640282325 Henry Cohn, 2026, needs more optimization.
6 161 0.656360259547 Henry Cohn, 2026, needs more optimization.
6 162 0.657161492941 Henry Cohn, 2026, needs more optimization.
6 163 0.658150909560 Henry Cohn, 2026, needs more optimization.
6 164 0.658813957356 Henry Cohn, 2026, needs more optimization.
6 165 0.659405569935 Henry Cohn, 2026, needs more optimization.
6 166 0.659972001819 Henry Cohn, 2026, needs more optimization.
6 167 0.660494089825 Henry Cohn, 2026, needs more optimization.
6 168 0.660627648513 Henry Cohn, 2026, needs more optimization.
6 169 0.661755325566 Henry Cohn, 2026, needs more optimization.
6 170 0.662756856934 Henry Cohn, 2026, needs more optimization.
6 171 0.663988514301 Henry Cohn, 2026, needs more optimization.
6 172 0.664140280503 Henry Cohn, 2026, needs more optimization.
6 173 0.664476768323 Henry Cohn, 2026, needs more optimization.
6 174 0.664871187770 Henry Cohn, 2026, needs more optimization.
6 175 0.665500995714 Henry Cohn, 2026, needs more optimization.
6 176 0.666108528160 Henry Cohn, 2026, needs more optimization.
6 177 0.667713757965 Henry Cohn, 2026, needs more optimization.
6 178 0.668956384255 Henry Cohn, 2026, needs more optimization.
6 179 0.671279706232 Henry Cohn, 2026, needs more optimization.
6 180 0.671725786395 Henry Cohn, 2026, needs more optimization.
6 181 0.672461654795 Henry Cohn, 2026, needs more optimization.
6 182 0.672777046941 Henry Cohn, 2026, needs more optimization.
6 183 0.673135121733 Henry Cohn, 2026, needs more optimization.
6 184 0.673943980589 Henry Cohn, 2026, needs more optimization.
6 185 0.674404473917 Henry Cohn, 2026, needs more optimization.
6 186 0.674794519800 Henry Cohn, 2026, needs more optimization.
6 187 0.676017773194 Henry Cohn, 2026, needs more optimization.
6 188 0.676616728423 Henry Cohn, 2026, needs more optimization.
6 189 0.677344948548 Henry Cohn, 2026, needs more optimization.
6 190 0.677463792353 Henry Cohn, 2026, needs more optimization.
6 191 0.678569102470 Henry Cohn, 2026, needs more optimization.
6 192 0.679806475502 Henry Cohn, 2026, needs more optimization.
6 193 0.680040880240 Henry Cohn, 2026, needs more optimization.
6 194 0.680581238632 Henry Cohn, 2026, needs more optimization.
6 195 0.681332783642 Henry Cohn, 2026, needs more optimization.
6 196 0.682089675791 Henry Cohn, 2026, needs more optimization.
6 197 0.682649173285 Henry Cohn, 2026, needs more optimization.
6 198 0.682995389789 Henry Cohn, 2026, needs more optimization.
6 199 0.683553802145 Henry Cohn, 2026, needs more optimization.
6 200 0.684414501169 Henry Cohn, 2026, needs more optimization.
6 201 0.684726017350 Henry Cohn, 2026, needs more optimization.
6 202 0.685171065066 Henry Cohn, 2026, needs more optimization.
6 203 0.685504498318 Henry Cohn, 2026, needs more optimization.
6 204 0.686221850185 Henry Cohn, 2026, needs more optimization.
6 205 0.686851753715 Henry Cohn, 2026, needs more optimization.
6 206 0.687366549612 Henry Cohn, 2025, needs more optimization.
6 207 0.687889167838 Henry Cohn, 2026, needs more optimization.
6 208 0.688118226108 Henry Cohn, 2026, needs more optimization.
6 209 0.689078356902 Henry Cohn, 2026, needs more optimization.
6 210 0.689987287290 Henry Cohn, 2026, needs more optimization.
6 211 0.690720340466 Henry Cohn, 2026, needs more optimization.
6 212 0.691250741906 Henry Cohn, 2026, needs more optimization.
6 213 0.691959302440 Henry Cohn, 2026, needs more optimization.
6 214 0.692440482721 Henry Cohn, 2026, needs more optimization.
6 215 0.692811674168 Henry Cohn, 2026, needs more optimization.
6 216 0.693500746182 Henry Cohn, 2026, needs more optimization.
6 217 0.694032285129 Henry Cohn, 2026, needs more optimization.
6 218 0.694567151107 Henry Cohn, 2026, needs more optimization.
6 219 0.695680798199 Henry Cohn, 2026, needs more optimization.
6 220 0.695984596122 Henry Cohn, 2026, needs more optimization.
6 221 0.696511789747 Henry Cohn, 2026, needs more optimization.
6 222 0.697193437135 Henry Cohn, 2026, needs more optimization.
6 223 0.697502441237 Henry Cohn, 2026, needs more optimization.
6 224 0.697765509403 Henry Cohn, 2026, needs more optimization.
6 225 0.698267581092 Henry Cohn, 2026, needs more optimization.
6 226 0.698679875171 Henry Cohn, 2026, needs more optimization.
6 227 0.699036614892 Henry Cohn, 2026, needs more optimization.
6 228 0.699679796894 Henry Cohn, 2026, needs more optimization.
6 243 0.7 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−7
6 247 0.704240154258 Henry Cohn, 2026, needs more optimization.
6 248 0.704281793354 Henry Cohn, 2026, needs more optimization.
6 249 0.704335287719 Henry Cohn, 2026, needs more optimization.
6 250 0.704522625931 Henry Cohn, 2026, needs more optimization.
6 251 0.704691605800 Henry Cohn, 2026, needs more optimization.
6 252 0.704768099691 Henry Cohn, 2026, needs more optimization.
6 253 0.704969745337 Henry Cohn, 2026, needs more optimization.
6 254 0.705162936639 Henry Cohn, 2026, needs more optimization.
6 255 0.705338500574 Henry Cohn, 2026, needs more optimization.
6 256 0.705400024585 Henry Cohn, 2026, needs more optimization.
6 257 0.705733804180 Henry Cohn, 2026, needs more optimization.
6 258 0.706255650576 Henry Cohn, 2026, needs more optimization.
6 259 0.706859108128 Henry Cohn, 2026, needs more optimization.
6 260 0.707250637972 Henry Cohn, 2026, needs more optimization.
6 261 0.707874147681 Henry Cohn, 2026, needs more optimization.
6 262 0.709136328720 Henry Cohn, 2026, needs more optimization.
6 263 0.710517309341 Henry Cohn, 2026, needs more optimization.
6 264 0.710659608962 Henry Cohn, 2026, needs more optimization.
6 265 0.711702774569 Henry Cohn, 2026, needs more optimization.
6 266 0.712074459262 Henry Cohn, 2026, needs more optimization.
6 267 0.713848802660 Henry Cohn, 2026, needs more optimization.
6 268 0.714481332930 Henry Cohn, 2026, needs more optimization.
6 270 0.715237409629 Henry Cohn, 2026, needs more optimization.
6 271 0.715857970144 Henry Cohn, 2026, needs more optimization.
6 272 0.716690193432 Henry Cohn, 2026, needs more optimization.
6 273 0.717514986838 Henry Cohn, 2026, needs more optimization.
6 274 0.717514986937 Henry Cohn, 2026, needs more optimization.
6 275 0.718346002250 Henry Cohn, 2026, needs more optimization.
6 276 0.718975395786 Henry Cohn, 2026, needs more optimization.
6 277 0.719606800478 Henry Cohn, 2026, needs more optimization.
6 278 0.720093556033 Henry Cohn, 2026, needs more optimization.
6 279 0.720982579108 Henry Cohn, 2026, needs more optimization.
6 280 0.721821771810 Henry Cohn, 2026, needs more optimization.
6 281 0.722571602346 Henry Cohn, 2026, needs more optimization.
6 282 0.723043863505 Henry Cohn, 2026, needs more optimization.
6 283 0.723553405127 Henry Cohn, 2026, needs more optimization.
6 284 0.724218988089 Henry Cohn, 2026, needs more optimization.
6 285 0.724666293887 Henry Cohn, 2026, needs more optimization.
6 286 0.725124817630 Henry Cohn, 2026, needs more optimization.
6 287 0.725259249179 Henry Cohn, 2026, needs more optimization.
6 288 0.726007945905 Henry Cohn, 2026, needs more optimization.
6 289 0.726377973200 Henry Cohn, 2026, needs more optimization.
6 290 0.726443968762 Henry Cohn, 2026, needs more optimization.
6 291 0.727106350307 Henry Cohn, 2026, needs more optimization.
6 292 0.728174504449 Henry Cohn, 2025, needs more optimization.
6 293 0.728584606835 Henry Cohn, 2026, needs more optimization.
6 294 0.728962205967 Henry Cohn, 2026, needs more optimization.
6 295 0.729392940759 Henry Cohn, 2026, needs more optimization.
6 296 0.729954045937 Henry Cohn, 2026, needs more optimization.
6 297 0.730503281239 Henry Cohn, 2026, needs more optimization.
6 298 0.730956846166 Henry Cohn, 2026, needs more optimization.
6 299 0.731272376823 Henry Cohn, 2026, needs more optimization.
6 300 0.731906534742 Henry Cohn, 2026, needs more optimization.
6 301 0.732416678518 Henry Cohn, 2025, needs more optimization.
6 302 0.733154597342 Henry Cohn, 2025, needs more optimization.
6 303 0.733265144419 Henry Cohn, 2025, needs more optimization.
6 304 0.733474326159 Henry Cohn, 2025, needs more optimization.
6 305 0.733794655030 Henry Cohn, 2025, needs more optimization.
6 306 0.733866177993 Henry Cohn, 2025, needs more optimization.
6 307 0.734390329949 Henry Cohn, 2025, needs more optimization.
6 308 0.735132508610 Henry Cohn, 2026, needs more optimization.
6 309 0.735661892248 Henry Cohn, 2025, needs more optimization.
6 310 0.736073358656 Henry Cohn, 2025, needs more optimization.
6 311 0.736181169237 Henry Cohn, 2026, needs more optimization.
6 312 0.736700074960 Henry Cohn, 2025, needs more optimization.
6 313 0.737357322296 Henry Cohn, 2025, needs more optimization.
6 314 0.737761728767 Henry Cohn, 2025, needs more optimization.
6 315 0.737831637343 Henry Cohn, 2025, needs more optimization.
6 316 0.738209850784 Henry Cohn, 2026, needs more optimization.
6 317 0.738613322480 Henry Cohn, 2025, needs more optimization.
6 318 0.739530231283 Henry Cohn, 2025, needs more optimization.
6 319 0.740040267366 Henry Cohn, 2026, needs more optimization.
6 320 0.740195855213 Henry Cohn, 2025, needs more optimization.
6 321 0.740402273601 Henry Cohn, 2026, needs more optimization.
6 322 0.740872947420 Henry Cohn, 2026, needs more optimization.
6 323 0.741323429328 Henry Cohn, 2025, needs more optimization.
6 324 0.741693742410 Henry Cohn, 2026, needs more optimization.
6 325 0.742218586647 Henry Cohn, 2026, needs more optimization.
6 326 0.742456930608 Henry Cohn, 2025, needs more optimization.
6 327 0.742951316911 Henry Cohn, 2025, needs more optimization.
6 328 0.743206035143 Henry Cohn, 2026, needs more optimization.
6 329 0.743917206939 Henry Cohn, 2025, needs more optimization.
6 330 0.744395552873 Henry Cohn, 2026, needs more optimization.
6 331 0.744800502360 Henry Cohn, 2025, needs more optimization.
6 332 0.745075935606 Henry Cohn, 2025, needs more optimization.
6 333 0.745467810779 Henry Cohn, 2025, needs more optimization.
6 334 0.745876428076 Henry Cohn, 2025, needs more optimization.
6 335 0.746518221120 Henry Cohn, 2026, needs more optimization.
6 336 0.746526630978 Henry Cohn, 2026, needs more optimization.
6 338 0.746760290311 Henry Cohn, 2026, needs more optimization.
6 340 0.746778829562 Henry Cohn, 2026, needs more optimization.
6 342 0.746783383823 Henry Cohn, 2026, needs more optimization.
6 343 0.748841050044 Henry Cohn, 2025, needs more optimization.
6 344 0.749056432048 Henry Cohn, 2026, needs more optimization.
6 345 0.749265236147 Henry Cohn, 2026, needs more optimization.
6 346 0.749564741696 Henry Cohn, 2025, needs more optimization.
6 347 0.749797304227 Henry Cohn, 2026, needs more optimization.
6 348 0.750331506180 Henry Cohn, 2025, needs more optimization.
6 349 0.750503191071 Henry Cohn, 2025, needs more optimization.
6 350 0.750780551529 Henry Cohn, 2026, needs more optimization.
6 351 0.750837736399 Henry Cohn, 2025, needs more optimization.
6 352 0.751253722010 Henry Cohn, 2025, needs more optimization.
6 353 0.751714863962 Henry Cohn, 2025, needs more optimization.
6 354 0.751805047730 Henry Cohn, 2025, needs more optimization.
6 355 0.751934926381 Henry Cohn, 2025, needs more optimization.
6 356 0.752284354827 Henry Cohn, 2025, needs more optimization.
6 357 0.752897715808 Henry Cohn, 2026, needs more optimization.
6 358 0.752944135015 Henry Cohn, 2025, needs more optimization.
6 359 0.753290360804 Henry Cohn, 2025, needs more optimization.
6 360 0.753398391402 Henry Cohn, 2025, needs more optimization.
6 361 0.753737071365 Henry Cohn, 2025, needs more optimization.
6 362 0.754060455855 Henry Cohn, 2025, needs more optimization.
6 363 0.754391381517 Henry Cohn, 2025, needs more optimization.
6 364 0.754666347797 Henry Cohn, 2025, needs more optimization.
6 365 0.754818502152 Henry Cohn, 2025, needs more optimization.
6 366 0.755036821765 Henry Cohn, 2026, needs more optimization.
6 367 0.755458232833 Henry Cohn, 2025, needs more optimization.
6 368 0.755618078029 Henry Cohn, 2026, needs more optimization.
6 369 0.756134137839 Henry Cohn, 2025, needs more optimization.
6 370 0.756490885955 Henry Cohn, 2026, needs more optimization.
6 371 0.756625060003 Henry Cohn, 2025, needs more optimization.
6 372 0.756759262628 Henry Cohn, 2025, needs more optimization.
6 373 0.757132722236 Henry Cohn, 2025, needs more optimization.
6 374 0.757313417240 Henry Cohn, 2026, needs more optimization.
6 375 0.757922987508 Henry Cohn, 2025, needs more optimization.
6 376 0.757993367495 Henry Cohn, 2025, needs more optimization.
6 377 0.758664541092 Henry Cohn, 2025, needs more optimization.
6 378 0.758717144387 Henry Cohn, 2025, needs more optimization.
6 379 0.758939583890 Ilmari Vahteristo, 2026.
6 380 0.759289338453 Henry Cohn, 2025, needs more optimization.
6 381 0.759421496990 Henry Cohn, 2026, needs more optimization.
6 382 0.759586923897 Henry Cohn, 2026, needs more optimization.
6 383 0.759892829859 Henry Cohn, 2025, needs more optimization.
6 384 0.759900544934 Henry Cohn, 2026, needs more optimization.
6 385 0.760347676343 Henry Cohn, 2025, needs more optimization.
6 386 0.760469383839 Henry Cohn, 2025, needs more optimization.
6 387 0.760835708448 Henry Cohn, 2025, needs more optimization.
6 388 0.761166611751 Henry Cohn, 2026, needs more optimization.
6 389 0.761392923324 Henry Cohn, 2025, needs more optimization.
6 390 0.761779583649 Henry Cohn, 2025, needs more optimization.
6 391 0.761801350661 Henry Cohn, 2025, needs more optimization.
6 392 0.762156311332 Henry Cohn, 2026, needs more optimization.
6 393 0.762160511164 Henry Cohn, 2025, needs more optimization.
6 394 0.762460815016 Henry Cohn, 2026, needs more optimization.
6 395 0.762824595902 Henry Cohn, 2026, needs more optimization.
6 396 0.763226986795 Henry Cohn, 2025, needs more optimization.
6 397 0.763265417521 Henry Cohn, 2025, needs more optimization.
6 398 0.763667586383 Henry Cohn, 2025, needs more optimization.
6 399 0.763778015015 Henry Cohn, 2025, needs more optimization.
6 400 0.764313410189 Henry Cohn, 2025, needs more optimization.
6 401 0.764321098938 Henry Cohn, 2025, needs more optimization.
6 402 0.764359402081 Henry Cohn, 2026, needs more optimization.
6 403 0.764572152690 Henry Cohn, 2025, needs more optimization.
6 404 0.764948720712 Henry Cohn, 2025, needs more optimization.
6 405 0.765119391862 Henry Cohn, 2025, needs more optimization.
6 406 0.765531096457 Henry Cohn, 2026, needs more optimization.
6 407 0.765562373015 Henry Cohn, 2025, needs more optimization.
6 408 0.765843084808 Henry Cohn, 2025, needs more optimization.
6 409 0.765847573501 Henry Cohn, 2025, needs more optimization.
6 410 0.766034682898 Henry Cohn, 2026, needs more optimization.
6 411 0.766428857285 Henry Cohn, 2026, needs more optimization.
6 412 0.766619840406 Henry Cohn, 2025, needs more optimization.
6 413 0.766783053501 Henry Cohn, 2025, needs more optimization.
6 414 0.767103548283 Henry Cohn, 2026, needs more optimization.
6 415 0.767558038199 Henry Cohn, 2025, needs more optimization.
6 416 0.767822571162 Henry Cohn, 2025, needs more optimization.
6 417 0.768110015375 Ilmari Vahteristo, 2026.
6 418 0.768325691504 Henry Cohn, 2025, needs more optimization.
6 419 0.768667400220 Ilmari Vahteristo, 2026.
6 420 0.768700416304 Henry Cohn, 2026, needs more optimization.
6 421 0.768870069376 Henry Cohn, 2025, needs more optimization.
6 422 0.769139383101 Henry Cohn, 2026, needs more optimization.
6 423 0.769380268362 Henry Cohn, 2026, needs more optimization.
6 424 0.769735933377 Henry Cohn, 2026, needs more optimization.
6 425 0.769905701850 Henry Cohn, 2026, needs more optimization.
6 426 0.770200252343 Ilmari Vahteristo, 2026.
6 427 0.770470798880 Henry Cohn, 2025, needs more optimization.
6 428 0.770653463637 Ilmari Vahteristo, 2026.
6 429 0.770681981055 Henry Cohn, 2025, needs more optimization.
6 430 0.770908838569 Henry Cohn, 2026, needs more optimization.
6 431 0.770929384281 Henry Cohn, 2025, needs more optimization.
6 432 0.771241013622 Henry Cohn, 2026, needs more optimization.
6 433 0.771382581330 Henry Cohn, 2025, needs more optimization.
6 434 0.771535594990 Henry Cohn, 2025, needs more optimization.
6 435 0.771885822672 Henry Cohn, 2025, needs more optimization.
6 436 0.771888185017 Henry Cohn, 2026, needs more optimization.
6 437 0.772029819935 Henry Cohn, 2025, needs more optimization.
6 438 0.772265509671 Henry Cohn, 2025, needs more optimization.
6 439 0.772523939817 Henry Cohn, 2025, needs more optimization.
6 440 0.772663149453 Henry Cohn, 2025, needs more optimization.
6 441 0.772955200339 Henry Cohn, 2025, needs more optimization.
6 442 0.773109581137 Henry Cohn, 2026, needs more optimization.
6 443 0.773310557624 Henry Cohn, 2025, needs more optimization.
6 444 0.773776268957 Henry Cohn, 2026, needs more optimization.
6 445 0.773983280335 Henry Cohn, 2025, needs more optimization.
6 446 0.774219246104 Henry Cohn, 2025, needs more optimization.
6 447 0.774236279177 Henry Cohn, 2025, needs more optimization.
6 448 0.774534657349 Henry Cohn, 2026, needs more optimization.
6 449 0.774731477728 Henry Cohn, 2025, needs more optimization.
6 450 0.775053295714 Henry Cohn, 2026, needs more optimization.
6 451 0.775063237723 Henry Cohn, 2026, needs more optimization.
6 452 0.775246412303 Henry Cohn, 2025, needs more optimization.
6 453 0.775432127164 Henry Cohn, 2026, needs more optimization.
6 454 0.775505106768 Henry Cohn, 2025, needs more optimization.
6 455 0.775855579167 Henry Cohn, 2026, needs more optimization.
6 456 0.776068757202 Henry Cohn, 2025, needs more optimization.
6 457 0.776321955413 Henry Cohn, 2025, needs more optimization.
6 458 0.776539310055 Henry Cohn, 2026, needs more optimization.
6 459 0.776803861429 Henry Cohn, 2026, needs more optimization.
6 460 0.776807101274 Henry Cohn, 2025, needs more optimization.
6 461 0.776809166143 Henry Cohn, 2025, needs more optimization.
6 462 0.777190441084 Henry Cohn, 2026, needs more optimization.
6 463 0.777434326346 Henry Cohn, 2025, needs more optimization.
6 464 0.777508700669 Henry Cohn, 2025, needs more optimization.
6 465 0.777692189029 Henry Cohn, 2026, needs more optimization.
6 466 0.777951652917 Henry Cohn, 2026, needs more optimization.
6 467 0.778148493090 Henry Cohn, 2026, needs more optimization.
6 468 0.778287393273 Henry Cohn, 2025, needs more optimization.
6 469 0.778345056785 Henry Cohn, 2026, needs more optimization.
6 470 0.779001228385 Henry Cohn, 2025, needs more optimization.
6 471 0.779024956635 Henry Cohn, 2025, needs more optimization.
6 472 0.779181329561 Henry Cohn, 2025, needs more optimization.
6 473 0.779488936123 Henry Cohn, 2025, needs more optimization.
6 474 0.779723666725 Henry Cohn, 2026, needs more optimization.
6 475 0.779753504424 Henry Cohn, 2025, needs more optimization.
6 476 0.779768569425 Henry Cohn, 2025, needs more optimization.
6 477 0.780128871313 Henry Cohn, 2025, needs more optimization.
6 478 0.780205950103 Henry Cohn, 2025, needs more optimization.
6 479 0.780501205782 Henry Cohn, 2025, needs more optimization.
6 480 0.780553951214 Henry Cohn, 2025, needs more optimization.
6 481 0.780794006151 Henry Cohn, 2026, needs more optimization.
6 482 0.780976751883 Henry Cohn, 2026, needs more optimization.
6 483 0.781178259455 Henry Cohn, 2026, needs more optimization.
6 484 0.781464673023 Henry Cohn, 2026, needs more optimization.
6 485 0.781607451896 Henry Cohn, 2025, needs more optimization.
6 486 0.781666833507 Henry Cohn, 2026, needs more optimization.
6 487 0.782092404018 Henry Cohn, 2025, needs more optimization.
6 488 0.782189214112 Henry Cohn, 2026, needs more optimization.
6 489 0.782411616128 Henry Cohn, 2026, needs more optimization.
6 490 0.782461906213 Henry Cohn, 2026, needs more optimization.
6 491 0.782767005066 Henry Cohn, 2026, needs more optimization.
6 492 0.782865245898 Henry Cohn, 2025, needs more optimization.
6 493 0.783018604741 Henry Cohn, 2026, needs more optimization.
6 494 0.783328089629 Henry Cohn, 2025, needs more optimization.
6 495 0.783396974283 Henry Cohn, 2025, needs more optimization.
6 496 0.783465207879 Henry Cohn, 2026, needs more optimization.
6 497 0.783759592457 Henry Cohn, 2026, needs more optimization.
6 498 0.783946677385 Henry Cohn, 2025, needs more optimization.
6 499 0.783955309086 Henry Cohn, 2025, needs more optimization.
6 500 0.784225819721 Henry Cohn, 2025, needs more optimization.
6 501 0.784506246453 Henry Cohn, 2025, needs more optimization.
6 502 0.784696939909 Henry Cohn, 2025, needs more optimization.
6 503 0.784879873306 Henry Cohn, 2025, needs more optimization.
6 504 0.785043563985 Henry Cohn, 2026, needs more optimization.
6 505 0.785179710994 Henry Cohn, 2026, needs more optimization.
6 506 0.785426852564 Henry Cohn, 2026, needs more optimization.
6 507 0.785540748252 Henry Cohn, 2026, needs more optimization.
6 508 0.785799771003 Henry Cohn, 2026, needs more optimization.
6 509 0.785963085809 Henry Cohn, 2025, needs more optimization.
6 510 0.786068209087 Henry Cohn, 2026, needs more optimization.
6 511 0.786344662388 Henry Cohn, 2025, needs more optimization.
6 512 0.786379684678 Henry Cohn, 2026, needs more optimization.
6 513 0.786463332303 Henry Cohn, 2026, needs more optimization.
6 514 0.786694907764 Henry Cohn, 2026, needs more optimization.
6 515 0.786913884715 Henry Cohn, 2025, needs more optimization.
6 516 0.787047171505 Henry Cohn, 2026, needs more optimization.
6 517 0.787230377399 Henry Cohn, 2026, needs more optimization.
6 518 0.787272798145 Henry Cohn, 2025, needs more optimization.
6 519 0.787318272676 Henry Cohn, 2025, needs more optimization.
6 520 0.787617124479 Henry Cohn, 2025, needs more optimization.
6 521 0.787734926114 Henry Cohn, 2025, needs more optimization.
6 522 0.788137976651 Henry Cohn, 2025, needs more optimization.
6 523 0.788156267395 Henry Cohn, 2025, needs more optimization.
6 524 0.788441800907 Henry Cohn, 2026, needs more optimization.
6 525 0.788608388669 Henry Cohn, 2025, needs more optimization.
6 526 0.788709148657 Henry Cohn, 2025, needs more optimization.
6 527 0.788874161694 Henry Cohn, 2026, needs more optimization.
6 528 0.788926543638 Henry Cohn, 2026, needs more optimization.
6 529 0.789134700458 Henry Cohn, 2025, needs more optimization.
6 530 0.789414103146 Henry Cohn, 2026, needs more optimization.
6 531 0.789428246829 Henry Cohn, 2026, needs more optimization.
6 532 0.789787457345 Henry Cohn, 2026, needs more optimization.
6 533 0.789792757309 Henry Cohn, 2025, needs more optimization.
6 534 0.789817192244 Henry Cohn, 2025, needs more optimization.
6 535 0.790045702885 Henry Cohn, 2025, needs more optimization.
6 536 0.790080666571 Henry Cohn, 2025, needs more optimization.
6 537 0.790456481764 Henry Cohn, 2026, needs more optimization.
6 538 0.790512511145 Henry Cohn, 2026, needs more optimization.
6 539 0.790575573190 Henry Cohn, 2025, needs more optimization.
6 540 0.790802834220 Henry Cohn, 2026, needs more optimization.
6 541 0.790905992923 Henry Cohn, 2026, needs more optimization.
6 542 0.790912425048 Henry Cohn, 2025, needs more optimization.
6 543 0.791109702429 Henry Cohn, 2025, needs more optimization.
6 544 0.791482114125 Henry Cohn, 2026, needs more optimization.
6 545 0.791558205412 Henry Cohn, 2026, needs more optimization.
6 546 0.791791197806 Henry Cohn, 2026, needs more optimization.
6 547 0.791817853845 Henry Cohn, 2025, needs more optimization.
6 548 0.792007169007 Henry Cohn, 2026, needs more optimization.
6 549 0.792120458535 Henry Cohn, 2025, needs more optimization.
6 550 0.792394874086 Henry Cohn, 2026, needs more optimization.
6 551 0.792571287759 Henry Cohn, 2025, needs more optimization.
6 552 0.792575911224 Henry Cohn, 2026, needs more optimization.
6 553 0.792720237063 Henry Cohn, 2025, needs more optimization.
6 554 0.792991123280 Henry Cohn, 2025, needs more optimization.
6 555 0.793030377786 Henry Cohn, 2025, needs more optimization.
6 556 0.793345560359 Henry Cohn, 2025, needs more optimization.
6 557 0.793375623664 Henry Cohn, 2025, needs more optimization.
6 558 0.793391752086 Henry Cohn, 2026, needs more optimization.
6 559 0.793540032966 Henry Cohn, 2026, needs more optimization.
6 560 0.793970939934 Henry Cohn, 2026, needs more optimization.
6 561 0.793997720863 Henry Cohn, 2025, needs more optimization.
6 562 0.793999096351 Henry Cohn, 2025, needs more optimization.
6 563 0.794253599934 Henry Cohn, 2025, needs more optimization.
6 564 0.794345967712 Henry Cohn, 2025, needs more optimization.
6 565 0.794514240296 Henry Cohn, 2025, needs more optimization.
6 566 0.794720999866 Henry Cohn, 2025, needs more optimization.
6 567 0.794822227717 Henry Cohn, 2026, needs more optimization.
6 568 0.795027686258 Henry Cohn, 2026, needs more optimization.
6 569 0.795033176405 Henry Cohn, 2026, needs more optimization.
6 570 0.795265951322 Henry Cohn, 2026, needs more optimization.
6 571 0.795288705125 Henry Cohn, 2025, needs more optimization.
6 572 0.795516409345 Henry Cohn, 2025, needs more optimization.
6 573 0.795829156946 Henry Cohn, 2025, needs more optimization.
6 574 0.795900175913 Henry Cohn, 2025, needs more optimization.
6 575 0.795904568008 Henry Cohn, 2025, needs more optimization.
6 576 0.796101080809 Henry Cohn, 2025, needs more optimization.
6 577 0.796256548729 Henry Cohn, 2025, needs more optimization.
6 578 0.796571670123 Henry Cohn, 2025, needs more optimization.
6 579 0.796576792514 Henry Cohn, 2026, needs more optimization.
6 580 0.796751653475 Henry Cohn, 2025, needs more optimization.
6 581 0.796786785592 Henry Cohn, 2026, needs more optimization.
6 582 0.797057202471 Henry Cohn, 2025, needs more optimization.
6 583 0.797104811578 Henry Cohn, 2025, needs more optimization.
6 584 0.797356665470 Henry Cohn, 2026, needs more optimization.
6 585 0.797384718954 Henry Cohn, 2025, needs more optimization.
6 586 0.797385241881 Henry Cohn, 2026, needs more optimization.
6 587 0.797603948018 Henry Cohn, 2025, needs more optimization.
6 588 0.797789322431 Henry Cohn, 2026, needs more optimization.
6 589 0.797840114335 Henry Cohn, 2026, needs more optimization.
6 590 0.798162548924 Henry Cohn, 2026, needs more optimization.
6 591 0.798166091649 Henry Cohn, 2025, needs more optimization.
6 592 0.798376791335 Henry Cohn, 2025, needs more optimization.
6 593 0.798472384327 Henry Cohn, 2025, needs more optimization.
6 594 0.798669532087 Henry Cohn, 2026, needs more optimization.
6 595 0.798805187978 Henry Cohn, 2025, needs more optimization.
6 596 0.799063819653 Henry Cohn, 2026, needs more optimization.
6 597 0.799214553851 Henry Cohn, 2025, needs more optimization.
6 598 0.799240654751 Henry Cohn, 2026, needs more optimization.
6 599 0.799406794187 Henry Cohn, 2025, needs more optimization.
6 600 0.799541345677 Henry Cohn, 2026, needs more optimization.
6 601 0.799696542620 Henry Cohn, 2025, needs more optimization.
6 602 0.799818854650 Henry Cohn, 2026, needs more optimization.
6 603 0.799927083241 Henry Cohn, 2025, needs more optimization.
6 604 0.800237726072 Henry Cohn, 2025, needs more optimization.
6 605 0.800238223191 Henry Cohn, 2025, needs more optimization.
6 606 0.800239423949 Henry Cohn, 2025, needs more optimization.
6 607 0.800492441363 Henry Cohn, 2025, needs more optimization.
6 608 0.800495024091 Henry Cohn, 2026, needs more optimization.
6 609 0.800688709880 Henry Cohn, 2025, needs more optimization.
6 610 0.801072650459 Henry Cohn, 2025, needs more optimization.
6 611 0.801085375103 Henry Cohn, 2026, needs more optimization.
6 612 0.801133000500 Henry Cohn, 2025, needs more optimization.
6 613 0.801192982451 Henry Cohn, 2025, needs more optimization.
6 614 0.801482225961 Henry Cohn, 2026, needs more optimization.
6 615 0.801487334924 Henry Cohn, 2025, needs more optimization.
6 616 0.801657461132 Henry Cohn, 2026, needs more optimization.
6 617 0.801682559413 Henry Cohn, 2026, needs more optimization.
6 618 0.801908204381 Henry Cohn, 2026, needs more optimization.
6 619 0.801914036391 Henry Cohn, 2026, needs more optimization.
6 620 0.802028436564 Henry Cohn, 2026, needs more optimization.
6 621 0.802209048142 Henry Cohn, 2026, needs more optimization.
6 622 0.802454074297 Henry Cohn, 2025, needs more optimization.
6 623 0.802568688111 Henry Cohn, 2025, needs more optimization.
6 624 0.802580355221 Henry Cohn, 2026, needs more optimization.
6 625 0.802875169852 Henry Cohn, 2025, needs more optimization.
6 626 0.802899751488 Henry Cohn, 2026, needs more optimization.
6 627 0.802921218541 Henry Cohn, 2025, needs more optimization.
6 628 0.803035532929 Henry Cohn, 2026, needs more optimization.
6 629 0.803299590474 Henry Cohn, 2026, needs more optimization.
6 630 0.803301323863 Henry Cohn, 2026, needs more optimization.
6 631 0.803487382574 Henry Cohn, 2025, needs more optimization.
6 632 0.803728175116 Henry Cohn, 2026, needs more optimization.
6 633 0.803849473735 Henry Cohn, 2026, needs more optimization.
6 634 0.804007465348 Henry Cohn, 2026, needs more optimization.
6 635 0.804025542024 Henry Cohn, 2025, needs more optimization.
6 636 0.804180065316 Henry Cohn, 2026, needs more optimization.
6 637 0.804238749445 Henry Cohn, 2026, needs more optimization.
6 638 0.804384859272 Henry Cohn, 2025, needs more optimization.
6 639 0.804386938080 Henry Cohn, 2026, needs more optimization.
6 640 0.804616355202 Henry Cohn, 2025, needs more optimization.
6 641 0.804666298456 Henry Cohn, 2025, needs more optimization.
6 642 0.804672578592 Henry Cohn, 2025, needs more optimization.
6 643 0.804842333605 Henry Cohn, 2026, needs more optimization.
6 644 0.805068138518 Henry Cohn, 2026, needs more optimization.
6 645 0.805285069869 Henry Cohn, 2025, needs more optimization.
6 646 0.805384911647 Henry Cohn, 2025, needs more optimization.
6 647 0.805448187462 Henry Cohn, 2025, needs more optimization.
6 648 0.805456820919 Henry Cohn, 2025, needs more optimization.
6 649 0.805642092642 Henry Cohn, 2025, needs more optimization.
6 650 0.805657404477 Henry Cohn, 2026, needs more optimization.
6 651 0.805913789108 Henry Cohn, 2026, needs more optimization.
6 652 0.805952437252 Henry Cohn, 2026, needs more optimization.
6 653 0.806116288247 Henry Cohn, 2026, needs more optimization.
6 654 0.806370880524 Henry Cohn, 2025, needs more optimization.
6 655 0.806375912850 Henry Cohn, 2025, needs more optimization.
6 656 0.806422253369 Henry Cohn, 2026, needs more optimization.
6 657 0.806640579298 Henry Cohn, 2025, needs more optimization.
6 658 0.806678026189 Henry Cohn, 2026, needs more optimization.
6 659 0.806730375136 Henry Cohn, 2025, needs more optimization.
6 660 0.806757030490 Henry Cohn, 2025, needs more optimization.
6 661 0.806983357269 Henry Cohn, 2025, needs more optimization.
6 662 0.807247874962 Henry Cohn, 2025, needs more optimization.
6 663 0.807373630299 Henry Cohn, 2026, needs more optimization.
6 664 0.807378892261 Henry Cohn, 2026, needs more optimization.
6 665 0.807624736629 Henry Cohn, 2026, needs more optimization.
6 666 0.807660969307 Henry Cohn, 2026, needs more optimization.
6 667 0.807795326218 Henry Cohn, 2025, needs more optimization.
6 668 0.807828789748 Henry Cohn, 2025, needs more optimization.
6 669 0.807833607483 Henry Cohn, 2025, needs more optimization.
6 670 0.807898038068 Henry Cohn, 2026, needs more optimization.
6 671 0.808077665747 Henry Cohn, 2026, needs more optimization.
6 672 0.808175676168 Henry Cohn, 2026, needs more optimization.
6 673 0.808414765330 Henry Cohn, 2025, needs more optimization.
6 674 0.808465382532 Henry Cohn, 2026, needs more optimization.
6 676 0.808770309220 Henry Cohn, 2026, needs more optimization.
6 677 0.808946782452 Henry Cohn, 2025, needs more optimization.
6 678 0.809095726889 Henry Cohn, 2026, needs more optimization.
6 679 0.809105555259 Henry Cohn, 2025, needs more optimization.
6 680 0.809285168486 Henry Cohn, 2025, needs more optimization.
6 681 0.809550813598 Henry Cohn, 2025, needs more optimization.
6 682 0.809556610555 Henry Cohn, 2026, needs more optimization.
6 683 0.809593568170 Henry Cohn, 2025, needs more optimization.
6 684 0.809809729757 Henry Cohn, 2026, needs more optimization.
6 685 0.809815681557 Henry Cohn, 2025, needs more optimization.
6 686 0.809957609025 Henry Cohn, 2026, needs more optimization.
6 687 0.809987501148 Henry Cohn, 2026, needs more optimization.
6 688 0.810216131855 Henry Cohn, 2025, needs more optimization.
6 689 0.810286164813 Henry Cohn, 2025, needs more optimization.
6 690 0.810404495670 Henry Cohn, 2025, needs more optimization.
6 691 0.810680318644 Henry Cohn, 2025, needs more optimization.
6 692 0.810691458399 Henry Cohn, 2026, needs more optimization.
6 693 0.810692518870 Henry Cohn, 2026, needs more optimization.
6 694 0.810880398447 Henry Cohn, 2026, needs more optimization.
6 695 0.810944407206 Henry Cohn, 2026, needs more optimization.
6 696 0.811134509113 Henry Cohn, 2026, needs more optimization.
6 697 0.811178575942 Henry Cohn, 2026, needs more optimization.
6 698 0.811436541795 Henry Cohn, 2025, needs more optimization.
6 699 0.811556195073 Henry Cohn, 2025, needs more optimization.
6 700 0.811692885419 Henry Cohn, 2026, needs more optimization.
6 701 0.811698474053 Henry Cohn, 2026, needs more optimization.
6 702 0.811787077923 Henry Cohn, 2025, needs more optimization.
6 703 0.811896779748 Henry Cohn, 2026, needs more optimization.
6 704 0.811933453698 Henry Cohn, 2026, needs more optimization.
6 705 0.812056196050 Henry Cohn, 2026, needs more optimization.
6 706 0.812327856122 Henry Cohn, 2026, needs more optimization.
6 707 0.812337579657 Henry Cohn, 2026, needs more optimization.
6 708 0.812521323092 Henry Cohn, 2025, needs more optimization.
6 709 0.812709123718 Henry Cohn, 2026, needs more optimization.
6 710 0.812869067662 Henry Cohn, 2026, needs more optimization.
6 711 0.812870939378 Henry Cohn, 2025, needs more optimization.
6 712 0.812909766290 Henry Cohn, 2026, needs more optimization.
6 713 0.813168514782 Henry Cohn, 2025, needs more optimization.
6 714 0.813189998744 Henry Cohn, 2026, needs more optimization.
6 715 0.813306799649 Henry Cohn, 2025, needs more optimization.
6 716 0.813312306830 Henry Cohn, 2025, needs more optimization.
6 717 0.813339672183 Henry Cohn, 2026, needs more optimization.
6 718 0.813642939265 Henry Cohn, 2026, needs more optimization.
6 719 0.813647808802 Henry Cohn, 2025, needs more optimization.
6 720 0.813677877521 Henry Cohn, 2026, needs more optimization.
6 721 0.813962266975 Henry Cohn, 2025, needs more optimization.
6 722 0.814008585494 Henry Cohn, 2025, needs more optimization.
6 723 0.814032728403 Henry Cohn, 2026, needs more optimization.
6 724 0.814066976477 Henry Cohn, 2026, needs more optimization.
6 725 0.814205535670 Henry Cohn, 2026, needs more optimization.
6 726 0.814326606162 Henry Cohn, 2026, needs more optimization.
6 727 0.814502502478 Henry Cohn, 2026, needs more optimization.
6 728 0.814503288797 Henry Cohn, 2025, needs more optimization.
6 729 0.814570219480 Henry Cohn, 2026, needs more optimization.
6 730 0.814691836372 Henry Cohn, 2026, needs more optimization.
6 731 0.814856583331 Henry Cohn, 2026, needs more optimization.
6 732 0.814941616114 Henry Cohn, 2026, needs more optimization.
6 733 0.815064098749 Henry Cohn, 2026, needs more optimization.
6 734 0.815069220671 Henry Cohn, 2026, needs more optimization.
6 735 0.815126481815 Henry Cohn, 2026, needs more optimization.
6 736 0.815223603952 Henry Cohn, 2025, needs more optimization.
6 737 0.815682268478 Henry Cohn, 2026, needs more optimization.
6 738 0.815693468417 Henry Cohn, 2026, needs more optimization.
6 739 0.815709376578 Henry Cohn, 2025, needs more optimization.
6 740 0.815877414246 Henry Cohn, 2026, needs more optimization.
6 741 0.815898132314 Henry Cohn, 2026, needs more optimization.
6 742 0.816035439694 Henry Cohn, 2026, needs more optimization.
6 743 0.816066005174 Henry Cohn, 2026, needs more optimization.
6 744 0.816072924951 Henry Cohn, 2026, needs more optimization.
6 745 0.816297758800 Henry Cohn, 2025, needs more optimization.
6 746 0.816305246119 Henry Cohn, 2026, needs more optimization.
6 747 0.816590719307 Henry Cohn, 2026, needs more optimization.
6 748 0.816629818356 Henry Cohn, 2025, needs more optimization.
6 749 0.816636310815 Henry Cohn, 2025, needs more optimization.
6 750 0.816834403280 Henry Cohn, 2026, needs more optimization.
6 751 0.816988092892 Henry Cohn, 2026, needs more optimization.
6 752 0.817000737748 Henry Cohn, 2026, needs more optimization.
6 753 0.817252063848 Henry Cohn, 2025, needs more optimization.
6 754 0.817260199019 Henry Cohn, 2025, needs more optimization.
6 755 0.817289678208 Henry Cohn, 2026, needs more optimization.
6 756 0.817435527872 Henry Cohn, 2026, needs more optimization.
6 757 0.817474379864 Henry Cohn, 2026, needs more optimization.
6 758 0.817494710876 Henry Cohn, 2026, needs more optimization.
6 759 0.817679682538 Henry Cohn, 2025, needs more optimization.
6 760 0.817728595799 Henry Cohn, 2026, needs more optimization.
6 761 0.817737248258 Henry Cohn, 2026, needs more optimization.
6 762 0.818009280002 Henry Cohn, 2025, needs more optimization.
6 763 0.818125060239 Henry Cohn, 2026, needs more optimization.
6 764 0.818293022730 Henry Cohn, 2026, needs more optimization.
6 765 0.818386820456 Henry Cohn, 2026, needs more optimization.
6 766 0.818390063895 Henry Cohn, 2026, needs more optimization.
6 767 0.818394454662 Henry Cohn, 2025, needs more optimization.
6 768 0.818596596606 Henry Cohn, 2025, needs more optimization.
6 769 0.818775965803 Henry Cohn, 2025, needs more optimization.
6 770 0.818805061007 Henry Cohn, 2026, needs more optimization.
6 771 0.818923267989 Henry Cohn, 2026, needs more optimization.
6 772 0.818932450167 Henry Cohn, 2026, needs more optimization.
6 773 0.818970769208 Henry Cohn, 2025, needs more optimization.
6 774 0.819128780864 Henry Cohn, 2026, needs more optimization.
6 775 0.819129055822 Henry Cohn, 2026, needs more optimization.
6 776 0.819373850853 Henry Cohn, 2026, needs more optimization.
6 777 0.819409159888 Henry Cohn, 2026, needs more optimization.
6 778 0.819549833203 Henry Cohn, 2025, needs more optimization.
6 779 0.819551772387 Henry Cohn, 2026, needs more optimization.
6 780 0.819703678444 Henry Cohn, 2026, needs more optimization.
6 781 0.819710578070 Henry Cohn, 2026, needs more optimization.
6 782 0.819732926480 Henry Cohn, 2026, needs more optimization.
6 783 0.819933707254 Henry Cohn, 2025, needs more optimization.
6 784 0.819960428163 Henry Cohn, 2026, needs more optimization.
6 785 0.820143659869 Henry Cohn, 2025, needs more optimization.
6 786 0.820162296273 Henry Cohn, 2026, needs more optimization.
6 787 0.820192193425 Henry Cohn, 2026, needs more optimization.
6 788 0.820407823502 Henry Cohn, 2026, needs more optimization.
6 789 0.820418485236 Henry Cohn, 2025, needs more optimization.
6 790 0.820541743786 Henry Cohn, 2026, needs more optimization.
6 791 0.820646161966 Henry Cohn, 2026, needs more optimization.
6 792 0.820801628820 Henry Cohn, 2026, needs more optimization.
6 793 0.820844938450 Henry Cohn, 2026, needs more optimization.
6 794 0.820992944116 Henry Cohn, 2026, needs more optimization.
6 795 0.820998941353 Henry Cohn, 2025, needs more optimization.
6 796 0.821019788207 Henry Cohn, 2025, needs more optimization.
6 797 0.821161818773 Henry Cohn, 2026, needs more optimization.
6 798 0.821167863597 Henry Cohn, 2026, needs more optimization.
6 799 0.821268664848 Henry Cohn, 2026, needs more optimization.
6 800 0.821599446854 Henry Cohn, 2025, needs more optimization.
6 801 0.821655585342 Henry Cohn, 2025, needs more optimization.
6 802 0.821670709678 Henry Cohn, 2026, needs more optimization.
6 803 0.821753358327 Henry Cohn, 2026, needs more optimization.
6 804 0.821760010760 Henry Cohn, 2026, needs more optimization.
6 805 0.821921704628 Henry Cohn, 2025, needs more optimization.
6 806 0.821925354397 Henry Cohn, 2025, needs more optimization.
6 807 0.822127138753 Henry Cohn, 2025, needs more optimization.
6 808 0.822136942702 Henry Cohn, 2026, needs more optimization.
6 809 0.822274739568 Henry Cohn, 2025, needs more optimization.
6 810 0.822299924242 Henry Cohn, 2025, needs more optimization.
6 811 0.822379403637 Henry Cohn, 2026, needs more optimization.
6 812 0.822493820161 Henry Cohn, 2026, needs more optimization.
6 813 0.822711901212 Henry Cohn, 2026, needs more optimization.
6 814 0.822717523257 Henry Cohn, 2026, needs more optimization.
6 815 0.822810732997 Henry Cohn, 2025, needs more optimization.
6 816 0.822862618507 Henry Cohn, 2026, needs more optimization.
6 817 0.823003742491 Henry Cohn, 2025, needs more optimization.
6 818 0.823195043696 Henry Cohn, 2026, needs more optimization.
6 820 0.823199035966 Henry Cohn, 2026, needs more optimization.
6 821 0.823455597756 Henry Cohn, 2026, needs more optimization.
6 822 0.823659438728 Henry Cohn, 2026, needs more optimization.
6 824 0.823661404172 Henry Cohn, 2025, needs more optimization.
6 825 0.823727831164 Henry Cohn, 2025, needs more optimization.
6 826 0.823991086599 Henry Cohn, 2026, needs more optimization.
6 827 0.823997725332 Henry Cohn, 2026, needs more optimization.
6 828 0.824000600074 Henry Cohn, 2026, needs more optimization.
6 829 0.824087347346 Henry Cohn, 2026, needs more optimization.
6 830 0.824248007756 Henry Cohn, 2026, needs more optimization.
6 831 0.824253060781 Henry Cohn, 2025, needs more optimization.
6 832 0.824405563460 Henry Cohn, 2026, needs more optimization.
6 833 0.824410474997 Henry Cohn, 2026, needs more optimization.
6 834 0.824560460920 Henry Cohn, 2025, needs more optimization.
6 835 0.824562867216 Henry Cohn, 2025, needs more optimization.
6 836 0.824565043044 Henry Cohn, 2025, needs more optimization.
6 837 0.824856286512 Henry Cohn, 2026, needs more optimization.
6 838 0.824860456156 Henry Cohn, 2026, needs more optimization.
6 839 0.824886179725 Henry Cohn, 2026, needs more optimization.
6 840 0.824920182114 Henry Cohn, 2025, needs more optimization.
6 841 0.824997445981 Henry Cohn, 2026, needs more optimization.
6 842 0.825315243286 Henry Cohn, 2026, needs more optimization.
6 843 0.825320807229 Henry Cohn, 2025, needs more optimization.
6 844 0.825332142790 Henry Cohn, 2026, needs more optimization.
6 845 0.825431145892 Henry Cohn, 2025, needs more optimization.
6 846 0.825565311431 Henry Cohn, 2026, needs more optimization.
6 847 0.825575914986 Henry Cohn, 2026, needs more optimization.
6 848 0.825586029457 Henry Cohn, 2026, needs more optimization.
6 849 0.825838964850 Henry Cohn, 2026, needs more optimization.
6 850 0.825859233687 Henry Cohn, 2026, needs more optimization.
6 851 0.825867145117 Henry Cohn, 2026, needs more optimization.
6 852 0.826024374941 Henry Cohn, 2026, needs more optimization.
6 853 0.826141135886 Henry Cohn, 2026, needs more optimization.
6 854 0.826367084565 Henry Cohn, 2026, needs more optimization.
6 855 0.826400472648 Henry Cohn, 2025, needs more optimization.
6 856 0.826415296291 Henry Cohn, 2026, needs more optimization.
6 857 0.826652046639 Henry Cohn, 2025, needs more optimization.
6 858 0.826659628926 Henry Cohn, 2025, needs more optimization.
6 859 0.826687113923 Henry Cohn, 2026, needs more optimization.
6 860 0.826841472698 Henry Cohn, 2026, needs more optimization.
6 861 0.826932469101 Henry Cohn, 2026, needs more optimization.
6 862 0.826936718325 Henry Cohn, 2026, needs more optimization.
6 863 0.827094871902 Henry Cohn, 2026, needs more optimization.
6 864 0.827100003459 Henry Cohn, 2026, needs more optimization.
6 865 0.827296940286 Henry Cohn, 2026, needs more optimization.
6 867 0.827303375728 Henry Cohn, 2025, needs more optimization.
6 868 0.827394189128 Henry Cohn, 2026, needs more optimization.
6 869 0.827396755599 Henry Cohn, 2026, needs more optimization.
6 870 0.827591086516 Henry Cohn, 2026, needs more optimization.
6 871 0.827597158369 Henry Cohn, 2025, needs more optimization.
6 872 0.827728271232 Henry Cohn, 2026, needs more optimization.
6 873 0.827729680529 Henry Cohn, 2026, needs more optimization.
6 874 0.827730794125 Henry Cohn, 2025, needs more optimization.
6 875 0.827737392377 Henry Cohn, 2025, needs more optimization.
6 876 0.827801485706 Henry Cohn, 2026, needs more optimization.
6 877 0.827866203405 Henry Cohn, 2026, needs more optimization.
6 878 0.827995146225 Henry Cohn, 2026, needs more optimization.
6 879 0.828001895957 Henry Cohn, 2026, needs more optimization.
6 880 0.828018048100 Henry Cohn, 2026, needs more optimization.
6 881 0.828029296896 Henry Cohn, 2026, needs more optimization.
6 882 0.828043374383 Henry Cohn, 2026, needs more optimization.
6 883 0.828094035035 Henry Cohn, 2026, needs more optimization.
6 884 0.828212504038 Henry Cohn, 2026, needs more optimization.
6 885 0.828338428446 Henry Cohn, 2026, needs more optimization.
6 886 0.828367158085 Henry Cohn, 2026, needs more optimization.
6 887 0.828495265806 Henry Cohn, 2026, needs more optimization.
6 888 0.828533748457 Henry Cohn, 2026, needs more optimization.
6 890 0.828644258996 Henry Cohn, 2025, needs more optimization.
6 891 0.828686193879 Henry Cohn, 2026, needs more optimization.
6 892 0.828880658446 Henry Cohn, 2026, needs more optimization.
6 894 0.828882968640 Henry Cohn, 2026, needs more optimization.
6 895 0.828942339148 Henry Cohn, 2026, needs more optimization.
6 896 0.828942922823 Henry Cohn, 2025, needs more optimization.
6 897 0.829139780938 Henry Cohn, 2026, needs more optimization.
6 898 0.829142880376 Henry Cohn, 2025, needs more optimization.
6 899 0.829152200876 Henry Cohn, 2026, needs more optimization.
6 900 0.829310619521 Henry Cohn, 2026, needs more optimization.
6 901 0.829417197627 Henry Cohn, 2026, needs more optimization.
6 902 0.829425911396 Henry Cohn, 2026, needs more optimization.
6 904 0.829628240514 Henry Cohn, 2026, needs more optimization.
6 905 0.829683541482 Henry Cohn, 2026, needs more optimization.
6 906 0.829812045947 Henry Cohn, 2025, needs more optimization.
6 907 0.829817198209 Henry Cohn, 2025, needs more optimization.
6 908 0.829818655010 Henry Cohn, 2025, needs more optimization.
6 909 0.830020033127 Henry Cohn, 2026, needs more optimization.
6 910 0.830022358121 Henry Cohn, 2026, needs more optimization.
6 911 0.830065610631 Henry Cohn, 2025, needs more optimization.
6 912 0.830113517537 Henry Cohn, 2026, needs more optimization.
6 913 0.830239845292 Henry Cohn, 2026, needs more optimization.
6 914 0.830242519417 Henry Cohn, 2025, needs more optimization.
6 916 0.830521683842 Henry Cohn, 2026, needs more optimization.
6 917 0.830522878283 Henry Cohn, 2025, needs more optimization.
6 918 0.830527013915 Henry Cohn, 2025, needs more optimization.
6 919 0.830527776902 Henry Cohn, 2025, needs more optimization.
6 920 0.830717981265 Henry Cohn, 2026, needs more optimization.
6 921 0.830721961270 Henry Cohn, 2026, needs more optimization.
6 922 0.830829231774 Henry Cohn, 2025, needs more optimization.
6 923 0.830840743540 Henry Cohn, 2025, needs more optimization.
6 924 0.830903672293 Henry Cohn, 2026, needs more optimization.
6 925 0.830906862451 Henry Cohn, 2025, needs more optimization.
6 926 0.830908268155 Henry Cohn, 2025, needs more optimization.
6 928 0.831284349465 Henry Cohn, 2025, needs more optimization.
6 929 0.831287055099 Henry Cohn, 2025, needs more optimization.
6 930 0.831324563680 Henry Cohn, 2026, needs more optimization.
6 931 0.831468398894 Henry Cohn, 2026, needs more optimization.
6 932 0.831470102843 Henry Cohn, 2026, needs more optimization.
6 933 0.831470915442 Henry Cohn, 2026, needs more optimization.
6 934 0.831471312652 Henry Cohn, 2026, needs more optimization.
6 935 0.831494689356 Henry Cohn, 2026, needs more optimization.
6 936 0.831503858491 Henry Cohn, 2026, needs more optimization.
6 937 0.831654977354 Henry Cohn, 2025, needs more optimization.
6 938 0.831657240242 Henry Cohn, 2025, needs more optimization.
6 939 0.831778720014 Henry Cohn, 2026, needs more optimization.
6 941 0.831799180282 Henry Cohn, 2026, needs more optimization.
6 942 0.831841531793 Henry Cohn, 2026, needs more optimization.
6 944 0.831997404175 Henry Cohn, 2026, needs more optimization.
6 945 0.831997660390 Henry Cohn, 2026, needs more optimization.
6 946 0.831998896870 Henry Cohn, 2026, needs more optimization.
6 947 0.832020842073 Henry Cohn, 2026, needs more optimization.
6 948 0.832138138234 Henry Cohn, 2025, needs more optimization.
6 949 0.832143197266 Henry Cohn, 2026, needs more optimization.
6 950 0.832149915545 Henry Cohn, 2026, needs more optimization.
6 951 0.832288455846 Henry Cohn, 2026, needs more optimization.
6 952 0.832294478981 Henry Cohn, 2026, needs more optimization.
6 953 0.832299324236 Henry Cohn, 2026, needs more optimization.
6 954 0.832417246251 Henry Cohn, 2026, needs more optimization.
6 955 0.832430215495 Henry Cohn, 2026, needs more optimization.
6 956 0.832433305929 Henry Cohn, 2026, needs more optimization.
6 957 0.832443618756 Henry Cohn, 2025, needs more optimization.
6 958 0.832590542539 Henry Cohn, 2026, needs more optimization.
6 959 0.832608439140 Henry Cohn, 2025, needs more optimization.
6 960 0.832608515714 Henry Cohn, 2025, needs more optimization.
6 961 0.832622827750 Henry Cohn, 2026, needs more optimization.
6 962 0.832768207726 Henry Cohn, 2026, needs more optimization.
6 963 0.832769541550 Henry Cohn, 2026, needs more optimization.
6 964 0.832772805190 Henry Cohn, 2026, needs more optimization.
6 965 0.832775002865 Henry Cohn, 2026, needs more optimization.
6 966 0.832897436776 Henry Cohn, 2026, needs more optimization.
6 967 0.832901388916 Henry Cohn, 2025, needs more optimization.
6 968 0.832904729760 Henry Cohn, 2026, needs more optimization.
6 970 0.832913668308 Henry Cohn, 2026, needs more optimization.
6 972 0.832923583366 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
6 991 0.835256925020 Henry Cohn, 2026, needs more optimization.
6 992 0.836344602402 Henry Cohn, 2026, needs more optimization.
6 993 0.836365663324 Henry Cohn, 2025, needs more optimization.
6 994 0.836412974463 Henry Cohn, 2026, needs more optimization.
6 995 0.836413523076 Henry Cohn, 2025, needs more optimization.
6 996 0.836586134983 Henry Cohn, 2025, needs more optimization.
6 997 0.836735501990 Henry Cohn, 2026, needs more optimization.
6 998 0.836761414944 Henry Cohn, 2026, needs more optimization.
6 999 0.836916042999 Henry Cohn, 2025, needs more optimization.
6 1000 0.836920990870 Henry Cohn, 2026, needs more optimization.
6 1001 0.836925063933 Henry Cohn, 2026, needs more optimization.
6 1002 0.836953091035 Henry Cohn, 2026, needs more optimization.
6 1003 0.837120279195 Henry Cohn, 2026, needs more optimization.
6 1004 0.837120788733 Henry Cohn, 2025, needs more optimization.
6 1005 0.837371159708 Henry Cohn, 2026, needs more optimization.
6 1006 0.837374559607 Henry Cohn, 2026, needs more optimization.
6 1007 0.837387988124 Henry Cohn, 2026, needs more optimization.
6 1008 0.837393643211 Henry Cohn, 2026, needs more optimization.
6 1009 0.837520820339 Henry Cohn, 2026, needs more optimization.
6 1010 0.837636537050 Henry Cohn, 2025, needs more optimization.
6 1011 0.837673892136 Henry Cohn, 2026, needs more optimization.
6 1012 0.837675282618 Henry Cohn, 2026, needs more optimization.
6 1013 0.837801849982 Henry Cohn, 2026, needs more optimization.
6 1014 0.837809886773 Henry Cohn, 2026, needs more optimization.
6 1015 0.837940910005 Henry Cohn, 2025, needs more optimization.
6 1016 0.837946894777 Henry Cohn, 2025, needs more optimization.
6 1017 0.837961382298 Henry Cohn, 2026, needs more optimization.
6 1018 0.838155652623 Henry Cohn, 2026, needs more optimization.
6 1019 0.838159994174 Henry Cohn, 2026, needs more optimization.
6 1020 0.838339854919 Henry Cohn, 2025, needs more optimization.
6 1021 0.838343021300 Henry Cohn, 2026, needs more optimization.
6 1022 0.838428949157 Henry Cohn, 2026, needs more optimization.
6 1023 0.838510633068 Henry Cohn, 2026, needs more optimization.
6 1024 0.838621267399 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 0.333312302687 Henry Cohn, 2025.
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 0.414766349117 Henry Cohn, 2025.
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 0.428235713853 Henry Cohn, 2025.
7 69 0.428531302684 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 0.453278412444 Henry Cohn, 2024.
7 80 0.453887992064 Henry Cohn, 2024.
7 81 0.459667826759 Henry Cohn, 2025.
7 82 0.461219223470 Henry Cohn, 2025.
7 83 0.461669205843 Henry Cohn, 2024.
7 84 0.465073032663 Henry Cohn, 2025.
7 86 0.466580867327 Henry Cohn, 2025, needs more optimization.
7 87 0.469578821552 Henry Cohn, 2024.
7 88 0.473067267884 Henry Cohn, 2024.
7 89 0.474988257844 Henry Cohn, 2024.
7 90 0.475294477919 Henry Cohn, 2024.
7 91 0.479167604557 Henry Cohn, 2026.
7 92 0.480306853225 Henry Cohn, 2025.
7 93 0.482408792669 Henry Cohn, 2026.
7 94 0.483507258083 Henry Cohn, 2025.
7 96 0.486808303779 Henry Cohn, 2025.
7 97 0.487296284314 Henry Cohn, 2025.
7 98 0.489141129031 Henry Cohn, 2026.
7 99 0.494785280364 Henry Cohn, 2026, needs more optimization.
7 101 0.496533689719 Henry Cohn, 2026, needs more optimization.
7 102 0.496928744650 Henry Cohn, 2026, needs more optimization.
7 103 0.498534303908 Henry Cohn, 2026, needs more optimization.
7 106 0.499144603452 Henry Cohn, 2026, needs more optimization.
7 107 0.499575980041 Henry Cohn, 2026, needs more optimization.
7 108 0.499944082669 Henry Cohn, 2026, needs more optimization.
7 109 0.499990542788 Henry Cohn, 2026, needs more optimization.
7 110 0.499997318619 Henry Cohn, 2026, needs more optimization.
7 111 0.499999997332 Henry Cohn, 2026, needs more optimization.
7 112 0.499999997662 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 0.509963471599 Henry Cohn, 2025.
7 128 0.513867786045 Henry Cohn, 2026, needs more optimization.
7 129 0.518845401605 Henry Cohn, 2026, needs more optimization.
7 132 0.519151939790 Henry Cohn, 2026, needs more optimization.
7 134 0.519151940482 Henry Cohn, 2026, needs more optimization.
7 135 0.519152051057 Henry Cohn, 2026, needs more optimization.
7 136 0.519153914325 Henry Cohn, 2026, needs more optimization.
7 137 0.519751518195 Henry Cohn, 2024.
7 138 0.527218738805 Henry Cohn, 2025.
7 141 0.531596764994 Henry Cohn, 2026, needs more optimization.
7 142 0.531598439418 Henry Cohn, 2026, needs more optimization.
7 144 0.531670507033 Henry Cohn, 2026, needs more optimization.
7 145 0.532801092831 Henry Cohn, 2026, needs more optimization.
7 146 0.532883690322 Henry Cohn, 2025.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.533995828316 Henry Cohn, 2026.
7 149 0.546228057898 Henry Cohn, 2026, needs more optimization.
7 150 0.546228537761 Henry Cohn, 2026, needs more optimization.
7 151 0.546228627347 Henry Cohn, 2026, needs more optimization.
7 152 0.546229235067 Henry Cohn, 2026, needs more optimization.
7 153 0.546281099580 Henry Cohn, 2026, needs more optimization.
7 154 0.546281370439 Henry Cohn, 2026, needs more optimization.
7 155 0.548973616291 Henry Cohn, 2026, needs more optimization.
7 156 0.552241692045 Henry Cohn, 2026, needs more optimization.
7 157 0.557021206861 Henry Cohn, 2026, needs more optimization.
7 158 0.559633811542 Henry Cohn, 2026, needs more optimization.
7 159 0.559651386412 Henry Cohn, 2026, needs more optimization.
7 161 0.560446499777 Henry Cohn, 2026, needs more optimization.
7 162 0.561765794056 Henry Cohn, 2026, needs more optimization.
7 163 0.561766516654 Henry Cohn, 2026, needs more optimization.
7 168 0.563371438124 Henry Cohn, 2026, needs more optimization.
7 169 0.563588109639 Henry Cohn, 2026, needs more optimization.
7 170 0.563592084341 Henry Cohn, 2026, needs more optimization.
7 171 0.569095738748 Henry Cohn, 2026, needs more optimization.
7 173 0.570436755960 Henry Cohn, 2026, needs more optimization.
7 174 0.570442857883 Henry Cohn, 2026, needs more optimization.
7 176 0.570443889073 Henry Cohn, 2026, needs more optimization.
7 177 0.570454519168 Henry Cohn, 2026, needs more optimization.
7 178 0.570455862570 Henry Cohn, 2026, needs more optimization.
7 180 0.570549323514 Henry Cohn, 2026, needs more optimization.
7 181 0.573146880911 Henry Cohn, 2025, 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 0.587541965804 Ilmari Vahteristo, 2026.
7 184 0.589941685631 Henry Cohn, 2026, needs more optimization.
7 185 0.591807964460 Henry Cohn, 2026, needs more optimization.
7 186 0.592606737675 Henry Cohn, 2026, needs more optimization.
7 188 0.593606290207 Henry Cohn, 2026, needs more optimization.
7 190 0.593913496248 Henry Cohn, 2026, needs more optimization.
7 191 0.594817168173 Henry Cohn, 2026, needs more optimization.
7 192 0.595580103106 Henry Cohn, 2026, needs more optimization.
7 193 0.596000048894 Henry Cohn, 2026, needs more optimization.
7 194 0.599360499965 Henry Cohn, 2024, needs more optimization.
7 195 0.601485464264 Henry Cohn, 2026, needs more optimization.
7 196 0.601777579786 Henry Cohn, 2026, needs more optimization.
7 197 0.603178792619 Henry Cohn, 2026, needs more optimization.
7 198 0.603898124210 Henry Cohn, 2026, needs more optimization.
7 199 0.605261083349 Henry Cohn, 2024, needs more optimization.
7 200 0.605866105540 Henry Cohn, 2024, needs more optimization.
7 201 0.606526030920 Henry Cohn, 2026, needs more optimization.
7 202 0.607761565343 Henry Cohn, 2026, needs more optimization.
7 203 0.608067965677 Henry Cohn, 2026, needs more optimization.
7 204 0.608994271275 Henry Cohn, 2026, needs more optimization.
7 205 0.610362711212 Henry Cohn, 2026, needs more optimization.
7 206 0.611945534082 Henry Cohn, 2024, needs more optimization.
7 207 0.612711767950 Henry Cohn, 2026, needs more optimization.
7 208 0.613445099966 Henry Cohn, 2026, needs more optimization.
7 209 0.614588496520 Henry Cohn, 2026, needs more optimization.
7 210 0.614894346303 Henry Cohn, 2024, needs more optimization.
7 211 0.615997059701 Henry Cohn, 2026, needs more optimization.
7 212 0.616282950118 Henry Cohn, 2026, needs more optimization.
7 213 0.617073701156 Henry Cohn, 2024, needs more optimization.
7 214 0.617517287064 Henry Cohn, 2026, needs more optimization.
7 215 0.618573245085 Henry Cohn, 2026, needs more optimization.
7 216 0.619599983206 Henry Cohn, 2024, needs more optimization.
7 217 0.620462147152 Henry Cohn, 2026, needs more optimization.
7 218 0.621368072363 Henry Cohn, 2024, needs more optimization.
7 219 0.621876747898 Henry Cohn, 2026, needs more optimization.
7 220 0.622558844415 Henry Cohn, 2026, needs more optimization.
7 221 0.623342873403 Henry Cohn, 2026, needs more optimization.
7 222 0.624378330934 Henry Cohn, 2026, needs more optimization.
7 223 0.624821718955 Henry Cohn, 2026, needs more optimization.
7 224 0.625196948482 Henry Cohn, 2026, needs more optimization.
7 225 0.625872966956 Henry Cohn, 2024, needs more optimization.
7 226 0.627152303608 Henry Cohn, 2026, needs more optimization.
7 227 0.627342518255 Henry Cohn, 2026, needs more optimization.
7 228 0.628120990435 Henry Cohn, 2026, needs more optimization.
7 229 0.629153255261 Henry Cohn, 2026, needs more optimization.
7 230 0.629909510207 Henry Cohn, 2026, needs more optimization.
7 231 0.630549078404 Henry Cohn, 2024, needs more optimization.
7 232 0.631246982226 Henry Cohn, 2026, needs more optimization.
7 233 0.631901836958 Henry Cohn, 2024, needs more optimization.
7 234 0.632529093827 Henry Cohn, 2026, needs more optimization.
7 235 0.633010619003 Henry Cohn, 2026, needs more optimization.
7 236 0.633943127321 Henry Cohn, 2024, needs more optimization.
7 237 0.634228377169 Henry Cohn, 2026, needs more optimization.
7 238 0.634654815026 Henry Cohn, 2026, needs more optimization.
7 239 0.635356766795 Henry Cohn, 2024, needs more optimization.
7 240 0.635658801272 Henry Cohn, 2026, needs more optimization.
7 241 0.636611518385 Henry Cohn, 2026, needs more optimization.
7 242 0.636956653067 Henry Cohn, 2026, needs more optimization.
7 243 0.637507090261 Henry Cohn, 2026, needs more optimization.
7 244 0.638074677610 Henry Cohn, 2024, needs more optimization.
7 245 0.638570541491 Henry Cohn, 2026, needs more optimization.
7 246 0.638764849762 Henry Cohn, 2026, needs more optimization.
7 247 0.639330346902 Henry Cohn, 2026, needs more optimization.
7 248 0.640032835036 Henry Cohn, 2024, needs more optimization.
7 249 0.640392373037 Henry Cohn, 2026, needs more optimization.
7 250 0.640818441217 Henry Cohn, 2026, needs more optimization.
7 251 0.641158392745 Henry Cohn, 2026, needs more optimization.
7 252 0.641627501594 Henry Cohn, 2026, needs more optimization.
7 253 0.641863049753 Henry Cohn, 2026, needs more optimization.
7 254 0.642224260070 Henry Cohn, 2026, needs more optimization.
7 255 0.643053811435 Henry Cohn, 2026, needs more optimization.
7 256 0.643605698550 Henry Cohn, 2026, needs more optimization.
7 257 0.644333209005 Henry Cohn, 2026, needs more optimization.
7 258 0.644862333677 Henry Cohn, 2026, needs more optimization.
7 259 0.645196148266 Henry Cohn, 2026, needs more optimization.
7 260 0.645630270654 Henry Cohn, 2026, needs more optimization.
7 261 0.645766214910 Henry Cohn, 2026, needs more optimization.
7 262 0.646108227697 Henry Cohn, 2026, needs more optimization.
7 263 0.646792647073 Henry Cohn, 2026, needs more optimization.
7 264 0.647387571259 Henry Cohn, 2026, needs more optimization.
7 265 0.648257069747 Henry Cohn, 2026, needs more optimization.
7 266 0.648403234025 Henry Cohn, 2026, needs more optimization.
7 267 0.648852960515 Henry Cohn, 2026, needs more optimization.
7 268 0.649240401163 Henry Cohn, 2026, needs more optimization.
7 269 0.649474936929 Henry Cohn, 2026, needs more optimization.
7 270 0.649753870520 Henry Cohn, 2026, needs more optimization.
7 271 0.650140295058 Henry Cohn, 2026, needs more optimization.
7 272 0.650599075448 Henry Cohn, 2026, needs more optimization.
7 273 0.651217014390 Henry Cohn, 2026, needs more optimization.
7 274 0.651405724817 Henry Cohn, 2026, needs more optimization.
7 275 0.651721175314 Henry Cohn, 2026, needs more optimization.
7 276 0.652377390243 Henry Cohn, 2026, needs more optimization.
7 277 0.652608875266 Henry Cohn, 2026, needs more optimization.
7 278 0.653250169720 Henry Cohn, 2026, needs more optimization.
7 279 0.653595323014 Henry Cohn, 2026, needs more optimization.
7 280 0.654148024436 Henry Cohn, 2026, needs more optimization.
7 281 0.654906638703 Henry Cohn, 2026, needs more optimization.
7 282 0.655071481483 Henry Cohn, 2025, needs more optimization.
7 283 0.655666676836 Henry Cohn, 2026, needs more optimization.
7 284 0.655832274881 Henry Cohn, 2026, needs more optimization.
7 285 0.656367203749 Henry Cohn, 2026, needs more optimization.
7 286 0.656971056238 Henry Cohn, 2026, needs more optimization.
7 287 0.657327617485 Henry Cohn, 2026, needs more optimization.
7 288 0.657534749623 Henry Cohn, 2026, needs more optimization.
7 289 0.657971728976 Henry Cohn, 2026, needs more optimization.
7 290 0.658620662878 Henry Cohn, 2026, needs more optimization.
7 291 0.658962667319 Henry Cohn, 2026, needs more optimization.
7 292 0.659216678686 Henry Cohn, 2026, needs more optimization.
7 293 0.659660932297 Henry Cohn, 2026, needs more optimization.
7 294 0.660018961385 Henry Cohn, 2026, needs more optimization.
7 295 0.660494500375 Henry Cohn, 2026, needs more optimization.
7 296 0.661004239670 Henry Cohn, 2026, needs more optimization.
7 297 0.661206513040 Henry Cohn, 2026, needs more optimization.
7 298 0.661765003451 Henry Cohn, 2026, needs more optimization.
7 299 0.662357090607 Henry Cohn, 2026, needs more optimization.
7 300 0.662639501416 Henry Cohn, 2026, needs more optimization.
7 301 0.663282861097 Henry Cohn, 2026, needs more optimization.
7 302 0.663759454150 Henry Cohn, 2025, needs more optimization.
7 303 0.663998669282 Henry Cohn, 2026, needs more optimization.
7 304 0.664599851270 Henry Cohn, 2026, needs more optimization.
7 305 0.664628042274 Henry Cohn, 2025, needs more optimization.
7 306 0.664738733263 Henry Cohn, 2026, needs more optimization.
7 307 0.665702963255 Henry Cohn, 2025, needs more optimization.
7 308 0.666037244322 Henry Cohn, 2025, needs more optimization.
7 309 0.666452865264 Henry Cohn, 2026, needs more optimization.
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 0.668524326970 Henry Cohn, 2026, needs more optimization.
7 360 0.675672261492 Henry Cohn, 2026, needs more optimization.
7 361 0.675712378451 Henry Cohn, 2026, needs more optimization.
7 362 0.675759836804 Henry Cohn, 2026, needs more optimization.
7 363 0.675811653557 Henry Cohn, 2026, needs more optimization.
7 364 0.675854054558 Henry Cohn, 2026, needs more optimization.
7 365 0.675946641714 Henry Cohn, 2026, needs more optimization.
7 366 0.676099020958 Henry Cohn, 2026, needs more optimization.
7 367 0.676399959676 Henry Cohn, 2026, needs more optimization.
7 368 0.676415352949 Henry Cohn, 2026, needs more optimization.
7 369 0.676479305561 Henry Cohn, 2026, needs more optimization.
7 370 0.676494876240 Henry Cohn, 2026, needs more optimization.
7 372 0.676737424673 Henry Cohn, 2026, needs more optimization.
7 373 0.676833567738 Henry Cohn, 2026, needs more optimization.
7 374 0.677036925378 Henry Cohn, 2026, needs more optimization.
7 376 0.677059596678 Henry Cohn, 2026, needs more optimization.
7 378 0.677062824127 Henry Cohn, 2026, needs more optimization.
7 380 0.677085973391 Henry Cohn, 2026, needs more optimization.
7 382 0.677410372200 Henry Cohn, 2026, needs more optimization.
7 383 0.678022967422 Henry Cohn, 2026, needs more optimization.
7 384 0.679172662319 Henry Cohn, 2026, needs more optimization.
7 385 0.679178805122 Henry Cohn, 2026, needs more optimization.
7 386 0.679753598396 Henry Cohn, 2026, needs more optimization.
7 388 0.680312167273 Henry Cohn, 2026, needs more optimization.
7 389 0.680994589993 Henry Cohn, 2026, needs more optimization.
7 390 0.681038152614 Henry Cohn, 2026, needs more optimization.
7 391 0.681263351807 Henry Cohn, 2026, needs more optimization.
7 392 0.681696095783 Henry Cohn, 2026, needs more optimization.
7 394 0.681765586423 Henry Cohn, 2026, needs more optimization.
7 395 0.681798498173 Henry Cohn, 2026, needs more optimization.
7 396 0.682955969683 Henry Cohn, 2026, needs more optimization.
7 397 0.682997247619 Henry Cohn, 2026, needs more optimization.
7 398 0.683036748947 Henry Cohn, 2026, needs more optimization.
7 399 0.683110520018 Henry Cohn, 2026, needs more optimization.
7 400 0.683129736371 Henry Cohn, 2026, needs more optimization.
7 401 0.683185948128 Henry Cohn, 2026, needs more optimization.
7 402 0.683291958276 Henry Cohn, 2026, needs more optimization.
7 403 0.683318714028 Henry Cohn, 2026, needs more optimization.
7 404 0.683320042580 Henry Cohn, 2026, needs more optimization.
7 405 0.683357014411 Henry Cohn, 2026, needs more optimization.
7 406 0.690932444651 Henry Cohn, 2025, needs more optimization.
7 407 0.691685829843 Henry Cohn, 2026, needs more optimization.
7 408 0.692257645580 Henry Cohn, 2026, needs more optimization.
7 409 0.692332039010 Henry Cohn, 2025, needs more optimization.
7 410 0.692414746541 Henry Cohn, 2025, needs more optimization.
7 411 0.692787928477 Henry Cohn, 2025, needs more optimization.
7 412 0.692958018599 Henry Cohn, 2026, needs more optimization.
7 413 0.693125695547 Henry Cohn, 2025, needs more optimization.
7 414 0.693154749248 Henry Cohn, 2025, needs more optimization.
7 415 0.693162668354 Henry Cohn, 2025, needs more optimization.
7 416 0.694123742176 Henry Cohn, 2025, needs more optimization.
7 417 0.694287009188 Henry Cohn, 2025, needs more optimization.
7 418 0.694523585349 Henry Cohn, 2025, needs more optimization.
7 419 0.694815792826 Henry Cohn, 2026, needs more optimization.
7 420 0.695128563933 Henry Cohn, 2025, needs more optimization.
7 421 0.695130508518 Henry Cohn, 2025, needs more optimization.
7 422 0.695176221166 Henry Cohn, 2025, needs more optimization.
7 423 0.695830132382 Henry Cohn, 2025, needs more optimization.
7 424 0.695880985033 Henry Cohn, 2025, needs more optimization.
7 425 0.696154846704 Henry Cohn, 2025, needs more optimization.
7 426 0.696220870137 Henry Cohn, 2025, needs more optimization.
7 427 0.696335833512 Henry Cohn, 2025, needs more optimization.
7 428 0.696904394283 Henry Cohn, 2026, needs more optimization.
7 429 0.696957305399 Henry Cohn, 2025, needs more optimization.
7 430 0.697019949514 Henry Cohn, 2026, needs more optimization.
7 431 0.697198226158 Henry Cohn, 2025, needs more optimization.
7 432 0.697758355591 Henry Cohn, 2025, needs more optimization.
7 434 0.698064930275 Henry Cohn, 2026, needs more optimization.
7 436 0.698129161773 Henry Cohn, 2025, needs more optimization.
7 438 0.698768530471 Henry Cohn, 2025, needs more optimization.
7 439 0.699057471161 Henry Cohn, 2025, needs more optimization.
7 440 0.699564497374 Henry Cohn, 2025, needs more optimization.
7 441 0.699943203361 Henry Cohn, 2026, needs more optimization.
7 442 0.700293285076 Henry Cohn, 2025, needs more optimization.
7 444 0.700938073780 Henry Cohn, 2025, needs more optimization.
7 445 0.700946567027 Henry Cohn, 2025, needs more optimization.
7 446 0.700962130467 Henry Cohn, 2025, needs more optimization.
7 447 0.701190449341 Henry Cohn, 2025, needs more optimization.
7 448 0.701776571024 Henry Cohn, 2025, needs more optimization.
7 449 0.702022842893 Henry Cohn, 2025, needs more optimization.
7 450 0.702810548686 Henry Cohn, 2025, needs more optimization.
7 451 0.702836794920 Henry Cohn, 2026, needs more optimization.
7 452 0.703104019437 Henry Cohn, 2026, needs more optimization.
7 453 0.703553853189 Henry Cohn, 2025, needs more optimization.
7 454 0.703590992781 Henry Cohn, 2025, needs more optimization.
7 455 0.703646141098 Henry Cohn, 2025, needs more optimization.
7 458 0.704114722772 Henry Cohn, 2025, needs more optimization.
7 459 0.704603392874 Henry Cohn, 2025, needs more optimization.
7 460 0.704691314146 Henry Cohn, 2026, needs more optimization.
7 461 0.705051861668 Henry Cohn, 2026, needs more optimization.
7 462 0.705056506687 Henry Cohn, 2025, needs more optimization.
7 463 0.705379494979 Henry Cohn, 2025, needs more optimization.
7 464 0.705388063719 Henry Cohn, 2025, needs more optimization.
7 466 0.705390639937 Henry Cohn, 2026, needs more optimization.
7 467 0.705764381751 Henry Cohn, 2025, needs more optimization.
7 468 0.705859692358 Henry Cohn, 2025, needs more optimization.
7 469 0.705879757078 Henry Cohn, 2025, needs more optimization.
7 472 0.706158356996 Henry Cohn, 2025, needs more optimization.
7 473 0.706329190915 Henry Cohn, 2025, needs more optimization.
7 474 0.706685568025 Henry Cohn, 2026, needs more optimization.
7 475 0.707007270167 Henry Cohn, 2025, needs more optimization.
7 476 0.707415911476 Henry Cohn, 2025, needs more optimization.
7 477 0.707552845511 Henry Cohn, 2025, needs more optimization.
7 478 0.707831690404 Henry Cohn, 2026, needs more optimization.
7 479 0.708089164268 Henry Cohn, 2026, needs more optimization.
7 480 0.708092903508 Henry Cohn, 2026, needs more optimization.
7 481 0.708095396023 Henry Cohn, 2025, needs more optimization.
7 482 0.708101389020 Henry Cohn, 2025, needs more optimization.
7 484 0.708113876563 Henry Cohn, 2026, needs more optimization.
7 486 0.708180044040 Henry Cohn, 2026, needs more optimization.
7 488 0.708460763259 Henry Cohn, 2026, needs more optimization.
7 489 0.708483139185 Henry Cohn, 2026, needs more optimization.
7 490 0.708523196112 Henry Cohn, 2026, needs more optimization.
7 491 0.708679022412 Henry Cohn, 2026, needs more optimization.
7 492 0.708950875015 Henry Cohn, 2026, needs more optimization.
7 493 0.709329693366 Henry Cohn, 2026, needs more optimization.
7 495 0.709342566356 Henry Cohn, 2026, needs more optimization.
7 497 0.709385652205 Henry Cohn, 2026, needs more optimization.
7 498 0.709968198579 Henry Cohn, 2026, needs more optimization.
7 500 0.710662666537 Henry Cohn, 2026, needs more optimization.
7 502 0.710707989177 Henry Cohn, 2026, needs more optimization.
7 503 0.710804090259 Henry Cohn, 2026, needs more optimization.
7 504 0.711088772535 Henry Cohn, 2026, needs more optimization.
7 505 0.711110226360 Henry Cohn, 2026, needs more optimization.
7 506 0.711124169425 Henry Cohn, 2026, needs more optimization.
7 508 0.711500454141 Henry Cohn, 2026, needs more optimization.
7 510 0.711522337911 Henry Cohn, 2026, needs more optimization.
7 512 0.712280029239 Henry Cohn, 2026, needs more optimization.
7 514 0.712451797743 Henry Cohn, 2026, needs more optimization.
7 524 0.713306211333 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 0.718530723442 Henry Cohn, 2026, needs more optimization.
7 634 0.720182447113 Henry Cohn, 2026, needs more optimization.
7 635 0.722270041976 Henry Cohn, 2026, needs more optimization.
7 636 0.722561757329 Henry Cohn, 2026, needs more optimization.
7 637 0.722910969918 Henry Cohn, 2026, needs more optimization.
7 638 0.723719902423 Henry Cohn, 2026, needs more optimization.
7 639 0.724503501230 Henry Cohn, 2026, needs more optimization.
7 640 0.724996131554 Henry Cohn, 2026, needs more optimization.
7 641 0.725515318615 Henry Cohn, 2026, needs more optimization.
7 642 0.726062360201 Henry Cohn, 2026, needs more optimization.
7 643 0.726419686186 Henry Cohn, 2026, needs more optimization.
7 644 0.726767117197 Henry Cohn, 2026, needs more optimization.
7 645 0.727072134418 Henry Cohn, 2026, needs more optimization.
7 646 0.727523405252 Henry Cohn, 2026, needs more optimization.
7 647 0.727899087192 Henry Cohn, 2026, needs more optimization.
7 648 0.728313923636 Henry Cohn, 2026, needs more optimization.
7 649 0.728646716928 Henry Cohn, 2026, needs more optimization.
7 650 0.729059260572 Henry Cohn, 2026, needs more optimization.
7 651 0.729305084691 Henry Cohn, 2026, needs more optimization.
7 652 0.729576868838 Henry Cohn, 2026, needs more optimization.
7 653 0.729815561629 Henry Cohn, 2026, needs more optimization.
7 654 0.729996592871 Henry Cohn, 2026, needs more optimization.
7 655 0.730250916152 Henry Cohn, 2026, needs more optimization.
7 656 0.730587976885 Henry Cohn, 2026, needs more optimization.
7 657 0.730832199313 Henry Cohn, 2026, needs more optimization.
7 658 0.731124097256 Henry Cohn, 2026, needs more optimization.
7 659 0.731381460642 Henry Cohn, 2026, needs more optimization.
7 660 0.731490849512 Henry Cohn, 2026, needs more optimization.
7 661 0.731872017300 Henry Cohn, 2026, needs more optimization.
7 662 0.732093874471 Henry Cohn, 2026, needs more optimization.
7 663 0.732308754339 Henry Cohn, 2026, needs more optimization.
7 664 0.732501362566 Henry Cohn, 2026, needs more optimization.
7 665 0.732902368392 Henry Cohn, 2026, needs more optimization.
7 666 0.733220652475 Henry Cohn, 2026, needs more optimization.
7 667 0.733498879536 Henry Cohn, 2026, needs more optimization.
7 668 0.733766249988 Henry Cohn, 2026, needs more optimization.
7 669 0.734023928351 Henry Cohn, 2026, needs more optimization.
7 670 0.734314293833 Henry Cohn, 2026, needs more optimization.
7 671 0.734592193721 Henry Cohn, 2026, needs more optimization.
7 672 0.734857439461 Henry Cohn, 2026, needs more optimization.
7 673 0.735102023732 Henry Cohn, 2026, needs more optimization.
7 674 0.735521894407 Henry Cohn, 2026, needs more optimization.
7 675 0.735699324019 Henry Cohn, 2026, needs more optimization.
7 676 0.735890167055 Henry Cohn, 2026, needs more optimization.
7 677 0.736132969679 Henry Cohn, 2026, needs more optimization.
7 678 0.736353938019 Henry Cohn, 2026, needs more optimization.
7 679 0.736587018803 Henry Cohn, 2026, needs more optimization.
7 680 0.736873070816 Henry Cohn, 2026, needs more optimization.
7 681 0.737106791343 Henry Cohn, 2026, needs more optimization.
7 682 0.737358675376 Henry Cohn, 2026, needs more optimization.
7 683 0.737527047925 Henry Cohn, 2026, needs more optimization.
7 684 0.737637782629 Henry Cohn, 2026, needs more optimization.
7 685 0.737773808026 Henry Cohn, 2026, needs more optimization.
7 686 0.738007645100 Henry Cohn, 2026, needs more optimization.
7 687 0.738342505381 Henry Cohn, 2026, needs more optimization.
7 688 0.738619338161 Henry Cohn, 2026, needs more optimization.
7 689 0.738955558058 Henry Cohn, 2026, needs more optimization.
7 690 0.739303005167 Henry Cohn, 2026, needs more optimization.
7 691 0.739508897096 Henry Cohn, 2026, needs more optimization.
7 692 0.739703818069 Henry Cohn, 2026, needs more optimization.
7 693 0.740099578487 Henry Cohn, 2026, needs more optimization.
7 694 0.740344319636 Henry Cohn, 2026, needs more optimization.
7 695 0.740478276360 Henry Cohn, 2026, needs more optimization.
7 696 0.740594204948 Henry Cohn, 2026, needs more optimization.
7 697 0.740815085689 Henry Cohn, 2026, needs more optimization.
7 698 0.741232571703 Henry Cohn, 2026, needs more optimization.
7 699 0.741467077937 Henry Cohn, 2026, needs more optimization.
7 700 0.741601948227 Henry Cohn, 2026, needs more optimization.
7 701 0.741898654856 Henry Cohn, 2026, needs more optimization.
7 702 0.742062476670 Henry Cohn, 2026, needs more optimization.
7 703 0.742116118054 Henry Cohn, 2026, needs more optimization.
7 704 0.742396288906 Henry Cohn, 2026, needs more optimization.
7 705 0.742921607558 Henry Cohn, 2026, needs more optimization.
7 706 0.743445190779 Henry Cohn, 2026, needs more optimization.
7 707 0.743835042789 Henry Cohn, 2026, needs more optimization.
7 708 0.744164171034 Henry Cohn, 2026, needs more optimization.
7 709 0.744478515632 Henry Cohn, 2026, needs more optimization.
7 710 0.744745900665 Henry Cohn, 2026, needs more optimization.
7 711 0.745059673446 Henry Cohn, 2026, needs more optimization.
7 712 0.745329029114 Henry Cohn, 2026, needs more optimization.
7 713 0.745580733395 Henry Cohn, 2026, needs more optimization.
7 714 0.745798844097 Henry Cohn, 2026, needs more optimization.
7 715 0.749221951020 Henry Cohn, 2025, needs more optimization.
7 716 0.749387656241 Henry Cohn, 2026, needs more optimization.
7 717 0.749648394970 Henry Cohn, 2026, needs more optimization.
7 718 0.749816872874 Henry Cohn, 2026, needs more optimization.
7 719 0.749928903028 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 0.756664682984 Henry Cohn, 2026, needs more optimization.
7 884 0.766418771944 Henry Cohn, 2025, needs more optimization.
7 885 0.766524752233 Henry Cohn, 2026, needs more optimization.
7 886 0.766527594674 Henry Cohn, 2025, needs more optimization.
7 887 0.766864236744 Henry Cohn, 2026, needs more optimization.
7 888 0.766885779552 Henry Cohn, 2026, needs more optimization.
7 889 0.766887386394 Henry Cohn, 2026, needs more optimization.
7 890 0.767018124487 Henry Cohn, 2025, needs more optimization.
7 891 0.767082538566 Henry Cohn, 2026, needs more optimization.
7 892 0.767231569550 Henry Cohn, 2025, needs more optimization.
7 893 0.767251169955 Henry Cohn, 2026, needs more optimization.
7 894 0.767257094381 Henry Cohn, 2026, needs more optimization.
7 895 0.767391546637 Henry Cohn, 2025, needs more optimization.
7 896 0.767401946186 Henry Cohn, 2025, needs more optimization.
7 897 0.767681720564 Henry Cohn, 2025, needs more optimization.
7 898 0.767731229371 Henry Cohn, 2026, needs more optimization.
7 899 0.767736873146 Henry Cohn, 2025, needs more optimization.
7 900 0.767809065227 Henry Cohn, 2026, needs more optimization.
7 901 0.768010126256 Henry Cohn, 2026, needs more optimization.
7 902 0.768013173488 Henry Cohn, 2025, needs more optimization.
7 904 0.768138005293 Henry Cohn, 2025, needs more optimization.
7 905 0.768349270409 Henry Cohn, 2025, needs more optimization.
7 906 0.768388903761 Henry Cohn, 2026, needs more optimization.
7 907 0.768518067748 Henry Cohn, 2025, needs more optimization.
7 908 0.768580271112 Henry Cohn, 2025, needs more optimization.
7 909 0.768713496939 Henry Cohn, 2025, needs more optimization.
7 910 0.768739341134 Henry Cohn, 2025, needs more optimization.
7 911 0.768770505285 Henry Cohn, 2026, needs more optimization.
7 913 0.768957366848 Henry Cohn, 2025, needs more optimization.
7 914 0.768959087661 Henry Cohn, 2026, needs more optimization.
7 915 0.769192254989 Henry Cohn, 2025, needs more optimization.
7 916 0.769195854871 Henry Cohn, 2026, needs more optimization.
7 917 0.769205025913 Henry Cohn, 2025, needs more optimization.
7 918 0.769532233218 Henry Cohn, 2025, needs more optimization.
7 919 0.769536044854 Henry Cohn, 2025, needs more optimization.
7 920 0.769700440865 Henry Cohn, 2025, needs more optimization.
7 921 0.769706695485 Henry Cohn, 2026, needs more optimization.
7 922 0.769879798173 Henry Cohn, 2026, needs more optimization.
7 923 0.769903571307 Henry Cohn, 2026, needs more optimization.
7 924 0.769923720137 Henry Cohn, 2026, needs more optimization.
7 925 0.769964729931 Henry Cohn, 2025, needs more optimization.
7 926 0.769997961235 Henry Cohn, 2025, needs more optimization.
7 927 0.770123058479 Henry Cohn, 2025, needs more optimization.
7 928 0.770256536122 Henry Cohn, 2026, needs more optimization.
7 929 0.770260744309 Henry Cohn, 2026, needs more optimization.
7 930 0.770302505224 Henry Cohn, 2025, needs more optimization.
7 931 0.770575401025 Henry Cohn, 2026, needs more optimization.
7 932 0.770579743316 Henry Cohn, 2025, needs more optimization.
7 933 0.770595690567 Henry Cohn, 2025, needs more optimization.
7 934 0.770626503767 Henry Cohn, 2026, needs more optimization.
7 935 0.770770123599 Henry Cohn, 2026, needs more optimization.
7 937 0.770899391053 Henry Cohn, 2026, needs more optimization.
7 938 0.771165856307 Henry Cohn, 2025, needs more optimization.
7 939 0.771169572134 Henry Cohn, 2025, needs more optimization.
7 940 0.771215436337 Henry Cohn, 2026, needs more optimization.
7 941 0.771237395615 Henry Cohn, 2026, needs more optimization.
7 943 0.771360024917 Henry Cohn, 2026, needs more optimization.
7 944 0.771503310438 Henry Cohn, 2025, needs more optimization.
7 945 0.771522679568 Henry Cohn, 2026, needs more optimization.
7 946 0.771742521096 Henry Cohn, 2025, needs more optimization.
7 948 0.771748841996 Henry Cohn, 2025, needs more optimization.
7 949 0.771756780691 Henry Cohn, 2026, needs more optimization.
7 950 0.771897005109 Henry Cohn, 2026, needs more optimization.
7 951 0.772123382659 Henry Cohn, 2025, needs more optimization.
7 952 0.772237080380 Henry Cohn, 2026, needs more optimization.
7 953 0.772237817687 Henry Cohn, 2026, needs more optimization.
7 954 0.772255181222 Henry Cohn, 2026, needs more optimization.
7 955 0.772542061754 Henry Cohn, 2026, needs more optimization.
7 956 0.772595320218 Henry Cohn, 2025, needs more optimization.
7 957 0.772601217064 Henry Cohn, 2026, needs more optimization.
7 959 0.772738527814 Henry Cohn, 2025, needs more optimization.
7 960 0.772837170696 Henry Cohn, 2026, needs more optimization.
7 961 0.772840763944 Henry Cohn, 2026, needs more optimization.
7 962 0.772920980658 Henry Cohn, 2026, needs more optimization.
7 963 0.773161630297 Henry Cohn, 2025, needs more optimization.
7 965 0.773200621725 Henry Cohn, 2025, needs more optimization.
7 966 0.773221993721 Henry Cohn, 2026, needs more optimization.
7 967 0.773310420734 Henry Cohn, 2026, needs more optimization.
7 968 0.773534895672 Henry Cohn, 2025, needs more optimization.
7 969 0.773631869817 Henry Cohn, 2026, needs more optimization.
7 970 0.773634633709 Henry Cohn, 2026, needs more optimization.
7 971 0.773822099300 Henry Cohn, 2025, needs more optimization.
7 972 0.773827494958 Henry Cohn, 2025, needs more optimization.
7 973 0.773834788495 Henry Cohn, 2025, needs more optimization.
7 974 0.773950544892 Henry Cohn, 2026, needs more optimization.
7 975 0.774070487691 Henry Cohn, 2026, needs more optimization.
7 976 0.774179541403 Henry Cohn, 2026, needs more optimization.
7 977 0.774221215285 Henry Cohn, 2026, needs more optimization.
7 978 0.774231409619 Henry Cohn, 2025, needs more optimization.
7 979 0.774442604987 Henry Cohn, 2026, needs more optimization.
7 980 0.774464634630 Henry Cohn, 2026, needs more optimization.
7 981 0.774489936361 Henry Cohn, 2025, needs more optimization.
7 982 0.774495818164 Henry Cohn, 2026, needs more optimization.
7 983 0.774644331561 Henry Cohn, 2026, needs more optimization.
7 985 0.774756465462 Henry Cohn, 2025, needs more optimization.
7 986 0.774774748227 Henry Cohn, 2025, needs more optimization.
7 987 0.774871634708 Henry Cohn, 2026, needs more optimization.
7 988 0.775041594845 Henry Cohn, 2025, needs more optimization.
7 989 0.775060031414 Henry Cohn, 2026, needs more optimization.
7 990 0.775268368778 Henry Cohn, 2025, needs more optimization.
7 991 0.775275612377 Henry Cohn, 2025, needs more optimization.
7 992 0.775423925764 Henry Cohn, 2025, needs more optimization.
7 993 0.775430697361 Henry Cohn, 2026, needs more optimization.
7 994 0.775449990401 Henry Cohn, 2026, needs more optimization.
7 995 0.775632598837 Henry Cohn, 2025, needs more optimization.
7 996 0.775669217867 Henry Cohn, 2026, needs more optimization.
7 997 0.775704293887 Henry Cohn, 2025, needs more optimization.
7 998 0.775770821979 Henry Cohn, 2026, needs more optimization.
7 999 0.775775434402 Henry Cohn, 2026, needs more optimization.
7 1000 0.775855223040 Henry Cohn, 2026, needs more optimization.
7 1001 0.776024150867 Henry Cohn, 2025, needs more optimization.
7 1002 0.776036634130 Henry Cohn, 2026, needs more optimization.
7 1003 0.776176572478 Henry Cohn, 2025, needs more optimization.
7 1004 0.776184751487 Henry Cohn, 2025, needs more optimization.
7 1005 0.776327111003 Henry Cohn, 2025, needs more optimization.
7 1006 0.776380105971 Henry Cohn, 2025, needs more optimization.
7 1007 0.776425871372 Henry Cohn, 2025, needs more optimization.
7 1008 0.776753227999 Henry Cohn, 2025, needs more optimization.
7 1009 0.776757501902 Henry Cohn, 2025, needs more optimization.
7 1010 0.776791148616 Henry Cohn, 2026, needs more optimization.
7 1012 0.776978114898 Henry Cohn, 2025, needs more optimization.
7 1013 0.777161042973 Henry Cohn, 2025, needs more optimization.
7 1014 0.777180183121 Henry Cohn, 2025, needs more optimization.
7 1015 0.777230269753 Henry Cohn, 2026, needs more optimization.
7 1016 0.777352916164 Henry Cohn, 2026, needs more optimization.
7 1017 0.777362033599 Henry Cohn, 2025, needs more optimization.
7 1018 0.777407561032 Henry Cohn, 2026, needs more optimization.
7 1019 0.777478741294 Henry Cohn, 2026, needs more optimization.
7 1020 0.777811702770 Henry Cohn, 2025, needs more optimization.
7 1021 0.777828074942 Henry Cohn, 2026, needs more optimization.
7 1022 0.777990478570 Henry Cohn, 2025, needs more optimization.
7 1023 0.777994305436 Henry Cohn, 2025, needs more optimization.
7 1024 0.778006655112 Henry Cohn, 2025, 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 0.315283655377 Henry Cohn, 2025.
8 51 0.316850575857 Henry Cohn, 2023.
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 0.374360545517 Henry Cohn, 2023.
8 74 0.375030122030 Henry Cohn, 2025.
8 75 0.380147254829 Henry Cohn, 2024.
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 0.399272012697 Henry Cohn, 2024.
8 81 0.401670700481 Henry Cohn, 2026.
8 82 0.402283801532 Henry Cohn, 2025.
8 83 0.405303858040 Henry Cohn, 2026.
8 84 0.405589808949 Henry Cohn, 2026.
8 85 0.413778833762 Henry Cohn, 2025.
8 86 0.416818893963 Henry Cohn, 2026, needs more optimization.
8 88 0.418782717642 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.
32⁢x3−8⁢x+1
8 89 0.421006969523 Henry Cohn, 2026.
8 90 0.422051749186 Henry Cohn, 2026.
8 91 0.422503445662 Henry Cohn, 2026.
8 92 0.423356339274 Henry Cohn, 2026, needs more optimization.
8 93 0.425292960391 Henry Cohn, 2026.
8 94 0.425630619041 Henry Cohn, 2026, needs more optimization.
8 95 0.426690121416 Henry Cohn, 2026, needs more optimization.
8 96 0.427525768702 Henry Cohn, 2026, needs more optimization.
8 97 0.428526010827 Henry Cohn, 2025.
8 99 0.428564490087 Henry Cohn, 2025.
8 100 0.428571420298 Henry Cohn, 2026, needs more optimization.
8 101 0.428571428376 Henry Cohn, 2026, needs more optimization.
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 0.447648896804 Henry Cohn, 2026, needs more optimization.
8 116 0.448022446705 Henry Cohn, 2026, needs more optimization.
8 117 0.451867492073 Henry Cohn, 2026.
8 118 0.455382682228 Henry Cohn, 2026.
8 119 0.461439500217 Henry Cohn, 2026, needs more optimization.
8 121 0.461746553489 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 0.468486456439 Henry Cohn, 2026, needs more optimization.
8 139 0.468833039278 Henry Cohn, 2026, needs more optimization.
8 140 0.470970373659 Henry Cohn, 2026, needs more optimization.
8 141 0.472529423812 Henry Cohn, 2026, needs more optimization.
8 143 0.476795268384 Henry Cohn, 2026, needs more optimization.
8 144 0.482744215104 Henry Cohn, 2026, needs more optimization.
8 145 0.485609722267 Henry Cohn, 2026, needs more optimization.
8 146 0.488485081287 Henry Cohn, 2026, needs more optimization.
8 147 0.488694984260 Henry Cohn, 2026, needs more optimization.
8 148 0.489572056479 Henry Cohn, 2026, needs more optimization.
8 149 0.489727764203 Henry Cohn, 2026, needs more optimization.
8 150 0.489754949602 Henry Cohn, 2026, needs more optimization.
8 151 0.490701500207 Henry Cohn, 2026, needs more optimization.
8 152 0.491601025841 Henry Cohn, 2026, needs more optimization.
8 153 0.492433667672 Henry Cohn, 2026, needs more optimization.
8 154 0.492643283453 Henry Cohn, 2026, needs more optimization.
8 155 0.493163193440 Henry Cohn, 2026, needs more optimization.
8 156 0.494129971018 Henry Cohn, 2026, needs more optimization.
8 157 0.494372949940 Henry Cohn, 2026, needs more optimization.
8 158 0.494814853408 Henry Cohn, 2026, needs more optimization.
8 159 0.495415668269 Henry Cohn, 2026, needs more optimization.
8 160 0.496350818438 Henry Cohn, 2026, needs more optimization.
8 161 0.496788326141 Henry Cohn, 2026, needs more optimization.
8 162 0.496914471295 Henry Cohn, 2026, needs more optimization.
8 164 0.497382420937 Henry Cohn, 2026, needs more optimization.
8 166 0.497613945133 Henry Cohn, 2026, needs more optimization.
8 167 0.498497861414 Henry Cohn, 2026, needs more optimization.
8 169 0.499345550174 Henry Cohn, 2026, needs more optimization.
8 171 0.499383078665 Henry Cohn, 2026, needs more optimization.
8 173 0.499958493808 Henry Cohn, 2026, needs more optimization.
8 174 0.499997147138 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 0.544194168465 Henry Cohn, 2026, needs more optimization.
8 243 0.547495291094 Henry Cohn, 2026, needs more optimization.
8 244 0.549897410528 Henry Cohn, 2026, needs more optimization.
8 245 0.552064076011 Henry Cohn, 2026, needs more optimization.
8 246 0.554019096006 Henry Cohn, 2026, needs more optimization.
8 247 0.555292483399 Henry Cohn, 2026, needs more optimization.
8 248 0.557108921844 Henry Cohn, 2026, needs more optimization.
8 249 0.559315600847 Henry Cohn, 2026, needs more optimization.
8 250 0.560773679637 Henry Cohn, 2026, needs more optimization.
8 251 0.561873071359 Henry Cohn, 2026, needs more optimization.
8 252 0.562957018710 Henry Cohn, 2026, needs more optimization.
8 253 0.564127528515 Henry Cohn, 2026, needs more optimization.
8 255 0.564249171508 Henry Cohn, 2026, needs more optimization.
8 256 0.564581910925 Henry Cohn, 2026, needs more optimization.
8 257 0.565098477571 Henry Cohn, 2026, needs more optimization.
8 258 0.566782153247 Henry Cohn, 2026, needs more optimization.
8 259 0.568671809459 Henry Cohn, 2026, needs more optimization.
8 260 0.568881675719 Henry Cohn, 2026, needs more optimization.
8 261 0.569927286382 Henry Cohn, 2026, needs more optimization.
8 262 0.570036496934 Henry Cohn, 2026, needs more optimization.
8 263 0.571303669465 Henry Cohn, 2026, needs more optimization.
8 264 0.571822508600 Henry Cohn, 2026, needs more optimization.
8 265 0.572361297084 Henry Cohn, 2026, needs more optimization.
8 266 0.572640483762 Henry Cohn, 2026, needs more optimization.
8 267 0.573732348533 Henry Cohn, 2026, needs more optimization.
8 268 0.574050946564 Henry Cohn, 2026, needs more optimization.
8 269 0.574572552605 Henry Cohn, 2026, needs more optimization.
8 270 0.574981577864 Henry Cohn, 2026, needs more optimization.
8 271 0.575558470571 Henry Cohn, 2026, needs more optimization.
8 272 0.576615984979 Henry Cohn, 2026, needs more optimization.
8 273 0.577453125906 Henry Cohn, 2026, needs more optimization.
8 274 0.578153814079 Henry Cohn, 2026, needs more optimization.
8 275 0.579054340964 Henry Cohn, 2026, needs more optimization.
8 276 0.579507267496 Henry Cohn, 2026, needs more optimization.
8 277 0.580134726000 Henry Cohn, 2026, needs more optimization.
8 278 0.580619391990 Henry Cohn, 2026, needs more optimization.
8 279 0.581100276737 Henry Cohn, 2026, needs more optimization.
8 280 0.581727950853 Henry Cohn, 2026, needs more optimization.
8 281 0.582158964397 Henry Cohn, 2026, needs more optimization.
8 282 0.582289893392 Henry Cohn, 2026, needs more optimization.
8 283 0.582808118615 Henry Cohn, 2026, needs more optimization.
8 284 0.584952708964 Henry Cohn, 2026, needs more optimization.
8 285 0.584981872151 Henry Cohn, 2026, needs more optimization.
8 287 0.585238953225 Henry Cohn, 2026, needs more optimization.
8 288 0.585442959557 Henry Cohn, 2026, needs more optimization.
8 289 0.585738964792 Henry Cohn, 2026, needs more optimization.
8 290 0.586218352795 Henry Cohn, 2026, needs more optimization.
8 291 0.586517901751 Henry Cohn, 2026, needs more optimization.
8 292 0.586643796622 Henry Cohn, 2026, needs more optimization.
8 293 0.586664580411 Henry Cohn, 2026, needs more optimization.
8 294 0.586813253705 Henry Cohn, 2026, needs more optimization.
8 295 0.588221500687 Henry Cohn, 2026, needs more optimization.
8 296 0.588668544068 Henry Cohn, 2026, needs more optimization.
8 297 0.589691135429 Henry Cohn, 2026, needs more optimization.
8 300 0.590795419317 Henry Cohn, 2026, needs more optimization.
8 301 0.590822129591 Henry Cohn, 2026, needs more optimization.
8 302 0.591336973921 Henry Cohn, 2026, needs more optimization.
8 304 0.591537423177 Henry Cohn, 2026, needs more optimization.
8 306 0.591618046832 Henry Cohn, 2026, needs more optimization.
8 308 0.591841300958 Henry Cohn, 2026, needs more optimization.
8 310 0.591890247514 Henry Cohn, 2026, needs more optimization.
8 311 0.600392682840 Henry Cohn, 2025, needs more optimization.
8 312 0.600857275911 Henry Cohn, 2025, needs more optimization.
8 313 0.601247557345 Henry Cohn, 2025, needs more optimization.
8 314 0.601604875833 Henry Cohn, 2025, needs more optimization.
8 315 0.601754794772 Henry Cohn, 2025, needs more optimization.
8 316 0.601883016118 Henry Cohn, 2026, needs more optimization.
8 317 0.602304929605 Henry Cohn, 2025, needs more optimization.
8 318 0.604495111714 Henry Cohn, 2025, needs more optimization.
8 319 0.604822638198 Henry Cohn, 2025, needs more optimization.
8 320 0.605769909395 Henry Cohn, 2026, needs more optimization.
8 321 0.606080632890 Henry Cohn, 2025, needs more optimization.
8 322 0.606676646313 Henry Cohn, 2025, needs more optimization.
8 323 0.606748296967 Henry Cohn, 2025, needs more optimization.
8 325 0.606875669076 Henry Cohn, 2025, needs more optimization.
8 326 0.607207281517 Henry Cohn, 2025, needs more optimization.
8 327 0.608149701647 Henry Cohn, 2025, needs more optimization.
8 328 0.608181717009 Henry Cohn, 2026, needs more optimization.
8 329 0.608320338402 Henry Cohn, 2025, needs more optimization.
8 330 0.609064020319 Henry Cohn, 2025, needs more optimization.
8 331 0.609197149344 Henry Cohn, 2025, needs more optimization.
8 332 0.609790935425 Henry Cohn, 2025, needs more optimization.
8 333 0.609869023821 Henry Cohn, 2025, needs more optimization.
8 334 0.610018411770 Henry Cohn, 2025, needs more optimization.
8 335 0.610073776765 Henry Cohn, 2025, needs more optimization.
8 336 0.610729053233 Henry Cohn, 2026, needs more optimization.
8 337 0.610839137829 Henry Cohn, 2025, needs more optimization.
8 338 0.611570317481 Henry Cohn, 2026, needs more optimization.
8 340 0.611870699584 Henry Cohn, 2026, needs more optimization.
8 341 0.612146643052 Henry Cohn, 2025, needs more optimization.
8 342 0.612148803025 Henry Cohn, 2025, needs more optimization.
8 343 0.612154038153 Henry Cohn, 2025, needs more optimization.
8 344 0.612780479272 Henry Cohn, 2026, needs more optimization.
8 346 0.612819000288 Henry Cohn, 2026, needs more optimization.
8 348 0.613901448115 Henry Cohn, 2025, needs more optimization.
8 349 0.613958393143 Henry Cohn, 2025, needs more optimization.
8 350 0.614066362464 Henry Cohn, 2026, needs more optimization.
8 351 0.614693773399 Henry Cohn, 2025, needs more optimization.
8 352 0.615043453221 Henry Cohn, 2026, needs more optimization.
8 353 0.615891488252 Henry Cohn, 2025, needs more optimization.
8 354 0.616147123726 Henry Cohn, 2025, needs more optimization.
8 355 0.616343028699 Henry Cohn, 2025, needs more optimization.
8 356 0.616552318905 Henry Cohn, 2025, needs more optimization.
8 357 0.616557922801 Henry Cohn, 2025, needs more optimization.
8 358 0.616753657402 Henry Cohn, 2025, needs more optimization.
8 359 0.617239684539 Henry Cohn, 2025, needs more optimization.
8 360 0.617327508249 Henry Cohn, 2026, needs more optimization.
8 361 0.617622312575 Henry Cohn, 2025, needs more optimization.
8 362 0.618194789446 Henry Cohn, 2026, needs more optimization.
8 363 0.618218429962 Henry Cohn, 2025, needs more optimization.
8 364 0.618861448418 Henry Cohn, 2026, needs more optimization.
8 365 0.618946330794 Henry Cohn, 2025, needs more optimization.
8 366 0.619533958360 Henry Cohn, 2025, needs more optimization.
8 367 0.619566098791 Henry Cohn, 2025, needs more optimization.
8 368 0.620019189187 Henry Cohn, 2025, needs more optimization.
8 369 0.620799329733 Henry Cohn, 2025, needs more optimization.
8 370 0.621206572985 Henry Cohn, 2026, needs more optimization.
8 371 0.621219399291 Henry Cohn, 2025, needs more optimization.
8 372 0.621278546847 Henry Cohn, 2025, needs more optimization.
8 373 0.621439323831 Henry Cohn, 2025, needs more optimization.
8 374 0.621792945272 Henry Cohn, 2026, needs more optimization.
8 375 0.622680026091 Henry Cohn, 2025, needs more optimization.
8 376 0.622721928823 Henry Cohn, 2026, needs more optimization.
8 377 0.623361057450 Henry Cohn, 2025, needs more optimization.
8 378 0.623375974656 Henry Cohn, 2025, needs more optimization.
8 379 0.623561181724 Henry Cohn, 2025, needs more optimization.
8 380 0.623729549220 Henry Cohn, 2026, needs more optimization.
8 381 0.624750658484 Henry Cohn, 2025, needs more optimization.
8 382 0.624770012520 Henry Cohn, 2025, needs more optimization.
8 383 0.624991249003 Henry Cohn, 2025, needs more optimization.
8 384 0.625403316793 Henry Cohn, 2025, needs more optimization.
8 385 0.625724677010 Henry Cohn, 2025, needs more optimization.
8 386 0.626127695908 Henry Cohn, 2025, needs more optimization.
8 388 0.626432231530 Henry Cohn, 2025, needs more optimization.
8 389 0.626962564375 Henry Cohn, 2025, needs more optimization.
8 390 0.627640882088 Henry Cohn, 2025, needs more optimization.
8 391 0.628205858700 Henry Cohn, 2025, needs more optimization.
8 392 0.628294232678 Henry Cohn, 2025, needs more optimization.
8 393 0.628396377236 Henry Cohn, 2025, needs more optimization.
8 394 0.628399885301 Henry Cohn, 2025, needs more optimization.
8 395 0.628659533842 Henry Cohn, 2025, needs more optimization.
8 396 0.629105201649 Henry Cohn, 2025, needs more optimization.
8 397 0.629169317910 Henry Cohn, 2025, needs more optimization.
8 398 0.629863388803 Henry Cohn, 2026, needs more optimization.
8 399 0.629897232379 Henry Cohn, 2025, needs more optimization.
8 400 0.630174839577 Henry Cohn, 2025, needs more optimization.
8 401 0.631382584291 Henry Cohn, 2025, needs more optimization.
8 402 0.631390153886 Henry Cohn, 2025, needs more optimization.
8 403 0.631491811937 Henry Cohn, 2025, needs more optimization.
8 404 0.631523250496 Henry Cohn, 2025, needs more optimization.
8 405 0.632217833561 Henry Cohn, 2025, needs more optimization.
8 406 0.632349801223 Henry Cohn, 2025, needs more optimization.
8 407 0.632398200978 Henry Cohn, 2025, needs more optimization.
8 408 0.632751021452 Henry Cohn, 2025, needs more optimization.
8 409 0.632771125197 Henry Cohn, 2025, needs more optimization.
8 410 0.633663719121 Henry Cohn, 2025, needs more optimization.
8 411 0.633684274566 Henry Cohn, 2025, needs more optimization.
8 412 0.634038324108 Henry Cohn, 2025, needs more optimization.
8 413 0.634054592998 Henry Cohn, 2025, needs more optimization.
8 414 0.634320629040 Henry Cohn, 2025, needs more optimization.
8 415 0.634728376576 Henry Cohn, 2025, needs more optimization.
8 416 0.634814438444 Henry Cohn, 2025, needs more optimization.
8 417 0.634837438867 Henry Cohn, 2025, needs more optimization.
8 418 0.634934621158 Henry Cohn, 2025, needs more optimization.
8 419 0.635070107909 Henry Cohn, 2025, needs more optimization.
8 420 0.635468466546 Henry Cohn, 2026, needs more optimization.
8 421 0.636141198917 Henry Cohn, 2025, needs more optimization.
8 422 0.636167082174 Henry Cohn, 2026, needs more optimization.
8 423 0.636176710499 Henry Cohn, 2025, needs more optimization.
8 424 0.636318728782 Henry Cohn, 2026, needs more optimization.
8 425 0.637001897162 Henry Cohn, 2025, needs more optimization.
8 426 0.637023119393 Henry Cohn, 2025, needs more optimization.
8 427 0.637087408572 Henry Cohn, 2025, needs more optimization.
8 428 0.637089357587 Henry Cohn, 2025, needs more optimization.
8 429 0.637091035838 Henry Cohn, 2025, needs more optimization.
8 430 0.637597366016 Henry Cohn, 2025, needs more optimization.
8 431 0.637929976400 Henry Cohn, 2026, needs more optimization.
8 432 0.638116238897 Henry Cohn, 2025, needs more optimization.
8 433 0.638534297751 Henry Cohn, 2025, needs more optimization.
8 434 0.638897270433 Henry Cohn, 2025, needs more optimization.
8 435 0.639069879825 Henry Cohn, 2025, needs more optimization.
8 436 0.639792064682 Henry Cohn, 2025, needs more optimization.
8 437 0.639809402862 Henry Cohn, 2025, needs more optimization.
8 438 0.640047960605 Henry Cohn, 2025, needs more optimization.
8 439 0.640157825639 Henry Cohn, 2025, needs more optimization.
8 440 0.640469991884 Henry Cohn, 2025, needs more optimization.
8 441 0.640506385547 Henry Cohn, 2025, needs more optimization.
8 443 0.640766099500 Henry Cohn, 2025, needs more optimization.
8 445 0.641262965109 Henry Cohn, 2025, needs more optimization.
8 446 0.641438529490 Henry Cohn, 2025, needs more optimization.
8 447 0.641482891413 Henry Cohn, 2025, needs more optimization.
8 448 0.641496880893 Henry Cohn, 2025, needs more optimization.
8 449 0.641578861091 Henry Cohn, 2025, needs more optimization.
8 450 0.641627464306 Henry Cohn, 2026, needs more optimization.
8 451 0.641797750053 Henry Cohn, 2025, needs more optimization.
8 452 0.641811557867 Henry Cohn, 2025, needs more optimization.
8 453 0.641908870744 Henry Cohn, 2025, needs more optimization.
8 454 0.641974822647 Henry Cohn, 2026, needs more optimization.
8 455 0.642174437296 Henry Cohn, 2025, needs more optimization.
8 456 0.642217378185 Henry Cohn, 2025, needs more optimization.
8 457 0.642229200426 Henry Cohn, 2025, needs more optimization.
8 458 0.642270284839 Henry Cohn, 2025, needs more optimization.
8 459 0.642632119105 Henry Cohn, 2025, needs more optimization.
8 460 0.643398235197 Henry Cohn, 2026, needs more optimization.
8 461 0.643491563350 Henry Cohn, 2025, needs more optimization.
8 462 0.643496044258 Henry Cohn, 2025, needs more optimization.
8 463 0.643541281167 Henry Cohn, 2025, needs more optimization.
8 464 0.643549393561 Henry Cohn, 2025, needs more optimization.
8 465 0.643579577026 Henry Cohn, 2025, needs more optimization.
8 466 0.643718584379 Henry Cohn, 2025, needs more optimization.
8 467 0.643732809840 Henry Cohn, 2025, needs more optimization.
8 468 0.644388241331 Henry Cohn, 2026, needs more optimization.
8 469 0.644393228166 Henry Cohn, 2025, needs more optimization.
8 470 0.644444228630 Henry Cohn, 2026, needs more optimization.
8 471 0.645133996535 Henry Cohn, 2025, needs more optimization.
8 472 0.645158393914 Henry Cohn, 2025, needs more optimization.
8 473 0.645195224081 Henry Cohn, 2025, needs more optimization.
8 474 0.645233527519 Henry Cohn, 2026, needs more optimization.
8 475 0.645262692751 Henry Cohn, 2025, needs more optimization.
8 476 0.646060671921 Henry Cohn, 2026, needs more optimization.
8 477 0.646072431746 Henry Cohn, 2025, needs more optimization.
8 478 0.646125842259 Henry Cohn, 2025, needs more optimization.
8 479 0.647189050236 Henry Cohn, 2025, needs more optimization.
8 480 0.648172971263 Henry Cohn, 2026, needs more optimization.
8 481 0.648203278480 Henry Cohn, 2025, needs more optimization.
8 482 0.648231152639 Henry Cohn, 2025, needs more optimization.
8 483 0.648257524986 Henry Cohn, 2025, needs more optimization.
8 484 0.648301006016 Henry Cohn, 2025, needs more optimization.
8 485 0.648304156375 Henry Cohn, 2025, needs more optimization.
8 486 0.648378747748 Henry Cohn, 2026, needs more optimization.
8 488 0.648409107473 Henry Cohn, 2025, needs more optimization.
8 489 0.648878574511 Henry Cohn, 2025, needs more optimization.
8 490 0.648968769590 Henry Cohn, 2026, needs more optimization.
8 491 0.648969005235 Henry Cohn, 2025, needs more optimization.
8 492 0.649044714764 Henry Cohn, 2026, needs more optimization.
8 495 0.649395489506 Henry Cohn, 2025, needs more optimization.
8 496 0.650342450429 Henry Cohn, 2026, needs more optimization.
8 497 0.650460855550 Henry Cohn, 2026, needs more optimization.
8 498 0.651812874290 Henry Cohn, 2025, needs more optimization.
8 499 0.651821743715 Henry Cohn, 2025, needs more optimization.
8 500 0.651864776838 Henry Cohn, 2025, needs more optimization.
8 501 0.651903079136 Henry Cohn, 2025, needs more optimization.
8 502 0.651950881169 Henry Cohn, 2026, needs more optimization.
8 504 0.651983459840 Henry Cohn, 2026, needs more optimization.
8 506 0.652606806992 Henry Cohn, 2025, needs more optimization.
8 508 0.652625400184 Henry Cohn, 2026, needs more optimization.
8 509 0.652692843143 Henry Cohn, 2025, needs more optimization.
8 510 0.652761675344 Henry Cohn, 2025, needs more optimization.
8 511 0.653822844364 Henry Cohn, 2025, needs more optimization.
8 512 0.653824945416 Henry Cohn, 2025, needs more optimization.
8 514 0.653915965662 Henry Cohn, 2026, needs more optimization.
8 515 0.653957938818 Henry Cohn, 2025, needs more optimization.
8 517 0.654161754594 Henry Cohn, 2025, needs more optimization.
8 519 0.654636126810 Henry Cohn, 2025, needs more optimization.
8 520 0.655352966131 Henry Cohn, 2025, needs more optimization.
8 522 0.655378986905 Henry Cohn, 2025, needs more optimization.
8 523 0.655409138883 Henry Cohn, 2025, needs more optimization.
8 524 0.655432550572 Henry Cohn, 2025, needs more optimization.
8 526 0.656607371810 Henry Cohn, 2025, needs more optimization.
8 528 0.656622819844 Henry Cohn, 2026, needs more optimization.
8 529 0.656662772223 Henry Cohn, 2025, needs more optimization.
8 530 0.656667219490 Henry Cohn, 2025, needs more optimization.
8 531 0.656677786317 Henry Cohn, 2025, needs more optimization.
8 532 0.656705658565 Henry Cohn, 2026, needs more optimization.
8 534 0.656808887119 Henry Cohn, 2026, needs more optimization.
8 535 0.657707828098 Henry Cohn, 2025, needs more optimization.
8 536 0.657712569744 Henry Cohn, 2025, needs more optimization.
8 537 0.657727538788 Henry Cohn, 2025, needs more optimization.
8 538 0.657873599784 Henry Cohn, 2026, needs more optimization.
8 539 0.659017871832 Henry Cohn, 2025, needs more optimization.
8 540 0.659064677191 Henry Cohn, 2026, needs more optimization.
8 541 0.659074917342 Henry Cohn, 2025, needs more optimization.
8 542 0.659252551474 Henry Cohn, 2026, needs more optimization.
8 543 0.660020360645 Henry Cohn, 2025, needs more optimization.
8 544 0.660026024022 Henry Cohn, 2025, needs more optimization.
8 545 0.660034658104 Henry Cohn, 2025, needs more optimization.
8 546 0.660039231384 Henry Cohn, 2025, needs more optimization.
8 547 0.660052739108 Henry Cohn, 2025, needs more optimization.
8 548 0.660077488246 Henry Cohn, 2026, needs more optimization.
8 551 0.660974086809 Henry Cohn, 2025, needs more optimization.
8 552 0.660987073712 Henry Cohn, 2025, needs more optimization.
8 553 0.661549468537 Henry Cohn, 2025, needs more optimization.
8 554 0.661937000088 Henry Cohn, 2025, needs more optimization.
8 555 0.661938005024 Henry Cohn, 2025, needs more optimization.
8 556 0.661961369488 Henry Cohn, 2025, needs more optimization.
8 557 0.662037705835 Henry Cohn, 2025, needs more optimization.
8 558 0.662464118455 Henry Cohn, 2026, needs more optimization.
8 561 0.662973680970 Henry Cohn, 2025, needs more optimization.
8 562 0.663010324820 Henry Cohn, 2026, needs more optimization.
8 563 0.663021420021 Henry Cohn, 2025, needs more optimization.
8 564 0.663029029492 Henry Cohn, 2025, needs more optimization.
8 565 0.663035818985 Henry Cohn, 2025, needs more optimization.
8 566 0.663098851934 Henry Cohn, 2026, needs more optimization.
8 567 0.663892412862 Henry Cohn, 2025, needs more optimization.
8 568 0.663926371318 Henry Cohn, 2025, needs more optimization.
8 569 0.664046024545 Henry Cohn, 2025, needs more optimization.
8 570 0.664623961042 Henry Cohn, 2025, needs more optimization.
8 571 0.664637068515 Henry Cohn, 2025, needs more optimization.
8 572 0.664702818723 Henry Cohn, 2026, needs more optimization.
8 574 0.665244636737 Henry Cohn, 2026, needs more optimization.
8 576 0.665248884435 Henry Cohn, 2026, needs more optimization.
8 580 0.665302826327 Henry Cohn, 2026, needs more optimization.
8 581 0.665350887801 Henry Cohn, 2025, needs more optimization.
8 584 0.665379649120 Henry Cohn, 2025, needs more optimization.
8 586 0.665380549827 Henry Cohn, 2025, needs more optimization.
8 587 0.665435047722 Henry Cohn, 2025, needs more optimization.
8 588 0.665445319204 Henry Cohn, 2025, needs more optimization.
8 590 0.665549666817 Henry Cohn, 2026, needs more optimization.
8 592 0.665561282339 Henry Cohn, 2025, needs more optimization.
8 594 0.666112815539 Henry Cohn, 2026, needs more optimization.
8 595 0.666130895254 Henry Cohn, 2025, needs more optimization.
8 596 0.666387024705 Henry Cohn, 2025, needs more optimization.
8 599 0.666397358052 Henry Cohn, 2025, needs more optimization.
8 600 0.666602509895 Henry Cohn, 2026, needs more optimization.
8 601 0.666965063068 Henry Cohn, 2025, needs more optimization.
8 603 0.666985574341 Henry Cohn, 2025, needs more optimization.
8 604 0.667055396755 Henry Cohn, 2026, needs more optimization.
8 605 0.667060658637 Henry Cohn, 2025, needs more optimization.
8 606 0.667072130559 Henry Cohn, 2025, needs more optimization.
8 607 0.667087479684 Henry Cohn, 2025, needs more optimization.
8 608 0.667089302599 Henry Cohn, 2025, needs more optimization.
8 609 0.667095398399 Henry Cohn, 2025, needs more optimization.
8 610 0.667099364039 Henry Cohn, 2025, needs more optimization.
8 611 0.667108979091 Henry Cohn, 2025, needs more optimization.
8 613 0.667111574246 Henry Cohn, 2025, needs more optimization.
8 614 0.667138324876 Henry Cohn, 2025, needs more optimization.
8 615 0.667483585956 Henry Cohn, 2025, needs more optimization.
8 616 0.667623615616 Henry Cohn, 2025, needs more optimization.
8 617 0.667658585372 Henry Cohn, 2025, needs more optimization.
8 618 0.667665939580 Henry Cohn, 2025, needs more optimization.
8 620 0.667678310990 Henry Cohn, 2025, needs more optimization.
8 621 0.667691025236 Henry Cohn, 2025, needs more optimization.
8 622 0.667692412190 Henry Cohn, 2025, needs more optimization.
8 623 0.667736479972 Henry Cohn, 2025, needs more optimization.
8 624 0.667737235348 Henry Cohn, 2025, needs more optimization.
8 625 0.667790082788 Henry Cohn, 2025, needs more optimization.
8 626 0.667846604599 Henry Cohn, 2026, needs more optimization.
8 628 0.667862843031 Henry Cohn, 2026, needs more optimization.
8 630 0.667964357919 Henry Cohn, 2026, needs more optimization.
8 632 0.667996157491 Henry Cohn, 2026, needs more optimization.
8 633 0.668028469835 Henry Cohn, 2025, needs more optimization.
8 634 0.668097362317 Henry Cohn, 2026, needs more optimization.
8 635 0.668103995122 Henry Cohn, 2025, needs more optimization.
8 636 0.668296451526 Henry Cohn, 2026, needs more optimization.
8 637 0.668744675880 Henry Cohn, 2025, needs more optimization.
8 638 0.668765396908 Henry Cohn, 2025, needs more optimization.
8 639 0.668781500950 Henry Cohn, 2025, needs more optimization.
8 640 0.668796717281 Henry Cohn, 2026, needs more optimization.
8 641 0.668821436898 Henry Cohn, 2025, needs more optimization.
8 642 0.668825887669 Henry Cohn, 2026, needs more optimization.
8 643 0.668849763782 Henry Cohn, 2025, needs more optimization.
8 644 0.668888933796 Henry Cohn, 2026, needs more optimization.
8 645 0.668913424501 Henry Cohn, 2025, needs more optimization.
8 646 0.668925108447 Henry Cohn, 2025, needs more optimization.
8 648 0.670118418002 Henry Cohn, 2025, needs more optimization.
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8 650 0.670157075400 Henry Cohn, 2026, needs more optimization.
8 651 0.670169070821 Henry Cohn, 2025, needs more optimization.
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8 653 0.670249265653 Henry Cohn, 2025, needs more optimization.
8 654 0.670496836573 Henry Cohn, 2025, needs more optimization.
8 656 0.670540356874 Henry Cohn, 2025, needs more optimization.
8 657 0.670625558936 Henry Cohn, 2026, needs more optimization.
8 658 0.670718764970 Henry Cohn, 2026, needs more optimization.
8 660 0.671405900252 Henry Cohn, 2026, needs more optimization.
8 661 0.671576063393 Henry Cohn, 2026, needs more optimization.
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8 663 0.672376082884 Henry Cohn, 2025, needs more optimization.
8 664 0.672381833357 Henry Cohn, 2025, needs more optimization.
8 665 0.672388136782 Henry Cohn, 2025, needs more optimization.
8 668 0.672402986964 Henry Cohn, 2025, needs more optimization.
8 669 0.672405478766 Henry Cohn, 2025, needs more optimization.
8 671 0.672433821191 Henry Cohn, 2025, needs more optimization.
8 673 0.672444029762 Henry Cohn, 2025, needs more optimization.
8 674 0.672920393834 Henry Cohn, 2025, needs more optimization.
8 675 0.673610862017 Henry Cohn, 2025, needs more optimization.
8 676 0.673615460560 Henry Cohn, 2025, needs more optimization.
8 677 0.673654129403 Henry Cohn, 2025, needs more optimization.
8 678 0.673656323795 Henry Cohn, 2025, needs more optimization.
8 681 0.673674600224 Henry Cohn, 2025, needs more optimization.
8 682 0.673708965600 Henry Cohn, 2025, needs more optimization.
8 683 0.676263648596 Henry Cohn, 2025, needs more optimization.
8 684 0.676421990904 Henry Cohn, 2026, needs more optimization.
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8 689 0.677559094580 Henry Cohn, 2025, needs more optimization.
8 690 0.677573227978 Henry Cohn, 2025, needs more optimization.
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8 692 0.678679769647 Henry Cohn, 2025, needs more optimization.
8 693 0.678688084707 Henry Cohn, 2025, needs more optimization.
8 694 0.678720290855 Henry Cohn, 2025, needs more optimization.
8 695 0.678729793454 Henry Cohn, 2025, needs more optimization.
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8 697 0.678782198352 Henry Cohn, 2025, needs more optimization.
8 698 0.678784004008 Henry Cohn, 2025, needs more optimization.
8 700 0.679658794379 Henry Cohn, 2025, needs more optimization.
8 701 0.680815834525 Henry Cohn, 2025, needs more optimization.
8 702 0.680825164121 Henry Cohn, 2025, needs more optimization.
8 704 0.680860712448 Henry Cohn, 2025, needs more optimization.
8 705 0.681761519941 Henry Cohn, 2025, needs more optimization.
8 706 0.681769565159 Henry Cohn, 2026, needs more optimization.
8 707 0.681783437957 Henry Cohn, 2025, needs more optimization.
8 708 0.681790375821 Henry Cohn, 2025, needs more optimization.
8 709 0.681807845025 Henry Cohn, 2025, needs more optimization.
8 710 0.681819621502 Henry Cohn, 2025, needs more optimization.
8 711 0.682547829724 Henry Cohn, 2025, needs more optimization.
8 712 0.682556151636 Henry Cohn, 2025, needs more optimization.
8 713 0.682631957791 Henry Cohn, 2025, needs more optimization.
8 714 0.682647104955 Henry Cohn, 2025, needs more optimization.
8 715 0.682720970670 Henry Cohn, 2026, needs more optimization.
8 716 0.683299678822 Henry Cohn, 2025, needs more optimization.
8 717 0.683347815941 Henry Cohn, 2025, needs more optimization.
8 718 0.684191236637 Henry Cohn, 2025, needs more optimization.
8 720 0.684198725768 Henry Cohn, 2025, needs more optimization.
8 721 0.684209256236 Henry Cohn, 2025, needs more optimization.
8 722 0.684552996041 Henry Cohn, 2025, needs more optimization.
8 723 0.684597203485 Henry Cohn, 2025, needs more optimization.
8 725 0.685637290899 Henry Cohn, 2025, needs more optimization.
8 727 0.685651013687 Henry Cohn, 2025, needs more optimization.
8 728 0.686655440089 Henry Cohn, 2025, needs more optimization.
8 730 0.686764596522 Henry Cohn, 2025, needs more optimization.
8 731 0.687195507005 Henry Cohn, 2025, needs more optimization.
8 732 0.687199858892 Henry Cohn, 2025, needs more optimization.
8 733 0.687556618604 Henry Cohn, 2025, needs more optimization.
8 734 0.687560122508 Henry Cohn, 2025, needs more optimization.
8 735 0.687565651641 Henry Cohn, 2025, needs more optimization.
8 736 0.687595156374 Henry Cohn, 2025, needs more optimization.
8 737 0.688314662407 Henry Cohn, 2026, needs more optimization.
8 738 0.688324275861 Henry Cohn, 2026, needs more optimization.
8 739 0.688340073834 Henry Cohn, 2025, needs more optimization.
8 741 0.688352439514 Henry Cohn, 2025, needs more optimization.
8 742 0.688380495694 Henry Cohn, 2026, needs more optimization.
8 743 0.689087386175 Henry Cohn, 2025, needs more optimization.
8 744 0.689093364046 Henry Cohn, 2025, needs more optimization.
8 745 0.689245371248 Henry Cohn, 2025, needs more optimization.
8 746 0.689257208969 Henry Cohn, 2025, needs more optimization.
8 747 0.689285686948 Henry Cohn, 2025, needs more optimization.
8 748 0.689650119683 Henry Cohn, 2025, needs more optimization.
8 749 0.689654681524 Henry Cohn, 2025, needs more optimization.
8 750 0.689712410927 Henry Cohn, 2026, needs more optimization.
8 751 0.689712820395 Henry Cohn, 2025, needs more optimization.
8 753 0.690221625290 Henry Cohn, 2025, needs more optimization.
8 754 0.690249738820 Henry Cohn, 2025, needs more optimization.
8 756 0.690254002412 Henry Cohn, 2025, needs more optimization.
8 757 0.690262706824 Henry Cohn, 2025, needs more optimization.
8 758 0.690269097024 Henry Cohn, 2025, needs more optimization.
8 760 0.690275149052 Henry Cohn, 2025, needs more optimization.
8 761 0.690397754931 Henry Cohn, 2026, needs more optimization.
8 762 0.690931028446 Henry Cohn, 2025, needs more optimization.
8 763 0.690985339857 Henry Cohn, 2025, needs more optimization.
8 764 0.691649582708 Henry Cohn, 2025, needs more optimization.
8 765 0.691657242200 Henry Cohn, 2025, needs more optimization.
8 766 0.691660459895 Henry Cohn, 2025, needs more optimization.
8 767 0.691733318685 Henry Cohn, 2025, needs more optimization.
8 768 0.691738086675 Henry Cohn, 2025, needs more optimization.
8 770 0.691756855104 Henry Cohn, 2025, needs more optimization.
8 771 0.691764059186 Henry Cohn, 2025, needs more optimization.
8 772 0.691769701878 Henry Cohn, 2025, needs more optimization.
8 773 0.692182103909 Henry Cohn, 2026, needs more optimization.
8 774 0.692427638048 Henry Cohn, 2025, needs more optimization.
8 775 0.692465210450 Henry Cohn, 2025, needs more optimization.
8 776 0.692503031109 Henry Cohn, 2026, needs more optimization.
8 777 0.692507780945 Henry Cohn, 2025, needs more optimization.
8 778 0.692685446443 Henry Cohn, 2025, needs more optimization.
8 779 0.692696406897 Henry Cohn, 2025, needs more optimization.
8 780 0.692703051394 Henry Cohn, 2025, needs more optimization.
8 781 0.692707887399 Henry Cohn, 2025, needs more optimization.
8 782 0.692758858442 Henry Cohn, 2025, needs more optimization.
8 783 0.692780451895 Henry Cohn, 2025, needs more optimization.
8 784 0.692817786168 Henry Cohn, 2025, needs more optimization.
8 785 0.693746730553 Henry Cohn, 2025, needs more optimization.
8 786 0.693749065175 Henry Cohn, 2025, needs more optimization.
8 787 0.693809101014 Henry Cohn, 2025, needs more optimization.
8 788 0.693820391069 Henry Cohn, 2025, needs more optimization.
8 789 0.694266147106 Henry Cohn, 2026, needs more optimization.
8 790 0.694297113974 Henry Cohn, 2025, needs more optimization.
8 791 0.694304362807 Henry Cohn, 2025, needs more optimization.
8 792 0.694317963429 Henry Cohn, 2025, needs more optimization.
8 794 0.694664633550 Henry Cohn, 2025, needs more optimization.
8 795 0.694703983569 Henry Cohn, 2025, needs more optimization.
8 797 0.694715522952 Henry Cohn, 2025, needs more optimization.
8 799 0.694912235139 Henry Cohn, 2025, needs more optimization.
8 800 0.695331096435 Henry Cohn, 2025, needs more optimization.
8 801 0.695383678268 Henry Cohn, 2025, needs more optimization.
8 802 0.695653080170 Henry Cohn, 2025, needs more optimization.
8 803 0.695703246342 Henry Cohn, 2025, needs more optimization.
8 804 0.696078886015 Henry Cohn, 2025, needs more optimization.
8 805 0.696401640756 Henry Cohn, 2026, needs more optimization.
8 806 0.696420678624 Henry Cohn, 2025, needs more optimization.
8 807 0.696427726754 Henry Cohn, 2025, needs more optimization.
8 808 0.696450883362 Henry Cohn, 2025, needs more optimization.
8 809 0.696493755900 Henry Cohn, 2025, needs more optimization.
8 810 0.696521885117 Henry Cohn, 2026, needs more optimization.
8 811 0.696770658267 Henry Cohn, 2026, needs more optimization.
8 812 0.696772875652 Henry Cohn, 2025, needs more optimization.
8 813 0.696926164631 Henry Cohn, 2025, needs more optimization.
8 814 0.697612546310 Henry Cohn, 2025, needs more optimization.
8 815 0.697613780682 Henry Cohn, 2025, needs more optimization.
8 817 0.697625402129 Henry Cohn, 2025, needs more optimization.
8 818 0.697635270970 Henry Cohn, 2025, needs more optimization.
8 819 0.697656849098 Henry Cohn, 2025, needs more optimization.
8 820 0.697735882156 Henry Cohn, 2025, needs more optimization.
8 821 0.697769959461 Henry Cohn, 2026, needs more optimization.
8 822 0.698090630860 Henry Cohn, 2026, needs more optimization.
8 823 0.698109445083 Henry Cohn, 2025, needs more optimization.
8 824 0.698158922001 Henry Cohn, 2025, needs more optimization.
8 825 0.698171458389 Henry Cohn, 2025, needs more optimization.
8 826 0.698267233858 Henry Cohn, 2025, needs more optimization.
8 828 0.698680526523 Henry Cohn, 2025, needs more optimization.
8 829 0.698698277435 Henry Cohn, 2025, needs more optimization.
8 833 0.699228866288 Henry Cohn, 2025, needs more optimization.
8 834 0.699236866590 Henry Cohn, 2025, needs more optimization.
8 835 0.699533746117 Henry Cohn, 2026, needs more optimization.
8 838 0.699976879270 Henry Cohn, 2025, needs more optimization.
8 839 0.699989920786 Henry Cohn, 2025, needs more optimization.
8 840 0.700052149297 Henry Cohn, 2025, needs more optimization.
8 842 0.700535494509 Henry Cohn, 2026, needs more optimization.
8 844 0.700579575605 Henry Cohn, 2025, needs more optimization.
8 846 0.700582454670 Henry Cohn, 2025, needs more optimization.
8 847 0.700585511073 Henry Cohn, 2025, needs more optimization.
8 848 0.700783071915 Henry Cohn, 2026, needs more optimization.
8 850 0.701194373603 Henry Cohn, 2025, needs more optimization.
8 851 0.701205442734 Henry Cohn, 2025, needs more optimization.
8 852 0.701300853845 Henry Cohn, 2025, needs more optimization.
8 853 0.701627111266 Henry Cohn, 2025, needs more optimization.
8 854 0.701647154743 Henry Cohn, 2025, needs more optimization.
8 856 0.702140146489 Henry Cohn, 2025, needs more optimization.
8 857 0.702140752693 Henry Cohn, 2025, needs more optimization.
8 858 0.702158024689 Henry Cohn, 2026, needs more optimization.
8 859 0.702361464710 Henry Cohn, 2026, needs more optimization.
8 860 0.702635130955 Henry Cohn, 2026, needs more optimization.
8 861 0.702639415712 Henry Cohn, 2025, needs more optimization.
8 862 0.703046881118 Henry Cohn, 2026, needs more optimization.
8 863 0.703047455658 Henry Cohn, 2025, needs more optimization.
8 864 0.703075542271 Henry Cohn, 2025, needs more optimization.
8 865 0.703086668407 Henry Cohn, 2025, needs more optimization.
8 866 0.703089439857 Henry Cohn, 2025, needs more optimization.
8 867 0.703394919194 Henry Cohn, 2026, needs more optimization.
8 868 0.703400832635 Henry Cohn, 2025, needs more optimization.
8 869 0.703488766318 Henry Cohn, 2026, needs more optimization.
8 870 0.703489788978 Henry Cohn, 2026, needs more optimization.
8 871 0.703725472340 Henry Cohn, 2026, needs more optimization.
8 872 0.703743378781 Henry Cohn, 2026, needs more optimization.
8 873 0.703890487142 Henry Cohn, 2025, needs more optimization.
8 874 0.703929272417 Henry Cohn, 2025, needs more optimization.
8 875 0.703937923467 Henry Cohn, 2025, needs more optimization.
8 876 0.703952340476 Henry Cohn, 2025, needs more optimization.
8 877 0.704409953183 Henry Cohn, 2025, needs more optimization.
8 879 0.704413282221 Henry Cohn, 2025, needs more optimization.
8 880 0.704445046575 Henry Cohn, 2025, needs more optimization.
8 881 0.704454523140 Henry Cohn, 2025, needs more optimization.
8 882 0.704494807984 Henry Cohn, 2026, needs more optimization.
8 883 0.704812314689 Henry Cohn, 2025, needs more optimization.
8 884 0.704825256769 Henry Cohn, 2025, needs more optimization.
8 886 0.705062062139 Henry Cohn, 2025, needs more optimization.
8 887 0.705062193245 Henry Cohn, 2025, needs more optimization.
8 888 0.705070441205 Henry Cohn, 2025, needs more optimization.
8 889 0.705080235144 Henry Cohn, 2025, needs more optimization.
8 890 0.705113042198 Henry Cohn, 2025, needs more optimization.
8 891 0.705712899680 Henry Cohn, 2025, needs more optimization.
8 892 0.705721402518 Henry Cohn, 2025, needs more optimization.
8 893 0.705729660190 Henry Cohn, 2025, needs more optimization.
8 894 0.705734532374 Henry Cohn, 2025, needs more optimization.
8 895 0.705745173745 Henry Cohn, 2025, needs more optimization.
8 896 0.705761190193 Henry Cohn, 2025, needs more optimization.
8 897 0.705764606541 Henry Cohn, 2025, needs more optimization.
8 899 0.705821749669 Henry Cohn, 2025, needs more optimization.
8 902 0.705829679270 Henry Cohn, 2025, needs more optimization.
8 903 0.705835670346 Henry Cohn, 2025, needs more optimization.
8 904 0.706104844872 Henry Cohn, 2025, needs more optimization.
8 905 0.706106342062 Henry Cohn, 2025, needs more optimization.
8 908 0.706543218819 Henry Cohn, 2025, needs more optimization.
8 909 0.706548180413 Henry Cohn, 2025, needs more optimization.
8 910 0.706549815083 Henry Cohn, 2025, needs more optimization.
8 911 0.706561407014 Henry Cohn, 2025, needs more optimization.
8 914 0.706571631333 Henry Cohn, 2025, needs more optimization.
8 915 0.707003548339 Henry Cohn, 2026, needs more optimization.
8 916 0.707012136771 Henry Cohn, 2025, needs more optimization.
8 917 0.707013838812 Henry Cohn, 2025, needs more optimization.
8 918 0.707186141715 Henry Cohn, 2026, needs more optimization.
8 919 0.707190386128 Henry Cohn, 2025, needs more optimization.
8 920 0.707192636288 Henry Cohn, 2025, needs more optimization.
8 921 0.707670415856 Henry Cohn, 2025, needs more optimization.
8 923 0.707676716516 Henry Cohn, 2025, needs more optimization.
8 925 0.707694037021 Henry Cohn, 2025, needs more optimization.
8 926 0.707707856101 Henry Cohn, 2025, needs more optimization.
8 928 0.707991000305 Henry Cohn, 2025, needs more optimization.
8 930 0.707996589845 Henry Cohn, 2025, needs more optimization.
8 931 0.708050920570 Henry Cohn, 2026, needs more optimization.
8 932 0.708150395923 Henry Cohn, 2026, needs more optimization.
8 933 0.708152389831 Henry Cohn, 2025, needs more optimization.
8 934 0.708470511601 Henry Cohn, 2026, needs more optimization.
8 935 0.708473659723 Henry Cohn, 2026, needs more optimization.
8 936 0.708482055285 Henry Cohn, 2026, needs more optimization.
8 937 0.708543268831 Henry Cohn, 2026, needs more optimization.
8 938 0.708946530234 Henry Cohn, 2026, needs more optimization.
8 939 0.708951251854 Henry Cohn, 2026, needs more optimization.
8 941 0.708963902315 Henry Cohn, 2025, needs more optimization.
8 942 0.708966792925 Henry Cohn, 2026, needs more optimization.
8 943 0.709002441249 Henry Cohn, 2026, needs more optimization.
8 944 0.709064950292 Henry Cohn, 2025, needs more optimization.
8 946 0.709192766988 Henry Cohn, 2026, needs more optimization.
8 947 0.709246845504 Henry Cohn, 2026, needs more optimization.
8 949 0.709561805584 Henry Cohn, 2025, needs more optimization.
8 950 0.709568370738 Henry Cohn, 2025, needs more optimization.
8 952 0.709580083659 Henry Cohn, 2025, needs more optimization.
8 953 0.709592878533 Henry Cohn, 2026, needs more optimization.
8 954 0.709618223393 Henry Cohn, 2026, needs more optimization.
8 955 0.710013127623 Henry Cohn, 2025, needs more optimization.
8 956 0.710025120237 Henry Cohn, 2025, needs more optimization.
8 957 0.710043299869 Henry Cohn, 2026, needs more optimization.
8 958 0.710045768660 Henry Cohn, 2026, needs more optimization.
8 960 0.710351161619 Henry Cohn, 2026, needs more optimization.
8 961 0.710358683147 Henry Cohn, 2026, needs more optimization.
8 962 0.710752798997 Henry Cohn, 2026, needs more optimization.
8 963 0.710768583393 Henry Cohn, 2026, needs more optimization.
8 964 0.710786430671 Henry Cohn, 2026, needs more optimization.
8 967 0.710794195804 Henry Cohn, 2025, needs more optimization.
8 968 0.710800955289 Henry Cohn, 2025, needs more optimization.
8 969 0.710847532911 Henry Cohn, 2025, needs more optimization.
8 970 0.710949866180 Henry Cohn, 2025, needs more optimization.
8 971 0.711446368805 Henry Cohn, 2026, needs more optimization.
8 972 0.711498673462 Henry Cohn, 2026, needs more optimization.
8 973 0.711510485535 Henry Cohn, 2026, needs more optimization.
8 974 0.711571576014 Henry Cohn, 2025, needs more optimization.
8 975 0.711583352192 Henry Cohn, 2026, needs more optimization.
8 976 0.711588575557 Henry Cohn, 2026, needs more optimization.
8 977 0.711611710434 Henry Cohn, 2025, needs more optimization.
8 978 0.711671964312 Henry Cohn, 2026, needs more optimization.
8 979 0.711962486346 Henry Cohn, 2025, needs more optimization.
8 980 0.711968317112 Henry Cohn, 2026, needs more optimization.
8 981 0.712055090895 Henry Cohn, 2026, needs more optimization.
8 983 0.712080270091 Henry Cohn, 2025, needs more optimization.
8 984 0.712092572803 Henry Cohn, 2026, needs more optimization.
8 986 0.712394668618 Henry Cohn, 2025, needs more optimization.
8 987 0.712408844609 Henry Cohn, 2025, needs more optimization.
8 988 0.712468855396 Henry Cohn, 2026, needs more optimization.
8 989 0.712714678610 Henry Cohn, 2025, needs more optimization.
8 990 0.713101116160 Henry Cohn, 2026, needs more optimization.
8 991 0.713103386410 Henry Cohn, 2025, needs more optimization.
8 992 0.713104668986 Henry Cohn, 2025, needs more optimization.
8 997 0.713123846310 Henry Cohn, 2026, needs more optimization.
8 998 0.713167095763 Henry Cohn, 2026, needs more optimization.
8 1000 0.713202920821 Henry Cohn, 2026, needs more optimization.
8 1001 0.713332075457 Henry Cohn, 2026, needs more optimization.
8 1002 0.713378981153 Henry Cohn, 2026, needs more optimization.
8 1004 0.713385229889 Henry Cohn, 2026, needs more optimization.
8 1005 0.713502674043 Henry Cohn, 2026, needs more optimization.
8 1006 0.713539780676 Henry Cohn, 2026, needs more optimization.
8 1007 0.713618320729 Henry Cohn, 2026, needs more optimization.
8 1008 0.713720370882 Henry Cohn, 2026, needs more optimization.
8 1009 0.713721529006 Henry Cohn, 2026, needs more optimization.
8 1011 0.713736698650 Henry Cohn, 2026, needs more optimization.
8 1012 0.713825874255 Henry Cohn, 2026, needs more optimization.
8 1014 0.713855643489 Henry Cohn, 2026, needs more optimization.
8 1015 0.713893833812 Henry Cohn, 2026, needs more optimization.
8 1016 0.713895154713 Henry Cohn, 2026, needs more optimization.
8 1017 0.713928471654 Henry Cohn, 2026, needs more optimization.
8 1018 0.713969814791 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 0.2 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
9 37 0.213781170696 Henry Cohn, 2025.
9 38 0.217703240659 Henry Cohn, 2025.
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 0.266202150382 Henry Cohn, 2025.
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 0.297700422270 Henry Cohn, 2023.
9 62 0.299407593895 Henry Cohn, 2026.
9 63 0.302685227391 Henry Cohn, 2025.
9 64 0.306653313780 Henry Cohn, 2023.
9 65 0.310476186338 Henry Cohn, 2026, needs more optimization.
9 66 0.314219501967 Henry Cohn, 2024.
9 67 0.319305112920 Henry Cohn, 2025.
9 68 0.322050465427 Henry Cohn, 2025.
9 69 0.324666182383 Henry Cohn, 2025.
9 70 0.328147252748 Henry Cohn, 2026, needs more optimization.
9 71 0.329165247504 Henry Cohn, 2026.
9 72 0.330036093460 Henry Cohn, 2025, needs more optimization.
9 73 0.330041808451 Henry Cohn, 2025, needs more optimization.
9 74 0.330099461319 Henry Cohn, 2026, needs more optimization.
9 75 0.330101783843 Henry Cohn, 2025, needs more optimization.
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 0.378530782312 Henry Cohn, 2026, needs more optimization.
9 103 0.378850283307 Henry Cohn, 2026, needs more optimization.
9 104 0.379137241782 Henry Cohn, 2025, needs more optimization.
9 105 0.391682453674 Henry Cohn, 2026, needs more optimization.
9 106 0.395189700208 Henry Cohn, 2026, needs more optimization.
9 107 0.398154357334 Henry Cohn, 2026, needs more optimization.
9 108 0.400036532419 Henry Cohn, 2026, needs more optimization.
9 109 0.403046937070 Henry Cohn, 2026, needs more optimization.
9 110 0.405589538580 Henry Cohn, 2026, needs more optimization.
9 111 0.407513805241 Henry Cohn, 2026, needs more optimization.
9 112 0.408810852793 Henry Cohn, 2026, needs more optimization.
9 113 0.411622580981 Henry Cohn, 2026, needs more optimization.
9 114 0.413210493268 Henry Cohn, 2026, needs more optimization.
9 115 0.413676808831 Henry Cohn, 2026, needs more optimization.
9 116 0.414183003841 Henry Cohn, 2026, needs more optimization.
9 117 0.415197525333 Henry Cohn, 2026, needs more optimization.
9 118 0.416489360388 Henry Cohn, 2026, needs more optimization.
9 119 0.417729288063 Henry Cohn, 2026, needs more optimization.
9 120 0.418016338583 Henry Cohn, 2026, needs more optimization.
9 121 0.418782043207 Henry Cohn, 2026, needs more optimization.
9 122 0.420072737098 Henry Cohn, 2026, needs more optimization.
9 123 0.421372141538 Henry Cohn, 2026, needs more optimization.
9 124 0.422247974303 Henry Cohn, 2026, needs more optimization.
9 125 0.422393887846 Henry Cohn, 2026, needs more optimization.
9 126 0.423481497602 Henry Cohn, 2026, needs more optimization.
9 127 0.424951818474 Henry Cohn, 2026, needs more optimization.
9 128 0.426691463492 Henry Cohn, 2026, needs more optimization.
9 129 0.428279428430 Henry Cohn, 2026, needs more optimization.
9 130 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
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 0.441717675398 Henry Cohn, 2026, needs more optimization.
9 148 0.444897053449 Henry Cohn, 2026, needs more optimization.
9 149 0.448505735205 Henry Cohn, 2026, needs more optimization.
9 150 0.450521552080 Henry Cohn, 2026, needs more optimization.
9 151 0.452124462437 Henry Cohn, 2026, needs more optimization.
9 152 0.453419450442 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
9 167 0.462218526406 Henry Cohn, 2026, needs more optimization.
9 168 0.463306430381 Henry Cohn, 2026, needs more optimization.
9 169 0.465249009709 Henry Cohn, 2026, needs more optimization.
9 170 0.469053924614 Henry Cohn, 2026, needs more optimization.
9 171 0.471015417577 Henry Cohn, 2026, needs more optimization.
9 172 0.471827959303 Henry Cohn, 2026, needs more optimization.
9 173 0.472363916154 Henry Cohn, 2026, needs more optimization.
9 174 0.473604016858 Henry Cohn, 2026, needs more optimization.
9 175 0.473730901892 Henry Cohn, 2026, needs more optimization.
9 176 0.474074558258 Henry Cohn, 2026, needs more optimization.
9 177 0.474576234826 Henry Cohn, 2026, needs more optimization.
9 178 0.475491112223 Henry Cohn, 2026, needs more optimization.
9 179 0.475568890322 Henry Cohn, 2026, needs more optimization.
9 180 0.476087415470 Henry Cohn, 2026, needs more optimization.
9 181 0.476802597534 Henry Cohn, 2026, needs more optimization.
9 182 0.476813502445 Henry Cohn, 2026, needs more optimization.
9 183 0.477078950744 Henry Cohn, 2026, needs more optimization.
9 184 0.477280494821 Henry Cohn, 2026, needs more optimization.
9 185 0.477631553395 Henry Cohn, 2026, needs more optimization.
9 186 0.478987829193 Henry Cohn, 2026, needs more optimization.
9 187 0.479092975713 Henry Cohn, 2026, needs more optimization.
9 188 0.479360904333 Henry Cohn, 2026, needs more optimization.
9 189 0.479831149793 Henry Cohn, 2026, needs more optimization.
9 190 0.480108793056 Henry Cohn, 2026, needs more optimization.
9 191 0.480356031645 Henry Cohn, 2026, needs more optimization.
9 192 0.481341369030 Henry Cohn, 2026, needs more optimization.
9 193 0.482434790702 Henry Cohn, 2026, needs more optimization.
9 194 0.483134582492 Henry Cohn, 2026, needs more optimization.
9 195 0.484529379205 Henry Cohn, 2026, needs more optimization.
9 196 0.484941534529 Henry Cohn, 2026, needs more optimization.
9 197 0.485125511701 Henry Cohn, 2026, needs more optimization.
9 198 0.486052454172 Henry Cohn, 2026, needs more optimization.
9 199 0.486277500563 Henry Cohn, 2026, needs more optimization.
9 200 0.486578547550 Henry Cohn, 2026, needs more optimization.
9 201 0.486852059183 Henry Cohn, 2026, needs more optimization.
9 202 0.487411547824 Henry Cohn, 2026, needs more optimization.
9 203 0.487804985508 Henry Cohn, 2026, needs more optimization.
9 204 0.488684114628 Henry Cohn, 2026, needs more optimization.
9 205 0.489745011461 Henry Cohn, 2026, needs more optimization.
9 206 0.489798052300 Henry Cohn, 2026, needs more optimization.
9 207 0.490227719340 Henry Cohn, 2026, needs more optimization.
9 208 0.490784742807 Henry Cohn, 2026, needs more optimization.
9 209 0.490838542660 Henry Cohn, 2026, needs more optimization.
9 210 0.491411418334 Henry Cohn, 2026, needs more optimization.
9 211 0.492031663133 Henry Cohn, 2026, needs more optimization.
9 212 0.493185696336 Henry Cohn, 2026, needs more optimization.
9 213 0.494001370998 Henry Cohn, 2026, needs more optimization.
9 215 0.494432920860 Henry Cohn, 2026, needs more optimization.
9 216 0.494830482939 Henry Cohn, 2026, needs more optimization.
9 217 0.495761490523 Henry Cohn, 2026, needs more optimization.
9 218 0.495793440845 Henry Cohn, 2026, needs more optimization.
9 219 0.496342839960 Henry Cohn, 2026, needs more optimization.
9 220 0.496770891183 Henry Cohn, 2026, needs more optimization.
9 221 0.496992034446 Henry Cohn, 2026, needs more optimization.
9 222 0.497393841789 Henry Cohn, 2026, needs more optimization.
9 224 0.497881103412 Henry Cohn, 2026, needs more optimization.
9 225 0.498065058788 Henry Cohn, 2026, needs more optimization.
9 227 0.498306952482 Henry Cohn, 2026, needs more optimization.
9 228 0.498615615347 Henry Cohn, 2026, needs more optimization.
9 229 0.498698229647 Henry Cohn, 2026, needs more optimization.
9 230 0.498752790904 Henry Cohn, 2026, needs more optimization.
9 233 0.499062749764 Henry Cohn, 2026, needs more optimization.
9 234 0.499432116864 Henry Cohn, 2026, needs more optimization.
9 235 0.499470799374 Henry Cohn, 2026, needs more optimization.
9 236 0.499552245672 Henry Cohn, 2026, needs more optimization.
9 237 0.499633595401 Henry Cohn, 2026, needs more optimization.
9 238 0.499718818967 Henry Cohn, 2026, needs more optimization.
9 240 0.499743050848 Henry Cohn, 2026, needs more optimization.
9 241 0.499799044040 Henry Cohn, 2026, needs more optimization.
9 242 0.499919910490 Henry Cohn, 2026, needs more optimization.
9 244 0.499925433886 Henry Cohn, 2026, needs more optimization.
9 245 0.499949443295 Henry Cohn, 2026, needs more optimization.
9 246 0.499969930363 Henry Cohn, 2026, needs more optimization.
9 247 0.499986522082 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 0.517341896236 Henry Cohn, 2024, needs more optimization.
9 308 0.523809525477 Henry Cohn, 2026, needs more optimization.
9 310 0.525542622648 Henry Cohn, 2026, needs more optimization.
9 311 0.536081422599 Henry Cohn, 2025, needs more optimization.
9 312 0.536116067832 Henry Cohn, 2026, needs more optimization.
9 314 0.536129423307 Henry Cohn, 2025, needs more optimization.
9 318 0.536750390731 Henry Cohn, 2026, needs more optimization.
9 322 0.536792455461 Henry Cohn, 2026, needs more optimization.
9 324 0.536804014874 Henry Cohn, 2026, needs more optimization.
9 326 0.536813535400 Henry Cohn, 2026, needs more optimization.
9 330 0.536824983719 Henry Cohn, 2026, needs more optimization.
9 332 0.536838164256 Henry Cohn, 2026, needs more optimization.
9 333 0.537239953366 Henry Cohn, 2026, needs more optimization.
9 334 0.537906269092 Henry Cohn, 2026, needs more optimization.
9 335 0.537980963423 Henry Cohn, 2026, needs more optimization.
9 336 0.539493189916 Henry Cohn, 2026, needs more optimization.
9 337 0.540140136178 Henry Cohn, 2025, needs more optimization.
9 338 0.540874199116 Henry Cohn, 2026, needs more optimization.
9 342 0.542144699890 Henry Cohn, 2026, needs more optimization.
9 343 0.543041335903 Henry Cohn, 2026, needs more optimization.
9 344 0.543752408221 Henry Cohn, 2026, needs more optimization.
9 345 0.544511556930 Henry Cohn, 2026, needs more optimization.
9 346 0.544523298108 Henry Cohn, 2026, needs more optimization.
9 348 0.544955695509 Henry Cohn, 2026, needs more optimization.
9 349 0.545185501587 Henry Cohn, 2026, needs more optimization.
9 350 0.545756768291 Henry Cohn, 2026, needs more optimization.
9 351 0.546514033030 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
9 484 0.559333706661 Henry Cohn, 2026, needs more optimization.
9 485 0.563034805828 Henry Cohn, 2026, needs more optimization.
9 486 0.565467939542 Henry Cohn, 2026, needs more optimization.
9 487 0.568432385645 Henry Cohn, 2026, needs more optimization.
9 488 0.570789116964 Henry Cohn, 2026, needs more optimization.
9 489 0.570985963078 Henry Cohn, 2026, needs more optimization.
9 490 0.572639878396 Henry Cohn, 2026, needs more optimization.
9 491 0.574216378832 Henry Cohn, 2026, needs more optimization.
9 492 0.575114890807 Henry Cohn, 2026, needs more optimization.
9 493 0.576794006130 Henry Cohn, 2026, needs more optimization.
9 494 0.578198785456 Henry Cohn, 2026, needs more optimization.
9 495 0.579097300812 Henry Cohn, 2026, needs more optimization.
9 496 0.580225710181 Henry Cohn, 2026, needs more optimization.
9 497 0.581195944076 Henry Cohn, 2026, needs more optimization.
9 498 0.582083521605 Henry Cohn, 2026, needs more optimization.
9 499 0.583367175839 Henry Cohn, 2026, needs more optimization.
9 500 0.584189754620 Henry Cohn, 2026, needs more optimization.
9 501 0.584916769307 Henry Cohn, 2026, needs more optimization.
9 502 0.585872262657 Henry Cohn, 2026, needs more optimization.
9 503 0.586651007671 Henry Cohn, 2026, needs more optimization.
9 504 0.587382890326 Henry Cohn, 2026, needs more optimization.
9 505 0.587619208643 Henry Cohn, 2026, needs more optimization.
9 506 0.588350562263 Henry Cohn, 2026, needs more optimization.
9 507 0.588537818149 Henry Cohn, 2026, needs more optimization.
9 508 0.589239589787 Henry Cohn, 2026, needs more optimization.
9 509 0.590162175823 Henry Cohn, 2026, needs more optimization.
9 510 0.590607082850 Henry Cohn, 2026, needs more optimization.
9 511 0.590986798472 Henry Cohn, 2026, needs more optimization.
9 512 0.591350014799 Henry Cohn, 2026, needs more optimization.
9 513 0.591868210832 Henry Cohn, 2026, needs more optimization.
9 514 0.592241460879 Henry Cohn, 2026, needs more optimization.
9 515 0.592682255423 Henry Cohn, 2026, needs more optimization.
9 516 0.593160233720 Henry Cohn, 2026, needs more optimization.
9 517 0.593440530740 Henry Cohn, 2026, needs more optimization.
9 518 0.593728065552 Henry Cohn, 2026, needs more optimization.
9 519 0.594229771975 Henry Cohn, 2026, needs more optimization.
9 520 0.594529192698 Henry Cohn, 2026, needs more optimization.
9 521 0.594978597895 Henry Cohn, 2026, needs more optimization.
9 522 0.595288143250 Henry Cohn, 2026, needs more optimization.
9 523 0.595852039089 Henry Cohn, 2026, needs more optimization.
9 524 0.596118975349 Henry Cohn, 2026, needs more optimization.
9 525 0.596432362797 Henry Cohn, 2026, needs more optimization.
9 526 0.596916361234 Henry Cohn, 2026, needs more optimization.
9 527 0.597075023194 Henry Cohn, 2026, needs more optimization.
9 528 0.597203491293 Henry Cohn, 2026, needs more optimization.
9 529 0.597318504551 Henry Cohn, 2026, needs more optimization.
9 530 0.597789948857 Henry Cohn, 2026, needs more optimization.
9 531 0.597952390182 Henry Cohn, 2026, needs more optimization.
9 532 0.598044969241 Henry Cohn, 2026, needs more optimization.
9 533 0.598443943788 Henry Cohn, 2026, needs more optimization.
9 534 0.598551453851 Henry Cohn, 2026, needs more optimization.
9 535 0.598932080179 Henry Cohn, 2026, needs more optimization.
9 536 0.599119887031 Henry Cohn, 2026, needs more optimization.
9 538 0.599238627137 Henry Cohn, 2026, needs more optimization.
9 539 0.599609488334 Henry Cohn, 2026, needs more optimization.
9 540 0.599915477236 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 0.605363653247 Henry Cohn, 2026, needs more optimization.
9 614 0.614786340484 Henry Cohn, 2025, needs more optimization.
9 615 0.614905078465 Henry Cohn, 2025, needs more optimization.
9 616 0.615168409892 Henry Cohn, 2026, needs more optimization.
9 617 0.616077792127 Henry Cohn, 2025, needs more optimization.
9 618 0.616086937851 Henry Cohn, 2026, needs more optimization.
9 620 0.616371048168 Henry Cohn, 2026, needs more optimization.
9 621 0.616457216116 Henry Cohn, 2026, needs more optimization.
9 622 0.616652401298 Henry Cohn, 2026, needs more optimization.
9 623 0.616770298760 Henry Cohn, 2026, needs more optimization.
9 624 0.616854969423 Henry Cohn, 2026, needs more optimization.
9 625 0.617118237893 Henry Cohn, 2026, needs more optimization.
9 626 0.617273015032 Henry Cohn, 2026, needs more optimization.
9 627 0.617429175646 Henry Cohn, 2026, needs more optimization.
9 628 0.617609123757 Henry Cohn, 2026, needs more optimization.
9 629 0.617673240500 Henry Cohn, 2026, needs more optimization.
9 630 0.617795206600 Henry Cohn, 2026, needs more optimization.
9 631 0.617849568314 Henry Cohn, 2026, needs more optimization.
9 632 0.617863619858 Henry Cohn, 2026, needs more optimization.
9 633 0.617943462736 Henry Cohn, 2026, needs more optimization.
9 638 0.618033982583 Henry Cohn, 2026, needs more optimization.
9 640 0.618033987180 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 0.624191863384 Henry Cohn, 2026, needs more optimization.
9 724 0.642759824040 Henry Cohn, 2026, needs more optimization.
9 725 0.642940432076 Henry Cohn, 2026, needs more optimization.
9 726 0.643197872157 Henry Cohn, 2025, needs more optimization.
9 727 0.643254326513 Henry Cohn, 2026, needs more optimization.
9 728 0.643367753818 Henry Cohn, 2025, needs more optimization.
9 729 0.643667113761 Henry Cohn, 2026, needs more optimization.
9 730 0.643679183146 Henry Cohn, 2026, needs more optimization.
9 731 0.643707398203 Henry Cohn, 2026, needs more optimization.
9 732 0.643712370360 Henry Cohn, 2026, needs more optimization.
9 733 0.643833843770 Henry Cohn, 2025, needs more optimization.
9 734 0.644273059340 Henry Cohn, 2026, needs more optimization.
9 735 0.644275212489 Henry Cohn, 2026, needs more optimization.
9 736 0.644496407810 Henry Cohn, 2025, needs more optimization.
9 737 0.644577686472 Henry Cohn, 2025, needs more optimization.
9 738 0.644591860201 Henry Cohn, 2025, needs more optimization.
9 739 0.644984741360 Henry Cohn, 2026, needs more optimization.
9 740 0.645107975569 Henry Cohn, 2025, needs more optimization.
9 741 0.645116699616 Henry Cohn, 2025, needs more optimization.
9 742 0.645214426924 Henry Cohn, 2025, needs more optimization.
9 743 0.645220929540 Henry Cohn, 2025, needs more optimization.
9 744 0.645358015488 Henry Cohn, 2026, needs more optimization.
9 745 0.645658898983 Henry Cohn, 2026, needs more optimization.
9 746 0.645662904024 Henry Cohn, 2026, needs more optimization.
9 747 0.645674473369 Henry Cohn, 2026, needs more optimization.
9 748 0.645733908744 Henry Cohn, 2026, needs more optimization.
9 749 0.645791357303 Henry Cohn, 2026, needs more optimization.
9 750 0.646059931101 Henry Cohn, 2026, needs more optimization.
9 751 0.646116345826 Henry Cohn, 2026, needs more optimization.
9 752 0.646447386259 Henry Cohn, 2025, needs more optimization.
9 753 0.646633832580 Henry Cohn, 2026, needs more optimization.
9 754 0.646640495508 Henry Cohn, 2026, needs more optimization.
9 755 0.646651493345 Henry Cohn, 2026, needs more optimization.
9 756 0.646809620524 Henry Cohn, 2026, needs more optimization.
9 757 0.647012745042 Henry Cohn, 2026, needs more optimization.
9 758 0.647188302956 Henry Cohn, 2026, needs more optimization.
9 760 0.647415975407 Henry Cohn, 2025, needs more optimization.
9 761 0.647454310385 Henry Cohn, 2026, needs more optimization.
9 762 0.647502273069 Henry Cohn, 2026, needs more optimization.
9 763 0.647890382897 Henry Cohn, 2025, needs more optimization.
9 764 0.647911180488 Henry Cohn, 2026, needs more optimization.
9 765 0.648153586359 Henry Cohn, 2026, needs more optimization.
9 766 0.648179398056 Henry Cohn, 2025, needs more optimization.
9 767 0.648201575174 Henry Cohn, 2026, needs more optimization.
9 768 0.648276344216 Henry Cohn, 2026, needs more optimization.
9 769 0.648498850472 Henry Cohn, 2025, needs more optimization.
9 770 0.648525378931 Henry Cohn, 2026, needs more optimization.
9 771 0.648980224016 Henry Cohn, 2025, needs more optimization.
9 772 0.648988014765 Henry Cohn, 2025, needs more optimization.
9 773 0.649001453595 Henry Cohn, 2025, needs more optimization.
9 774 0.649049866559 Henry Cohn, 2026, needs more optimization.
9 775 0.649335423097 Henry Cohn, 2026, needs more optimization.
9 776 0.649337034538 Henry Cohn, 2026, needs more optimization.
9 777 0.649380032310 Henry Cohn, 2026, needs more optimization.
9 778 0.649386637141 Henry Cohn, 2025, needs more optimization.
9 779 0.649893766152 Henry Cohn, 2025, needs more optimization.
9 780 0.649924079901 Henry Cohn, 2025, needs more optimization.
9 781 0.649981132962 Henry Cohn, 2026, needs more optimization.
9 782 0.650115707659 Henry Cohn, 2025, needs more optimization.
9 783 0.650123145497 Henry Cohn, 2026, needs more optimization.
9 784 0.650177798115 Henry Cohn, 2026, needs more optimization.
9 785 0.650205564063 Henry Cohn, 2026, needs more optimization.
9 786 0.650691249426 Henry Cohn, 2026, needs more optimization.
9 787 0.650726527805 Henry Cohn, 2026, needs more optimization.
9 788 0.650760346949 Henry Cohn, 2026, needs more optimization.
9 789 0.650838057392 Henry Cohn, 2026, needs more optimization.
9 790 0.651076572262 Henry Cohn, 2026, needs more optimization.
9 791 0.651296506682 Henry Cohn, 2026, needs more optimization.
9 792 0.651301357390 Henry Cohn, 2025, needs more optimization.
9 793 0.651428922736 Henry Cohn, 2025, needs more optimization.
9 794 0.651526523791 Henry Cohn, 2026, needs more optimization.
9 795 0.651650729064 Henry Cohn, 2025, needs more optimization.
9 796 0.651657860374 Henry Cohn, 2025, needs more optimization.
9 797 0.651682645355 Henry Cohn, 2026, needs more optimization.
9 798 0.651897804106 Henry Cohn, 2026, needs more optimization.
9 799 0.652149293163 Henry Cohn, 2026, needs more optimization.
9 800 0.652161370068 Henry Cohn, 2026, needs more optimization.
9 801 0.652216667734 Henry Cohn, 2025, needs more optimization.
9 802 0.652274223271 Henry Cohn, 2026, needs more optimization.
9 803 0.652515969238 Henry Cohn, 2026, needs more optimization.
9 804 0.652549189881 Henry Cohn, 2026, needs more optimization.
9 805 0.652557977808 Henry Cohn, 2026, needs more optimization.
9 806 0.652702137773 Henry Cohn, 2026, needs more optimization.
9 807 0.652908801011 Henry Cohn, 2025, needs more optimization.
9 808 0.652955833314 Henry Cohn, 2026, needs more optimization.
9 809 0.653154055619 Henry Cohn, 2025, needs more optimization.
9 810 0.653167528053 Henry Cohn, 2026, needs more optimization.
9 811 0.653233776655 Henry Cohn, 2026, needs more optimization.
9 812 0.653369918581 Henry Cohn, 2025, needs more optimization.
9 813 0.653464181862 Henry Cohn, 2026, needs more optimization.
9 814 0.653677664001 Henry Cohn, 2026, needs more optimization.
9 815 0.653808986185 Henry Cohn, 2026, needs more optimization.
9 816 0.653818231082 Henry Cohn, 2025, needs more optimization.
9 817 0.653848628627 Henry Cohn, 2026, needs more optimization.
9 818 0.653919993720 Henry Cohn, 2026, needs more optimization.
9 819 0.654181938332 Henry Cohn, 2026, needs more optimization.
9 820 0.654189110499 Henry Cohn, 2026, needs more optimization.
9 821 0.654222384679 Henry Cohn, 2025, needs more optimization.
9 822 0.654258849453 Henry Cohn, 2025, needs more optimization.
9 823 0.654389441086 Henry Cohn, 2026, needs more optimization.
9 824 0.654468550447 Henry Cohn, 2025, needs more optimization.
9 825 0.654613358049 Henry Cohn, 2026, needs more optimization.
9 826 0.654819846122 Henry Cohn, 2026, needs more optimization.
9 827 0.654998406963 Henry Cohn, 2026, needs more optimization.
9 828 0.655004842296 Henry Cohn, 2025, needs more optimization.
9 829 0.655218926120 Henry Cohn, 2026, needs more optimization.
9 830 0.655442763615 Henry Cohn, 2025, needs more optimization.
9 831 0.655452949080 Henry Cohn, 2025, needs more optimization.
9 832 0.655463034710 Henry Cohn, 2026, needs more optimization.
9 833 0.655676995760 Henry Cohn, 2026, needs more optimization.
9 834 0.655681418143 Henry Cohn, 2026, needs more optimization.
9 835 0.655843661133 Henry Cohn, 2026, needs more optimization.
9 836 0.655868714138 Henry Cohn, 2026, needs more optimization.
9 837 0.656262456101 Henry Cohn, 2025, needs more optimization.
9 838 0.656288861246 Henry Cohn, 2026, needs more optimization.
9 839 0.656360663883 Henry Cohn, 2026, needs more optimization.
9 840 0.656565559996 Henry Cohn, 2025, needs more optimization.
9 842 0.656810400690 Henry Cohn, 2026, needs more optimization.
9 843 0.657094679486 Henry Cohn, 2025, needs more optimization.
9 844 0.657098253250 Henry Cohn, 2025, needs more optimization.
9 845 0.657205808161 Henry Cohn, 2026, needs more optimization.
9 846 0.657393872630 Henry Cohn, 2025, needs more optimization.
9 847 0.657414562303 Henry Cohn, 2026, needs more optimization.
9 848 0.657418448672 Henry Cohn, 2025, needs more optimization.
9 849 0.657451067624 Henry Cohn, 2025, needs more optimization.
9 850 0.657531881331 Henry Cohn, 2025, needs more optimization.
9 851 0.657751538905 Henry Cohn, 2025, needs more optimization.
9 852 0.657805663087 Henry Cohn, 2026, needs more optimization.
9 853 0.657806090386 Henry Cohn, 2026, needs more optimization.
9 854 0.657813045189 Henry Cohn, 2026, needs more optimization.
9 855 0.658000690184 Henry Cohn, 2026, needs more optimization.
9 856 0.658328451121 Henry Cohn, 2025, needs more optimization.
9 857 0.658388148399 Henry Cohn, 2026, needs more optimization.
9 858 0.658604634171 Henry Cohn, 2026, needs more optimization.
9 859 0.658611693231 Henry Cohn, 2026, needs more optimization.
9 861 0.658835417154 Henry Cohn, 2026, needs more optimization.
9 862 0.659031437873 Henry Cohn, 2025, needs more optimization.
9 863 0.659046632503 Henry Cohn, 2025, needs more optimization.
9 864 0.659261179677 Henry Cohn, 2025, needs more optimization.
9 865 0.659346409902 Henry Cohn, 2025, needs more optimization.
9 866 0.659356134011 Henry Cohn, 2025, needs more optimization.
9 867 0.659595134719 Henry Cohn, 2025, needs more optimization.
9 868 0.659605999850 Henry Cohn, 2025, needs more optimization.
9 869 0.659633383665 Henry Cohn, 2025, needs more optimization.
9 870 0.659782748322 Henry Cohn, 2026, needs more optimization.
9 871 0.659787821052 Henry Cohn, 2026, needs more optimization.
9 872 0.660017704676 Henry Cohn, 2026, needs more optimization.
9 873 0.660130318815 Henry Cohn, 2026, needs more optimization.
9 874 0.660230563294 Henry Cohn, 2026, needs more optimization.
9 875 0.660491797414 Henry Cohn, 2026, needs more optimization.
9 876 0.660497979113 Henry Cohn, 2026, needs more optimization.
9 877 0.660503958980 Henry Cohn, 2025, needs more optimization.
9 878 0.660528229665 Henry Cohn, 2026, needs more optimization.
9 879 0.660587138431 Henry Cohn, 2026, needs more optimization.
9 880 0.660632906756 Henry Cohn, 2026, needs more optimization.
9 881 0.660977096392 Henry Cohn, 2026, needs more optimization.
9 882 0.661023469661 Henry Cohn, 2026, needs more optimization.
9 883 0.661036789071 Henry Cohn, 2026, needs more optimization.
9 884 0.661155559221 Henry Cohn, 2026, needs more optimization.
9 885 0.661241996052 Henry Cohn, 2025, needs more optimization.
9 886 0.661245073071 Henry Cohn, 2025, needs more optimization.
9 887 0.661290839841 Henry Cohn, 2026, needs more optimization.
9 888 0.661647282768 Henry Cohn, 2026, needs more optimization.
9 889 0.661694799853 Henry Cohn, 2026, needs more optimization.
9 890 0.661734238751 Henry Cohn, 2026, needs more optimization.
9 891 0.661744138180 Henry Cohn, 2026, needs more optimization.
9 892 0.661934946059 Henry Cohn, 2026, needs more optimization.
9 893 0.661989531975 Henry Cohn, 2026, needs more optimization.
9 894 0.662032980058 Henry Cohn, 2026, needs more optimization.
9 895 0.662247016230 Henry Cohn, 2025, needs more optimization.
9 896 0.662283643031 Henry Cohn, 2026, needs more optimization.
9 897 0.662309815641 Henry Cohn, 2026, needs more optimization.
9 898 0.662524539542 Henry Cohn, 2026, needs more optimization.
9 899 0.662537919598 Henry Cohn, 2025, needs more optimization.
9 900 0.662636126846 Henry Cohn, 2025, needs more optimization.
9 901 0.662642382986 Henry Cohn, 2025, needs more optimization.
9 902 0.663087337091 Henry Cohn, 2026, needs more optimization.
9 903 0.663138760502 Henry Cohn, 2026, needs more optimization.
9 904 0.663151783688 Henry Cohn, 2025, needs more optimization.
9 905 0.663184166271 Henry Cohn, 2026, needs more optimization.
9 906 0.663321732544 Henry Cohn, 2025, needs more optimization.
9 907 0.663375383331 Henry Cohn, 2026, needs more optimization.
9 908 0.663412535064 Henry Cohn, 2026, needs more optimization.
9 909 0.663582763222 Henry Cohn, 2026, needs more optimization.
9 910 0.663640087295 Henry Cohn, 2026, needs more optimization.
9 911 0.663880013046 Henry Cohn, 2026, needs more optimization.
9 912 0.663891728453 Henry Cohn, 2026, needs more optimization.
9 913 0.663892753724 Henry Cohn, 2026, needs more optimization.
9 914 0.663907227269 Henry Cohn, 2026, needs more optimization.
9 915 0.664017810781 Henry Cohn, 2026, needs more optimization.
9 916 0.664221329263 Henry Cohn, 2026, needs more optimization.
9 917 0.664227497870 Henry Cohn, 2026, needs more optimization.
9 918 0.664316325074 Henry Cohn, 2026, needs more optimization.
9 919 0.664694543885 Henry Cohn, 2025, needs more optimization.
9 920 0.664707746199 Henry Cohn, 2026, needs more optimization.
9 921 0.664729861899 Henry Cohn, 2025, needs more optimization.
9 922 0.665008783421 Henry Cohn, 2025, needs more optimization.
9 923 0.665050102315 Henry Cohn, 2026, needs more optimization.
9 924 0.665085819662 Henry Cohn, 2026, needs more optimization.
9 925 0.665334306282 Henry Cohn, 2026, needs more optimization.
9 926 0.665358156161 Henry Cohn, 2026, needs more optimization.
9 927 0.665376436975 Henry Cohn, 2026, needs more optimization.
9 928 0.665655225021 Henry Cohn, 2025, needs more optimization.
9 929 0.665658867246 Henry Cohn, 2025, needs more optimization.
9 930 0.665736024728 Henry Cohn, 2026, needs more optimization.
9 931 0.666042254133 Henry Cohn, 2026, needs more optimization.
9 932 0.666231956226 Henry Cohn, 2026, needs more optimization.
9 933 0.666344124923 Henry Cohn, 2026, needs more optimization.
9 934 0.666553416310 Henry Cohn, 2026, needs more optimization.
9 935 0.666663195995 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 0.210550138817 Henry Cohn, 2025.
10 45 0.210753585520 Henry Cohn, 2025.
10 46 0.210850169054 Henry Cohn, 2025.
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 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 0.253695768464 Henry Cohn, 2024.
10 60 0.254730982571 Henry Cohn, 2026.
10 63 0.257944905339 Henry Cohn, 2025.
10 64 0.260558294031 Henry Cohn, 2026, needs more optimization.
10 65 0.264885834877 Henry Cohn, 2025.
10 66 0.265168946762 Henry Cohn, 2025.
10 67 0.268064425530 Henry Cohn, 2025.
10 68 0.269390887696 Henry Cohn, 2026, needs more optimization.
10 69 0.269775337251 Henry Cohn, 2026, needs more optimization.
10 70 0.271729029641 Henry Cohn, 2026, needs more optimization.
10 71 0.271905044086 Henry Cohn, 2026, needs more optimization.
10 72 0.274448309623 Henry Cohn, 2026, needs more optimization.
10 73 0.275987133320 Henry Cohn, 2025.
10 74 0.279604561566 Henry Cohn, 2025.
10 76 0.284096667917 Henry Cohn, 2025.
10 77 0.284910960402 Henry Cohn, 2025.
10 78 0.289897948557 Henry Cohn, 2026.
10 79 0.295299509598 Henry Cohn, 2026, needs more optimization.
10 80 0.299108514820 Henry Cohn, 2026, needs more optimization.
10 81 0.301784416185 Henry Cohn, 2026, needs more optimization.
10 82 0.304464263561 Henry Cohn, 2026, needs more optimization.
10 83 0.308260062052 Henry Cohn, 2026, needs more optimization.
10 84 0.311152230093 Henry Cohn, 2026, needs more optimization.
10 85 0.318255786436 Henry Cohn, 2026, needs more optimization.
10 86 0.322961942252 Henry Cohn, 2026, needs more optimization.
10 87 0.323798687008 Henry Cohn, 2026, needs more optimization.
10 88 0.324407524635 Henry Cohn, 2026, needs more optimization.
10 89 0.324779870327 Henry Cohn, 2026, needs more optimization.
10 90 0.325480249188 Henry Cohn, 2026, needs more optimization.
10 91 0.326611883339 Henry Cohn, 2026, needs more optimization.
10 92 0.328560709595 Henry Cohn, 2026, needs more optimization.
10 93 0.329063708307 Henry Cohn, 2026, needs more optimization.
10 94 0.329784568962 Henry Cohn, 2026, needs more optimization.
10 95 0.329854854198 Henry Cohn, 2025, needs more optimization.
10 96 0.330315697732 Henry Cohn, 2025, needs more optimization.
10 97 0.330623955280 Henry Cohn, 2026, needs more optimization.
10 98 0.330715006309 Henry Cohn, 2026, needs more optimization.
10 99 0.330884838125 Henry Cohn, 2026, needs more optimization.
10 100 0.331093369801 Henry Cohn, 2026, needs more optimization.
10 101 0.331208860419 Henry Cohn, 2026, needs more optimization.
10 102 0.331404553045 Henry Cohn, 2026, needs more optimization.
10 103 0.333258404202 Henry Cohn, 2025, needs more optimization.
10 104 0.333261975589 Henry Cohn, 2025, needs more optimization.
10 105 0.333276446551 Henry Cohn, 2025, needs more optimization.
10 107 0.333327625778 Henry Cohn, 2023, needs more optimization.
10 108 0.333329834036 Henry Cohn, 2023, needs more optimization.
10 109 0.335269304285 Henry Cohn, 2026, needs more optimization.
10 110 0.339665962344 Henry Cohn, 2026, needs more optimization.
10 111 0.342369261176 Henry Cohn, 2024, needs more optimization.
10 112 0.347037575649 Henry Cohn, 2023, needs more optimization.
10 113 0.348033782060 Henry Cohn, 2026, needs more optimization.
10 114 0.350518184001 Henry Cohn, 2026, needs more optimization.
10 115 0.352629567807 Henry Cohn, 2023, needs more optimization.
10 116 0.354011173451 Henry Cohn, 2026, needs more optimization.
10 117 0.360196526935 Henry Cohn, 2026, needs more optimization.
10 118 0.362483350895 Henry Cohn, 2026, needs more optimization.
10 119 0.363780154338 Henry Cohn, 2026, needs more optimization.
10 120 0.364675140118 Henry Cohn, 2026, needs more optimization.
10 121 0.365330574232 Henry Cohn, 2026, needs more optimization.
10 122 0.365464158252 Henry Cohn, 2026, needs more optimization.
10 123 0.365550207038 Henry Cohn, 2026, needs more optimization.
10 124 0.365550207044 Henry Cohn, 2026, needs more optimization.
10 125 0.365553853153 Henry Cohn, 2026, needs more optimization.
10 126 0.365563082891 Henry Cohn, 2026, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367843527953 Henry Cohn, 2026, needs more optimization.
10 129 0.370543052593 Henry Cohn, 2026, needs more optimization.
10 130 0.371247320309 Henry Cohn, 2026, needs more optimization.
10 131 0.371343753631 Henry Cohn, 2026, needs more optimization.
10 132 0.371409895415 Henry Cohn, 2026, needs more optimization.
10 133 0.385290000731 Henry Cohn, 2026, needs more optimization.
10 134 0.390086321049 Henry Cohn, 2026, needs more optimization.
10 135 0.392361953682 Henry Cohn, 2026, needs more optimization.
10 136 0.393476980357 Henry Cohn, 2026, needs more optimization.
10 137 0.396218518613 Henry Cohn, 2026, needs more optimization.
10 138 0.398651390978 Henry Cohn, 2026, needs more optimization.
10 139 0.400282439529 Henry Cohn, 2026, needs more optimization.
10 140 0.401787414255 Henry Cohn, 2026, needs more optimization.
10 141 0.403139490794 Henry Cohn, 2026, needs more optimization.
10 142 0.404397831501 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 0.413330114587 Henry Cohn, 2026, needs more optimization.
10 158 0.414341440809 Henry Cohn, 2026, needs more optimization.
10 159 0.415368955508 Henry Cohn, 2026, needs more optimization.
10 160 0.416899871465 Henry Cohn, 2026, needs more optimization.
10 161 0.417719534741 Henry Cohn, 2026, needs more optimization.
10 162 0.419439435006 Henry Cohn, 2026, needs more optimization.
10 163 0.419845846073 Henry Cohn, 2026, needs more optimization.
10 164 0.420594116242 Henry Cohn, 2026, needs more optimization.
10 165 0.421680629361 Henry Cohn, 2026, needs more optimization.
10 166 0.422486778390 Henry Cohn, 2026, needs more optimization.
10 167 0.423433552928 Henry Cohn, 2026, needs more optimization.
10 168 0.424392647086 Henry Cohn, 2026, needs more optimization.
10 169 0.425571935807 Henry Cohn, 2026, needs more optimization.
10 170 0.426224622819 Henry Cohn, 2026, needs more optimization.
10 171 0.427212004198 Henry Cohn, 2026, needs more optimization.
10 172 0.428496444999 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 0.438709439537 Henry Cohn, 2026, needs more optimization.
10 196 0.441243501882 Henry Cohn, 2026, needs more optimization.
10 197 0.443967343602 Henry Cohn, 2026, needs more optimization.
10 198 0.445553629705 Henry Cohn, 2026, needs more optimization.
10 199 0.447436717225 Henry Cohn, 2026, needs more optimization.
10 200 0.448481363416 Henry Cohn, 2026, needs more optimization.
10 201 0.449694739964 Henry Cohn, 2026, needs more optimization.
10 202 0.450529250281 Henry Cohn, 2026, needs more optimization.
10 203 0.452093688195 Henry Cohn, 2026, needs more optimization.
10 204 0.452721486138 Henry Cohn, 2026, needs more optimization.
10 205 0.453801832819 Henry Cohn, 2026, needs more optimization.
10 206 0.454861996257 Henry Cohn, 2026, needs more optimization.
10 207 0.456083226069 Henry Cohn, 2026, needs more optimization.
10 208 0.456936082730 Henry Cohn, 2026, needs more optimization.
10 209 0.457680820251 Henry Cohn, 2026, needs more optimization.
10 210 0.458850276228 Henry Cohn, 2026, needs more optimization.
10 211 0.459005550930 Henry Cohn, 2026, needs more optimization.
10 212 0.459497297349 Henry Cohn, 2026, needs more optimization.
10 213 0.460512036881 Henry Cohn, 2026, needs more optimization.
10 214 0.461002115929 Henry Cohn, 2026, needs more optimization.
10 215 0.462055765080 Henry Cohn, 2026, needs more optimization.
10 216 0.462876052471 Henry Cohn, 2026, needs more optimization.
10 217 0.463467203832 Henry Cohn, 2026, needs more optimization.
10 218 0.464495108128 Henry Cohn, 2026, needs more optimization.
10 219 0.464732264947 Henry Cohn, 2026, needs more optimization.
10 220 0.465421004402 Henry Cohn, 2026, needs more optimization.
10 221 0.466023267826 Henry Cohn, 2026, needs more optimization.
10 222 0.466764527412 Henry Cohn, 2026, needs more optimization.
10 223 0.467869465014 Henry Cohn, 2026, needs more optimization.
10 224 0.469073054854 Henry Cohn, 2026, needs more optimization.
10 225 0.469583006463 Henry Cohn, 2026, needs more optimization.
10 226 0.470434749719 Henry Cohn, 2026, needs more optimization.
10 227 0.470553137344 Henry Cohn, 2026, needs more optimization.
10 228 0.471384365227 Henry Cohn, 2026, needs more optimization.
10 229 0.471989199412 Henry Cohn, 2026, needs more optimization.
10 230 0.472162401928 Henry Cohn, 2026, needs more optimization.
10 231 0.472977583642 Henry Cohn, 2026, needs more optimization.
10 232 0.473539168082 Henry Cohn, 2026, needs more optimization.
10 233 0.474197855360 Henry Cohn, 2026, needs more optimization.
10 234 0.474838547550 Henry Cohn, 2026, needs more optimization.
10 235 0.475447411104 Henry Cohn, 2026, needs more optimization.
10 236 0.475673532407 Henry Cohn, 2026, needs more optimization.
10 237 0.476380944779 Henry Cohn, 2026, needs more optimization.
10 238 0.476799182540 Henry Cohn, 2026, needs more optimization.
10 239 0.477315070247 Henry Cohn, 2026, needs more optimization.
10 240 0.477981578139 Henry Cohn, 2026, needs more optimization.
10 241 0.478585529655 Henry Cohn, 2026, needs more optimization.
10 242 0.478815174563 Henry Cohn, 2026, needs more optimization.
10 243 0.479627627918 Henry Cohn, 2026, needs more optimization.
10 244 0.480086378940 Henry Cohn, 2026, needs more optimization.
10 245 0.480566468734 Henry Cohn, 2026, needs more optimization.
10 246 0.480774383974 Henry Cohn, 2026, needs more optimization.
10 247 0.481633203634 Henry Cohn, 2026, needs more optimization.
10 248 0.482075091394 Henry Cohn, 2026, needs more optimization.
10 249 0.482325592361 Henry Cohn, 2026, needs more optimization.
10 250 0.482729587567 Henry Cohn, 2026, needs more optimization.
10 251 0.483506878311 Henry Cohn, 2026, needs more optimization.
10 252 0.483896744548 Henry Cohn, 2026, needs more optimization.
10 253 0.484252687157 Henry Cohn, 2026, needs more optimization.
10 254 0.484823559891 Henry Cohn, 2026, needs more optimization.
10 255 0.485429598749 Henry Cohn, 2026, needs more optimization.
10 256 0.485586206383 Henry Cohn, 2026, needs more optimization.
10 257 0.486421235755 Henry Cohn, 2026, needs more optimization.
10 258 0.486765477266 Henry Cohn, 2026, needs more optimization.
10 259 0.486921926091 Henry Cohn, 2026, needs more optimization.
10 260 0.487130149433 Henry Cohn, 2026, needs more optimization.
10 261 0.487866345301 Henry Cohn, 2026, needs more optimization.
10 262 0.488010638917 Henry Cohn, 2026, needs more optimization.
10 263 0.488151735700 Henry Cohn, 2026, needs more optimization.
10 264 0.488264807789 Henry Cohn, 2026, needs more optimization.
10 265 0.488896264651 Henry Cohn, 2026, needs more optimization.
10 266 0.488946955579 Henry Cohn, 2026, needs more optimization.
10 267 0.489025212635 Henry Cohn, 2026, needs more optimization.
10 268 0.489035726104 Henry Cohn, 2026, needs more optimization.
10 269 0.489303349360 Henry Cohn, 2026, needs more optimization.
10 270 0.489529602023 Henry Cohn, 2026, needs more optimization.
10 271 0.490330414180 Henry Cohn, 2026, needs more optimization.
10 272 0.491170991695 Henry Cohn, 2026, needs more optimization.
10 273 0.491823319110 Henry Cohn, 2026, needs more optimization.
10 274 0.492524491247 Henry Cohn, 2026, needs more optimization.
10 275 0.492955302214 Henry Cohn, 2026, needs more optimization.
10 276 0.493608150761 Henry Cohn, 2026, needs more optimization.
10 277 0.493971430003 Henry Cohn, 2026, needs more optimization.
10 278 0.494362379438 Henry Cohn, 2026, needs more optimization.
10 279 0.494779766514 Henry Cohn, 2026, needs more optimization.
10 280 0.495215118237 Henry Cohn, 2026, needs more optimization.
10 281 0.495545922303 Henry Cohn, 2026, needs more optimization.
10 282 0.495978120641 Henry Cohn, 2026, needs more optimization.
10 283 0.496351927774 Henry Cohn, 2026, needs more optimization.
10 284 0.496801495945 Henry Cohn, 2026, needs more optimization.
10 285 0.497294395516 Henry Cohn, 2026, needs more optimization.
10 286 0.497459311151 Henry Cohn, 2026, needs more optimization.
10 287 0.497647335877 Henry Cohn, 2026, needs more optimization.
10 288 0.498091769281 Henry Cohn, 2026, needs more optimization.
10 289 0.498295800531 Henry Cohn, 2026, needs more optimization.
10 290 0.498647707934 Henry Cohn, 2026, needs more optimization.
10 291 0.499030763153 Henry Cohn, 2026, needs more optimization.
10 292 0.499452550184 Henry Cohn, 2026, needs more optimization.
10 293 0.499682098835 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 0.529313788325 Henry Cohn, 2026, needs more optimization.
10 512 0.532482681462 Henry Cohn, 2026, needs more optimization.
10 513 0.532937321731 Henry Cohn, 2026, needs more optimization.
10 514 0.534530943434 Henry Cohn, 2026, needs more optimization.
10 515 0.535498226265 Henry Cohn, 2026, needs more optimization.
10 516 0.537142804872 Henry Cohn, 2026, needs more optimization.
10 517 0.538476486280 Henry Cohn, 2026, needs more optimization.
10 518 0.539468980091 Henry Cohn, 2026, needs more optimization.
10 519 0.540625024351 Henry Cohn, 2026, needs more optimization.
10 520 0.541359299555 Henry Cohn, 2026, needs more optimization.
10 521 0.542387446634 Henry Cohn, 2026, needs more optimization.
10 522 0.543382562178 Henry Cohn, 2026, needs more optimization.
10 523 0.543843839915 Henry Cohn, 2026, needs more optimization.
10 524 0.544595814617 Henry Cohn, 2026, needs more optimization.
10 525 0.545430202242 Henry Cohn, 2026, needs more optimization.
10 526 0.546161671713 Henry Cohn, 2026, needs more optimization.
10 527 0.546726387753 Henry Cohn, 2026, needs more optimization.
10 528 0.547554055065 Henry Cohn, 2026, needs more optimization.
10 529 0.548200636752 Henry Cohn, 2026, needs more optimization.
10 530 0.548948996512 Henry Cohn, 2026, needs more optimization.
10 531 0.549553818988 Henry Cohn, 2026, needs more optimization.
10 532 0.549837989518 Henry Cohn, 2026, needs more optimization.
10 533 0.550565343595 Henry Cohn, 2026, needs more optimization.
10 534 0.551057819115 Henry Cohn, 2026, needs more optimization.
10 535 0.551471689238 Henry Cohn, 2026, needs more optimization.
10 536 0.552196170252 Henry Cohn, 2026, needs more optimization.
10 537 0.552743815083 Henry Cohn, 2026, needs more optimization.
10 538 0.553504561757 Henry Cohn, 2026, needs more optimization.
10 539 0.553729417059 Henry Cohn, 2026, needs more optimization.
10 540 0.554153259455 Henry Cohn, 2026, needs more optimization.
10 541 0.554598380421 Henry Cohn, 2026, needs more optimization.
10 542 0.555272704173 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 0.567879432830 Henry Cohn, 2026, needs more optimization.
10 773 0.570037614498 Henry Cohn, 2026, needs more optimization.
10 774 0.571081908435 Henry Cohn, 2026, needs more optimization.
10 775 0.572672491525 Henry Cohn, 2026, needs more optimization.
10 776 0.572845273843 Henry Cohn, 2026, needs more optimization.
10 778 0.573302457128 Henry Cohn, 2026, needs more optimization.
10 779 0.573464379228 Henry Cohn, 2026, needs more optimization.
10 780 0.573904979718 Henry Cohn, 2026, needs more optimization.
10 781 0.574193603648 Henry Cohn, 2026, needs more optimization.
10 782 0.574512896400 Henry Cohn, 2026, needs more optimization.
10 783 0.574541464999 Henry Cohn, 2026, needs more optimization.
10 784 0.575183404971 Henry Cohn, 2026, needs more optimization.
10 785 0.575732700572 Henry Cohn, 2026, needs more optimization.
10 786 0.576446001614 Henry Cohn, 2026, needs more optimization.
10 787 0.576783735663 Henry Cohn, 2026, needs more optimization.
10 788 0.577201402166 Henry Cohn, 2026, needs more optimization.
10 789 0.577635473124 Henry Cohn, 2026, needs more optimization.
10 790 0.577942986400 Henry Cohn, 2026, needs more optimization.
10 791 0.578430015898 Henry Cohn, 2026, needs more optimization.
10 792 0.578950765224 Henry Cohn, 2026, needs more optimization.
10 793 0.579177131099 Henry Cohn, 2026, needs more optimization.
10 794 0.579803576339 Henry Cohn, 2026, needs more optimization.
10 795 0.580119045570 Henry Cohn, 2026, needs more optimization.
10 797 0.580599397204 Henry Cohn, 2026, needs more optimization.
10 798 0.580713207213 Henry Cohn, 2026, needs more optimization.
10 799 0.582072136794 Henry Cohn, 2026, needs more optimization.
10 800 0.582242618725 Henry Cohn, 2026, needs more optimization.
10 801 0.583241667548 Henry Cohn, 2026, needs more optimization.
10 804 0.583760573490 Henry Cohn, 2026, needs more optimization.
10 805 0.584306498950 Henry Cohn, 2026, needs more optimization.
10 806 0.584492511797 Henry Cohn, 2026, needs more optimization.
10 807 0.584567947622 Henry Cohn, 2026, needs more optimization.
10 808 0.584606221846 Henry Cohn, 2026, needs more optimization.
10 809 0.584962108286 Henry Cohn, 2026, needs more optimization.
10 810 0.585403454250 Henry Cohn, 2026, needs more optimization.
10 811 0.585510106653 Henry Cohn, 2026, needs more optimization.
10 814 0.585629764392 Henry Cohn, 2026, needs more optimization.
10 815 0.585698434656 Henry Cohn, 2026, needs more optimization.
10 816 0.585844659288 Henry Cohn, 2026, needs more optimization.
10 817 0.586365840898 Henry Cohn, 2026, needs more optimization.
10 818 0.586714101802 Henry Cohn, 2026, needs more optimization.
10 820 0.586869335636 Henry Cohn, 2026, needs more optimization.
10 821 0.586937655518 Henry Cohn, 2026, needs more optimization.
10 822 0.587195723304 Henry Cohn, 2026, needs more optimization.
10 823 0.587450075707 Henry Cohn, 2026, needs more optimization.
10 824 0.588042947054 Henry Cohn, 2026, needs more optimization.
10 826 0.588174063605 Henry Cohn, 2026, needs more optimization.
10 827 0.588473979801 Henry Cohn, 2026, needs more optimization.
10 828 0.588648961363 Henry Cohn, 2026, needs more optimization.
10 829 0.588987485676 Henry Cohn, 2026, needs more optimization.
10 830 0.589333182456 Henry Cohn, 2026, needs more optimization.
10 831 0.589397546523 Henry Cohn, 2026, needs more optimization.
10 832 0.589661266454 Henry Cohn, 2026, needs more optimization.
10 833 0.589969578010 Henry Cohn, 2026, needs more optimization.
10 834 0.590352040140 Henry Cohn, 2026, needs more optimization.
10 835 0.590682232508 Henry Cohn, 2026, needs more optimization.
10 836 0.590852599131 Henry Cohn, 2026, needs more optimization.
10 837 0.591030888582 Henry Cohn, 2026, needs more optimization.
10 843 0.591205324988 Henry Cohn, 2026, needs more optimization.
10 844 0.591318856594 Henry Cohn, 2026, needs more optimization.
10 845 0.591319324997 Henry Cohn, 2026, needs more optimization.
10 846 0.591560025069 Henry Cohn, 2026, needs more optimization.
10 847 0.591655126527 Henry Cohn, 2026, needs more optimization.
10 848 0.591886844379 Henry Cohn, 2026, needs more optimization.
10 849 0.592129670761 Henry Cohn, 2026, needs more optimization.
10 850 0.592219266885 Henry Cohn, 2026, needs more optimization.
10 851 0.592235979391 Henry Cohn, 2026, needs more optimization.
10 853 0.592630131517 Henry Cohn, 2026, needs more optimization.
10 854 0.592760272232 Henry Cohn, 2026, needs more optimization.
10 855 0.592809292561 Henry Cohn, 2026, needs more optimization.
10 856 0.593043154050 Henry Cohn, 2026, needs more optimization.
10 857 0.593145507623 Henry Cohn, 2026, needs more optimization.
10 858 0.593485318056 Henry Cohn, 2026, needs more optimization.
10 859 0.593610476607 Henry Cohn, 2026, needs more optimization.
10 860 0.594039079151 Henry Cohn, 2026, needs more optimization.
10 861 0.594098381380 Henry Cohn, 2026, needs more optimization.
10 862 0.594338161087 Henry Cohn, 2026, needs more optimization.
10 863 0.594574921741 Henry Cohn, 2026, needs more optimization.
10 864 0.594687771344 Henry Cohn, 2026, needs more optimization.
10 867 0.594833312992 Henry Cohn, 2026, needs more optimization.
10 869 0.594968121057 Henry Cohn, 2026, needs more optimization.
10 872 0.594984409228 Henry Cohn, 2026, needs more optimization.
10 873 0.595193445237 Henry Cohn, 2026, needs more optimization.
10 874 0.595335667209 Henry Cohn, 2026, needs more optimization.
10 875 0.595459074522 Henry Cohn, 2026, needs more optimization.
10 876 0.595811303428 Henry Cohn, 2026, needs more optimization.
10 877 0.595833110230 Henry Cohn, 2026, needs more optimization.
10 878 0.596021534813 Henry Cohn, 2026, needs more optimization.
10 879 0.596022967129 Henry Cohn, 2026, needs more optimization.
10 880 0.596116413261 Henry Cohn, 2026, needs more optimization.
10 881 0.596319244435 Henry Cohn, 2026, needs more optimization.
10 882 0.596573491223 Henry Cohn, 2026, needs more optimization.
10 883 0.596718552662 Henry Cohn, 2026, needs more optimization.
10 884 0.596857402843 Henry Cohn, 2026, needs more optimization.
10 885 0.596944198936 Henry Cohn, 2026, needs more optimization.
10 886 0.597014472221 Henry Cohn, 2026, needs more optimization.
10 887 0.597047496220 Henry Cohn, 2026, needs more optimization.
10 888 0.597203344886 Henry Cohn, 2026, needs more optimization.
10 889 0.597263166153 Henry Cohn, 2026, needs more optimization.
10 896 0.597311859714 Henry Cohn, 2026, needs more optimization.
10 897 0.597478626924 Henry Cohn, 2026, needs more optimization.
10 898 0.597618530079 Henry Cohn, 2026, needs more optimization.
10 899 0.597797641355 Henry Cohn, 2026, needs more optimization.
10 900 0.597819493411 Henry Cohn, 2026, needs more optimization.
10 902 0.597922285142 Henry Cohn, 2026, needs more optimization.
10 903 0.598034202318 Henry Cohn, 2026, needs more optimization.
10 905 0.598147353443 Henry Cohn, 2026, needs more optimization.
10 906 0.598200548087 Henry Cohn, 2026, needs more optimization.
10 907 0.598332097393 Henry Cohn, 2026, needs more optimization.
10 908 0.598354947897 Henry Cohn, 2026, needs more optimization.
10 909 0.598395314958 Henry Cohn, 2026, needs more optimization.
10 911 0.598399874533 Henry Cohn, 2026, needs more optimization.
10 912 0.598480021360 Henry Cohn, 2026, needs more optimization.
10 914 0.598644279309 Henry Cohn, 2026, needs more optimization.
10 915 0.598703884300 Henry Cohn, 2026, needs more optimization.
10 916 0.598790357057 Henry Cohn, 2026, needs more optimization.
10 917 0.599133261035 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 0.204931262058 Henry Cohn, 2025.
11 51 0.204957387535 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
11 52 0.208005237402 Henry Cohn, 2024.
11 53 0.209775126698 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.
11 70 0.244726315701 Henry Cohn, 2026.
11 71 0.255919437719 Henry Cohn, 2026, needs more optimization.
11 72 0.256477843138 Henry Cohn, 2026, needs more optimization.
11 73 0.259177844497 Henry Cohn, 2026, needs more optimization.
11 74 0.259418448087 Henry Cohn, 2026, needs more optimization.
11 75 0.259732970444 Henry Cohn, 2026, needs more optimization.
11 76 0.260611782278 Henry Cohn, 2026, needs more optimization.
11 77 0.260659717349 Henry Cohn, 2026, needs more optimization.
11 78 0.260823410840 Henry Cohn, 2026, needs more optimization.
11 79 0.261256567266 Henry Cohn, 2026, needs more optimization.
11 80 0.261313611563 Henry Cohn, 2026, needs more optimization.
11 81 0.262008277852 Henry Cohn, 2026, needs more optimization.
11 82 0.263455942165 Henry Cohn, 2026, needs more optimization.
11 83 0.264198463434 Henry Cohn, 2026, needs more optimization.
11 84 0.265230263115 Henry Cohn, 2026, needs more optimization.
11 85 0.266218308143 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 0.280653491593 Henry Cohn, 2026, needs more optimization.
11 93 0.281719231974 Henry Cohn, 2026, needs more optimization.
11 94 0.282962812797 Henry Cohn, 2026, needs more optimization.
11 95 0.283938928367 Henry Cohn, 2026, needs more optimization.
11 96 0.285631420356 Henry Cohn, 2026, needs more optimization.
11 97 0.286255983593 Henry Cohn, 2026, needs more optimization.
11 98 0.287807016108 Henry Cohn, 2026, needs more optimization.
11 99 0.289831202843 Henry Cohn, 2026, needs more optimization.
11 100 0.299916029374 Henry Cohn, 2026, needs more optimization.
11 101 0.302929489511 Henry Cohn, 2026, needs more optimization.
11 102 0.304471825431 Henry Cohn, 2026, needs more optimization.
11 103 0.305756497969 Henry Cohn, 2026, needs more optimization.
11 104 0.306554011452 Henry Cohn, 2026, needs more optimization.
11 105 0.307098305054 Henry Cohn, 2026, needs more optimization.
11 106 0.307737954219 Henry Cohn, 2026, needs more optimization.
11 107 0.310786210625 Henry Cohn, 2026, needs more optimization.
11 108 0.317734326003 Henry Cohn, 2026, needs more optimization.
11 109 0.320412997083 Henry Cohn, 2026, needs more optimization.
11 110 0.321720197391 Henry Cohn, 2026, needs more optimization.
11 111 0.323862359645 Henry Cohn, 2026, needs more optimization.
11 112 0.324893580560 Henry Cohn, 2026, needs more optimization.
11 113 0.325064953334 Henry Cohn, 2026, needs more optimization.
11 114 0.325267864652 Henry Cohn, 2026, needs more optimization.
11 115 0.325412321402 Henry Cohn, 2026, needs more optimization.
11 116 0.325687792754 Henry Cohn, 2026, needs more optimization.
11 117 0.325913410900 Henry Cohn, 2026, needs more optimization.
11 118 0.326109011732 Henry Cohn, 2026, needs more optimization.
11 119 0.326373144328 Henry Cohn, 2026, needs more optimization.
11 120 0.326580746251 Henry Cohn, 2026, needs more optimization.
11 121 0.326847196383 Henry Cohn, 2026, needs more optimization.
11 122 0.327076280459 Henry Cohn, 2026, needs more optimization.
11 123 0.328161428278 Henry Cohn, 2026, needs more optimization.
11 124 0.328656833607 Henry Cohn, 2026, needs more optimization.
11 125 0.332602117631 Henry Cohn, 2026, needs more optimization.
11 126 0.332737064046 Henry Cohn, 2026, needs more optimization.
11 127 0.332908701031 Henry Cohn, 2026, needs more optimization.
11 128 0.333030047873 Henry Cohn, 2026, needs more optimization.
11 129 0.333205495741 Henry Cohn, 2026, needs more optimization.
11 130 0.333276029314 Henry Cohn, 2024, needs more optimization.
11 131 0.333319651971 Henry Cohn, 2026, needs more optimization.
11 132 0.333329701451 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 0.361630937422 Henry Cohn, 2026, needs more optimization.
11 158 0.366397797208 Henry Cohn, 2026, needs more optimization.
11 159 0.368577368410 Henry Cohn, 2026, needs more optimization.
11 160 0.371916368993 Henry Cohn, 2026, needs more optimization.
11 161 0.373303691468 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 0.387129126358 Henry Cohn, 2026, needs more optimization.
11 168 0.389144844342 Henry Cohn, 2026, needs more optimization.
11 169 0.390142039413 Henry Cohn, 2026, needs more optimization.
11 170 0.391448614267 Henry Cohn, 2026, needs more optimization.
11 172 0.392005839963 Henry Cohn, 2026, needs more optimization.
11 173 0.392240684230 Henry Cohn, 2026, needs more optimization.
11 174 0.392787733447 Henry Cohn, 2026, needs more optimization.
11 175 0.393623647013 Henry Cohn, 2026, needs more optimization.
11 176 0.394006755440 Henry Cohn, 2026, needs more optimization.
11 177 0.394295007446 Henry Cohn, 2026, needs more optimization.
11 178 0.394679752627 Henry Cohn, 2026, needs more optimization.
11 179 0.395494708029 Henry Cohn, 2026, needs more optimization.
11 180 0.395844925983 Henry Cohn, 2026, needs more optimization.
11 181 0.396178133935 Henry Cohn, 2026, needs more optimization.
11 182 0.396912796538 Henry Cohn, 2026, needs more optimization.
11 183 0.397403817336 Henry Cohn, 2026, needs more optimization.
11 184 0.397779288436 Henry Cohn, 2026, needs more optimization.
11 185 0.398636633114 Henry Cohn, 2026, needs more optimization.
11 186 0.399296822298 Henry Cohn, 2026, needs more optimization.
11 187 0.400687829283 Henry Cohn, 2026, needs more optimization.
11 188 0.401470057316 Henry Cohn, 2026, needs more optimization.
11 189 0.402343107224 Henry Cohn, 2026, needs more optimization.
11 190 0.403086926571 Henry Cohn, 2026, needs more optimization.
11 191 0.403720651282 Henry Cohn, 2026, needs more optimization.
11 192 0.403776436879 Henry Cohn, 2026, needs more optimization.
11 193 0.404374927657 Henry Cohn, 2026, needs more optimization.
11 194 0.404786773949 Henry Cohn, 2026, needs more optimization.
11 195 0.404900192101 Henry Cohn, 2026, needs more optimization.
11 196 0.407042981894 Henry Cohn, 2026, needs more optimization.
11 197 0.408235998788 Henry Cohn, 2026, needs more optimization.
11 198 0.409579218902 Henry Cohn, 2026, needs more optimization.
11 199 0.410366826855 Henry Cohn, 2026, needs more optimization.
11 200 0.410534703098 Henry Cohn, 2026, needs more optimization.
11 201 0.411042633265 Henry Cohn, 2026, needs more optimization.
11 202 0.411728345252 Henry Cohn, 2026, needs more optimization.
11 203 0.412155139559 Henry Cohn, 2026, needs more optimization.
11 204 0.412964194155 Henry Cohn, 2026, needs more optimization.
11 205 0.413254502021 Henry Cohn, 2026, needs more optimization.
11 206 0.413994797891 Henry Cohn, 2026, needs more optimization.
11 207 0.414145522921 Henry Cohn, 2026, needs more optimization.
11 208 0.414301134074 Henry Cohn, 2026, needs more optimization.
11 209 0.414793061121 Henry Cohn, 2026, needs more optimization.
11 210 0.415183505955 Henry Cohn, 2026, needs more optimization.
11 211 0.415522535332 Henry Cohn, 2026, needs more optimization.
11 212 0.416172021243 Henry Cohn, 2026, needs more optimization.
11 213 0.416642746252 Henry Cohn, 2026, needs more optimization.
11 214 0.417361530838 Henry Cohn, 2026, needs more optimization.
11 215 0.417930974678 Henry Cohn, 2026, needs more optimization.
11 216 0.418478858479 Henry Cohn, 2026, needs more optimization.
11 217 0.418802717440 Henry Cohn, 2026, needs more optimization.
11 218 0.419795134924 Henry Cohn, 2026, needs more optimization.
11 219 0.420159041152 Henry Cohn, 2026, needs more optimization.
11 220 0.420747325708 Henry Cohn, 2026, needs more optimization.
11 221 0.421090553670 Henry Cohn, 2026, needs more optimization.
11 222 0.421867941749 Henry Cohn, 2026, needs more optimization.
11 223 0.422308149279 Henry Cohn, 2026, needs more optimization.
11 224 0.422973289760 Henry Cohn, 2026, needs more optimization.
11 225 0.423309361542 Henry Cohn, 2026, needs more optimization.
11 226 0.423614038854 Henry Cohn, 2026, needs more optimization.
11 227 0.423771196426 Henry Cohn, 2026, needs more optimization.
11 228 0.424275873663 Henry Cohn, 2026, needs more optimization.
11 229 0.424446981791 Henry Cohn, 2026, needs more optimization.
11 230 0.425108488309 Henry Cohn, 2026, needs more optimization.
11 231 0.425452466489 Henry Cohn, 2026, needs more optimization.
11 232 0.425745164593 Henry Cohn, 2026, needs more optimization.
11 233 0.425938995729 Henry Cohn, 2026, needs more optimization.
11 234 0.426278827701 Henry Cohn, 2026, needs more optimization.
11 235 0.426733276267 Henry Cohn, 2026, needs more optimization.
11 236 0.426985620390 Henry Cohn, 2026, needs more optimization.
11 237 0.427270021733 Henry Cohn, 2026, needs more optimization.
11 238 0.427623337596 Henry Cohn, 2026, needs more optimization.
11 239 0.427918108521 Henry Cohn, 2026, needs more optimization.
11 240 0.428485958290 Henry Cohn, 2026, needs more optimization.
11 241 0.428899378945 Henry Cohn, 2026, needs more optimization.
11 242 0.429138872108 Henry Cohn, 2026, needs more optimization.
11 243 0.429627142599 Henry Cohn, 2026, needs more optimization.
11 244 0.430193487433 Henry Cohn, 2026, needs more optimization.
11 245 0.430432683005 Henry Cohn, 2026, needs more optimization.
11 246 0.430804963342 Henry Cohn, 2026, needs more optimization.
11 247 0.430852073654 Henry Cohn, 2026, needs more optimization.
11 248 0.431568183836 Henry Cohn, 2026, needs more optimization.
11 249 0.432406895783 Henry Cohn, 2026, needs more optimization.
11 250 0.433210624199 Henry Cohn, 2026, needs more optimization.
11 251 0.433762683999 Henry Cohn, 2026, needs more optimization.
11 252 0.434440815745 Henry Cohn, 2026, needs more optimization.
11 253 0.435850263707 Henry Cohn, 2026, needs more optimization.
11 254 0.437718076606 Henry Cohn, 2026, needs more optimization.
11 255 0.437858488632 Henry Cohn, 2026, needs more optimization.
11 256 0.438576028356 Henry Cohn, 2026, needs more optimization.
11 257 0.438603967406 Henry Cohn, 2026, needs more optimization.
11 258 0.438700898596 Henry Cohn, 2026, needs more optimization.
11 259 0.438829085513 Henry Cohn, 2026, needs more optimization.
11 261 0.438905180194 Henry Cohn, 2026, needs more optimization.
11 262 0.439085178112 Henry Cohn, 2026, needs more optimization.
11 263 0.439206756212 Henry Cohn, 2026, needs more optimization.
11 264 0.439573812563 Henry Cohn, 2026, needs more optimization.
11 265 0.439641951500 Henry Cohn, 2026, needs more optimization.
11 266 0.439689828105 Henry Cohn, 2026, needs more optimization.
11 267 0.439734100868 Henry Cohn, 2026, needs more optimization.
11 269 0.439810483743 Henry Cohn, 2026, needs more optimization.
11 270 0.439913484543 Henry Cohn, 2026, needs more optimization.
11 271 0.439934139961 Henry Cohn, 2026, needs more optimization.
11 272 0.440007855236 Henry Cohn, 2026, needs more optimization.
11 273 0.440341087280 Henry Cohn, 2026, needs more optimization.
11 274 0.440421644744 Henry Cohn, 2026, needs more optimization.
11 275 0.440533044057 Henry Cohn, 2026, needs more optimization.
11 276 0.440763037059 Henry Cohn, 2026, needs more optimization.
11 277 0.441106008217 Henry Cohn, 2026, needs more optimization.
11 278 0.441376731698 Henry Cohn, 2026, needs more optimization.
11 279 0.441568590074 Henry Cohn, 2026, needs more optimization.
11 280 0.441955516603 Henry Cohn, 2026, needs more optimization.
11 281 0.442498744228 Henry Cohn, 2026, needs more optimization.
11 283 0.442753869906 Henry Cohn, 2026, needs more optimization.
11 284 0.443024967025 Henry Cohn, 2026, needs more optimization.
11 285 0.443573763675 Henry Cohn, 2026, needs more optimization.
11 286 0.444109188055 Henry Cohn, 2026, needs more optimization.
11 287 0.444196051248 Henry Cohn, 2026, needs more optimization.
11 288 0.444766566191 Henry Cohn, 2026, needs more optimization.
11 289 0.445150354888 Henry Cohn, 2026, needs more optimization.
11 290 0.445402012752 Henry Cohn, 2026, needs more optimization.
11 291 0.446229949092 Henry Cohn, 2026, needs more optimization.
11 292 0.447157700560 Henry Cohn, 2026, needs more optimization.
11 293 0.447849180862 Henry Cohn, 2026, needs more optimization.
11 294 0.448448727116 Henry Cohn, 2026, needs more optimization.
11 295 0.450598258337 Henry Cohn, 2026, needs more optimization.
11 296 0.451500481431 Henry Cohn, 2026, needs more optimization.
11 297 0.452272890613 Henry Cohn, 2026, needs more optimization.
11 298 0.453745383501 Henry Cohn, 2026, needs more optimization.
11 299 0.454267648714 Henry Cohn, 2026, needs more optimization.
11 300 0.455250351004 Henry Cohn, 2026, needs more optimization.
11 301 0.455775597588 Henry Cohn, 2026, needs more optimization.
11 302 0.460192657659 Henry Cohn, 2026, needs more optimization.
11 303 0.460288477586 Henry Cohn, 2025, needs more optimization.
11 304 0.460862225321 Henry Cohn, 2026, needs more optimization.
11 305 0.461268830255 Henry Cohn, 2025, needs more optimization.
11 306 0.461690942609 Henry Cohn, 2026, needs more optimization.
11 307 0.462044048096 Henry Cohn, 2025, needs more optimization.
11 308 0.462383050078 Henry Cohn, 2026, needs more optimization.
11 309 0.462994444527 Henry Cohn, 2025, needs more optimization.
11 310 0.463544165000 Henry Cohn, 2025, needs more optimization.
11 311 0.463659643751 Henry Cohn, 2025, needs more optimization.
11 312 0.464359894912 Henry Cohn, 2026, needs more optimization.
11 313 0.464976892208 Henry Cohn, 2025, needs more optimization.
11 314 0.465026251850 Henry Cohn, 2026, needs more optimization.
11 315 0.465715320515 Henry Cohn, 2025, needs more optimization.
11 316 0.465897384515 Henry Cohn, 2026, needs more optimization.
11 317 0.465904310823 Henry Cohn, 2025, needs more optimization.
11 318 0.466067712918 Henry Cohn, 2026, needs more optimization.
11 319 0.466267282465 Henry Cohn, 2025, needs more optimization.
11 320 0.467028400033 Henry Cohn, 2026, needs more optimization.
11 321 0.467258854327 Henry Cohn, 2025, needs more optimization.
11 322 0.467503068269 Henry Cohn, 2026, needs more optimization.
11 323 0.468182878263 Henry Cohn, 2025, needs more optimization.
11 324 0.470460066007 Henry Cohn, 2026, needs more optimization.
11 325 0.471201521874 Henry Cohn, 2025, needs more optimization.
11 326 0.471690828070 Henry Cohn, 2026, needs more optimization.
11 327 0.471894887006 Henry Cohn, 2025, needs more optimization.
11 328 0.472633915840 Henry Cohn, 2026, needs more optimization.
11 329 0.472833096322 Henry Cohn, 2025, needs more optimization.
11 330 0.473096478358 Henry Cohn, 2026, needs more optimization.
11 331 0.473467506404 Henry Cohn, 2025, needs more optimization.
11 332 0.473850864192 Henry Cohn, 2026, needs more optimization.
11 333 0.473871803646 Henry Cohn, 2025, needs more optimization.
11 334 0.474236401896 Henry Cohn, 2025, needs more optimization.
11 335 0.474719431936 Henry Cohn, 2025, needs more optimization.
11 336 0.474724651842 Henry Cohn, 2026, needs more optimization.
11 337 0.475243110879 Henry Cohn, 2025, needs more optimization.
11 338 0.475606236134 Henry Cohn, 2026, needs more optimization.
11 339 0.475701250198 Henry Cohn, 2025, needs more optimization.
11 340 0.475915208916 Henry Cohn, 2026, needs more optimization.
11 341 0.476285444701 Henry Cohn, 2025, needs more optimization.
11 342 0.476352958676 Henry Cohn, 2026, needs more optimization.
11 343 0.476618421655 Henry Cohn, 2025, needs more optimization.
11 344 0.476716590023 Henry Cohn, 2026, needs more optimization.
11 345 0.476956469542 Henry Cohn, 2025, needs more optimization.
11 346 0.477294178606 Henry Cohn, 2026, needs more optimization.
11 347 0.478281760346 Henry Cohn, 2025, needs more optimization.
11 348 0.478297176307 Henry Cohn, 2026, needs more optimization.
11 349 0.479176122649 Henry Cohn, 2025, needs more optimization.
11 350 0.479203737767 Henry Cohn, 2026, needs more optimization.
11 351 0.479489173418 Henry Cohn, 2025, needs more optimization.
11 352 0.479982048056 Henry Cohn, 2025, needs more optimization.
11 353 0.480077140051 Henry Cohn, 2025, needs more optimization.
11 354 0.480174630259 Henry Cohn, 2026, needs more optimization.
11 355 0.480436888208 Henry Cohn, 2025, needs more optimization.
11 356 0.480487166888 Henry Cohn, 2025, needs more optimization.
11 357 0.480842494444 Henry Cohn, 2025, needs more optimization.
11 358 0.480888841970 Henry Cohn, 2026, needs more optimization.
11 359 0.481274495959 Henry Cohn, 2025, needs more optimization.
11 360 0.481291506240 Henry Cohn, 2025, needs more optimization.
11 361 0.481741529691 Henry Cohn, 2025, needs more optimization.
11 362 0.481989034025 Henry Cohn, 2026, needs more optimization.
11 363 0.482103941912 Henry Cohn, 2025, needs more optimization.
11 364 0.482276232393 Henry Cohn, 2026, needs more optimization.
11 365 0.482303853060 Henry Cohn, 2025, needs more optimization.
11 366 0.482497122627 Henry Cohn, 2026, needs more optimization.
11 367 0.483057849632 Henry Cohn, 2025, needs more optimization.
11 368 0.483246288551 Henry Cohn, 2026, needs more optimization.
11 369 0.483262726267 Henry Cohn, 2025, needs more optimization.
11 370 0.483583948555 Henry Cohn, 2025, needs more optimization.
11 371 0.483706899316 Henry Cohn, 2025, needs more optimization.
11 372 0.483716473185 Henry Cohn, 2026, needs more optimization.
11 373 0.484043235518 Henry Cohn, 2025, needs more optimization.
11 374 0.484092087038 Henry Cohn, 2026, needs more optimization.
11 376 0.484538913691 Henry Cohn, 2026, needs more optimization.
11 378 0.485140048196 Henry Cohn, 2026, needs more optimization.
11 379 0.485977589895 Henry Cohn, 2025, needs more optimization.
11 380 0.485977720696 Henry Cohn, 2026, needs more optimization.
11 381 0.486020085020 Henry Cohn, 2025, needs more optimization.
11 382 0.486040770663 Henry Cohn, 2025, needs more optimization.
11 383 0.486097954624 Henry Cohn, 2025, needs more optimization.
11 384 0.486113457975 Henry Cohn, 2026, needs more optimization.
11 385 0.486126091016 Henry Cohn, 2025, needs more optimization.
11 386 0.486360236976 Henry Cohn, 2026, needs more optimization.
11 387 0.486469389022 Henry Cohn, 2025, needs more optimization.
11 388 0.486486010528 Henry Cohn, 2025, needs more optimization.
11 389 0.486579853534 Henry Cohn, 2025, needs more optimization.
11 390 0.486582656635 Henry Cohn, 2026, needs more optimization.
11 392 0.487378958415 Henry Cohn, 2026, needs more optimization.
11 393 0.487401897134 Henry Cohn, 2025, needs more optimization.
11 394 0.487409887893 Henry Cohn, 2025, needs more optimization.
11 395 0.487417126467 Henry Cohn, 2025, needs more optimization.
11 396 0.487482175882 Henry Cohn, 2026, needs more optimization.
11 397 0.488352351257 Henry Cohn, 2026, needs more optimization.
11 398 0.488404349101 Henry Cohn, 2026, needs more optimization.
11 400 0.488675285089 Henry Cohn, 2026, needs more optimization.
11 402 0.490196056384 Henry Cohn, 2026, needs more optimization.
11 403 0.490210887455 Henry Cohn, 2025, needs more optimization.
11 404 0.490239534679 Henry Cohn, 2025, needs more optimization.
11 405 0.490253634370 Henry Cohn, 2025, needs more optimization.
11 406 0.491130227765 Henry Cohn, 2026, needs more optimization.
11 408 0.491614827339 Henry Cohn, 2026, needs more optimization.
11 409 0.491734488110 Henry Cohn, 2025, needs more optimization.
11 410 0.492445043192 Henry Cohn, 2026, needs more optimization.
11 411 0.492513511025 Henry Cohn, 2025, needs more optimization.
11 412 0.492596937457 Henry Cohn, 2026, needs more optimization.
11 414 0.492650825965 Henry Cohn, 2026, needs more optimization.
11 415 0.492734383686 Henry Cohn, 2026, needs more optimization.
11 416 0.492812844913 Henry Cohn, 2026, needs more optimization.
11 417 0.492828395878 Henry Cohn, 2025, needs more optimization.
11 418 0.492948724087 Henry Cohn, 2026, needs more optimization.
11 419 0.493274992243 Henry Cohn, 2026, needs more optimization.
11 421 0.493916610675 Henry Cohn, 2026, needs more optimization.
11 422 0.493945089141 Henry Cohn, 2025, needs more optimization.
11 423 0.493970791475 Henry Cohn, 2025, needs more optimization.
11 424 0.493985756792 Henry Cohn, 2025, needs more optimization.
11 425 0.494037829338 Henry Cohn, 2025, needs more optimization.
11 426 0.494051876349 Henry Cohn, 2025, needs more optimization.
11 427 0.494082410490 Henry Cohn, 2026, needs more optimization.
11 429 0.494119524472 Henry Cohn, 2026, needs more optimization.
11 430 0.494207621254 Henry Cohn, 2026, needs more optimization.
11 431 0.494208897310 Henry Cohn, 2026, needs more optimization.
11 432 0.494214749693 Henry Cohn, 2026, needs more optimization.
11 434 0.494311598236 Henry Cohn, 2025, needs more optimization.
11 435 0.494313766122 Henry Cohn, 2025, needs more optimization.
11 436 0.494531349276 Henry Cohn, 2026, needs more optimization.
11 438 0.494865572262 Henry Cohn, 2025, needs more optimization.
11 439 0.494939689263 Henry Cohn, 2026, needs more optimization.
11 440 0.495001803697 Henry Cohn, 2025, needs more optimization.
11 441 0.495208013246 Henry Cohn, 2025, needs more optimization.
11 442 0.495240503799 Henry Cohn, 2026, needs more optimization.
11 443 0.495240503803 Henry Cohn, 2026, needs more optimization.
11 445 0.496354649532 Henry Cohn, 2026, needs more optimization.
11 446 0.496423782539 Henry Cohn, 2025, needs more optimization.
11 454 0.496499610859 Henry Cohn, 2026, needs more optimization.
11 455 0.496508114731 Henry Cohn, 2026, needs more optimization.
11 456 0.496517169073 Henry Cohn, 2026, needs more optimization.
11 457 0.496524167338 Henry Cohn, 2026, needs more optimization.
11 458 0.496592601188 Henry Cohn, 2026, needs more optimization.
11 459 0.496660396715 Henry Cohn, 2026, needs more optimization.
11 460 0.496951851616 Henry Cohn, 2026, needs more optimization.
11 461 0.497315230015 Henry Cohn, 2026, needs more optimization.
11 462 0.497402030874 Henry Cohn, 2026, needs more optimization.
11 463 0.497537485225 Henry Cohn, 2026, needs more optimization.
11 464 0.497707827952 Henry Cohn, 2026, needs more optimization.
11 465 0.497962433687 Henry Cohn, 2026, needs more optimization.
11 466 0.497988264619 Henry Cohn, 2026, needs more optimization.
11 467 0.498106928931 Henry Cohn, 2026, needs more optimization.
11 468 0.498329875719 Henry Cohn, 2026, needs more optimization.
11 469 0.498381790957 Henry Cohn, 2026, needs more optimization.
11 470 0.498485035615 Henry Cohn, 2026, needs more optimization.
11 471 0.498558722677 Henry Cohn, 2026, needs more optimization.
11 472 0.498898532612 Henry Cohn, 2026, needs more optimization.
11 473 0.499072820930 Henry Cohn, 2026, needs more optimization.
11 474 0.499080847543 Henry Cohn, 2026, needs more optimization.
11 475 0.499177555032 Henry Cohn, 2026, needs more optimization.
11 476 0.499235658393 Henry Cohn, 2026, needs more optimization.
11 477 0.499356987778 Henry Cohn, 2026, needs more optimization.
11 478 0.499715608344 Henry Cohn, 2026, needs more optimization.
11 479 0.499729766170 Henry Cohn, 2026, needs more optimization.
11 480 0.499807577818 Henry Cohn, 2026, needs more optimization.
11 481 0.499939897604 Henry Cohn, 2026, needs more optimization.
11 593 0.499999989608 A. Novikov, N. Vu, M. Eisenberger, E. Dupont, P.-S. Huang, A. Z. Wagner, S. Shirobokov, B. Kozlovskii, F. J. R. Ruiz, A. Mehrabian, M. P. Kumar, A. See, S. Chaudhuri, G. Holland, A. Davies, S. Nowozin, P. Kohli, and M. Balog, AlphaEvolve: A coding agent for scientific and algorithmic discovery, Google DeepMind white paper, 2025, after some further optimization.
11 594 0.500141289029 Ilmari Vahteristo, 2026.
11 595 0.500925697544 Ilmari Vahteristo, 2026.
11 596 0.501441454208 Henry Cohn, 2026, needs more optimization.
11 597 0.520255490104 Henry Cohn, 2025, needs more optimization.
11 598 0.520285971454 Henry Cohn, 2026, needs more optimization.
11 600 0.520405377653 Henry Cohn, 2026, needs more optimization.
11 602 0.520958515128 Henry Cohn, 2026, needs more optimization.
11 604 0.521043245819 Henry Cohn, 2026, needs more optimization.
11 606 0.521184748058 Henry Cohn, 2026, needs more optimization.
11 608 0.521425128897 Henry Cohn, 2026, needs more optimization.
11 609 0.521600438331 Henry Cohn, 2026, needs more optimization.
11 610 0.521853428711 Henry Cohn, 2026, needs more optimization.
11 611 0.521854890548 Henry Cohn, 2025, needs more optimization.
11 612 0.523617017905 Henry Cohn, 2026, needs more optimization.
11 614 0.523744504132 Henry Cohn, 2026, needs more optimization.
11 616 0.523839473739 Henry Cohn, 2026, needs more optimization.
11 618 0.523989391604 Henry Cohn, 2026, needs more optimization.
11 620 0.524033456003 Henry Cohn, 2026, needs more optimization.
11 622 0.524058891940 Henry Cohn, 2026, needs more optimization.
11 623 0.524096196647 Henry Cohn, 2025, needs more optimization.
11 624 0.525155603305 Henry Cohn, 2026, needs more optimization.
11 626 0.525218734855 Henry Cohn, 2026, needs more optimization.
11 628 0.525283801910 Henry Cohn, 2026, needs more optimization.
11 630 0.525522374852 Henry Cohn, 2026, needs more optimization.
11 631 0.525682491562 Henry Cohn, 2025, needs more optimization.
11 632 0.525941594293 Henry Cohn, 2026, needs more optimization.
11 633 0.527485789217 Henry Cohn, 2025, needs more optimization.
11 634 0.527520865245 Henry Cohn, 2026, needs more optimization.
11 636 0.527549701492 Henry Cohn, 2026, needs more optimization.
11 637 0.527569511004 Henry Cohn, 2025, needs more optimization.
11 638 0.528782436687 Henry Cohn, 2026, needs more optimization.
11 640 0.528850538035 Henry Cohn, 2026, needs more optimization.
11 642 0.529121716864 Henry Cohn, 2026, needs more optimization.
11 644 0.529185588858 Henry Cohn, 2026, needs more optimization.
11 646 0.529279865757 Henry Cohn, 2026, needs more optimization.
11 647 0.530846594391 Henry Cohn, 2025, needs more optimization.
11 648 0.530881393746 Henry Cohn, 2026, needs more optimization.
11 649 0.531044621234 Henry Cohn, 2025, needs more optimization.
11 650 0.531073068385 Henry Cohn, 2026, needs more optimization.
11 652 0.532332389863 Henry Cohn, 2026, needs more optimization.
11 654 0.532366976431 Henry Cohn, 2026, needs more optimization.
11 656 0.532386749828 Henry Cohn, 2026, needs more optimization.
11 657 0.532392160573 Henry Cohn, 2025, needs more optimization.
11 658 0.532394056432 Henry Cohn, 2026, needs more optimization.
11 659 0.532467715439 Henry Cohn, 2025, needs more optimization.
11 660 0.532683682665 Henry Cohn, 2026, needs more optimization.
11 662 0.534382259437 Henry Cohn, 2026, needs more optimization.
11 663 0.534422746084 Henry Cohn, 2025, needs more optimization.
11 664 0.535698338176 Henry Cohn, 2026, needs more optimization.
11 665 0.535702593944 Henry Cohn, 2025, needs more optimization.
11 666 0.535705528207 Henry Cohn, 2026, needs more optimization.
11 667 0.535746493888 Henry Cohn, 2025, needs more optimization.
11 668 0.536717879016 Henry Cohn, 2026, needs more optimization.
11 669 0.536758892961 Henry Cohn, 2025, needs more optimization.
11 670 0.536780315419 Henry Cohn, 2026, needs more optimization.
11 672 0.536789415949 Henry Cohn, 2026, needs more optimization.
11 673 0.536806501096 Henry Cohn, 2025, needs more optimization.
11 674 0.539045252006 Henry Cohn, 2026, needs more optimization.
11 678 0.539137574051 Henry Cohn, 2026, needs more optimization.
11 679 0.539314255561 Henry Cohn, 2026, needs more optimization.
11 680 0.539330726828 Henry Cohn, 2026, needs more optimization.
11 681 0.539565443765 Henry Cohn, 2026, needs more optimization.
11 682 0.541582375258 Henry Cohn, 2026, needs more optimization.
11 683 0.541618940674 Henry Cohn, 2025, needs more optimization.
11 684 0.541626134008 Henry Cohn, 2026, needs more optimization.
11 686 0.541652564397 Henry Cohn, 2026, needs more optimization.
11 687 0.541917098259 Henry Cohn, 2025, needs more optimization.
11 688 0.542939046711 Henry Cohn, 2026, needs more optimization.
11 690 0.543023508841 Henry Cohn, 2026, needs more optimization.
11 692 0.543069833915 Henry Cohn, 2026, needs more optimization.
11 693 0.543266949617 Henry Cohn, 2026, needs more optimization.
11 694 0.545955087139 Henry Cohn, 2026, needs more optimization.
11 695 0.545958643601 Henry Cohn, 2026, needs more optimization.
11 696 0.546017681485 Henry Cohn, 2026, needs more optimization.
11 697 0.546037295528 Henry Cohn, 2026, needs more optimization.
11 698 0.546903607132 Henry Cohn, 2026, needs more optimization.
11 699 0.546910821915 Henry Cohn, 2026, needs more optimization.
11 700 0.546970395971 Henry Cohn, 2026, needs more optimization.
11 701 0.547096089307 Henry Cohn, 2026, needs more optimization.
11 702 0.549143958357 Henry Cohn, 2026, needs more optimization.
11 703 0.550237672454 Henry Cohn, 2026, needs more optimization.
11 704 0.550609210994 Henry Cohn, 2026, needs more optimization.
11 705 0.550840491602 Henry Cohn, 2026, needs more optimization.
11 706 0.551099415000 Henry Cohn, 2026, needs more optimization.
11 707 0.551243083167 Henry Cohn, 2026, needs more optimization.
11 708 0.551428326567 Henry Cohn, 2026, needs more optimization.
11 709 0.551646934396 Henry Cohn, 2026, needs more optimization.
11 710 0.551795950756 Henry Cohn, 2026, needs more optimization.
11 711 0.552028085616 Henry Cohn, 2026, needs more optimization.
11 712 0.552161515032 Henry Cohn, 2026, needs more optimization.
11 713 0.552306280882 Henry Cohn, 2026, needs more optimization.
11 714 0.552519375391 Henry Cohn, 2026, needs more optimization.
11 715 0.552749290562 Henry Cohn, 2026, needs more optimization.
11 716 0.552975357980 Henry Cohn, 2026, needs more optimization.
11 717 0.553200107219 Henry Cohn, 2026, needs more optimization.
11 718 0.553397382647 Henry Cohn, 2026, needs more optimization.
11 719 0.553586129079 Henry Cohn, 2026, needs more optimization.
11 720 0.553781399919 Henry Cohn, 2026, needs more optimization.
11 721 0.553899127605 Henry Cohn, 2026, needs more optimization.
11 722 0.554108948073 Henry Cohn, 2026, needs more optimization.
11 723 0.554235721644 Henry Cohn, 2026, needs more optimization.
11 724 0.554462712741 Henry Cohn, 2026, needs more optimization.
11 725 0.554618834877 Henry Cohn, 2026, needs more optimization.
11 726 0.554823880422 Henry Cohn, 2026, needs more optimization.
11 727 0.555054152097 Henry Cohn, 2026, needs more optimization.
11 728 0.555345816733 Henry Cohn, 2026, needs more optimization.
11 729 0.555537938147 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 0.560846309520 Henry Cohn, 2026, needs more optimization.
11 984 0.588842803390 Henry Cohn, 2026, needs more optimization.
11 985 0.589065237636 Henry Cohn, 2026, needs more optimization.
11 986 0.589074288260 Henry Cohn, 2026, needs more optimization.
11 987 0.589333322167 Henry Cohn, 2026, needs more optimization.
11 988 0.589474269186 Henry Cohn, 2026, needs more optimization.
11 989 0.589482576433 Henry Cohn, 2026, needs more optimization.
11 990 0.589483899310 Henry Cohn, 2026, needs more optimization.
11 991 0.589721431077 Henry Cohn, 2026, needs more optimization.
11 992 0.589729337081 Henry Cohn, 2026, needs more optimization.
11 993 0.589746793340 Henry Cohn, 2026, needs more optimization.
11 994 0.589775579041 Henry Cohn, 2026, needs more optimization.
11 995 0.589926808863 Henry Cohn, 2026, needs more optimization.
11 996 0.589929252049 Henry Cohn, 2026, needs more optimization.
11 997 0.590217455898 Henry Cohn, 2025, needs more optimization.
11 998 0.590283232759 Henry Cohn, 2026, needs more optimization.
11 999 0.590289818313 Henry Cohn, 2026, needs more optimization.
11 1000 0.590342544738 Henry Cohn, 2026, needs more optimization.
11 1001 0.590361195019 Henry Cohn, 2026, needs more optimization.
11 1002 0.590628709920 Henry Cohn, 2025, needs more optimization.
11 1003 0.590659823164 Henry Cohn, 2025, needs more optimization.
11 1004 0.590674113006 Henry Cohn, 2026, needs more optimization.
11 1005 0.590845424995 Henry Cohn, 2026, needs more optimization.
11 1006 0.590979127066 Henry Cohn, 2026, needs more optimization.
11 1007 0.591020937710 Henry Cohn, 2026, needs more optimization.
11 1008 0.591238716992 Henry Cohn, 2026, needs more optimization.
11 1009 0.591281113006 Henry Cohn, 2026, needs more optimization.
11 1010 0.591399096240 Henry Cohn, 2026, needs more optimization.
11 1011 0.591405377429 Henry Cohn, 2025, needs more optimization.
11 1012 0.591437856314 Henry Cohn, 2026, needs more optimization.
11 1013 0.591619911381 Henry Cohn, 2026, needs more optimization.
11 1014 0.591652512963 Henry Cohn, 2026, needs more optimization.
11 1015 0.591878012420 Henry Cohn, 2026, needs more optimization.
11 1016 0.591904113557 Henry Cohn, 2026, needs more optimization.
11 1017 0.591908369313 Henry Cohn, 2026, needs more optimization.
11 1018 0.592152389992 Henry Cohn, 2026, needs more optimization.
11 1019 0.592163433490 Henry Cohn, 2026, needs more optimization.
11 1020 0.592205871152 Henry Cohn, 2026, needs more optimization.
11 1021 0.592231154376 Henry Cohn, 2026, needs more optimization.
11 1022 0.592579532885 Henry Cohn, 2026, needs more optimization.
11 1023 0.592590665440 Henry Cohn, 2026, needs more optimization.
11 1024 0.592628472863 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 0.187411648808 Henry Cohn, 2025.
12 54 0.189746662791 Henry Cohn, 2024.
12 55 0.193319611131 Henry Cohn, 2025.
12 56 0.200925636261 Henry Cohn, 2025.
12 57 0.201958116645 Henry Cohn, 2025.
12 58 0.203749632752 Henry Cohn, 2025.
12 59 0.205147720753 Henry Cohn, 2025.
12 60 0.207643910372 Henry Cohn, 2026, needs more optimization.
12 61 0.211404126394 Henry Cohn, 2025.
12 62 0.213688242265 Henry Cohn, 2025.
12 63 0.213962909655 Henry Cohn, 2026, needs more optimization.
12 64 0.214090056231 Henry Cohn, 2026, needs more optimization.
12 65 0.214410531368 Henry Cohn, 2026, needs more optimization.
12 66 0.215064206569 Henry Cohn, 2026, needs more optimization.
12 67 0.220118787411 Henry Cohn, 2026, needs more optimization.
12 68 0.220696215390 Henry Cohn, 2026.
12 69 0.225802384453 Henry Cohn, 2026, needs more optimization.
12 70 0.228644883302 Henry Cohn, 2026, needs more optimization.
12 71 0.232255775950 Henry Cohn, 2025.
12 72 0.233344424897 Henry Cohn, 2026.
12 73 0.234628823173 Henry Cohn, 2026, needs more optimization.
12 74 0.235166207807 Henry Cohn, 2026, needs more optimization.
12 75 0.236566179190 Henry Cohn, 2026, needs more optimization.
12 76 0.237336218342 Henry Cohn, 2025.
12 77 0.237968057446 Henry Cohn, 2025.
12 78 0.241648057068 Henry Cohn, 2025.
12 79 0.243234050771 Henry Cohn, 2025.
12 80 0.247423220389 Henry Cohn, 2026, needs more optimization.
12 81 0.25 C. Ma, T. T. Zhaowei, 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
12 82 0.255753795402 Henry Cohn, 2026, needs more optimization.
12 83 0.258657193037 Henry Cohn, 2026, needs more optimization.
12 84 0.259079120305 Henry Cohn, 2026, needs more optimization.
12 85 0.260700618907 Henry Cohn, 2026, needs more optimization.
12 86 0.261584332921 Henry Cohn, 2026, needs more optimization.
12 87 0.261666113899 Henry Cohn, 2026, needs more optimization.
12 88 0.261873213364 Henry Cohn, 2026, needs more optimization.
12 89 0.262198886446 Henry Cohn, 2026, needs more optimization.
12 90 0.262685089966 Henry Cohn, 2026, needs more optimization.
12 91 0.263153154395 Henry Cohn, 2026, needs more optimization.
12 92 0.263539603169 Henry Cohn, 2026, needs more optimization.
12 93 0.264145860551 Henry Cohn, 2026, needs more optimization.
12 94 0.264787772857 Henry Cohn, 2026, needs more optimization.
12 95 0.265466972449 Henry Cohn, 2026, needs more optimization.
12 96 0.265976743015 Henry Cohn, 2026, needs more optimization.
12 97 0.266109762761 Henry Cohn, 2026, needs more optimization.
12 98 0.266808143783 Henry Cohn, 2026, needs more optimization.
12 100 0.267113377119 Henry Cohn, 2026, needs more optimization.
12 102 0.267196354918 Henry Cohn, 2026, needs more optimization.
12 103 0.269155523217 Henry Cohn, 2026, needs more optimization.
12 104 0.271860966378 Henry Cohn, 2026, needs more optimization.
12 105 0.273461339500 Henry Cohn, 2026, needs more optimization.
12 106 0.274917636997 Henry Cohn, 2026, needs more optimization.
12 107 0.276795572600 Henry Cohn, 2026, needs more optimization.
12 108 0.276965352595 Henry Cohn, 2026, needs more optimization.
12 109 0.277603311786 Henry Cohn, 2026, needs more optimization.
12 110 0.278352312623 Henry Cohn, 2026, needs more optimization.
12 111 0.278780094721 Henry Cohn, 2026, needs more optimization.
12 112 0.281101493533 Henry Cohn, 2026, needs more optimization.
12 113 0.282021066887 Henry Cohn, 2026, needs more optimization.
12 114 0.291610551004 Henry Cohn, 2026, needs more optimization.
12 115 0.292492359176 Henry Cohn, 2026, needs more optimization.
12 116 0.292850742670 Henry Cohn, 2026, needs more optimization.
12 117 0.294031290192 Henry Cohn, 2026, needs more optimization.
12 118 0.294318328878 Henry Cohn, 2026, needs more optimization.
12 121 0.294708984744 Henry Cohn, 2026, needs more optimization.
12 122 0.304154401283 Henry Cohn, 2026, needs more optimization.
12 123 0.305712625663 Henry Cohn, 2026, needs more optimization.
12 124 0.305740747326 Henry Cohn, 2026, needs more optimization.
12 125 0.305884478708 Henry Cohn, 2026, needs more optimization.
12 126 0.306637345132 Henry Cohn, 2026, needs more optimization.
12 127 0.306792319535 Henry Cohn, 2026, needs more optimization.
12 128 0.308118108015 Henry Cohn, 2026, needs more optimization.
12 129 0.309039263634 Henry Cohn, 2026, needs more optimization.
12 130 0.310042584977 Henry Cohn, 2026, needs more optimization.
12 131 0.310604397540 Henry Cohn, 2026, needs more optimization.
12 132 0.312278318395 Henry Cohn, 2026, needs more optimization.
12 133 0.314602741601 Henry Cohn, 2026, needs more optimization.
12 134 0.316445584225 Henry Cohn, 2026, needs more optimization.
12 135 0.318189744399 Henry Cohn, 2026, needs more optimization.
12 136 0.318840926164 Henry Cohn, 2026, needs more optimization.
12 137 0.320444473048 Henry Cohn, 2026, needs more optimization.
12 138 0.321868031180 Henry Cohn, 2026, needs more optimization.
12 139 0.322266997399 Henry Cohn, 2026, needs more optimization.
12 140 0.322387362910 Henry Cohn, 2026, needs more optimization.
12 141 0.322661553921 Henry Cohn, 2026, needs more optimization.
12 142 0.322936703966 Henry Cohn, 2026, needs more optimization.
12 143 0.323138043691 Henry Cohn, 2026, needs more optimization.
12 144 0.323768007807 Henry Cohn, 2026, needs more optimization.
12 145 0.323966814278 Henry Cohn, 2026, needs more optimization.
12 146 0.324331025508 Henry Cohn, 2026, needs more optimization.
12 147 0.324845364097 Henry Cohn, 2026, needs more optimization.
12 148 0.325225283163 Henry Cohn, 2026, needs more optimization.
12 149 0.325540813445 Henry Cohn, 2026, needs more optimization.
12 150 0.326790061973 Henry Cohn, 2026, needs more optimization.
12 151 0.327152196741 Henry Cohn, 2026, needs more optimization.
12 152 0.327641655930 Henry Cohn, 2026, needs more optimization.
12 153 0.328491179040 Henry Cohn, 2026, needs more optimization.
12 154 0.329005175892 Henry Cohn, 2026, needs more optimization.
12 155 0.329459602094 Henry Cohn, 2026, needs more optimization.
12 156 0.329661839906 Henry Cohn, 2026, needs more optimization.
12 157 0.329880841682 Henry Cohn, 2026, needs more optimization.
12 162 0.330019428096 Henry Cohn, 2026, needs more optimization.
12 163 0.331522338406 Henry Cohn, 2026, needs more optimization.
12 164 0.331688062371 Henry Cohn, 2026, needs more optimization.
12 165 0.332062460897 Henry Cohn, 2026, needs more optimization.
12 166 0.332679518472 Henry Cohn, 2026, needs more optimization.
12 167 0.332835294745 Henry Cohn, 2026, needs more optimization.
12 168 0.332860991124 Henry Cohn, 2026, needs more optimization.
12 169 0.332943961443 Henry Cohn, 2026, needs more optimization.
12 170 0.333013371069 Henry Cohn, 2026, needs more optimization.
12 171 0.333040658194 Henry Cohn, 2026, needs more optimization.
12 172 0.333069117050 Henry Cohn, 2026, needs more optimization.
12 173 0.333113077021 Henry Cohn, 2026, needs more optimization.
12 174 0.333166286813 Henry Cohn, 2026, needs more optimization.
12 175 0.333177015583 Henry Cohn, 2026, needs more optimization.
12 176 0.333193477401 Henry Cohn, 2026, needs more optimization.
12 177 0.333210673395 Henry Cohn, 2026, needs more optimization.
12 178 0.333243522241 Henry Cohn, 2026, needs more optimization.
12 179 0.333513639422 Henry Cohn, 2026, needs more optimization.
12 180 0.336146562269 Henry Cohn, 2026, needs more optimization.
12 181 0.344464564798 Henry Cohn, 2026, needs more optimization.
12 182 0.345968739384 Henry Cohn, 2026, needs more optimization.
12 183 0.349297837951 Henry Cohn, 2026, needs more optimization.
12 184 0.351145642701 Henry Cohn, 2026, needs more optimization.
12 185 0.352294056027 Henry Cohn, 2026, needs more optimization.
12 186 0.354383585886 Henry Cohn, 2026, needs more optimization.
12 187 0.354467608505 Henry Cohn, 2026, needs more optimization.
12 188 0.355333266111 Henry Cohn, 2026, needs more optimization.
12 189 0.355546128939 Henry Cohn, 2026, needs more optimization.
12 190 0.356784389138 Henry Cohn, 2026, needs more optimization.
12 191 0.358056123344 Henry Cohn, 2026, needs more optimization.
12 192 0.359681654804 Henry Cohn, 2026, needs more optimization.
12 193 0.361072554024 Henry Cohn, 2026, needs more optimization.
12 194 0.362209800520 Henry Cohn, 2026, needs more optimization.
12 195 0.364002573331 Henry Cohn, 2026, needs more optimization.
12 196 0.365814999174 Henry Cohn, 2026, needs more optimization.
12 197 0.366442193887 Henry Cohn, 2026, needs more optimization.
12 198 0.366479789275 Henry Cohn, 2026, needs more optimization.
12 199 0.367194691824 Henry Cohn, 2026, needs more optimization.
12 200 0.368667224605 Henry Cohn, 2026, needs more optimization.
12 201 0.368988020878 Henry Cohn, 2026, needs more optimization.
12 202 0.370200319717 Henry Cohn, 2026, needs more optimization.
12 203 0.371036411146 Henry Cohn, 2026, needs more optimization.
12 204 0.371810017800 Henry Cohn, 2026, needs more optimization.
12 205 0.373199681876 Henry Cohn, 2026, needs more optimization.
12 206 0.373883478647 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 0.378110897165 Henry Cohn, 2026, needs more optimization.
12 212 0.381290018352 Henry Cohn, 2026, needs more optimization.
12 213 0.381795264857 Henry Cohn, 2026, needs more optimization.
12 214 0.382736357354 Henry Cohn, 2026, needs more optimization.
12 215 0.382913282458 Henry Cohn, 2026, needs more optimization.
12 216 0.384007317852 Henry Cohn, 2026, needs more optimization.
12 217 0.384574981452 Henry Cohn, 2026, needs more optimization.
12 218 0.385469670402 Henry Cohn, 2026, needs more optimization.
12 219 0.386603967618 Henry Cohn, 2026, needs more optimization.
12 220 0.387210680561 Henry Cohn, 2026, needs more optimization.
12 221 0.387727395941 Henry Cohn, 2026, needs more optimization.
12 222 0.388337778609 Henry Cohn, 2026, needs more optimization.
12 223 0.388998542920 Henry Cohn, 2026, needs more optimization.
12 224 0.389489683580 Henry Cohn, 2026, needs more optimization.
12 225 0.390285221425 Henry Cohn, 2026, needs more optimization.
12 226 0.390655502867 Henry Cohn, 2026, needs more optimization.
12 227 0.391288008131 Henry Cohn, 2026, needs more optimization.
12 228 0.391392272442 Henry Cohn, 2026, needs more optimization.
12 229 0.392345408549 Henry Cohn, 2026, needs more optimization.
12 230 0.392815018982 Henry Cohn, 2026, needs more optimization.
12 231 0.393316901944 Henry Cohn, 2026, needs more optimization.
12 232 0.393564856076 Henry Cohn, 2026, needs more optimization.
12 233 0.393713712385 Henry Cohn, 2026, needs more optimization.
12 234 0.393764867445 Henry Cohn, 2026, needs more optimization.
12 235 0.394404836160 Henry Cohn, 2026, needs more optimization.
12 236 0.394751191478 Henry Cohn, 2026, needs more optimization.
12 237 0.396443750804 Henry Cohn, 2026, needs more optimization.
12 238 0.396726795406 Henry Cohn, 2026, needs more optimization.
12 239 0.397725587111 Henry Cohn, 2026, needs more optimization.
12 240 0.398783631745 Henry Cohn, 2026, needs more optimization.
12 241 0.399753215203 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
12 289 0.401524963289 Henry Cohn, 2026, needs more optimization.
12 290 0.401886182100 Henry Cohn, 2026, needs more optimization.
12 291 0.406428946037 Henry Cohn, 2026, needs more optimization.
12 292 0.407300537869 Henry Cohn, 2026, needs more optimization.
12 293 0.409580705125 Henry Cohn, 2026, needs more optimization.
12 294 0.410797725394 Henry Cohn, 2026, needs more optimization.
12 295 0.414538692872 Henry Cohn, 2026, needs more optimization.
12 296 0.416295551198 Henry Cohn, 2026, needs more optimization.
12 297 0.417881692055 Henry Cohn, 2026, needs more optimization.
12 298 0.418638288776 Henry Cohn, 2026, needs more optimization.
12 299 0.419385940827 Henry Cohn, 2026, needs more optimization.
12 300 0.420533822647 Henry Cohn, 2026, needs more optimization.
12 301 0.421826565508 Henry Cohn, 2026, needs more optimization.
12 302 0.423079311208 Henry Cohn, 2026, needs more optimization.
12 303 0.424060494462 Henry Cohn, 2026, needs more optimization.
12 304 0.425101113128 Henry Cohn, 2026, needs more optimization.
12 305 0.426479699899 Henry Cohn, 2026, needs more optimization.
12 306 0.427644274004 Henry Cohn, 2026, needs more optimization.
12 307 0.428498502883 Henry Cohn, 2026, needs more optimization.
12 308 0.429280602326 Henry Cohn, 2026, needs more optimization.
12 309 0.430089001065 Henry Cohn, 2026, needs more optimization.
12 310 0.430528770155 Henry Cohn, 2026, needs more optimization.
12 311 0.431238411999 Henry Cohn, 2026, needs more optimization.
12 312 0.432215691131 Henry Cohn, 2026, needs more optimization.
12 313 0.433197532730 Henry Cohn, 2026, needs more optimization.
12 314 0.433537112441 Henry Cohn, 2026, needs more optimization.
12 315 0.434202361544 Henry Cohn, 2026, needs more optimization.
12 316 0.434804695072 Henry Cohn, 2026, needs more optimization.
12 317 0.435333633981 Henry Cohn, 2026, needs more optimization.
12 318 0.436004481272 Henry Cohn, 2026, needs more optimization.
12 319 0.436763109904 Henry Cohn, 2026, needs more optimization.
12 320 0.437247426746 Henry Cohn, 2026, needs more optimization.
12 321 0.437584274483 Henry Cohn, 2026, needs more optimization.
12 322 0.438073652916 Henry Cohn, 2026, needs more optimization.
12 323 0.438436912102 Henry Cohn, 2026, needs more optimization.
12 324 0.439044373537 Henry Cohn, 2026, needs more optimization.
12 325 0.439557635200 Henry Cohn, 2026, needs more optimization.
12 326 0.440059049272 Henry Cohn, 2026, needs more optimization.
12 327 0.440340606330 Henry Cohn, 2026, needs more optimization.
12 328 0.440899729790 Henry Cohn, 2026, needs more optimization.
12 329 0.441363597293 Henry Cohn, 2026, needs more optimization.
12 332 0.441787873769 Henry Cohn, 2026, needs more optimization.
12 333 0.442192336225 Henry Cohn, 2026, needs more optimization.
12 334 0.442527419534 Henry Cohn, 2026, needs more optimization.
12 335 0.442819488796 Henry Cohn, 2026, needs more optimization.
12 336 0.443066448963 Henry Cohn, 2026, needs more optimization.
12 337 0.443468076353 Henry Cohn, 2026, needs more optimization.
12 338 0.443799036320 Henry Cohn, 2026, needs more optimization.
12 339 0.444158775581 Henry Cohn, 2026, needs more optimization.
12 340 0.444374885618 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 0.455617041495 Henry Cohn, 2026, needs more optimization.
12 410 0.460770729125 Henry Cohn, 2026, needs more optimization.
12 411 0.460890339256 Henry Cohn, 2025, needs more optimization.
12 412 0.460911075715 Henry Cohn, 2026, needs more optimization.
12 414 0.461335246734 Henry Cohn, 2026, needs more optimization.
12 416 0.461623163776 Henry Cohn, 2026, needs more optimization.
12 417 0.462223153465 Henry Cohn, 2025, needs more optimization.
12 418 0.462240021104 Henry Cohn, 2026, needs more optimization.
12 419 0.462598213897 Henry Cohn, 2025, needs more optimization.
12 420 0.462966625030 Henry Cohn, 2026, needs more optimization.
12 422 0.463280003332 Henry Cohn, 2025, needs more optimization.
12 423 0.463392436162 Henry Cohn, 2025, needs more optimization.
12 424 0.464265187939 Henry Cohn, 2025, needs more optimization.
12 425 0.464291111787 Henry Cohn, 2025, needs more optimization.
12 426 0.464311724026 Henry Cohn, 2025, needs more optimization.
12 427 0.464333823925 Henry Cohn, 2025, needs more optimization.
12 428 0.464616426642 Henry Cohn, 2026, needs more optimization.
12 429 0.464633106668 Henry Cohn, 2025, needs more optimization.
12 430 0.464847152738 Henry Cohn, 2026, needs more optimization.
12 431 0.465132401439 Henry Cohn, 2025, needs more optimization.
12 432 0.465182768608 Henry Cohn, 2026, needs more optimization.
12 433 0.465278387386 Henry Cohn, 2025, needs more optimization.
12 434 0.465315241331 Henry Cohn, 2026, needs more optimization.
12 435 0.465390209709 Henry Cohn, 2025, needs more optimization.
12 436 0.465431254972 Henry Cohn, 2025, needs more optimization.
12 437 0.466609299805 Henry Cohn, 2025, needs more optimization.
12 438 0.466672002977 Henry Cohn, 2026, needs more optimization.
12 439 0.466712521703 Henry Cohn, 2025, needs more optimization.
12 440 0.466742768731 Henry Cohn, 2026, needs more optimization.
12 441 0.467305772666 Henry Cohn, 2025, needs more optimization.
12 442 0.467360243002 Henry Cohn, 2025, needs more optimization.
12 443 0.468001139329 Henry Cohn, 2025, needs more optimization.
12 444 0.468106256221 Henry Cohn, 2026, needs more optimization.
12 445 0.468136232732 Henry Cohn, 2025, needs more optimization.
12 446 0.468143718124 Henry Cohn, 2025, needs more optimization.
12 447 0.468255536845 Henry Cohn, 2025, needs more optimization.
12 448 0.468743091391 Henry Cohn, 2026, needs more optimization.
12 449 0.468997460954 Henry Cohn, 2025, needs more optimization.
12 450 0.469051089502 Henry Cohn, 2026, needs more optimization.
12 452 0.469731464656 Henry Cohn, 2025, needs more optimization.
12 453 0.469782575302 Henry Cohn, 2025, needs more optimization.
12 454 0.470043941291 Henry Cohn, 2026, needs more optimization.
12 455 0.470156999977 Henry Cohn, 2025, needs more optimization.
12 456 0.470337981255 Henry Cohn, 2026, needs more optimization.
12 457 0.470513260720 Henry Cohn, 2025, needs more optimization.
12 458 0.471171521321 Henry Cohn, 2026, needs more optimization.
12 459 0.471208941422 Henry Cohn, 2025, needs more optimization.
12 460 0.471276953125 Henry Cohn, 2025, needs more optimization.
12 461 0.471288301089 Henry Cohn, 2025, needs more optimization.
12 462 0.471675612043 Henry Cohn, 2026, needs more optimization.
12 463 0.471694744636 Henry Cohn, 2025, needs more optimization.
12 464 0.471725401825 Henry Cohn, 2026, needs more optimization.
12 465 0.472115369833 Henry Cohn, 2025, needs more optimization.
12 466 0.472246013089 Henry Cohn, 2026, needs more optimization.
12 467 0.472299875569 Henry Cohn, 2025, needs more optimization.
12 468 0.472594888906 Henry Cohn, 2026, needs more optimization.
12 470 0.472727425964 Henry Cohn, 2026, needs more optimization.
12 471 0.472810005882 Henry Cohn, 2025, needs more optimization.
12 472 0.473173758951 Henry Cohn, 2026, needs more optimization.
12 473 0.473794201790 Henry Cohn, 2025, needs more optimization.
12 474 0.473863242716 Henry Cohn, 2025, needs more optimization.
12 475 0.473893985623 Henry Cohn, 2025, needs more optimization.
12 476 0.474320570192 Henry Cohn, 2026, needs more optimization.
12 477 0.474360536795 Henry Cohn, 2025, needs more optimization.
12 478 0.474469715393 Henry Cohn, 2026, needs more optimization.
12 480 0.474794911276 Henry Cohn, 2026, needs more optimization.
12 481 0.474879578957 Henry Cohn, 2025, needs more optimization.
12 482 0.474910307680 Henry Cohn, 2026, needs more optimization.
12 484 0.475384553366 Henry Cohn, 2025, needs more optimization.
12 485 0.475402119032 Henry Cohn, 2025, needs more optimization.
12 486 0.475729166398 Henry Cohn, 2026, needs more optimization.
12 487 0.475962860199 Henry Cohn, 2025, needs more optimization.
12 488 0.475978252243 Henry Cohn, 2025, needs more optimization.
12 489 0.476034756004 Henry Cohn, 2025, needs more optimization.
12 490 0.476066967305 Henry Cohn, 2025, needs more optimization.
12 491 0.476292844955 Henry Cohn, 2025, needs more optimization.
12 492 0.476360069412 Henry Cohn, 2026, needs more optimization.
12 493 0.476671821079 Henry Cohn, 2025, needs more optimization.
12 494 0.476681822735 Henry Cohn, 2026, needs more optimization.
12 495 0.476903460299 Henry Cohn, 2025, needs more optimization.
12 496 0.476988548405 Henry Cohn, 2026, needs more optimization.
12 498 0.477402155072 Henry Cohn, 2026, needs more optimization.
12 499 0.477742523402 Henry Cohn, 2025, needs more optimization.
12 500 0.477788141354 Henry Cohn, 2026, needs more optimization.
12 501 0.477904125544 Henry Cohn, 2025, needs more optimization.
12 502 0.478121477354 Henry Cohn, 2026, needs more optimization.
12 503 0.478244559820 Henry Cohn, 2025, needs more optimization.
12 504 0.478375815422 Henry Cohn, 2026, needs more optimization.
12 506 0.479030756034 Henry Cohn, 2026, needs more optimization.
12 507 0.479068778130 Henry Cohn, 2025, needs more optimization.
12 508 0.479086144303 Henry Cohn, 2025, needs more optimization.
12 510 0.479615699285 Henry Cohn, 2026, needs more optimization.
12 512 0.480566845577 Henry Cohn, 2026, needs more optimization.
12 514 0.481009164290 Henry Cohn, 2026, needs more optimization.
12 516 0.481445633633 Henry Cohn, 2026, needs more optimization.
12 518 0.481528563822 Henry Cohn, 2026, needs more optimization.
12 519 0.481578191340 Henry Cohn, 2025, needs more optimization.
12 520 0.482341468928 Henry Cohn, 2026, needs more optimization.
12 521 0.482378058943 Henry Cohn, 2025, needs more optimization.
12 522 0.483147276361 Henry Cohn, 2026, needs more optimization.
12 524 0.483206384836 Henry Cohn, 2026, needs more optimization.
12 525 0.483287748702 Henry Cohn, 2025, needs more optimization.
12 526 0.483299604430 Henry Cohn, 2026, needs more optimization.
12 527 0.483322567657 Henry Cohn, 2025, needs more optimization.
12 528 0.483329276639 Henry Cohn, 2026, needs more optimization.
12 529 0.483358658357 Henry Cohn, 2025, needs more optimization.
12 530 0.484540695644 Henry Cohn, 2026, needs more optimization.
12 532 0.484699586469 Henry Cohn, 2026, needs more optimization.
12 534 0.484742595283 Henry Cohn, 2026, needs more optimization.
12 536 0.484768870016 Henry Cohn, 2026, needs more optimization.
12 537 0.484864119566 Henry Cohn, 2025, needs more optimization.
12 538 0.484883911620 Henry Cohn, 2026, needs more optimization.
12 539 0.484958011729 Henry Cohn, 2025, needs more optimization.
12 540 0.485896973842 Henry Cohn, 2026, needs more optimization.
12 542 0.486047046950 Henry Cohn, 2026, needs more optimization.
12 543 0.486597296157 Henry Cohn, 2025, needs more optimization.
12 544 0.486636925471 Henry Cohn, 2026, needs more optimization.
12 545 0.486766063233 Henry Cohn, 2025, needs more optimization.
12 546 0.487154543953 Henry Cohn, 2026, needs more optimization.
12 547 0.487239709562 Henry Cohn, 2025, needs more optimization.
12 548 0.487250378747 Henry Cohn, 2026, needs more optimization.
12 549 0.487273017307 Henry Cohn, 2025, needs more optimization.
12 550 0.487290268268 Henry Cohn, 2025, needs more optimization.
12 552 0.487400548117 Henry Cohn, 2026, needs more optimization.
12 554 0.487457326796 Henry Cohn, 2026, needs more optimization.
12 555 0.488070925645 Henry Cohn, 2025, needs more optimization.
12 556 0.488235125090 Henry Cohn, 2026, needs more optimization.
12 558 0.488289315535 Henry Cohn, 2026, needs more optimization.
12 560 0.488333474035 Henry Cohn, 2026, needs more optimization.
12 562 0.488600301489 Henry Cohn, 2026, needs more optimization.
12 563 0.488692205136 Henry Cohn, 2025, needs more optimization.
12 564 0.488697936674 Henry Cohn, 2025, needs more optimization.
12 565 0.488729497352 Henry Cohn, 2025, needs more optimization.
12 567 0.488739871268 Henry Cohn, 2025, needs more optimization.
12 569 0.488805387350 Henry Cohn, 2025, needs more optimization.
12 570 0.488818462647 Henry Cohn, 2025, needs more optimization.
12 571 0.488851947408 Henry Cohn, 2025, needs more optimization.
12 572 0.488933504580 Henry Cohn, 2026, needs more optimization.
12 573 0.488973658224 Henry Cohn, 2025, needs more optimization.
12 574 0.490298112699 Henry Cohn, 2026, needs more optimization.
12 576 0.490363963922 Henry Cohn, 2026, needs more optimization.
12 577 0.490399992850 Henry Cohn, 2025, needs more optimization.
12 578 0.490414553485 Henry Cohn, 2026, needs more optimization.
12 580 0.490441894573 Henry Cohn, 2025, needs more optimization.
12 581 0.490446236902 Henry Cohn, 2025, needs more optimization.
12 582 0.490480495880 Henry Cohn, 2026, needs more optimization.
12 583 0.490489697030 Henry Cohn, 2025, needs more optimization.
12 584 0.490498468096 Henry Cohn, 2025, needs more optimization.
12 585 0.490571683932 Henry Cohn, 2025, needs more optimization.
12 586 0.490637670147 Henry Cohn, 2026, needs more optimization.
12 587 0.490727775175 Henry Cohn, 2025, needs more optimization.
12 588 0.491084938853 Henry Cohn, 2026, needs more optimization.
12 590 0.492053535745 Henry Cohn, 2026, needs more optimization.
12 592 0.492137811490 Henry Cohn, 2026, needs more optimization.
12 594 0.492176094697 Henry Cohn, 2026, needs more optimization.
12 595 0.492685621409 Henry Cohn, 2025, needs more optimization.
12 596 0.492773181556 Henry Cohn, 2026, needs more optimization.
12 598 0.492837235041 Henry Cohn, 2026, needs more optimization.
12 599 0.494041598615 Henry Cohn, 2025, needs more optimization.
12 600 0.494044369153 Henry Cohn, 2025, needs more optimization.
12 601 0.494051376278 Henry Cohn, 2025, needs more optimization.
12 602 0.494067679491 Henry Cohn, 2025, needs more optimization.
12 603 0.494100934195 Henry Cohn, 2025, needs more optimization.
12 604 0.494121975732 Henry Cohn, 2025, needs more optimization.
12 605 0.494122442112 Henry Cohn, 2025, needs more optimization.
12 606 0.494177599242 Henry Cohn, 2026, needs more optimization.
12 607 0.494205393288 Henry Cohn, 2025, needs more optimization.
12 608 0.494260657622 Henry Cohn, 2026, needs more optimization.
12 610 0.494315912285 Henry Cohn, 2026, needs more optimization.
12 612 0.494325629276 Henry Cohn, 2025, needs more optimization.
12 613 0.494328327521 Henry Cohn, 2025, needs more optimization.
12 614 0.494501309900 Henry Cohn, 2026, needs more optimization.
12 615 0.495631117365 Henry Cohn, 2025, needs more optimization.
12 616 0.495637728423 Henry Cohn, 2025, needs more optimization.
12 619 0.495680470469 Henry Cohn, 2025, needs more optimization.
12 620 0.495681323654 Henry Cohn, 2025, needs more optimization.
12 621 0.495691130937 Henry Cohn, 2025, needs more optimization.
12 622 0.495692432016 Henry Cohn, 2025, needs more optimization.
12 623 0.495762354085 Henry Cohn, 2025, needs more optimization.
12 624 0.495762862636 Henry Cohn, 2025, needs more optimization.
12 625 0.495771634360 Henry Cohn, 2025, needs more optimization.
12 626 0.495841401097 Henry Cohn, 2026, needs more optimization.
12 628 0.495910771147 Henry Cohn, 2026, needs more optimization.
12 631 0.495949749227 Henry Cohn, 2025, needs more optimization.
12 635 0.496047783172 Henry Cohn, 2025, needs more optimization.
12 637 0.496050596998 Henry Cohn, 2025, needs more optimization.
12 638 0.496058274498 Henry Cohn, 2025, needs more optimization.
12 639 0.496064688904 Henry Cohn, 2025, needs more optimization.
12 643 0.496108643131 Henry Cohn, 2025, needs more optimization.
12 644 0.496129625185 Henry Cohn, 2025, needs more optimization.
12 645 0.496129835698 Henry Cohn, 2025, needs more optimization.
12 646 0.496131641462 Henry Cohn, 2025, needs more optimization.
12 647 0.496166216666 Henry Cohn, 2025, needs more optimization.
12 651 0.496193623279 Henry Cohn, 2025, needs more optimization.
12 653 0.496200069913 Henry Cohn, 2025, needs more optimization.
12 654 0.496204823044 Henry Cohn, 2025, needs more optimization.
12 655 0.496224318704 Henry Cohn, 2025, needs more optimization.
12 657 0.496249829119 Henry Cohn, 2025, needs more optimization.
12 658 0.496250534692 Henry Cohn, 2025, needs more optimization.
12 659 0.496251039019 Henry Cohn, 2025, needs more optimization.
12 662 0.496285882740 Henry Cohn, 2025, needs more optimization.
12 663 0.496286510903 Henry Cohn, 2025, needs more optimization.
12 665 0.496310481951 Henry Cohn, 2025, needs more optimization.
12 666 0.496347765652 Henry Cohn, 2025, needs more optimization.
12 669 0.496398243691 Henry Cohn, 2025, needs more optimization.
12 670 0.496539115043 Henry Cohn, 2025, needs more optimization.
12 671 0.496539947668 Henry Cohn, 2025, needs more optimization.
12 672 0.496554860611 Henry Cohn, 2025, needs more optimization.
12 674 0.496720703840 Henry Cohn, 2026, needs more optimization.
12 675 0.496751547917 Henry Cohn, 2025, needs more optimization.
12 676 0.496753236333 Henry Cohn, 2025, needs more optimization.
12 677 0.496783428091 Henry Cohn, 2025, needs more optimization.
12 678 0.496793437471 Henry Cohn, 2025, needs more optimization.
12 679 0.496795660943 Henry Cohn, 2025, needs more optimization.
12 680 0.496798825093 Henry Cohn, 2025, needs more optimization.
12 681 0.496812843857 Henry Cohn, 2025, needs more optimization.
12 682 0.496831444646 Henry Cohn, 2025, needs more optimization.
12 683 0.496845437127 Henry Cohn, 2025, needs more optimization.
12 685 0.496851590651 Henry Cohn, 2025, needs more optimization.
12 686 0.496851824199 Henry Cohn, 2025, needs more optimization.
12 687 0.496852290623 Henry Cohn, 2025, needs more optimization.
12 688 0.496853086617 Henry Cohn, 2025, needs more optimization.
12 689 0.496854473038 Henry Cohn, 2025, needs more optimization.
12 690 0.496856167771 Henry Cohn, 2025, needs more optimization.
12 691 0.496867036500 Henry Cohn, 2025, needs more optimization.
12 692 0.496916615838 Henry Cohn, 2025, needs more optimization.
12 693 0.496939035923 Henry Cohn, 2025, needs more optimization.
12 694 0.496939223105 Henry Cohn, 2025, needs more optimization.
12 695 0.496939429832 Henry Cohn, 2025, needs more optimization.
12 696 0.496987330577 Henry Cohn, 2025, needs more optimization.
12 697 0.497010713022 Henry Cohn, 2025, needs more optimization.
12 698 0.497019280717 Henry Cohn, 2025, needs more optimization.
12 699 0.497020722181 Henry Cohn, 2025, needs more optimization.
12 700 0.497021648148 Henry Cohn, 2025, needs more optimization.
12 701 0.497047186556 Henry Cohn, 2025, needs more optimization.
12 702 0.497047692253 Henry Cohn, 2025, needs more optimization.
12 703 0.497070451054 Henry Cohn, 2025, needs more optimization.
12 704 0.497074985031 Henry Cohn, 2025, needs more optimization.
12 705 0.497081067707 Henry Cohn, 2025, needs more optimization.
12 706 0.497085905576 Henry Cohn, 2025, needs more optimization.
12 707 0.497097469933 Henry Cohn, 2025, needs more optimization.
12 708 0.497117601389 Henry Cohn, 2025, needs more optimization.
12 712 0.497131515815 Henry Cohn, 2025, needs more optimization.
12 715 0.497132897391 Henry Cohn, 2025, needs more optimization.
12 716 0.497135687687 Henry Cohn, 2025, needs more optimization.
12 717 0.497143746739 Henry Cohn, 2025, needs more optimization.
12 718 0.497173466190 Henry Cohn, 2025, needs more optimization.
12 719 0.497263801905 Henry Cohn, 2025, needs more optimization.
12 721 0.497286042343 Henry Cohn, 2025, needs more optimization.
12 722 0.497290449234 Henry Cohn, 2025, needs more optimization.
12 723 0.497312775454 Henry Cohn, 2025, needs more optimization.
12 724 0.497329208844 Henry Cohn, 2025, needs more optimization.
12 725 0.497387109813 Henry Cohn, 2025, needs more optimization.
12 726 0.497394178916 Henry Cohn, 2025, needs more optimization.
12 728 0.497399332025 Henry Cohn, 2025, needs more optimization.
12 729 0.497420674493 Henry Cohn, 2025, needs more optimization.
12 730 0.497432979281 Henry Cohn, 2025, needs more optimization.
12 731 0.497433272235 Henry Cohn, 2025, needs more optimization.
12 735 0.497433741405 Henry Cohn, 2025, needs more optimization.
12 736 0.497434002036 Henry Cohn, 2025, needs more optimization.
12 737 0.497434977729 Henry Cohn, 2025, needs more optimization.
12 739 0.497438545873 Henry Cohn, 2025, needs more optimization.
12 740 0.497468963170 Henry Cohn, 2025, needs more optimization.
12 741 0.497479222995 Henry Cohn, 2025, needs more optimization.
12 742 0.497480363182 Henry Cohn, 2025, needs more optimization.
12 743 0.497482876559 Henry Cohn, 2025, needs more optimization.
12 744 0.497514619542 Henry Cohn, 2025, needs more optimization.
12 745 0.497543875236 Henry Cohn, 2025, needs more optimization.
12 746 0.497559732219 Henry Cohn, 2025, needs more optimization.
12 747 0.497577967446 Henry Cohn, 2025, needs more optimization.
12 748 0.497599189314 Henry Cohn, 2025, needs more optimization.
12 749 0.497680832175 Henry Cohn, 2025, needs more optimization.
12 750 0.497693229718 Henry Cohn, 2025, needs more optimization.
12 751 0.497710692954 Henry Cohn, 2025, needs more optimization.
12 752 0.497711277067 Henry Cohn, 2025, needs more optimization.
12 753 0.497838301804 Henry Cohn, 2025, needs more optimization.
12 754 0.497931271352 Henry Cohn, 2026, needs more optimization.
12 755 0.498105388971 Henry Cohn, 2026, needs more optimization.
12 756 0.499541791587 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, after some further optimization.
12 840 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, 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
12 841 0.510889073420 Henry Cohn, 2026, needs more optimization.
12 842 0.535503190469 Henry Cohn, 2026, needs more optimization.
12 843 0.535545961855 Henry Cohn, 2026, needs more optimization.
12 844 0.535853239784 Henry Cohn, 2026, needs more optimization.
12 845 0.535859114963 Henry Cohn, 2026, needs more optimization.
12 846 0.535864108463 Henry Cohn, 2026, needs more optimization.
12 847 0.536131518186 Henry Cohn, 2026, needs more optimization.
12 848 0.536193363348 Henry Cohn, 2026, needs more optimization.
12 849 0.536375325961 Henry Cohn, 2025, needs more optimization.
12 850 0.536420295280 Henry Cohn, 2026, needs more optimization.
12 851 0.536771725335 Henry Cohn, 2026, needs more optimization.
12 852 0.537229578938 Henry Cohn, 2026, needs more optimization.
12 853 0.537409326558 Henry Cohn, 2026, needs more optimization.
12 854 0.537422171407 Henry Cohn, 2026, needs more optimization.
12 855 0.537674136618 Henry Cohn, 2026, needs more optimization.
12 856 0.537757234848 Henry Cohn, 2026, needs more optimization.
12 857 0.537764198385 Henry Cohn, 2026, needs more optimization.
12 858 0.538135460468 Henry Cohn, 2026, needs more optimization.
12 859 0.538181862229 Henry Cohn, 2025, needs more optimization.
12 860 0.538272258203 Henry Cohn, 2026, needs more optimization.
12 861 0.538534955044 Henry Cohn, 2026, needs more optimization.
12 862 0.538787414143 Henry Cohn, 2026, needs more optimization.
12 863 0.538793495928 Henry Cohn, 2026, needs more optimization.
12 864 0.538971165052 Henry Cohn, 2026, needs more optimization.
12 865 0.539070917156 Henry Cohn, 2026, needs more optimization.
12 866 0.539097008848 Henry Cohn, 2026, needs more optimization.
12 867 0.539416526554 Henry Cohn, 2026, needs more optimization.
12 868 0.539434575143 Henry Cohn, 2026, needs more optimization.
12 869 0.539480505601 Henry Cohn, 2026, needs more optimization.
12 870 0.539713137269 Henry Cohn, 2026, needs more optimization.
12 871 0.539940914659 Henry Cohn, 2025, needs more optimization.
12 872 0.539941280606 Henry Cohn, 2025, needs more optimization.
12 873 0.539946671562 Henry Cohn, 2026, needs more optimization.
12 874 0.539952988405 Henry Cohn, 2026, needs more optimization.
12 875 0.540535685141 Henry Cohn, 2026, needs more optimization.
12 876 0.540539657177 Henry Cohn, 2026, needs more optimization.
12 877 0.540549574849 Henry Cohn, 2026, needs more optimization.
12 878 0.540633234207 Henry Cohn, 2026, needs more optimization.
12 879 0.541217329405 Henry Cohn, 2026, needs more optimization.
12 880 0.541219192725 Henry Cohn, 2026, needs more optimization.
12 881 0.541327585626 Henry Cohn, 2026, needs more optimization.
12 882 0.541339878624 Henry Cohn, 2026, needs more optimization.
12 883 0.541717510379 Henry Cohn, 2026, needs more optimization.
12 884 0.541997865472 Henry Cohn, 2026, needs more optimization.
12 885 0.542044694318 Henry Cohn, 2026, needs more optimization.
12 886 0.542061020507 Henry Cohn, 2026, needs more optimization.
12 887 0.542101600968 Henry Cohn, 2026, needs more optimization.
12 888 0.542472081129 Henry Cohn, 2026, needs more optimization.
12 889 0.542497414253 Henry Cohn, 2026, needs more optimization.
12 890 0.542500247999 Henry Cohn, 2026, needs more optimization.
12 891 0.542716966071 Henry Cohn, 2025, needs more optimization.
12 892 0.542782152692 Henry Cohn, 2026, needs more optimization.
12 893 0.543201117133 Henry Cohn, 2026, needs more optimization.
12 894 0.543439354489 Henry Cohn, 2026, needs more optimization.
12 895 0.543488133854 Henry Cohn, 2026, needs more optimization.
12 896 0.543547492757 Henry Cohn, 2026, needs more optimization.
12 897 0.543892335521 Henry Cohn, 2026, needs more optimization.
12 898 0.543900823672 Henry Cohn, 2025, needs more optimization.
12 899 0.543917569910 Henry Cohn, 2026, needs more optimization.
12 900 0.543925544989 Henry Cohn, 2026, needs more optimization.
12 901 0.544320840935 Henry Cohn, 2026, needs more optimization.
12 902 0.544374835174 Henry Cohn, 2026, needs more optimization.
12 903 0.544401358525 Henry Cohn, 2026, needs more optimization.
12 904 0.544629845122 Henry Cohn, 2026, needs more optimization.
12 905 0.544661206997 Henry Cohn, 2026, needs more optimization.
12 906 0.544833542818 Henry Cohn, 2026, needs more optimization.
12 907 0.544882912429 Henry Cohn, 2026, needs more optimization.
12 908 0.545184695362 Henry Cohn, 2026, needs more optimization.
12 909 0.545197677009 Henry Cohn, 2026, needs more optimization.
12 910 0.545439672598 Henry Cohn, 2026, needs more optimization.
12 911 0.545444590651 Henry Cohn, 2026, needs more optimization.
12 912 0.545451555011 Henry Cohn, 2026, needs more optimization.
12 913 0.545469063585 Henry Cohn, 2026, needs more optimization.
12 914 0.545740004124 Henry Cohn, 2026, needs more optimization.
12 915 0.545771016507 Henry Cohn, 2026, needs more optimization.
12 916 0.546071039392 Henry Cohn, 2026, needs more optimization.
12 917 0.546074754654 Henry Cohn, 2026, needs more optimization.
12 918 0.546194488677 Henry Cohn, 2026, needs more optimization.
12 919 0.546619818099 Henry Cohn, 2026, needs more optimization.
12 920 0.546633602871 Henry Cohn, 2026, needs more optimization.
12 921 0.546644832802 Henry Cohn, 2026, needs more optimization.
12 922 0.546646998141 Henry Cohn, 2026, needs more optimization.
12 923 0.546897034702 Henry Cohn, 2026, needs more optimization.
12 924 0.546995106625 Henry Cohn, 2026, needs more optimization.
12 925 0.547035580120 Henry Cohn, 2026, needs more optimization.
12 926 0.547177411079 Henry Cohn, 2026, needs more optimization.
12 927 0.547367612487 Henry Cohn, 2026, needs more optimization.
12 928 0.547395204939 Henry Cohn, 2026, needs more optimization.
12 929 0.547605995319 Henry Cohn, 2026, needs more optimization.
12 930 0.547618047478 Henry Cohn, 2026, needs more optimization.
12 931 0.547620577377 Henry Cohn, 2026, needs more optimization.
12 932 0.547983489649 Henry Cohn, 2026, needs more optimization.
12 933 0.548163066908 Henry Cohn, 2026, needs more optimization.
12 934 0.548174455525 Henry Cohn, 2025, needs more optimization.
12 935 0.548269809722 Henry Cohn, 2026, needs more optimization.
12 936 0.548438182116 Henry Cohn, 2026, needs more optimization.
12 937 0.548759002475 Henry Cohn, 2026, needs more optimization.
12 938 0.548955040248 Henry Cohn, 2026, needs more optimization.
12 939 0.548989051206 Henry Cohn, 2026, needs more optimization.
12 940 0.548989417186 Henry Cohn, 2026, needs more optimization.
12 941 0.549033151698 Henry Cohn, 2026, needs more optimization.
12 942 0.549046894383 Henry Cohn, 2026, needs more optimization.
12 943 0.549446993452 Henry Cohn, 2026, needs more optimization.
12 944 0.549474745499 Henry Cohn, 2026, needs more optimization.
12 945 0.549563428359 Henry Cohn, 2026, needs more optimization.
12 946 0.549700846868 Henry Cohn, 2026, needs more optimization.
12 947 0.549721990615 Henry Cohn, 2026, needs more optimization.
12 948 0.549763578707 Henry Cohn, 2026, needs more optimization.
12 949 0.550019754965 Henry Cohn, 2026, needs more optimization.
12 950 0.550029639616 Henry Cohn, 2026, needs more optimization.
12 951 0.550080634536 Henry Cohn, 2026, needs more optimization.
12 952 0.550572418929 Henry Cohn, 2026, needs more optimization.
12 953 0.550644237036 Henry Cohn, 2026, needs more optimization.
12 954 0.550660027253 Henry Cohn, 2026, needs more optimization.
12 955 0.550673642537 Henry Cohn, 2026, needs more optimization.
12 956 0.550681015515 Henry Cohn, 2026, needs more optimization.
12 957 0.551046621625 Henry Cohn, 2026, needs more optimization.
12 958 0.551084393944 Henry Cohn, 2026, needs more optimization.
12 959 0.551088939120 Henry Cohn, 2026, needs more optimization.
12 960 0.551241431542 Henry Cohn, 2026, needs more optimization.
12 961 0.551277319327 Henry Cohn, 2026, needs more optimization.
12 962 0.551283079098 Henry Cohn, 2026, needs more optimization.
12 963 0.551565168876 Henry Cohn, 2026, needs more optimization.
12 964 0.551614803955 Henry Cohn, 2026, needs more optimization.
12 965 0.551622605187 Henry Cohn, 2026, needs more optimization.
12 966 0.551882318610 Henry Cohn, 2026, needs more optimization.
12 967 0.551887701745 Henry Cohn, 2026, needs more optimization.
12 968 0.551963913130 Henry Cohn, 2026, needs more optimization.
12 969 0.552326081648 Henry Cohn, 2025, needs more optimization.
12 970 0.552368471158 Henry Cohn, 2026, needs more optimization.
12 971 0.552374235659 Henry Cohn, 2026, needs more optimization.
12 972 0.552387393943 Henry Cohn, 2026, needs more optimization.
12 973 0.552548949827 Henry Cohn, 2026, needs more optimization.
12 974 0.552601733015 Henry Cohn, 2026, needs more optimization.
12 975 0.552626390463 Henry Cohn, 2026, needs more optimization.
12 976 0.552926775811 Henry Cohn, 2026, needs more optimization.
12 977 0.552935976821 Henry Cohn, 2026, needs more optimization.
12 978 0.553176910874 Henry Cohn, 2026, needs more optimization.
12 979 0.553186524548 Henry Cohn, 2026, needs more optimization.
12 980 0.553236896900 Henry Cohn, 2026, needs more optimization.
12 981 0.553539091178 Henry Cohn, 2026, needs more optimization.
12 982 0.553616060670 Henry Cohn, 2026, needs more optimization.
12 983 0.553785438910 Henry Cohn, 2026, needs more optimization.
12 984 0.553797650615 Henry Cohn, 2026, needs more optimization.
12 985 0.553797696892 Henry Cohn, 2026, needs more optimization.
12 986 0.554010518638 Henry Cohn, 2026, needs more optimization.
12 987 0.554146076152 Henry Cohn, 2026, needs more optimization.
12 988 0.554375104397 Henry Cohn, 2026, needs more optimization.
12 989 0.554519236921 Henry Cohn, 2026, needs more optimization.
12 990 0.554659468953 Henry Cohn, 2026, needs more optimization.
12 991 0.554855886869 Henry Cohn, 2026, needs more optimization.
12 992 0.554951698605 Henry Cohn, 2026, needs more optimization.
12 993 0.555025705965 Henry Cohn, 2026, needs more optimization.
12 994 0.555160033658 Henry Cohn, 2026, needs more optimization.
12 995 0.555309110678 Henry Cohn, 2026, needs more optimization.
12 996 0.555440204498 Henry Cohn, 2026, needs more optimization.
12 997 0.555537774261 Henry Cohn, 2026, needs more optimization.
12 1024 0.555555555556 Subcode of a code of size 1144 from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−5
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 0.184601884691 Henry Cohn, 2025.
13 61 0.189133285981 Henry Cohn, 2026, needs more optimization.
13 62 0.189939244395 Henry Cohn, 2026.
13 63 0.193274783328 Henry Cohn, 2026.
13 64 0.194862550676 Henry Cohn, 2026, needs more optimization.
13 65 0.198938999914 Henry Cohn, 2026, needs more optimization.
13 66 0.201501645082 Henry Cohn, 2026, needs more optimization.
13 67 0.204060485677 Henry Cohn, 2026, needs more optimization.
13 68 0.207237119804 Henry Cohn, 2026, needs more optimization.
13 69 0.208427075365 Henry Cohn, 2025.
13 70 0.210762897393 Henry Cohn, 2026, needs more optimization.
13 71 0.212574330623 Henry Cohn, 2025.
13 72 0.214183844238 Henry Cohn, 2025.
13 73 0.216144703213 Henry Cohn, 2026, needs more optimization.
13 74 0.218072317405 Henry Cohn, 2026, needs more optimization.
13 75 0.219802379115 Henry Cohn, 2026, needs more optimization.
13 76 0.222090009062 Henry Cohn, 2026, needs more optimization.
13 77 0.224126205886 Henry Cohn, 2026, needs more optimization.
13 78 0.226253189158 Henry Cohn, 2026, needs more optimization.
13 79 0.228139500326 Henry Cohn, 2026, needs more optimization.
13 80 0.230720127190 Henry Cohn, 2026, needs more optimization.
13 81 0.232720216127 Henry Cohn, 2024, needs more optimization.
13 82 0.234416735243 Henry Cohn, 2026, needs more optimization.
13 83 0.236564048730 Henry Cohn, 2026, needs more optimization.
13 84 0.238167450282 Henry Cohn, 2026, needs more optimization.
13 85 0.240414219031 Henry Cohn, 2026, needs more optimization.
13 86 0.241747565738 Henry Cohn, 2026, needs more optimization.
13 87 0.243732895627 Henry Cohn, 2026, needs more optimization.
13 88 0.245463266601 Henry Cohn, 2026, needs more optimization.
13 89 0.247225983360 Henry Cohn, 2026, needs more optimization.
13 90 0.248473502762 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, needs more optimization.
13 107 0.258117011787 Henry Cohn, 2026, needs more optimization.
13 108 0.258372350014 Henry Cohn, 2026, needs more optimization.
13 109 0.259209674000 Henry Cohn, 2026, needs more optimization.
13 110 0.259525753325 Henry Cohn, 2026, needs more optimization.
13 111 0.259786920363 Henry Cohn, 2026, needs more optimization.
13 112 0.261427288349 Henry Cohn, 2026, needs more optimization.
13 113 0.263326655725 Henry Cohn, 2026, needs more optimization.
13 114 0.263627757025 Henry Cohn, 2026, needs more optimization.
13 115 0.264319176664 Henry Cohn, 2026, needs more optimization.
13 116 0.267844584869 Henry Cohn, 2026, needs more optimization.
13 117 0.270063561716 Henry Cohn, 2026, needs more optimization.
13 118 0.272924888843 Henry Cohn, 2026, needs more optimization.
13 119 0.275278661495 Henry Cohn, 2026, needs more optimization.
13 120 0.277450222629 Henry Cohn, 2026, needs more optimization.
13 121 0.278347119461 Henry Cohn, 2026, needs more optimization.
13 122 0.281090999555 Henry Cohn, 2026, needs more optimization.
13 123 0.282045173584 Henry Cohn, 2026, needs more optimization.
13 124 0.283991591644 Henry Cohn, 2026, needs more optimization.
13 125 0.285830527149 Henry Cohn, 2026, needs more optimization.
13 126 0.286739321680 Henry Cohn, 2026, needs more optimization.
13 127 0.288813726644 Henry Cohn, 2026, needs more optimization.
13 128 0.289858429057 Henry Cohn, 2026, needs more optimization.
13 129 0.290769562453 Henry Cohn, 2026, needs more optimization.
13 130 0.292567021091 Henry Cohn, 2026, needs more optimization.
13 131 0.293212558078 Henry Cohn, 2026, needs more optimization.
13 132 0.293701412623 Henry Cohn, 2026, needs more optimization.
13 133 0.294734908533 Henry Cohn, 2026, needs more optimization.
13 134 0.295302936789 Henry Cohn, 2026, needs more optimization.
13 135 0.295868709242 Henry Cohn, 2026, needs more optimization.
13 136 0.296740936115 Henry Cohn, 2026, needs more optimization.
13 137 0.297862084225 Henry Cohn, 2026, needs more optimization.
13 138 0.298953505410 Henry Cohn, 2026, needs more optimization.
13 139 0.299554546039 Henry Cohn, 2026, needs more optimization.
13 140 0.300703524113 Henry Cohn, 2026, needs more optimization.
13 141 0.301556501878 Henry Cohn, 2026, needs more optimization.
13 142 0.302544684723 Henry Cohn, 2026, needs more optimization.
13 143 0.303547343846 Henry Cohn, 2026, needs more optimization.
13 144 0.304000382163 Henry Cohn, 2026, needs more optimization.
13 145 0.305344309266 Henry Cohn, 2026, needs more optimization.
13 146 0.305525802699 Henry Cohn, 2026, needs more optimization.
13 147 0.306272881931 Henry Cohn, 2026, needs more optimization.
13 148 0.306931819194 Henry Cohn, 2026, needs more optimization.
13 149 0.307500412753 Henry Cohn, 2026, needs more optimization.
13 150 0.307711875033 Henry Cohn, 2026, needs more optimization.
13 151 0.308329513034 Henry Cohn, 2026, needs more optimization.
13 152 0.308804923456 Henry Cohn, 2026, needs more optimization.
13 153 0.309353871464 Henry Cohn, 2026, needs more optimization.
13 154 0.309802643932 Henry Cohn, 2026, needs more optimization.
13 155 0.310241966340 Henry Cohn, 2026, needs more optimization.
13 156 0.310821306924 Henry Cohn, 2026, needs more optimization.
13 157 0.311419143071 Henry Cohn, 2026, needs more optimization.
13 158 0.311968963155 Henry Cohn, 2026, needs more optimization.
13 159 0.312751890320 Henry Cohn, 2026, needs more optimization.
13 160 0.313429645346 Henry Cohn, 2026, needs more optimization.
13 161 0.314128763704 Henry Cohn, 2026, needs more optimization.
13 162 0.314412732235 Henry Cohn, 2026, needs more optimization.
13 163 0.315130081607 Henry Cohn, 2026, needs more optimization.
13 164 0.315592467627 Henry Cohn, 2026, needs more optimization.
13 165 0.316095535591 Henry Cohn, 2026, needs more optimization.
13 166 0.316863918970 Henry Cohn, 2026, needs more optimization.
13 167 0.317493577079 Henry Cohn, 2026, needs more optimization.
13 168 0.317708414801 Henry Cohn, 2026, needs more optimization.
13 169 0.318162443666 Henry Cohn, 2026, needs more optimization.
13 170 0.319149963078 Henry Cohn, 2026, needs more optimization.
13 171 0.319651084593 Henry Cohn, 2026, needs more optimization.
13 172 0.319861333905 Henry Cohn, 2026, needs more optimization.
13 173 0.320597581693 Henry Cohn, 2026, needs more optimization.
13 174 0.320938602328 Henry Cohn, 2026, needs more optimization.
13 175 0.321418317016 Henry Cohn, 2026, needs more optimization.
13 176 0.322087783508 Henry Cohn, 2026, needs more optimization.
13 177 0.322485620701 Henry Cohn, 2026, needs more optimization.
13 178 0.322765525610 Henry Cohn, 2026, needs more optimization.
13 179 0.323438842941 Henry Cohn, 2026, needs more optimization.
13 180 0.324034917271 Henry Cohn, 2026, needs more optimization.
13 181 0.324365389542 Henry Cohn, 2026, needs more optimization.
13 182 0.324628773164 Henry Cohn, 2026, needs more optimization.
13 183 0.324682565104 Henry Cohn, 2026, needs more optimization.
13 184 0.324854108179 Henry Cohn, 2026, needs more optimization.
13 185 0.325422984206 Henry Cohn, 2026, needs more optimization.
13 186 0.326248506816 Henry Cohn, 2026, needs more optimization.
13 187 0.326501763724 Henry Cohn, 2026, needs more optimization.
13 188 0.326839374146 Henry Cohn, 2026, needs more optimization.
13 189 0.326984442285 Henry Cohn, 2026, needs more optimization.
13 190 0.327484671980 Henry Cohn, 2026, needs more optimization.
13 191 0.327758411401 Henry Cohn, 2026, needs more optimization.
13 192 0.328096941479 Henry Cohn, 2026, needs more optimization.
13 193 0.328122344611 Henry Cohn, 2026, needs more optimization.
13 194 0.328326713928 Henry Cohn, 2026, needs more optimization.
13 195 0.328491276814 Henry Cohn, 2026, needs more optimization.
13 196 0.328736812038 Henry Cohn, 2026, needs more optimization.
13 197 0.328876787383 Henry Cohn, 2026, needs more optimization.
13 198 0.329077242297 Henry Cohn, 2026, needs more optimization.
13 199 0.329144461986 Henry Cohn, 2026, needs more optimization.
13 200 0.329387819196 Henry Cohn, 2026, needs more optimization.
13 201 0.329601465147 Henry Cohn, 2026, needs more optimization.
13 202 0.329823699345 Henry Cohn, 2026, needs more optimization.
13 203 0.332322810684 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 0.350454981883 Henry Cohn, 2026, needs more optimization.
13 210 0.351580184334 Henry Cohn, 2026, needs more optimization.
13 211 0.352249768849 Henry Cohn, 2026, needs more optimization.
13 212 0.352778179200 Henry Cohn, 2026, needs more optimization.
13 213 0.353908969601 Henry Cohn, 2026, needs more optimization.
13 214 0.354466062755 Henry Cohn, 2026, needs more optimization.
13 215 0.355369398891 Henry Cohn, 2026, needs more optimization.
13 216 0.355724894881 Henry Cohn, 2026, needs more optimization.
13 217 0.356444801918 Henry Cohn, 2026, needs more optimization.
13 218 0.357848603420 Henry Cohn, 2026, needs more optimization.
13 219 0.358097922353 Henry Cohn, 2026, needs more optimization.
13 220 0.358852636167 Henry Cohn, 2026, needs more optimization.
13 221 0.359893497825 Henry Cohn, 2026, needs more optimization.
13 222 0.360502750571 Henry Cohn, 2026, needs more optimization.
13 223 0.361604733961 Henry Cohn, 2026, needs more optimization.
13 224 0.362515409696 Henry Cohn, 2026, needs more optimization.
13 225 0.363377736204 Henry Cohn, 2026, needs more optimization.
13 226 0.364026553272 Henry Cohn, 2026, needs more optimization.
13 227 0.364774605284 Henry Cohn, 2026, needs more optimization.
13 228 0.365434943666 Henry Cohn, 2026, needs more optimization.
13 229 0.366367041868 Henry Cohn, 2026, needs more optimization.
13 230 0.366888670754 Henry Cohn, 2026, needs more optimization.
13 231 0.367686463085 Henry Cohn, 2026, needs more optimization.
13 232 0.368704853192 Henry Cohn, 2026, needs more optimization.
13 233 0.369233038758 Henry Cohn, 2026, needs more optimization.
13 234 0.369992288092 Henry Cohn, 2026, needs more optimization.
13 235 0.371072637880 Henry Cohn, 2026, needs more optimization.
13 236 0.371418565191 Henry Cohn, 2026, needs more optimization.
13 237 0.372099764297 Henry Cohn, 2026, needs more optimization.
13 238 0.372912056699 Henry Cohn, 2026, needs more optimization.
13 239 0.373572070877 Henry Cohn, 2026, needs more optimization.
13 240 0.374220160005 Henry Cohn, 2026, needs more optimization.
13 241 0.374832674099 Henry Cohn, 2026, needs more optimization.
13 242 0.375602005888 Henry Cohn, 2026, needs more optimization.
13 243 0.376259685927 Henry Cohn, 2026, needs more optimization.
13 244 0.376709523739 Henry Cohn, 2026, needs more optimization.
13 245 0.377647013567 Henry Cohn, 2026, needs more optimization.
13 246 0.378272266465 Henry Cohn, 2026, needs more optimization.
13 247 0.378820680341 Henry Cohn, 2026, needs more optimization.
13 248 0.379276158862 Henry Cohn, 2026, needs more optimization.
13 249 0.380069447935 Henry Cohn, 2026, needs more optimization.
13 250 0.380763937360 Henry Cohn, 2026, needs more optimization.
13 251 0.381485144531 Henry Cohn, 2026, needs more optimization.
13 252 0.381924747381 Henry Cohn, 2026, needs more optimization.
13 253 0.382855237546 Henry Cohn, 2026, needs more optimization.
13 254 0.383234990997 Henry Cohn, 2026, needs more optimization.
13 255 0.384355957547 Henry Cohn, 2026, needs more optimization.
13 306 0.384615384616 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−5
13 313 0.384615384616 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
13⁢x−5
13 314 0.390043042080 Henry Cohn, 2026, needs more optimization.
13 315 0.395309741901 Henry Cohn, 2026, needs more optimization.
13 316 0.397599719886 Henry Cohn, 2026, needs more optimization.
13 317 0.399689484624 Henry Cohn, 2026, needs more optimization.
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 0.402743868310 Henry Cohn, 2026, needs more optimization.
13 338 0.418428524196 Henry Cohn, 2026, needs more optimization.
13 339 0.418737825194 Henry Cohn, 2025, needs more optimization.
13 340 0.418875769127 Henry Cohn, 2025, needs more optimization.
13 341 0.419419034847 Henry Cohn, 2025, needs more optimization.
13 342 0.420041868205 Henry Cohn, 2026, needs more optimization.
13 343 0.420070225222 Henry Cohn, 2025, needs more optimization.
13 344 0.420389870109 Henry Cohn, 2026, needs more optimization.
13 345 0.420581365637 Henry Cohn, 2025, needs more optimization.
13 346 0.420692052532 Henry Cohn, 2026, needs more optimization.
13 347 0.421102107698 Henry Cohn, 2025, needs more optimization.
13 348 0.421543178185 Henry Cohn, 2026, needs more optimization.
13 349 0.421907425104 Henry Cohn, 2025, needs more optimization.
13 350 0.422003341351 Henry Cohn, 2026, needs more optimization.
13 351 0.422575939533 Henry Cohn, 2025, needs more optimization.
13 352 0.422858125025 Henry Cohn, 2026, needs more optimization.
13 353 0.423230257051 Henry Cohn, 2025, needs more optimization.
13 354 0.423705958035 Henry Cohn, 2026, needs more optimization.
13 355 0.424058260598 Henry Cohn, 2025, needs more optimization.
13 356 0.424139492882 Henry Cohn, 2026, needs more optimization.
13 357 0.424432715559 Henry Cohn, 2025, needs more optimization.
13 358 0.424990165310 Henry Cohn, 2026, needs more optimization.
13 359 0.425356584705 Henry Cohn, 2025, needs more optimization.
13 360 0.425473600075 Henry Cohn, 2026, needs more optimization.
13 361 0.426053892700 Henry Cohn, 2025, needs more optimization.
13 362 0.426380190775 Henry Cohn, 2026, needs more optimization.
13 363 0.426403543342 Henry Cohn, 2025, needs more optimization.
13 364 0.426672402227 Henry Cohn, 2026, needs more optimization.
13 365 0.427322675493 Henry Cohn, 2025, needs more optimization.
13 366 0.427754784345 Henry Cohn, 2026, needs more optimization.
13 367 0.428353186852 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
13 501 0.429715152009 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 0.459815216741 Henry Cohn, 2026, needs more optimization.
13 580 0.465789763135 Henry Cohn, 2026, needs more optimization.
13 581 0.465955526650 Henry Cohn, 2025, needs more optimization.
13 582 0.466245560670 Henry Cohn, 2026, needs more optimization.
13 584 0.466530373366 Henry Cohn, 2026, needs more optimization.
13 585 0.466832748141 Henry Cohn, 2025, needs more optimization.
13 586 0.467315367283 Henry Cohn, 2026, needs more optimization.
13 590 0.467465906002 Henry Cohn, 2026, needs more optimization.
13 594 0.467705720323 Henry Cohn, 2026, needs more optimization.
13 596 0.467769086876 Henry Cohn, 2026, needs more optimization.
13 598 0.470077705608 Henry Cohn, 2026, needs more optimization.
13 599 0.470605232123 Henry Cohn, 2026, needs more optimization.
13 600 0.470770397994 Henry Cohn, 2026, needs more optimization.
13 601 0.471026039091 Henry Cohn, 2025, needs more optimization.
13 602 0.472796352342 Henry Cohn, 2025, needs more optimization.
13 603 0.473262426000 Henry Cohn, 2025, needs more optimization.
13 604 0.473278998215 Henry Cohn, 2026, needs more optimization.
13 605 0.473324558816 Henry Cohn, 2025, needs more optimization.
13 606 0.473519402588 Henry Cohn, 2026, needs more optimization.
13 608 0.473604551063 Henry Cohn, 2026, needs more optimization.
13 609 0.473627679841 Henry Cohn, 2025, needs more optimization.
13 610 0.473665284087 Henry Cohn, 2026, needs more optimization.
13 611 0.473739534858 Henry Cohn, 2025, needs more optimization.
13 612 0.473965827048 Henry Cohn, 2026, needs more optimization.
13 613 0.474406686573 Henry Cohn, 2025, needs more optimization.
13 614 0.474466300754 Henry Cohn, 2026, needs more optimization.
13 615 0.474494086062 Henry Cohn, 2025, needs more optimization.
13 616 0.474905852839 Henry Cohn, 2026, needs more optimization.
13 617 0.474918963482 Henry Cohn, 2025, needs more optimization.
13 618 0.474944957609 Henry Cohn, 2026, needs more optimization.
13 619 0.475383863231 Henry Cohn, 2025, needs more optimization.
13 620 0.475415073774 Henry Cohn, 2026, needs more optimization.
13 621 0.475458135871 Henry Cohn, 2025, needs more optimization.
13 622 0.475526705956 Henry Cohn, 2026, needs more optimization.
13 623 0.475564411116 Henry Cohn, 2025, needs more optimization.
13 624 0.475772458391 Henry Cohn, 2025, needs more optimization.
13 625 0.476105619632 Henry Cohn, 2025, needs more optimization.
13 626 0.476123640269 Henry Cohn, 2026, needs more optimization.
13 627 0.476133672282 Henry Cohn, 2025, needs more optimization.
13 628 0.476274391676 Henry Cohn, 2026, needs more optimization.
13 629 0.476497765410 Henry Cohn, 2025, needs more optimization.
13 630 0.476681624640 Henry Cohn, 2026, needs more optimization.
13 632 0.476753462685 Henry Cohn, 2026, needs more optimization.
13 633 0.476779642724 Henry Cohn, 2025, needs more optimization.
13 634 0.476858156996 Henry Cohn, 2026, needs more optimization.
13 635 0.477164338899 Henry Cohn, 2025, needs more optimization.
13 636 0.477264749703 Henry Cohn, 2026, needs more optimization.
13 637 0.477285852944 Henry Cohn, 2025, needs more optimization.
13 638 0.477595922555 Henry Cohn, 2026, needs more optimization.
13 639 0.477701773044 Henry Cohn, 2025, needs more optimization.
13 640 0.477865043264 Henry Cohn, 2026, needs more optimization.
13 642 0.477875910369 Henry Cohn, 2026, needs more optimization.
13 644 0.478030845536 Henry Cohn, 2026, needs more optimization.
13 645 0.478368394521 Henry Cohn, 2025, needs more optimization.
13 646 0.478398455723 Henry Cohn, 2026, needs more optimization.
13 647 0.478492404615 Henry Cohn, 2025, needs more optimization.
13 648 0.478503335799 Henry Cohn, 2026, needs more optimization.
13 649 0.478509908716 Henry Cohn, 2025, needs more optimization.
13 650 0.478826305333 Henry Cohn, 2026, needs more optimization.
13 651 0.478838229297 Henry Cohn, 2025, needs more optimization.
13 652 0.478856464367 Henry Cohn, 2026, needs more optimization.
13 653 0.479050421989 Henry Cohn, 2025, needs more optimization.
13 654 0.479063218806 Henry Cohn, 2026, needs more optimization.
13 655 0.479603675125 Henry Cohn, 2025, needs more optimization.
13 656 0.479613974451 Henry Cohn, 2026, needs more optimization.
13 657 0.479687023902 Henry Cohn, 2025, needs more optimization.
13 658 0.479699271361 Henry Cohn, 2026, needs more optimization.
13 659 0.479730979245 Henry Cohn, 2025, needs more optimization.
13 660 0.480347440524 Henry Cohn, 2026, needs more optimization.
13 661 0.480364890268 Henry Cohn, 2025, needs more optimization.
13 662 0.480372895606 Henry Cohn, 2026, needs more optimization.
13 663 0.480405879307 Henry Cohn, 2025, needs more optimization.
13 664 0.480454278236 Henry Cohn, 2026, needs more optimization.
13 665 0.480771700158 Henry Cohn, 2025, needs more optimization.
13 666 0.480808035113 Henry Cohn, 2026, needs more optimization.
13 667 0.480821848300 Henry Cohn, 2025, needs more optimization.
13 668 0.480831213922 Henry Cohn, 2026, needs more optimization.
13 670 0.480884443442 Henry Cohn, 2026, needs more optimization.
13 672 0.481273438735 Henry Cohn, 2025, needs more optimization.
13 673 0.481283021102 Henry Cohn, 2025, needs more optimization.
13 674 0.481284347723 Henry Cohn, 2026, needs more optimization.
13 675 0.481644119395 Henry Cohn, 2025, needs more optimization.
13 676 0.481799113049 Henry Cohn, 2026, needs more optimization.
13 677 0.481830390467 Henry Cohn, 2025, needs more optimization.
13 678 0.481833814115 Henry Cohn, 2026, needs more optimization.
13 679 0.482152300430 Henry Cohn, 2025, needs more optimization.
13 680 0.482154819163 Henry Cohn, 2026, needs more optimization.
13 681 0.482169815140 Henry Cohn, 2025, needs more optimization.
13 682 0.482446092429 Henry Cohn, 2026, needs more optimization.
13 684 0.482480693519 Henry Cohn, 2026, needs more optimization.
13 685 0.482658262037 Henry Cohn, 2025, needs more optimization.
13 686 0.482707808246 Henry Cohn, 2026, needs more optimization.
13 687 0.482727338345 Henry Cohn, 2025, needs more optimization.
13 688 0.482904616258 Henry Cohn, 2026, needs more optimization.
13 690 0.482936949385 Henry Cohn, 2026, needs more optimization.
13 691 0.483009366512 Henry Cohn, 2025, needs more optimization.
13 692 0.483662493176 Henry Cohn, 2026, needs more optimization.
13 693 0.483679760956 Henry Cohn, 2026, needs more optimization.
13 694 0.483724892704 Henry Cohn, 2026, needs more optimization.
13 695 0.483787098673 Henry Cohn, 2026, needs more optimization.
13 696 0.483798522832 Henry Cohn, 2026, needs more optimization.
13 697 0.483876695006 Henry Cohn, 2026, needs more optimization.
13 698 0.484135521202 Henry Cohn, 2026, needs more optimization.
13 699 0.484199973268 Henry Cohn, 2026, needs more optimization.
13 700 0.484227609270 Henry Cohn, 2026, needs more optimization.
13 701 0.484239737748 Henry Cohn, 2026, needs more optimization.
13 702 0.484285803164 Henry Cohn, 2026, needs more optimization.
13 703 0.484302736505 Henry Cohn, 2026, needs more optimization.
13 704 0.484321914872 Henry Cohn, 2026, needs more optimization.
13 705 0.484422869747 Henry Cohn, 2026, needs more optimization.
13 706 0.484672767524 Henry Cohn, 2026, needs more optimization.
13 707 0.484732429220 Henry Cohn, 2026, needs more optimization.
13 708 0.484898375649 Henry Cohn, 2026, needs more optimization.
13 709 0.484916439382 Henry Cohn, 2026, needs more optimization.
13 710 0.484933992513 Henry Cohn, 2026, needs more optimization.
13 711 0.484975605774 Henry Cohn, 2026, needs more optimization.
13 712 0.484987569503 Henry Cohn, 2026, needs more optimization.
13 713 0.485212526103 Henry Cohn, 2026, needs more optimization.
13 714 0.485281723031 Henry Cohn, 2026, needs more optimization.
13 715 0.485372764905 Henry Cohn, 2026, needs more optimization.
13 716 0.485451228042 Henry Cohn, 2026, needs more optimization.
13 717 0.485454861353 Henry Cohn, 2026, needs more optimization.
13 718 0.485465400333 Henry Cohn, 2026, needs more optimization.
13 719 0.485468162774 Henry Cohn, 2025, needs more optimization.
13 720 0.485489349759 Henry Cohn, 2026, needs more optimization.
13 721 0.485590481749 Henry Cohn, 2026, needs more optimization.
13 722 0.485623534964 Henry Cohn, 2026, needs more optimization.
13 723 0.485665431561 Henry Cohn, 2026, needs more optimization.
13 724 0.486214777807 Henry Cohn, 2026, needs more optimization.
13 725 0.486252494691 Henry Cohn, 2026, needs more optimization.
13 726 0.486262022021 Henry Cohn, 2026, needs more optimization.
13 727 0.486295397213 Henry Cohn, 2026, needs more optimization.
13 728 0.486315569030 Henry Cohn, 2026, needs more optimization.
13 729 0.486332923651 Henry Cohn, 2026, needs more optimization.
13 730 0.486344751192 Henry Cohn, 2026, needs more optimization.
13 731 0.486386971428 Henry Cohn, 2026, needs more optimization.
13 732 0.486398271121 Henry Cohn, 2026, needs more optimization.
13 733 0.486407694694 Henry Cohn, 2026, needs more optimization.
13 734 0.486470573631 Henry Cohn, 2026, needs more optimization.
13 735 0.486510068810 Henry Cohn, 2026, needs more optimization.
13 736 0.486541827480 Henry Cohn, 2026, needs more optimization.
13 737 0.486590348277 Henry Cohn, 2026, needs more optimization.
13 738 0.486625678301 Henry Cohn, 2026, needs more optimization.
13 739 0.486645531175 Henry Cohn, 2026, needs more optimization.
13 740 0.486747665413 Henry Cohn, 2026, needs more optimization.
13 741 0.486757784174 Henry Cohn, 2026, needs more optimization.
13 742 0.486782295403 Henry Cohn, 2026, needs more optimization.
13 743 0.486797783725 Henry Cohn, 2026, needs more optimization.
13 744 0.486809080246 Henry Cohn, 2026, needs more optimization.
13 745 0.486828575373 Henry Cohn, 2026, needs more optimization.
13 746 0.486859781045 Henry Cohn, 2026, needs more optimization.
13 747 0.486976941830 Henry Cohn, 2026, needs more optimization.
13 748 0.487288300144 Henry Cohn, 2026, needs more optimization.
13 749 0.487297499593 Henry Cohn, 2025, needs more optimization.
13 750 0.487325957512 Henry Cohn, 2026, needs more optimization.
13 751 0.487367552569 Henry Cohn, 2026, needs more optimization.
13 752 0.487382031309 Henry Cohn, 2026, needs more optimization.
13 753 0.487389880484 Henry Cohn, 2026, needs more optimization.
13 754 0.487395788319 Henry Cohn, 2026, needs more optimization.
13 755 0.487488797036 Henry Cohn, 2026, needs more optimization.
13 756 0.487564772802 Henry Cohn, 2026, needs more optimization.
13 757 0.487717941281 Henry Cohn, 2026, needs more optimization.
13 758 0.487778612423 Henry Cohn, 2026, needs more optimization.
13 759 0.487799584568 Henry Cohn, 2026, needs more optimization.
13 760 0.487834969073 Henry Cohn, 2026, needs more optimization.
13 761 0.487884555595 Henry Cohn, 2026, needs more optimization.
13 762 0.487966859625 Henry Cohn, 2026, needs more optimization.
13 763 0.488026550395 Henry Cohn, 2026, needs more optimization.
13 764 0.488093397239 Henry Cohn, 2026, needs more optimization.
13 765 0.488121564610 Henry Cohn, 2026, needs more optimization.
13 766 0.488154726872 Henry Cohn, 2026, needs more optimization.
13 769 0.488174282443 Henry Cohn, 2026, needs more optimization.
13 770 0.488235441004 Henry Cohn, 2026, needs more optimization.
13 771 0.488351396155 Henry Cohn, 2026, needs more optimization.
13 772 0.488373464108 Henry Cohn, 2026, needs more optimization.
13 773 0.488420213503 Henry Cohn, 2026, needs more optimization.
13 774 0.488454070370 Henry Cohn, 2026, needs more optimization.
13 776 0.488472831823 Henry Cohn, 2026, needs more optimization.
13 777 0.488534261117 Henry Cohn, 2026, needs more optimization.
13 778 0.488582967968 Henry Cohn, 2026, needs more optimization.
13 779 0.488641812334 Henry Cohn, 2026, needs more optimization.
13 780 0.488652978943 Henry Cohn, 2026, needs more optimization.
13 781 0.488706694442 Henry Cohn, 2026, needs more optimization.
13 783 0.488742970113 Henry Cohn, 2026, needs more optimization.
13 784 0.488766702352 Henry Cohn, 2026, needs more optimization.
13 785 0.488845158247 Henry Cohn, 2026, needs more optimization.
13 786 0.488855043224 Henry Cohn, 2026, needs more optimization.
13 787 0.488874469850 Henry Cohn, 2026, needs more optimization.
13 788 0.488939559580 Henry Cohn, 2026, needs more optimization.
13 789 0.489073397216 Henry Cohn, 2026, needs more optimization.
13 790 0.489173658072 Henry Cohn, 2026, needs more optimization.
13 791 0.489183536067 Henry Cohn, 2026, needs more optimization.
13 792 0.489186890022 Henry Cohn, 2026, needs more optimization.
13 793 0.489323213786 Henry Cohn, 2026, needs more optimization.
13 794 0.489391064149 Henry Cohn, 2026, needs more optimization.
13 795 0.489469082070 Henry Cohn, 2026, needs more optimization.
13 796 0.489539713375 Henry Cohn, 2026, needs more optimization.
13 797 0.489602925537 Henry Cohn, 2026, needs more optimization.
13 800 0.489606815580 Henry Cohn, 2026, needs more optimization.
13 801 0.489689007180 Henry Cohn, 2026, needs more optimization.
13 803 0.489689603761 Henry Cohn, 2026, needs more optimization.
13 804 0.489733170731 Henry Cohn, 2026, needs more optimization.
13 805 0.489746583853 Henry Cohn, 2026, needs more optimization.
13 806 0.489849783294 Henry Cohn, 2026, needs more optimization.
13 807 0.489942616656 Henry Cohn, 2026, needs more optimization.
13 808 0.490072750203 Henry Cohn, 2026, needs more optimization.
13 809 0.490111765883 Henry Cohn, 2026, needs more optimization.
13 810 0.490124597435 Henry Cohn, 2026, needs more optimization.
13 811 0.490203978779 Henry Cohn, 2026, needs more optimization.
13 813 0.490234459693 Henry Cohn, 2026, needs more optimization.
13 814 0.490270385182 Henry Cohn, 2026, needs more optimization.
13 815 0.490308881783 Henry Cohn, 2026, needs more optimization.
13 817 0.490425243487 Henry Cohn, 2026, needs more optimization.
13 818 0.490613049609 Henry Cohn, 2026, needs more optimization.
13 819 0.490675490437 Henry Cohn, 2026, needs more optimization.
13 820 0.490785951877 Henry Cohn, 2026, needs more optimization.
13 821 0.490921498408 Henry Cohn, 2026, needs more optimization.
13 822 0.490958303049 Henry Cohn, 2026, needs more optimization.
13 823 0.491010447837 Henry Cohn, 2026, needs more optimization.
13 824 0.491066127526 Henry Cohn, 2026, needs more optimization.
13 826 0.491150285362 Henry Cohn, 2026, needs more optimization.
13 827 0.491217541538 Henry Cohn, 2026, needs more optimization.
13 828 0.491220260302 Henry Cohn, 2026, needs more optimization.
13 829 0.491338436111 Henry Cohn, 2026, needs more optimization.
13 830 0.491426807214 Henry Cohn, 2026, needs more optimization.
13 831 0.491494411301 Henry Cohn, 2026, needs more optimization.
13 832 0.491566759613 Henry Cohn, 2026, needs more optimization.
13 833 0.491654477358 Henry Cohn, 2026, needs more optimization.
13 834 0.491681551106 Henry Cohn, 2026, needs more optimization.
13 835 0.491722722640 Henry Cohn, 2026, needs more optimization.
13 836 0.491741045182 Henry Cohn, 2026, needs more optimization.
13 837 0.491844664645 Henry Cohn, 2026, needs more optimization.
13 842 0.491931171638 Henry Cohn, 2026, needs more optimization.
13 843 0.492013223904 Henry Cohn, 2026, needs more optimization.
13 844 0.492134401387 Henry Cohn, 2026, needs more optimization.
13 846 0.492213576413 Henry Cohn, 2026, needs more optimization.
13 847 0.492344271873 Henry Cohn, 2026, needs more optimization.
13 848 0.492446133470 Henry Cohn, 2026, needs more optimization.
13 849 0.492568053039 Henry Cohn, 2026, needs more optimization.
13 850 0.492694319902 Henry Cohn, 2026, needs more optimization.
13 851 0.492905638463 Henry Cohn, 2026, needs more optimization.
13 852 0.492999902420 Henry Cohn, 2026, needs more optimization.
13 853 0.493124177952 Henry Cohn, 2026, needs more optimization.
13 854 0.493256170735 Henry Cohn, 2026, needs more optimization.
13 855 0.493438425273 Henry Cohn, 2026, needs more optimization.
13 856 0.493599172978 Henry Cohn, 2026, needs more optimization.
13 857 0.493724237539 Henry Cohn, 2026, needs more optimization.
13 858 0.493915595949 Henry Cohn, 2026, needs more optimization.
13 859 0.494129487925 Henry Cohn, 2026, needs more optimization.
13 860 0.494278390579 Henry Cohn, 2026, needs more optimization.
13 861 0.494346204880 Henry Cohn, 2026, needs more optimization.
13 862 0.494534665185 Henry Cohn, 2026, needs more optimization.
13 863 0.494627348545 Henry Cohn, 2026, needs more optimization.
13 864 0.494769024438 Henry Cohn, 2026, needs more optimization.
13 865 0.494916035384 Henry Cohn, 2026, needs more optimization.
13 866 0.495059105976 Henry Cohn, 2026, needs more optimization.
13 867 0.495261851955 Henry Cohn, 2026, needs more optimization.
13 868 0.495400074182 Henry Cohn, 2026, needs more optimization.
13 869 0.495544057684 Henry Cohn, 2026, needs more optimization.
13 870 0.495762168565 Henry Cohn, 2026, needs more optimization.
13 871 0.495915909547 Henry Cohn, 2026, needs more optimization.
13 872 0.496018345558 Henry Cohn, 2026, needs more optimization.
13 874 0.496304834136 Henry Cohn, 2026, needs more optimization.
13 875 0.496416845255 Henry Cohn, 2026, needs more optimization.
13 876 0.496419974300 Henry Cohn, 2026, needs more optimization.
13 877 0.496823751126 Henry Cohn, 2026, needs more optimization.
13 878 0.496954262706 Henry Cohn, 2026, needs more optimization.
13 879 0.497087857398 Henry Cohn, 2026, needs more optimization.
13 880 0.497295006003 Henry Cohn, 2026, needs more optimization.
13 881 0.497357094722 Henry Cohn, 2026, needs more optimization.
13 882 0.497452655889 Henry Cohn, 2026, needs more optimization.
13 883 0.497738906212 Henry Cohn, 2026, needs more optimization.
13 884 0.498023877560 Henry Cohn, 2026, needs more optimization.
13 885 0.498201936366 Henry Cohn, 2026, needs more optimization.
13 886 0.498435066014 Henry Cohn, 2026, needs more optimization.
13 887 0.498612404172 Henry Cohn, 2026, needs more optimization.
13 888 0.498891722692 Henry Cohn, 2026, needs more optimization.
13 889 0.499071285711 Henry Cohn, 2026, needs more optimization.
13 890 0.499283746457 Henry Cohn, 2026, needs more optimization.
13 891 0.499423393292 Henry Cohn, 2026, needs more optimization.
13 892 0.499639900667 Henry Cohn, 2026, needs more optimization.
13 893 0.499857434534 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 0.180989672412 Henry Cohn, 2026.
14 73 0.184685922154 Henry Cohn, 2026, needs more optimization.
14 75 0.185110498567 Henry Cohn, 2026, needs more optimization.
14 76 0.189888326702 Henry Cohn, 2026, needs more optimization.
14 77 0.192041239872 Henry Cohn, 2026, needs more optimization.
14 78 0.192681299289 Henry Cohn, 2026, needs more optimization.
14 79 0.194319485351 Henry Cohn, 2026, needs more optimization.
14 80 0.195567887118 Henry Cohn, 2026, needs more optimization.
14 81 0.198109577704 Henry Cohn, 2026, needs more optimization.
14 83 0.198343910648 Henry Cohn, 2026, needs more optimization.
14 84 0.198352242086 Henry Cohn, 2026, needs more optimization.
14 85 0.198385543010 Henry Cohn, 2026, needs more optimization.
14 86 0.198455824029 Henry Cohn, 2026, needs more optimization.
14 87 0.198500556633 Henry Cohn, 2026, needs more optimization.
14 88 0.198573230999 Henry Cohn, 2026, needs more optimization.
14 89 0.198677263321 Henry Cohn, 2026, needs more optimization.
14 90 0.198771953024 Henry Cohn, 2026, needs more optimization.
14 91 0.198843416031 Henry Cohn, 2026, needs more optimization.
14 92 0.208457898342 Henry Cohn, 2026, needs more optimization.
14 93 0.212930218599 Henry Cohn, 2026, needs more optimization.
14 94 0.213929020886 Henry Cohn, 2026, needs more optimization.
14 95 0.217144961920 Henry Cohn, 2026, needs more optimization.
14 96 0.217581735483 Henry Cohn, 2026, needs more optimization.
14 97 0.217987275840 Henry Cohn, 2026, needs more optimization.
14 98 0.219808790643 Henry Cohn, 2026, needs more optimization.
14 99 0.222120043573 Henry Cohn, 2026, needs more optimization.
14 100 0.223728320054 Henry Cohn, 2026, needs more optimization.
14 101 0.225620988107 Henry Cohn, 2026, needs more optimization.
14 102 0.228335097166 Henry Cohn, 2026, needs more optimization.
14 112 0.229910395528 Henry Cohn, 2026, needs more optimization.
14 113 0.234903720985 Henry Cohn, 2026, needs more optimization.
14 114 0.237369497279 Henry Cohn, 2026, needs more optimization.
14 115 0.239325245580 Henry Cohn, 2026, needs more optimization.
14 116 0.240935156065 Henry Cohn, 2026, needs more optimization.
14 117 0.242371582782 Henry Cohn, 2026, needs more optimization.
14 118 0.244114685265 Henry Cohn, 2026, needs more optimization.
14 119 0.244941008540 Henry Cohn, 2026, needs more optimization.
14 120 0.246542776600 Henry Cohn, 2026, needs more optimization.
14 121 0.247804837635 Henry Cohn, 2026, needs more optimization.
14 122 0.249222342079 Henry Cohn, 2026, needs more optimization.
14 123 0.250379704223 Henry Cohn, 2026, needs more optimization.
14 124 0.251250704298 Henry Cohn, 2026, needs more optimization.
14 125 0.252289325846 Henry Cohn, 2026, needs more optimization.
14 126 0.253312836158 Henry Cohn, 2026, needs more optimization.
14 127 0.254061789773 Henry Cohn, 2026, needs more optimization.
14 128 0.254664003575 Henry Cohn, 2026, needs more optimization.
14 129 0.255355902029 Henry Cohn, 2026, needs more optimization.
14 130 0.256043761691 Henry Cohn, 2026, needs more optimization.
14 131 0.259573700404 Henry Cohn, 2026, needs more optimization.
14 132 0.261696058723 Henry Cohn, 2026, needs more optimization.
14 133 0.262945569771 Henry Cohn, 2026, needs more optimization.
14 134 0.264542191163 Henry Cohn, 2026, needs more optimization.
14 135 0.265754813181 Henry Cohn, 2026, needs more optimization.
14 136 0.266911524938 Henry Cohn, 2026, needs more optimization.
14 137 0.268345572335 Henry Cohn, 2026, needs more optimization.
14 138 0.269360778127 Henry Cohn, 2026, needs more optimization.
14 139 0.269360778215 Henry Cohn, 2026, needs more optimization.
14 140 0.269363487463 Henry Cohn, 2026, needs more optimization.
14 141 0.269364653598 Henry Cohn, 2026, needs more optimization.
14 142 0.269374502335 Henry Cohn, 2026, needs more optimization.
14 143 0.269376035730 Henry Cohn, 2026, needs more optimization.
14 144 0.269378796345 Henry Cohn, 2026, needs more optimization.
14 145 0.269385310491 Henry Cohn, 2026, needs more optimization.
14 146 0.269391870780 Henry Cohn, 2026, needs more optimization.
14 147 0.269406679844 Henry Cohn, 2026, needs more optimization.
14 148 0.269436221721 Henry Cohn, 2026, needs more optimization.
14 149 0.269471439877 Henry Cohn, 2026, needs more optimization.
14 150 0.269516324115 Henry Cohn, 2026, needs more optimization.
14 152 0.269752269749 Henry Cohn, 2026, needs more optimization.
14 153 0.273185531224 Henry Cohn, 2026, needs more optimization.
14 154 0.273861278753 Henry Cohn, 2026.
40⁢x2−3
14 156 0.283473354757 Henry Cohn, 2024.
112⁢x2−9
14 157 0.291874360089 Henry Cohn, 2026, needs more optimization.
14 158 0.292313560776 Henry Cohn, 2026, needs more optimization.
14 159 0.292613370098 Henry Cohn, 2026, needs more optimization.
14 160 0.293018166111 Henry Cohn, 2026, needs more optimization.
14 161 0.293282450482 Henry Cohn, 2026, needs more optimization.
14 162 0.293460417279 Henry Cohn, 2026, needs more optimization.
14 163 0.293843256947 Henry Cohn, 2026, needs more optimization.
14 164 0.294389313524 Henry Cohn, 2026, needs more optimization.
14 165 0.294761138488 Henry Cohn, 2026, needs more optimization.
14 166 0.294915118350 Henry Cohn, 2026, needs more optimization.
14 167 0.295209686292 Henry Cohn, 2026, needs more optimization.
14 168 0.295503189377 Henry Cohn, 2026, needs more optimization.
14 169 0.295903033027 Henry Cohn, 2026, needs more optimization.
14 170 0.296069867089 Henry Cohn, 2026, needs more optimization.
14 171 0.296373558678 Henry Cohn, 2026, needs more optimization.
14 172 0.296743192264 Henry Cohn, 2026, needs more optimization.
14 173 0.297333197311 Henry Cohn, 2026, needs more optimization.
14 174 0.298203122347 Henry Cohn, 2026, needs more optimization.
14 175 0.298918357813 Henry Cohn, 2026, needs more optimization.
14 176 0.299626167504 Henry Cohn, 2026, needs more optimization.
14 177 0.300872133328 Henry Cohn, 2026, needs more optimization.
14 178 0.301383882191 Henry Cohn, 2026, needs more optimization.
14 179 0.301974235178 Henry Cohn, 2026, needs more optimization.
14 180 0.302519384058 Henry Cohn, 2026, needs more optimization.
14 181 0.303196255754 Henry Cohn, 2026, needs more optimization.
14 182 0.303849848389 Henry Cohn, 2026, needs more optimization.
14 183 0.304088976452 Henry Cohn, 2026, needs more optimization.
14 184 0.304279563393 Henry Cohn, 2026, needs more optimization.
14 185 0.304681396403 Henry Cohn, 2026, needs more optimization.
14 186 0.304833574487 Henry Cohn, 2026, needs more optimization.
14 187 0.305009607834 Henry Cohn, 2026, needs more optimization.
14 188 0.305364169581 Henry Cohn, 2026, needs more optimization.
14 189 0.305514435865 Henry Cohn, 2026, needs more optimization.
14 190 0.305729414015 Henry Cohn, 2026, needs more optimization.
14 191 0.306011832450 Henry Cohn, 2026, needs more optimization.
14 192 0.306237359539 Henry Cohn, 2026, needs more optimization.
14 193 0.306423350022 Henry Cohn, 2026, needs more optimization.
14 194 0.306533060632 Henry Cohn, 2026, needs more optimization.
14 195 0.307191181438 Henry Cohn, 2026, needs more optimization.
14 196 0.308181996958 Henry Cohn, 2026, needs more optimization.
14 197 0.309388747861 Henry Cohn, 2026, needs more optimization.
14 198 0.310122136308 Henry Cohn, 2026, needs more optimization.
14 199 0.310697270757 Henry Cohn, 2026, needs more optimization.
14 200 0.311247704707 Henry Cohn, 2026, needs more optimization.
14 201 0.312455070761 Henry Cohn, 2026, needs more optimization.
14 202 0.313545758385 Henry Cohn, 2026, needs more optimization.
14 203 0.314864093760 Henry Cohn, 2026, needs more optimization.
14 204 0.315778330431 Henry Cohn, 2026, needs more optimization.
14 205 0.316641172779 Henry Cohn, 2026, needs more optimization.
14 206 0.317223057877 Henry Cohn, 2026, needs more optimization.
14 207 0.317654154004 Henry Cohn, 2026, needs more optimization.
14 210 0.318181818182 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
22⁢x−7
14 211 0.323538869870 Henry Cohn, 2026, needs more optimization.
14 212 0.323827678696 Henry Cohn, 2026, needs more optimization.
14 213 0.323855377135 Henry Cohn, 2026, needs more optimization.
14 214 0.323888934125 Henry Cohn, 2026, needs more optimization.
14 215 0.324219004032 Henry Cohn, 2026, needs more optimization.
14 216 0.324376738387 Henry Cohn, 2026, needs more optimization.
14 217 0.324414620466 Henry Cohn, 2026, needs more optimization.
14 218 0.324482493640 Henry Cohn, 2026, needs more optimization.
14 219 0.324849522938 Henry Cohn, 2026, needs more optimization.
14 220 0.325076988791 Henry Cohn, 2026, needs more optimization.
14 221 0.325415461477 Henry Cohn, 2026, needs more optimization.
14 222 0.325548028040 Henry Cohn, 2026, needs more optimization.
14 223 0.325916277422 Henry Cohn, 2026, needs more optimization.
14 224 0.325940873323 Henry Cohn, 2026, needs more optimization.
14 225 0.326076183289 Henry Cohn, 2026, needs more optimization.
14 226 0.326656095631 Henry Cohn, 2026, needs more optimization.
14 227 0.326918373400 Henry Cohn, 2026, needs more optimization.
14 228 0.327158972750 Henry Cohn, 2026, needs more optimization.
14 229 0.327348773089 Henry Cohn, 2026, needs more optimization.
14 230 0.327402971143 Henry Cohn, 2026, needs more optimization.
14 231 0.327680397329 Henry Cohn, 2026, needs more optimization.
14 232 0.328104201091 Henry Cohn, 2026, needs more optimization.
14 233 0.328778229383 Henry Cohn, 2026, needs more optimization.
14 234 0.329665952303 Henry Cohn, 2026, needs more optimization.
14 235 0.330548713354 Henry Cohn, 2026, needs more optimization.
14 236 0.331932737981 Henry Cohn, 2026, needs more optimization.
14 237 0.333260210248 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. T. Zhaowei, 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 0.346901134317 Henry Cohn, 2026, needs more optimization.
14 255 0.346930513781 Henry Cohn, 2026, needs more optimization.
14 256 0.347076392183 Henry Cohn, 2026, needs more optimization.
14 257 0.347152508792 Henry Cohn, 2026, needs more optimization.
14 258 0.347246645621 Henry Cohn, 2026, needs more optimization.
14 259 0.347398914511 Henry Cohn, 2026, needs more optimization.
14 260 0.347459063499 Henry Cohn, 2026, needs more optimization.
14 261 0.347501226873 Henry Cohn, 2026, needs more optimization.
14 262 0.347750689323 Henry Cohn, 2026, needs more optimization.
14 263 0.348057247434 Henry Cohn, 2026, needs more optimization.
14 264 0.348146436902 Henry Cohn, 2026, needs more optimization.
14 265 0.348241691464 Henry Cohn, 2026, needs more optimization.
14 266 0.348748993548 Henry Cohn, 2026, needs more optimization.
14 267 0.349032978811 Henry Cohn, 2026, needs more optimization.
14 268 0.349154435190 Henry Cohn, 2026, needs more optimization.
14 269 0.349245293862 Henry Cohn, 2026, needs more optimization.
14 270 0.349579462305 Henry Cohn, 2026, needs more optimization.
14 271 0.350189394089 Henry Cohn, 2026, needs more optimization.
14 272 0.350898578774 Henry Cohn, 2026, needs more optimization.
14 273 0.351350400262 Henry Cohn, 2026, needs more optimization.
14 274 0.351715999861 Henry Cohn, 2026, needs more optimization.
14 275 0.351971528212 Henry Cohn, 2026, needs more optimization.
14 276 0.352120541317 Henry Cohn, 2026, needs more optimization.
14 277 0.352372195071 Henry Cohn, 2026, needs more optimization.
14 278 0.352644178735 Henry Cohn, 2026, needs more optimization.
14 279 0.352929288107 Henry Cohn, 2026, needs more optimization.
14 280 0.353097248379 Henry Cohn, 2026, needs more optimization.
14 281 0.353358642142 Henry Cohn, 2026, needs more optimization.
14 282 0.353570650012 Henry Cohn, 2026, needs more optimization.
14 283 0.353698519353 Henry Cohn, 2026, needs more optimization.
14 284 0.353950965742 Henry Cohn, 2026, needs more optimization.
14 285 0.353960805901 Henry Cohn, 2026, needs more optimization.
14 286 0.354170929744 Henry Cohn, 2026, needs more optimization.
14 287 0.354321089826 Henry Cohn, 2026, needs more optimization.
14 289 0.354618865609 Henry Cohn, 2026, needs more optimization.
14 291 0.354659534312 Henry Cohn, 2026, needs more optimization.
14 292 0.354680317876 Henry Cohn, 2026, needs more optimization.
14 293 0.354787333854 Henry Cohn, 2026, needs more optimization.
14 294 0.354838946103 Henry Cohn, 2026, needs more optimization.
14 295 0.354959154455 Henry Cohn, 2026, needs more optimization.
14 296 0.355138059735 Henry Cohn, 2026, needs more optimization.
14 297 0.355188458536 Henry Cohn, 2026, needs more optimization.
14 298 0.355205968885 Henry Cohn, 2026, needs more optimization.
14 299 0.355210322860 Henry Cohn, 2026, needs more optimization.
14 300 0.355278140097 Henry Cohn, 2026, needs more optimization.
14 301 0.355408189315 Henry Cohn, 2026, needs more optimization.
14 304 0.355592458266 Henry Cohn, 2026, needs more optimization.
14 306 0.355595026220 Henry Cohn, 2026, needs more optimization.
14 307 0.355596245382 Henry Cohn, 2026, needs more optimization.
14 310 0.355596344014 Henry Cohn, 2026, needs more optimization.
14 317 0.355596615854 Henry Cohn, 2026, needs more optimization.
14 318 0.355598619036 Henry Cohn, 2026, needs more optimization.
14 320 0.355598733128 Henry Cohn, 2026, needs more optimization.
14 321 0.355603161787 Henry Cohn, 2026, needs more optimization.
14 322 0.355604049295 Henry Cohn, 2026, needs more optimization.
14 324 0.355612603920 Henry Cohn, 2026, needs more optimization.
14 325 0.355616443419 Henry Cohn, 2026, needs more optimization.
14 327 0.355620633097 Henry Cohn, 2026, needs more optimization.
14 328 0.355620672265 Henry Cohn, 2026, needs more optimization.
14 330 0.355621094000 Henry Cohn, 2026, needs more optimization.
14 331 0.355647861564 Henry Cohn, 2026, needs more optimization.
14 332 0.355662272317 Henry Cohn, 2026, needs more optimization.
14 334 0.356433769210 Henry Cohn, 2026, needs more optimization.
14 335 0.356523872657 Henry Cohn, 2026, needs more optimization.
14 336 0.356530903868 Henry Cohn, 2026, needs more optimization.
14 338 0.356633329284 Henry Cohn, 2026, needs more optimization.
14 339 0.358507191076 Henry Cohn, 2026, needs more optimization.
14 340 0.359862871314 Henry Cohn, 2026, needs more optimization.
14 341 0.360721335636 Henry Cohn, 2026, needs more optimization.
14 342 0.367763287129 Henry Cohn, 2026, needs more optimization.
14 343 0.367824826104 Henry Cohn, 2026, needs more optimization.
14 344 0.368268128693 Henry Cohn, 2026, needs more optimization.
14 346 0.368644934481 Henry Cohn, 2026, needs more optimization.
14 348 0.368808647722 Henry Cohn, 2026, needs more optimization.
14 350 0.368835384507 Henry Cohn, 2026, needs more optimization.
14 351 0.369397909736 Henry Cohn, 2026, needs more optimization.
14 352 0.370682642393 Henry Cohn, 2026, needs more optimization.
14 357 0.378276216277 Henry Cohn, 2026, needs more optimization.
14 358 0.378276216881 Henry Cohn, 2026, needs more optimization.
14 362 0.378279815438 Henry Cohn, 2026, needs more optimization.
14 364 0.378350393632 Henry Cohn, 2026, needs more optimization.
14 366 0.379470712799 Henry Cohn, 2026, needs more optimization.
14 368 0.379518558288 Henry Cohn, 2026, needs more optimization.
14 370 0.379535220280 Henry Cohn, 2026, needs more optimization.
14 372 0.379671965923 Henry Cohn, 2026, needs more optimization.
14 374 0.379676475179 Henry Cohn, 2026, needs more optimization.
14 376 0.379736746844 Henry Cohn, 2026, needs more optimization.
14 378 0.382548477035 Henry Cohn, 2026, needs more optimization.
14 380 0.382596035899 Henry Cohn, 2026, needs more optimization.
14 382 0.382601348572 Henry Cohn, 2026, needs more optimization.
14 384 0.382719113175 Henry Cohn, 2026, needs more optimization.
14 386 0.382850132255 Henry Cohn, 2026, needs more optimization.
14 387 0.383568966190 Henry Cohn, 2026, needs more optimization.
14 388 0.383846399026 Henry Cohn, 2026, needs more optimization.
14 389 0.385168796189 Henry Cohn, 2026, needs more optimization.
14 390 0.385393608823 Henry Cohn, 2026, needs more optimization.
14 391 0.385772743804 Henry Cohn, 2026, needs more optimization.
14 392 0.386946900953 Henry Cohn, 2026, needs more optimization.
14 393 0.387438680068 Henry Cohn, 2026, needs more optimization.
14 394 0.388277632423 Henry Cohn, 2026, needs more optimization.
14 395 0.388743895276 Henry Cohn, 2026, needs more optimization.
14 396 0.389069144467 Henry Cohn, 2026, needs more optimization.
14 397 0.389580870249 Henry Cohn, 2026, needs more optimization.
14 401 0.389991015343 Henry Cohn, 2026, needs more optimization.
14 402 0.389991015346 Henry Cohn, 2026, needs more optimization.
14 403 0.389991015351 Henry Cohn, 2026, needs more optimization.
14 404 0.389991015364 Henry Cohn, 2026, needs more optimization.
14 405 0.390407151109 Henry Cohn, 2026, needs more optimization.
14 407 0.390475616930 Henry Cohn, 2026, needs more optimization.
14 408 0.390708770529 Henry Cohn, 2026, needs more optimization.
14 409 0.390815994072 Henry Cohn, 2026, needs more optimization.
14 415 0.391188213680 Henry Cohn, 2026, needs more optimization.
14 416 0.392322352505 Henry Cohn, 2026, needs more optimization.
14 417 0.392771759196 Henry Cohn, 2026, needs more optimization.
14 419 0.393597883729 Henry Cohn, 2026, needs more optimization.
14 420 0.393868516811 Henry Cohn, 2026, needs more optimization.
14 423 0.393868516812 Henry Cohn, 2026, needs more optimization.
14 424 0.394524995836 Henry Cohn, 2026, needs more optimization.
14 425 0.395250647329 Henry Cohn, 2026, needs more optimization.
14 426 0.396262232864 Henry Cohn, 2026, needs more optimization.
14 427 0.396854602449 Henry Cohn, 2026, needs more optimization.
14 428 0.397243133691 Henry Cohn, 2026, needs more optimization.
14 429 0.397567154571 Henry Cohn, 2026, needs more optimization.
14 430 0.398722637195 Henry Cohn, 2026, needs more optimization.
14 431 0.399250805094 Henry Cohn, 2026, needs more optimization.
14 432 0.399698354205 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
14 492 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
14 493 0.407468460763 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 0.429748171333 Henry Cohn, 2026, needs more optimization.
14 602 0.430061691398 Henry Cohn, 2026, needs more optimization.
14 603 0.430255500551 Henry Cohn, 2025, needs more optimization.
14 604 0.430605377846 Henry Cohn, 2026, needs more optimization.
14 605 0.431095901490 Henry Cohn, 2025, needs more optimization.
14 606 0.431141998946 Henry Cohn, 2026, needs more optimization.
14 607 0.431236397848 Henry Cohn, 2025, needs more optimization.
14 608 0.431365482112 Henry Cohn, 2026, needs more optimization.
14 609 0.431552382817 Henry Cohn, 2025, needs more optimization.
14 610 0.431619232919 Henry Cohn, 2026, needs more optimization.
14 611 0.431687232253 Henry Cohn, 2025, needs more optimization.
14 612 0.432192772355 Henry Cohn, 2026, needs more optimization.
14 614 0.432335371455 Henry Cohn, 2026, needs more optimization.
14 616 0.432898752936 Henry Cohn, 2026, needs more optimization.
14 618 0.432937279627 Henry Cohn, 2026, needs more optimization.
14 620 0.433039391703 Henry Cohn, 2026, needs more optimization.
14 622 0.433079921836 Henry Cohn, 2026, needs more optimization.
14 624 0.433145754655 Henry Cohn, 2026, needs more optimization.
14 626 0.433223426889 Henry Cohn, 2026, needs more optimization.
14 627 0.433311094830 Henry Cohn, 2025, needs more optimization.
14 628 0.433563716319 Henry Cohn, 2026, needs more optimization.
14 630 0.433610534978 Henry Cohn, 2026, needs more optimization.
14 632 0.433688204409 Henry Cohn, 2026, needs more optimization.
14 634 0.433740695007 Henry Cohn, 2026, needs more optimization.
14 636 0.433832897674 Henry Cohn, 2026, needs more optimization.
14 637 0.433915481050 Henry Cohn, 2025, needs more optimization.
14 638 0.433931402932 Henry Cohn, 2026, needs more optimization.
14 639 0.433963466338 Henry Cohn, 2025, needs more optimization.
14 640 0.434234535028 Henry Cohn, 2026, needs more optimization.
14 642 0.434235518543 Henry Cohn, 2026, needs more optimization.
14 644 0.451502692839 Henry Cohn, 2026, needs more optimization.
14 646 0.451504559230 Henry Cohn, 2026, needs more optimization.
14 648 0.451555266873 Henry Cohn, 2026, needs more optimization.
14 649 0.451565788068 Henry Cohn, 2025, needs more optimization.
14 650 0.451676695627 Henry Cohn, 2026, needs more optimization.
14 654 0.451682985488 Henry Cohn, 2026, needs more optimization.
14 656 0.451788208457 Henry Cohn, 2026, needs more optimization.
14 658 0.452010725023 Henry Cohn, 2026, needs more optimization.
14 660 0.452033205431 Henry Cohn, 2026, needs more optimization.
14 667 0.452104481015 Henry Cohn, 2026, needs more optimization.
14 668 0.452120637291 Henry Cohn, 2026, needs more optimization.
14 669 0.452249589060 Henry Cohn, 2026, needs more optimization.
14 670 0.452362100028 Henry Cohn, 2026, needs more optimization.
14 671 0.452452360779 Henry Cohn, 2026, needs more optimization.
14 672 0.452618814252 Henry Cohn, 2026, needs more optimization.
14 673 0.452673179203 Henry Cohn, 2026, needs more optimization.
14 674 0.453194604273 Henry Cohn, 2026, needs more optimization.
14 675 0.453232898355 Henry Cohn, 2026, needs more optimization.
14 676 0.453306275693 Henry Cohn, 2026, needs more optimization.
14 678 0.453332242510 Henry Cohn, 2026, needs more optimization.
14 679 0.453365750682 Henry Cohn, 2026, needs more optimization.
14 680 0.453398481834 Henry Cohn, 2026, needs more optimization.
14 681 0.453452045068 Henry Cohn, 2026, needs more optimization.
14 682 0.453504546383 Henry Cohn, 2026, needs more optimization.
14 683 0.453553986151 Henry Cohn, 2026, needs more optimization.
14 684 0.453684243162 Henry Cohn, 2026, needs more optimization.
14 685 0.453867808833 Henry Cohn, 2026, needs more optimization.
14 688 0.453899317713 Henry Cohn, 2026, needs more optimization.
14 689 0.453934458557 Henry Cohn, 2026, needs more optimization.
14 690 0.454081479092 Henry Cohn, 2026, needs more optimization.
14 691 0.454135729789 Henry Cohn, 2026, needs more optimization.
14 692 0.454152143173 Henry Cohn, 2026, needs more optimization.
14 693 0.454181380020 Henry Cohn, 2026, needs more optimization.
14 694 0.454230726030 Henry Cohn, 2026, needs more optimization.
14 696 0.454336023536 Henry Cohn, 2026, needs more optimization.
14 697 0.454427760141 Henry Cohn, 2026, needs more optimization.
14 699 0.454441873936 Henry Cohn, 2026, needs more optimization.
14 700 0.454494098517 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 0.454719228552 Henry Cohn, 2026, needs more optimization.
14 898 0.454820209793 Henry Cohn, 2026, needs more optimization.
14 899 0.454843103974 Henry Cohn, 2026, needs more optimization.
14 900 0.454887890162 Henry Cohn, 2026, needs more optimization.
14 901 0.454908943607 Henry Cohn, 2026, needs more optimization.
14 902 0.454952665399 Henry Cohn, 2026, needs more optimization.
14 903 0.454978306178 Henry Cohn, 2026, needs more optimization.
14 904 0.455055416212 Henry Cohn, 2026, needs more optimization.
14 905 0.455090759574 Henry Cohn, 2026, needs more optimization.
14 906 0.455098117000 Henry Cohn, 2026, needs more optimization.
14 907 0.455109953199 Henry Cohn, 2026, needs more optimization.
14 908 0.455121613794 Henry Cohn, 2026, needs more optimization.
14 909 0.455141575289 Henry Cohn, 2026, needs more optimization.
14 910 0.455159335404 Henry Cohn, 2026, needs more optimization.
14 911 0.455176246333 Henry Cohn, 2026, needs more optimization.
14 912 0.455187226387 Henry Cohn, 2026, needs more optimization.
14 913 0.455198250727 Henry Cohn, 2026, needs more optimization.
14 914 0.455210036234 Henry Cohn, 2026, needs more optimization.
14 915 0.455224656761 Henry Cohn, 2026, needs more optimization.
14 916 0.455249105039 Henry Cohn, 2026, needs more optimization.
14 917 0.455260374478 Henry Cohn, 2026, needs more optimization.
14 918 0.455286091523 Henry Cohn, 2026, needs more optimization.
14 919 0.455316223489 Henry Cohn, 2026, needs more optimization.
14 920 0.455326887293 Henry Cohn, 2026, needs more optimization.
14 921 0.455339855729 Henry Cohn, 2026, needs more optimization.
14 922 0.455345687557 Henry Cohn, 2026, needs more optimization.
14 923 0.455350230940 Henry Cohn, 2026, needs more optimization.
14 924 0.492313427682 Henry Cohn, 2026, needs more optimization.
14 925 0.492324502055 Henry Cohn, 2026, needs more optimization.
14 926 0.492439035611 Henry Cohn, 2026, needs more optimization.
14 927 0.492661439025 Henry Cohn, 2026, needs more optimization.
14 928 0.492676366579 Henry Cohn, 2026, needs more optimization.
14 929 0.492689023063 Henry Cohn, 2026, needs more optimization.
14 930 0.492973056405 Henry Cohn, 2026, needs more optimization.
14 931 0.493017053994 Henry Cohn, 2026, needs more optimization.
14 932 0.493028038540 Henry Cohn, 2026, needs more optimization.
14 933 0.493095247549 Henry Cohn, 2026, needs more optimization.
14 934 0.493420721055 Henry Cohn, 2026, needs more optimization.
14 935 0.493431116869 Henry Cohn, 2026, needs more optimization.
14 936 0.493474884160 Henry Cohn, 2026, needs more optimization.
14 937 0.493638269990 Henry Cohn, 2026, needs more optimization.
14 938 0.493689294396 Henry Cohn, 2026, needs more optimization.
14 939 0.493697502046 Henry Cohn, 2026, needs more optimization.
14 940 0.493962683689 Henry Cohn, 2026, needs more optimization.
14 941 0.493969273812 Henry Cohn, 2026, needs more optimization.
14 942 0.494138863563 Henry Cohn, 2026, needs more optimization.
14 943 0.494146202233 Henry Cohn, 2026, needs more optimization.
14 944 0.494409198434 Henry Cohn, 2026, needs more optimization.
14 945 0.494434648440 Henry Cohn, 2026, needs more optimization.
14 946 0.494456422769 Henry Cohn, 2025, needs more optimization.
14 947 0.494688046624 Henry Cohn, 2026, needs more optimization.
14 948 0.494703928253 Henry Cohn, 2026, needs more optimization.
14 949 0.494748594954 Henry Cohn, 2026, needs more optimization.
14 950 0.495008690645 Henry Cohn, 2026, needs more optimization.
14 951 0.495020050231 Henry Cohn, 2026, needs more optimization.
14 952 0.495023447217 Henry Cohn, 2026, needs more optimization.
14 953 0.495027976260 Henry Cohn, 2026, needs more optimization.
14 954 0.495147935962 Henry Cohn, 2025, needs more optimization.
14 955 0.495162534668 Henry Cohn, 2026, needs more optimization.
14 956 0.495168651929 Henry Cohn, 2026, needs more optimization.
14 957 0.495367850435 Henry Cohn, 2026, needs more optimization.
14 958 0.495377637529 Henry Cohn, 2026, needs more optimization.
14 959 0.495654270934 Henry Cohn, 2026, needs more optimization.
14 960 0.495657184832 Henry Cohn, 2026, needs more optimization.
14 961 0.495747372287 Henry Cohn, 2026, needs more optimization.
14 962 0.496049763619 Henry Cohn, 2026, needs more optimization.
14 963 0.496053290706 Henry Cohn, 2026, needs more optimization.
14 964 0.496130338879 Henry Cohn, 2026, needs more optimization.
14 965 0.496343187653 Henry Cohn, 2026, needs more optimization.
14 966 0.496367793629 Henry Cohn, 2026, needs more optimization.
14 967 0.496382866709 Henry Cohn, 2026, needs more optimization.
14 968 0.496389619657 Henry Cohn, 2026, needs more optimization.
14 969 0.496650658465 Henry Cohn, 2026, needs more optimization.
14 970 0.496654723830 Henry Cohn, 2026, needs more optimization.
14 971 0.496919523514 Henry Cohn, 2026, needs more optimization.
14 972 0.496975899538 Henry Cohn, 2026, needs more optimization.
14 973 0.496991218031 Henry Cohn, 2026, needs more optimization.
14 974 0.497065736068 Henry Cohn, 2026, needs more optimization.
14 975 0.497286016665 Henry Cohn, 2026, needs more optimization.
14 976 0.497304672293 Henry Cohn, 2026, needs more optimization.
14 977 0.497359410487 Henry Cohn, 2026, needs more optimization.
14 978 0.497601982326 Henry Cohn, 2026, needs more optimization.
14 979 0.497648244447 Henry Cohn, 2026, needs more optimization.
14 980 0.497677114082 Henry Cohn, 2026, needs more optimization.
14 981 0.497737177065 Henry Cohn, 2026, needs more optimization.
14 982 0.497985418945 Henry Cohn, 2026, needs more optimization.
14 983 0.498010864853 Henry Cohn, 2026, needs more optimization.
14 984 0.498020685452 Henry Cohn, 2026, needs more optimization.
14 985 0.498027251417 Henry Cohn, 2026, needs more optimization.
14 986 0.498290396229 Henry Cohn, 2026, needs more optimization.
14 987 0.498474621937 Henry Cohn, 2026, needs more optimization.
14 988 0.498541834310 Henry Cohn, 2026, needs more optimization.
14 989 0.498574622810 Henry Cohn, 2026, needs more optimization.
14 990 0.498756442434 Henry Cohn, 2026, needs more optimization.
14 991 0.498956045858 Henry Cohn, 2026, needs more optimization.
14 992 0.499169595025 Henry Cohn, 2026, needs more optimization.
14 993 0.499337597710 Henry Cohn, 2026, needs more optimization.
14 994 0.499499886525 Henry Cohn, 2026, needs more optimization.
14 995 0.499584976373 Henry Cohn, 2026, needs more optimization.
14 996 0.499725881373 Henry Cohn, 2026, needs more optimization.
14 997 0.499859343626 Henry Cohn, 2026, needs more optimization.
14 998 0.499981323143 Henry Cohn, 2026, needs more optimization.
14 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
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 0.105767188891 Henry Cohn, 2023.
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 0.129619175385 Henry Cohn, 2025, needs more optimization.
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 71 0.166512948843 Henry Cohn, 2025.
15 72 0.166656830714 Henry Cohn, 2026, needs more optimization.
15 73 0.166704540358 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 0.186858652300 Henry Cohn, 2026, needs more optimization.
15 95 0.187145879513 Henry Cohn, 2026, needs more optimization.
15 96 0.188201821306 Henry Cohn, 2026, needs more optimization.
15 99 0.188682054198 Henry Cohn, 2026, needs more optimization.
15 100 0.189764265021 Henry Cohn, 2026, needs more optimization.
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 0.209693852059 Henry Cohn, 2026, needs more optimization.
15 130 0.216744767943 Henry Cohn, 2026, needs more optimization.
15 131 0.219841453017 Henry Cohn, 2026, needs more optimization.
15 132 0.221699429606 Henry Cohn, 2026, needs more optimization.
15 133 0.223240086287 Henry Cohn, 2026, needs more optimization.
15 134 0.226013010231 Henry Cohn, 2026, needs more optimization.
15 135 0.226122593087 Henry Cohn, 2026, needs more optimization.
15 136 0.226153149527 Henry Cohn, 2026, needs more optimization.
15 137 0.226888915734 Henry Cohn, 2026, needs more optimization.
15 142 0.227160244716 Henry Cohn, 2026, needs more optimization.
15 143 0.232905174657 Henry Cohn, 2026, needs more optimization.
15 144 0.236485146657 Henry Cohn, 2026, needs more optimization.
15 145 0.237675999094 Henry Cohn, 2026, needs more optimization.
15 146 0.238721219651 Henry Cohn, 2026, needs more optimization.
15 147 0.238762614221 Henry Cohn, 2026, needs more optimization.
15 150 0.239559038482 Henry Cohn, 2026, needs more optimization.
15 151 0.244766676204 Henry Cohn, 2026, needs more optimization.
15 152 0.245248898373 Henry Cohn, 2026, needs more optimization.
15 153 0.245510293391 Henry Cohn, 2026, needs more optimization.
15 157 0.249069470433 Henry Cohn, 2026.
15 158 0.254970525135 Henry Cohn, 2026.
15 159 0.261523033168 Henry Cohn, 2026, needs more optimization.
15 160 0.264450322591 Henry Cohn, 2026, needs more optimization.
15 161 0.265389041845 Henry Cohn, 2026, needs more optimization.
15 162 0.266601509974 Henry Cohn, 2026, needs more optimization.
15 163 0.267401037300 Henry Cohn, 2026, needs more optimization.
15 164 0.267913536818 Henry Cohn, 2026, needs more optimization.
15 165 0.268449269292 Henry Cohn, 2026, needs more optimization.
15 166 0.269139489004 Henry Cohn, 2026, needs more optimization.
15 167 0.269280737260 Henry Cohn, 2026, needs more optimization.
15 168 0.269370155087 Henry Cohn, 2026, needs more optimization.
15 169 0.269495222583 Henry Cohn, 2026, needs more optimization.
15 170 0.269652433255 Henry Cohn, 2026, needs more optimization.
15 171 0.269760333274 Henry Cohn, 2026, needs more optimization.
15 172 0.269850002255 Henry Cohn, 2026, needs more optimization.
15 173 0.269926266635 Henry Cohn, 2026, needs more optimization.
15 174 0.270214442213 Henry Cohn, 2026, needs more optimization.
15 175 0.270369853077 Henry Cohn, 2026, needs more optimization.
15 176 0.270472507931 Henry Cohn, 2026, needs more optimization.
15 177 0.270564586034 Henry Cohn, 2026, needs more optimization.
15 178 0.270603933063 Henry Cohn, 2026, needs more optimization.
15 179 0.270722449942 Henry Cohn, 2026, needs more optimization.
15 180 0.270853599817 Henry Cohn, 2026, needs more optimization.
15 181 0.270938799033 Henry Cohn, 2026, needs more optimization.
15 182 0.271104974687 Henry Cohn, 2026, needs more optimization.
15 183 0.271196570328 Henry Cohn, 2026, needs more optimization.
15 184 0.271314803183 Henry Cohn, 2026, needs more optimization.
15 185 0.271406579188 Henry Cohn, 2026, needs more optimization.
15 186 0.271477923533 Henry Cohn, 2026, needs more optimization.
15 187 0.271544896764 Henry Cohn, 2026, needs more optimization.
15 188 0.271591282404 Henry Cohn, 2026, needs more optimization.
15 189 0.271681295469 Henry Cohn, 2026, needs more optimization.
15 190 0.271716498710 Henry Cohn, 2026, needs more optimization.
15 191 0.271914022957 Henry Cohn, 2026, needs more optimization.
15 192 0.271978194245 Henry Cohn, 2026, needs more optimization.
15 193 0.272022075910 Henry Cohn, 2026, needs more optimization.
15 194 0.272044788672 Henry Cohn, 2026, needs more optimization.
15 195 0.272131992343 Henry Cohn, 2026, needs more optimization.
15 196 0.272161860577 Henry Cohn, 2026, needs more optimization.
15 197 0.272214514925 Henry Cohn, 2026, needs more optimization.
15 198 0.272247057122 Henry Cohn, 2026, needs more optimization.
15 199 0.272292198659 Henry Cohn, 2026, needs more optimization.
15 200 0.272330328921 Henry Cohn, 2026, needs more optimization.
15 201 0.272359118984 Henry Cohn, 2026, needs more optimization.
15 202 0.272398980857 Henry Cohn, 2026, needs more optimization.
15 203 0.272435043276 Henry Cohn, 2026, needs more optimization.
15 204 0.272466695373 Henry Cohn, 2026, needs more optimization.
15 205 0.272485700877 Henry Cohn, 2026, needs more optimization.
15 206 0.272519955596 Henry Cohn, 2026, needs more optimization.
15 207 0.272545322816 Henry Cohn, 2026, needs more optimization.
15 208 0.272572877496 Henry Cohn, 2026, needs more optimization.
15 209 0.272618691198 Henry Cohn, 2026, needs more optimization.
15 210 0.272645123909 Henry Cohn, 2026, needs more optimization.
15 211 0.272665338611 Henry Cohn, 2026, needs more optimization.
15 212 0.272714896336 Henry Cohn, 2026, needs more optimization.
15 213 0.272757894021 Henry Cohn, 2026, needs more optimization.
15 214 0.272777323867 Henry Cohn, 2026, needs more optimization.
15 215 0.272812458938 Henry Cohn, 2026, needs more optimization.
15 216 0.272875302011 Henry Cohn, 2026, needs more optimization.
15 217 0.272911619262 Henry Cohn, 2026, needs more optimization.
15 218 0.273001493315 Henry Cohn, 2026, needs more optimization.
15 219 0.273085901400 Henry Cohn, 2026, needs more optimization.
15 221 0.273150769652 Henry Cohn, 2026, needs more optimization.
15 222 0.293924008726 Henry Cohn, 2026, needs more optimization.
15 223 0.294641343789 Henry Cohn, 2026, needs more optimization.
15 224 0.296549074726 Henry Cohn, 2026, needs more optimization.
15 225 0.297567084022 Henry Cohn, 2026, needs more optimization.
15 226 0.297674150920 Henry Cohn, 2026, needs more optimization.
15 227 0.298458670130 Henry Cohn, 2026, needs more optimization.
15 228 0.299209134575 Henry Cohn, 2026, needs more optimization.
15 229 0.299666433962 Henry Cohn, 2026, needs more optimization.
15 230 0.300268183949 Henry Cohn, 2026, needs more optimization.
15 231 0.300750082652 Henry Cohn, 2026, needs more optimization.
15 232 0.301244274881 Henry Cohn, 2026, needs more optimization.
15 233 0.301706744594 Henry Cohn, 2026, needs more optimization.
15 234 0.302186512923 Henry Cohn, 2026, needs more optimization.
15 235 0.302372552357 Henry Cohn, 2026, needs more optimization.
15 240 0.304347826087 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x−7
15 256 0.304347826087 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.
23⁢x−7
15 257 0.304470555251 Henry Cohn, 2026, needs more optimization.
15 258 0.304781091027 Henry Cohn, 2026, needs more optimization.
15 259 0.305963607885 Henry Cohn, 2026, needs more optimization.
15 260 0.307205146825 Henry Cohn, 2026, needs more optimization.
15 261 0.308214305979 Henry Cohn, 2026, needs more optimization.
15 262 0.309457272981 Henry Cohn, 2026, needs more optimization.
15 263 0.309494745415 Henry Cohn, 2026, needs more optimization.
15 264 0.309633724236 Henry Cohn, 2026, needs more optimization.
15 265 0.312034060152 Henry Cohn, 2026, needs more optimization.
15 266 0.313632473517 Henry Cohn, 2026, needs more optimization.
15 267 0.315084175178 Henry Cohn, 2026, needs more optimization.
15 268 0.316247223831 Henry Cohn, 2026, needs more optimization.
15 269 0.316349075201 Henry Cohn, 2026, needs more optimization.
15 270 0.316569752116 Henry Cohn, 2026, needs more optimization.
15 271 0.319720751358 Henry Cohn, 2026, needs more optimization.
15 272 0.321672611599 Henry Cohn, 2026, needs more optimization.
15 273 0.325043042138 Henry Cohn, 2026, needs more optimization.
15 274 0.326571116049 Henry Cohn, 2026, needs more optimization.
15 275 0.328489908729 Henry Cohn, 2026, needs more optimization.
15 276 0.330124380806 Henry Cohn, 2026, needs more optimization.
15 277 0.331524001433 Henry Cohn, 2026, needs more optimization.
15 278 0.332349361550 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 0.339370412683 Henry Cohn, 2026, needs more optimization.
15 322 0.340377089292 Henry Cohn, 2026, needs more optimization.
15 323 0.353686979309 Henry Cohn, 2026, needs more optimization.
15 324 0.354487292678 Henry Cohn, 2026, needs more optimization.
15 326 0.354508123736 Henry Cohn, 2026, needs more optimization.
15 328 0.354566984239 Henry Cohn, 2026, needs more optimization.
15 329 0.354604194827 Henry Cohn, 2026, needs more optimization.
15 330 0.354626425661 Henry Cohn, 2026, needs more optimization.
15 331 0.354649136399 Henry Cohn, 2026, needs more optimization.
15 332 0.354679346979 Henry Cohn, 2026, needs more optimization.
15 334 0.354700635362 Henry Cohn, 2026, needs more optimization.
15 336 0.354741888911 Henry Cohn, 2026, needs more optimization.
15 337 0.354826816308 Henry Cohn, 2026, needs more optimization.
15 338 0.355237063746 Henry Cohn, 2026, needs more optimization.
15 340 0.355260132304 Henry Cohn, 2026, needs more optimization.
15 342 0.355278615966 Henry Cohn, 2026, needs more optimization.
15 344 0.355309909755 Henry Cohn, 2026, needs more optimization.
15 346 0.355331428719 Henry Cohn, 2026, needs more optimization.
15 347 0.355351162570 Henry Cohn, 2026, needs more optimization.
15 348 0.355353509195 Henry Cohn, 2026, needs more optimization.
15 350 0.355469506550 Henry Cohn, 2026, needs more optimization.
15 352 0.355493648494 Henry Cohn, 2026, needs more optimization.
15 354 0.355494422082 Henry Cohn, 2026, needs more optimization.
15 356 0.355527321103 Henry Cohn, 2026, needs more optimization.
15 358 0.355541652196 Henry Cohn, 2026, needs more optimization.
15 359 0.355600275452 Henry Cohn, 2026, needs more optimization.
15 360 0.355602110975 Henry Cohn, 2026, needs more optimization.
15 361 0.355610820517 Henry Cohn, 2026, needs more optimization.
15 362 0.355618827570 Henry Cohn, 2026, needs more optimization.
15 363 0.355650983568 Henry Cohn, 2026, needs more optimization.
15 364 0.355659351583 Henry Cohn, 2026, needs more optimization.
15 365 0.355680342401 Henry Cohn, 2026, needs more optimization.
15 366 0.355710147631 Henry Cohn, 2026, needs more optimization.
15 367 0.355716028864 Henry Cohn, 2026, needs more optimization.
15 368 0.355726879627 Henry Cohn, 2026, needs more optimization.
15 369 0.355772992600 Henry Cohn, 2026, needs more optimization.
15 370 0.355831769838 Henry Cohn, 2026, needs more optimization.
15 371 0.355865550171 Henry Cohn, 2026, needs more optimization.
15 372 0.355878923713 Henry Cohn, 2026, needs more optimization.
15 373 0.356896924733 Henry Cohn, 2026, needs more optimization.
15 374 0.357116370754 Henry Cohn, 2026, needs more optimization.
15 375 0.357327127633 Henry Cohn, 2026, needs more optimization.
15 376 0.359572438356 Henry Cohn, 2026, needs more optimization.
15 378 0.359619521534 Henry Cohn, 2026, needs more optimization.
15 380 0.360767005407 Henry Cohn, 2026, needs more optimization.
15 381 0.361027875254 Henry Cohn, 2026, needs more optimization.
15 382 0.361052934427 Henry Cohn, 2026, needs more optimization.
15 383 0.361793558670 Henry Cohn, 2026, needs more optimization.
15 384 0.362898403048 Henry Cohn, 2026, needs more optimization.
15 385 0.363400396726 Henry Cohn, 2026, needs more optimization.
15 386 0.364063907924 Henry Cohn, 2026, needs more optimization.
15 388 0.365849255935 Henry Cohn, 2026, needs more optimization.
15 389 0.383568966190 Orthogonal union of 387 points in 14 dimensions and 2 points in 1 dimension.
15 390 0.383846399026 Orthogonal union of 388 points in 14 dimensions and 2 points in 1 dimension.
15 391 0.385074975412 Henry Cohn, 2026, needs more optimization.
15 392 0.385393608823 Orthogonal union of 390 points in 14 dimensions and 2 points in 1 dimension.
15 393 0.385697573797 Henry Cohn, 2025, needs more optimization.
15 394 0.385981411644 Henry Cohn, 2026, needs more optimization.
15 395 0.386225226866 Henry Cohn, 2025, needs more optimization.
15 396 0.386591348150 Henry Cohn, 2026, needs more optimization.
15 397 0.387116282587 Henry Cohn, 2025, needs more optimization.
15 398 0.387166171787 Henry Cohn, 2026, needs more optimization.
15 399 0.387606636643 Henry Cohn, 2025, needs more optimization.
15 400 0.387878096356 Henry Cohn, 2026, needs more optimization.
15 401 0.387891088276 Henry Cohn, 2026, needs more optimization.
15 402 0.388335936402 Henry Cohn, 2026, needs more optimization.
15 403 0.388757758623 Henry Cohn, 2025, needs more optimization.
15 404 0.388759488830 Henry Cohn, 2026, needs more optimization.
15 405 0.388931907229 Henry Cohn, 2026, needs more optimization.
15 406 0.389246997759 Henry Cohn, 2026, needs more optimization.
15 407 0.389817861267 Henry Cohn, 2025, needs more optimization.
15 408 0.389821569051 Henry Cohn, 2026, needs more optimization.
15 409 0.390093941582 Henry Cohn, 2025, needs more optimization.
15 410 0.390216966887 Henry Cohn, 2026, needs more optimization.
15 411 0.390425306732 Henry Cohn, 2025, needs more optimization.
15 412 0.390743554804 Henry Cohn, 2026, needs more optimization.
15 417 0.391188213680 Orthogonal union of 415 points in 14 dimensions and 2 points in 1 dimension.
15 418 0.391876562826 Henry Cohn, 2026, needs more optimization.
15 422 0.391882000273 Henry Cohn, 2026, needs more optimization.
15 426 0.391883519698 Henry Cohn, 2026, needs more optimization.
15 430 0.391884408476 Henry Cohn, 2026, needs more optimization.
15 432 0.391885825686 Henry Cohn, 2026, needs more optimization.
15 433 0.391904247888 Henry Cohn, 2025, needs more optimization.
15 438 0.391905767205 Henry Cohn, 2026, needs more optimization.
15 442 0.391908466247 Henry Cohn, 2026, needs more optimization.
15 443 0.391960592920 Henry Cohn, 2026, needs more optimization.
15 444 0.391965011895 Henry Cohn, 2026, needs more optimization.
15 448 0.391969898330 Henry Cohn, 2026, needs more optimization.
15 449 0.391974552177 Henry Cohn, 2026, needs more optimization.
15 451 0.391982342905 Henry Cohn, 2026, needs more optimization.
15 452 0.391997881677 Henry Cohn, 2026, needs more optimization.
15 454 0.392007978704 Henry Cohn, 2026, needs more optimization.
15 456 0.392017018253 Henry Cohn, 2026, needs more optimization.
15 458 0.392020332370 Henry Cohn, 2026, needs more optimization.
15 459 0.392023857282 Henry Cohn, 2026, needs more optimization.
15 460 0.392040567096 Henry Cohn, 2026, needs more optimization.
15 462 0.392041602720 Henry Cohn, 2026, needs more optimization.
15 464 0.392065844463 Henry Cohn, 2026, needs more optimization.
15 465 0.392134371424 Henry Cohn, 2026, needs more optimization.
15 466 0.392145136407 Henry Cohn, 2026, needs more optimization.
15 468 0.392664769104 Henry Cohn, 2026, needs more optimization.
15 470 0.392686555526 Henry Cohn, 2026, needs more optimization.
15 471 0.392759590039 Henry Cohn, 2026, needs more optimization.
15 472 0.392830095296 Henry Cohn, 2026, needs more optimization.
15 473 0.392851877606 Henry Cohn, 2026, needs more optimization.
15 474 0.393137948926 Henry Cohn, 2026, needs more optimization.
15 475 0.393157298956 Henry Cohn, 2026, needs more optimization.
15 476 0.393197710439 Henry Cohn, 2026, needs more optimization.
15 477 0.393294692202 Henry Cohn, 2026, needs more optimization.
15 478 0.393410045160 Henry Cohn, 2026, needs more optimization.
15 479 0.393468087110 Henry Cohn, 2026, needs more optimization.
15 490 0.393595271752 Henry Cohn, 2026, needs more optimization.
15 491 0.393649079161 Henry Cohn, 2026, needs more optimization.
15 492 0.393810449924 Henry Cohn, 2026, needs more optimization.
15 494 0.393870150942 Henry Cohn, 2026, needs more optimization.
15 495 0.393938600254 Henry Cohn, 2026, needs more optimization.
15 507 0.393947143859 Henry Cohn, 2026, needs more optimization.
15 508 0.394082809098 Henry Cohn, 2026, needs more optimization.
15 509 0.394303227452 Henry Cohn, 2026, needs more optimization.
15 510 0.394717887547 Henry Cohn, 2026, needs more optimization.
15 511 0.395232609126 Henry Cohn, 2026, needs more optimization.
15 512 0.395339138517 Henry Cohn, 2026, needs more optimization.
15 513 0.395339138520 Henry Cohn, 2026, needs more optimization.
15 514 0.395592115088 Henry Cohn, 2026, needs more optimization.
15 515 0.395809664499 Henry Cohn, 2026, needs more optimization.
15 516 0.395876406343 Henry Cohn, 2026, needs more optimization.
15 517 0.396119343499 Henry Cohn, 2026, needs more optimization.
15 518 0.396548958528 Henry Cohn, 2026, needs more optimization.
15 519 0.396905469061 Henry Cohn, 2026, needs more optimization.
15 521 0.396940776706 Henry Cohn, 2026, needs more optimization.
15 522 0.397245350396 Henry Cohn, 2026, needs more optimization.
15 523 0.397608829281 Henry Cohn, 2026, needs more optimization.
15 524 0.397714019388 Henry Cohn, 2026, needs more optimization.
15 525 0.397787643464 Henry Cohn, 2026, needs more optimization.
15 526 0.397926057261 Henry Cohn, 2026, needs more optimization.
15 527 0.398326937846 Henry Cohn, 2026, needs more optimization.
15 528 0.398455476995 Henry Cohn, 2026, needs more optimization.
15 530 0.398559698347 Henry Cohn, 2026, needs more optimization.
15 531 0.398628134643 Henry Cohn, 2026, needs more optimization.
15 532 0.398858027388 Henry Cohn, 2026, needs more optimization.
15 533 0.398883314685 Henry Cohn, 2026, needs more optimization.
15 536 0.399002219814 Henry Cohn, 2026, needs more optimization.
15 537 0.399285589794 Henry Cohn, 2026, needs more optimization.
15 538 0.399487186834 Henry Cohn, 2026, needs more optimization.
15 539 0.399661982305 Henry Cohn, 2026, needs more optimization.
15 540 0.399719167567 Henry Cohn, 2026, needs more optimization.
15 542 0.399789139197 Henry Cohn, 2026, needs more optimization.
15 543 0.399854720341 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 0.404117037755 Henry Cohn, 2026, needs more optimization.
15 690 0.407439006131 Henry Cohn, 2026, needs more optimization.
15 691 0.410997419515 Henry Cohn, 2026, needs more optimization.
15 692 0.413802612393 Henry Cohn, 2026, needs more optimization.
15 693 0.415502525739 Henry Cohn, 2026, needs more optimization.
15 694 0.416786804091 Henry Cohn, 2026, needs more optimization.
15 695 0.417817202074 Henry Cohn, 2026, needs more optimization.
15 696 0.419452889511 Henry Cohn, 2026, needs more optimization.
15 697 0.420223621407 Henry Cohn, 2026, needs more optimization.
15 698 0.420583895388 Henry Cohn, 2026, needs more optimization.
15 699 0.420961787181 Henry Cohn, 2026, needs more optimization.
15 701 0.421321344666 Henry Cohn, 2026, needs more optimization.
15 711 0.421321344667 Henry Cohn, 2026, needs more optimization.
15 712 0.421407386297 Henry Cohn, 2026, needs more optimization.
15 713 0.421458797488 Henry Cohn, 2026, needs more optimization.
15 714 0.421553874169 Henry Cohn, 2026, needs more optimization.
15 715 0.421615047725 Henry Cohn, 2026, needs more optimization.
15 716 0.421825515925 Henry Cohn, 2026, needs more optimization.
15 717 0.422140327002 Henry Cohn, 2026, needs more optimization.
15 718 0.422376275795 Henry Cohn, 2026, needs more optimization.
15 719 0.422695142085 Henry Cohn, 2026, needs more optimization.
15 720 0.422890834349 Henry Cohn, 2026, needs more optimization.
15 721 0.423103555517 Henry Cohn, 2026, needs more optimization.
15 722 0.423268839180 Henry Cohn, 2026, needs more optimization.
15 723 0.423578807409 Henry Cohn, 2026, needs more optimization.
15 724 0.423854831735 Henry Cohn, 2026, needs more optimization.
15 725 0.424193225923 Henry Cohn, 2026, needs more optimization.
15 726 0.424397600913 Henry Cohn, 2026, needs more optimization.
15 727 0.424535970435 Henry Cohn, 2026, needs more optimization.
15 728 0.424767084761 Henry Cohn, 2026, needs more optimization.
15 729 0.425074531384 Henry Cohn, 2026, needs more optimization.
15 730 0.425235665989 Henry Cohn, 2026, needs more optimization.
15 731 0.425350491089 Henry Cohn, 2026, needs more optimization.
15 732 0.425492991503 Henry Cohn, 2026, needs more optimization.
15 733 0.425666573820 Henry Cohn, 2026, needs more optimization.
15 734 0.425838548018 Henry Cohn, 2026, needs more optimization.
15 735 0.426051572669 Henry Cohn, 2026, needs more optimization.
15 736 0.426218532832 Henry Cohn, 2026, needs more optimization.
15 737 0.426475649842 Henry Cohn, 2026, needs more optimization.
15 738 0.426699589170 Henry Cohn, 2026, needs more optimization.
15 739 0.426803651130 Henry Cohn, 2026, needs more optimization.
15 740 0.427119677451 Henry Cohn, 2026, needs more optimization.
15 741 0.427364806719 Henry Cohn, 2026, needs more optimization.
15 742 0.427478336924 Henry Cohn, 2026, needs more optimization.
15 743 0.427654716527 Henry Cohn, 2026, needs more optimization.
15 744 0.427723806330 Henry Cohn, 2026, needs more optimization.
15 745 0.427891014609 Henry Cohn, 2026, needs more optimization.
15 746 0.428010850027 Henry Cohn, 2026, needs more optimization.
15 747 0.428168251195 Henry Cohn, 2026, needs more optimization.
15 748 0.428377372301 Henry Cohn, 2026, needs more optimization.
15 749 0.428536554402 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 0.439838684253 Henry Cohn, 2026, needs more optimization.
15 993 0.454632239891 Henry Cohn, 2026, needs more optimization.
15 995 0.454643962041 Henry Cohn, 2026, needs more optimization.
15 997 0.454650675032 Henry Cohn, 2026, needs more optimization.
15 998 0.454656625504 Henry Cohn, 2026, needs more optimization.
15 999 0.454659862656 Henry Cohn, 2026, needs more optimization.
15 1001 0.454664391668 Henry Cohn, 2026, needs more optimization.
15 1002 0.454734240452 Henry Cohn, 2026, needs more optimization.
15 1003 0.454761356592 Henry Cohn, 2026, needs more optimization.
15 1005 0.454779645951 Henry Cohn, 2026, needs more optimization.
15 1006 0.454789504648 Henry Cohn, 2026, needs more optimization.
15 1007 0.454792546035 Henry Cohn, 2026, needs more optimization.
15 1008 0.454800278479 Henry Cohn, 2026, needs more optimization.
15 1010 0.454831522563 Henry Cohn, 2026, needs more optimization.
15 1011 0.454837749616 Henry Cohn, 2025, needs more optimization.
15 1012 0.454838359249 Henry Cohn, 2026, needs more optimization.
15 1013 0.454838884992 Henry Cohn, 2026, needs more optimization.
15 1015 0.454895768401 Henry Cohn, 2026, needs more optimization.
15 1017 0.454906903624 Henry Cohn, 2026, needs more optimization.
15 1018 0.454913946680 Henry Cohn, 2026, needs more optimization.
15 1020 0.454926265220 Henry Cohn, 2026, needs more optimization.
15 1022 0.454944092149 Henry Cohn, 2026, needs more optimization.
15 1023 0.454956921972 Henry Cohn, 2026, needs more optimization.
15 1024 0.454977519070 Henry Cohn, 2026, needs more optimization.
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 53 0.112902421936 Henry Cohn, 2025.
16 54 0.112907159448 Henry Cohn, 2025.
16 55 0.113137877868 Henry Cohn, 2026.
16 58 0.113835450316 Henry Cohn, 2026.
288⁢x2−24⁢x−1
16 59 0.115469803431 Henry Cohn, 2023, needs more optimization.
16 60 0.115470801109 Henry Cohn, 2026, needs more optimization.
16 61 0.119371454413 Henry Cohn, 2025.
16 62 0.125768177302 Henry Cohn, 2025.
16 74 0.127284656799 Henry Cohn, 2023.
156⁢x2−12⁢x−1
16 75 0.142415975160 Henry Cohn, 2025, needs more optimization.
16 76 0.157616857308 Henry Cohn, 2025.
16 77 0.161334829806 Henry Cohn, 2026, needs more optimization.
16 78 0.164417462768 Henry Cohn, 2026, needs more optimization.
16 79 0.167447335055 Henry Cohn, 2026, needs more optimization.
16 80 0.167545425773 Henry Cohn, 2026, needs more optimization.
16 81 0.167725167768 Henry Cohn, 2026, needs more optimization.
16 82 0.167867078730 Henry Cohn, 2026, needs more optimization.
16 83 0.168279307188 Henry Cohn, 2026, needs more optimization.
16 84 0.168596157094 Henry Cohn, 2026, needs more optimization.
16 85 0.168666428099 Henry Cohn, 2025, needs more optimization.
16 88 0.168668499420 Henry Cohn, 2025, needs more optimization.
16 92 0.168684604646 Henry Cohn, 2025, needs more optimization.
16 94 0.168684943107 Henry Cohn, 2025, needs more optimization.
16 96 0.168685705337 Henry Cohn, 2026, needs more optimization.
16 97 0.169880759680 Henry Cohn, 2026, needs more optimization.
16 102 0.170753175474 Henry Cohn, 2026.
128⁢x2−16⁢x−1
16 103 0.174178397918 Henry Cohn, 2026, needs more optimization.
16 104 0.179379121134 Henry Cohn, 2026, needs more optimization.
16 105 0.183420437163 Henry Cohn, 2026, needs more optimization.
16 106 0.185897329735 Henry Cohn, 2025, needs more optimization.
16 107 0.188035141309 Henry Cohn, 2026, needs more optimization.
16 108 0.191385007681 Henry Cohn, 2026, needs more optimization.
16 117 0.192450089730 Henry Cohn, 2026.
27⁢x2−1
16 118 0.197168274348 Henry Cohn, 2026, needs more optimization.
16 119 0.198900207109 Henry Cohn, 2026, needs more optimization.
16 122 0.199966091100 Henry Cohn, 2025, needs more optimization.
16 124 0.199989165771 Henry Cohn, 2025, needs more optimization.
16 126 0.199994691163 Henry Cohn, 2025, needs more optimization.
16 127 0.199995845425 Henry Cohn, 2025, needs more optimization.
16 130 0.199999918321 Henry Cohn, 2025, needs more optimization.
16 159 0.202913709779 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
44⁢x2−4⁢x−1
16 160 0.204975438260 Henry Cohn, 2026, needs more optimization.
16 161 0.221710856855 Henry Cohn, 2026, needs more optimization.
16 162 0.229583868962 Henry Cohn, 2026, needs more optimization.
16 163 0.233467253797 Henry Cohn, 2026, needs more optimization.
16 164 0.236108845761 Henry Cohn, 2026, needs more optimization.
16 165 0.237979017074 Henry Cohn, 2026, needs more optimization.
16 166 0.239581539503 Henry Cohn, 2026, needs more optimization.
16 167 0.240932114456 Henry Cohn, 2026, needs more optimization.
16 168 0.242177810266 Henry Cohn, 2026, needs more optimization.
16 169 0.243006571449 Henry Cohn, 2026, needs more optimization.
16 170 0.244083626556 Henry Cohn, 2026, needs more optimization.
16 171 0.245111782438 Henry Cohn, 2026, needs more optimization.
16 172 0.245709211951 Henry Cohn, 2026, needs more optimization.
16 173 0.245923763864 Henry Cohn, 2026, needs more optimization.
16 174 0.246394977527 Henry Cohn, 2026, needs more optimization.
16 175 0.246779948013 Henry Cohn, 2026, needs more optimization.
16 176 0.247721311182 Henry Cohn, 2026, needs more optimization.
16 177 0.248072831383 Henry Cohn, 2026, needs more optimization.
16 178 0.248073537627 Henry Cohn, 2026, needs more optimization.
16 179 0.248209942447 Henry Cohn, 2026, needs more optimization.
16 180 0.248536890053 Henry Cohn, 2026, needs more optimization.
16 181 0.248726584311 Henry Cohn, 2026, needs more optimization.
16 182 0.248863477054 Henry Cohn, 2026, needs more optimization.
16 183 0.249122006211 Henry Cohn, 2026, needs more optimization.
16 184 0.249278564574 Henry Cohn, 2026, needs more optimization.
16 185 0.249491816651 Henry Cohn, 2026, needs more optimization.
16 186 0.249492146216 Henry Cohn, 2026, needs more optimization.
16 187 0.249494880756 Henry Cohn, 2026, needs more optimization.
16 188 0.249555068845 Henry Cohn, 2026, needs more optimization.
16 189 0.249772784404 Henry Cohn, 2026, needs more optimization.
16 190 0.249821947229 Henry Cohn, 2026, needs more optimization.
16 191 0.249924937240 Henry Cohn, 2026, needs more optimization.
16 192 0.249933781267 Henry Cohn, 2026, needs more optimization.
16 193 0.249935260467 Henry Cohn, 2026, needs more optimization.
16 194 0.249944304308 Henry Cohn, 2026, needs more optimization.
16 195 0.249952701646 Henry Cohn, 2026, needs more optimization.
16 196 0.249965429051 Henry Cohn, 2026, needs more optimization.
16 197 0.249996709528 Henry Cohn, 2026, needs more optimization.
16 198 0.249999483726 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 0.287615532262 Henry Cohn, 2026, needs more optimization.
16 290 0.292889040387 Henry Cohn, 2026, needs more optimization.
16 291 0.296805126973 Henry Cohn, 2026, needs more optimization.
16 292 0.301075723808 Henry Cohn, 2026, needs more optimization.
16 293 0.302766155559 Henry Cohn, 2026, needs more optimization.
16 294 0.304407786154 Henry Cohn, 2026, needs more optimization.
16 295 0.305623894266 Henry Cohn, 2026, needs more optimization.
16 296 0.307612845517 Henry Cohn, 2026, needs more optimization.
16 297 0.309265685788 Henry Cohn, 2026, needs more optimization.
16 298 0.310799800423 Henry Cohn, 2026, needs more optimization.
16 299 0.311849578176 Henry Cohn, 2026, needs more optimization.
16 300 0.313782436670 Henry Cohn, 2026, needs more optimization.
16 301 0.314992675969 Henry Cohn, 2026, needs more optimization.
16 302 0.325179202759 Henry Cohn, 2026, needs more optimization.
16 304 0.325250802196 Henry Cohn, 2026, needs more optimization.
16 305 0.325530267005 Henry Cohn, 2026, needs more optimization.
16 306 0.325811391350 Henry Cohn, 2026, needs more optimization.
16 308 0.326004103681 Henry Cohn, 2026, needs more optimization.
16 310 0.327820093467 Henry Cohn, 2026, needs more optimization.
16 311 0.327940969500 Henry Cohn, 2026, needs more optimization.
16 312 0.328117052249 Henry Cohn, 2026, needs more optimization.
16 314 0.328216973365 Henry Cohn, 2026, needs more optimization.
16 315 0.328328223943 Henry Cohn, 2026, needs more optimization.
16 316 0.328385208881 Henry Cohn, 2026, needs more optimization.
16 318 0.328510565855 Henry Cohn, 2026, needs more optimization.
16 320 0.328848737906 Henry Cohn, 2026, needs more optimization.
16 322 0.328876625407 Henry Cohn, 2026, needs more optimization.
16 324 0.328966130649 Henry Cohn, 2026, needs more optimization.
16 325 0.329147111466 Henry Cohn, 2026, needs more optimization.
16 326 0.329226170045 Henry Cohn, 2026, needs more optimization.
16 327 0.329306507742 Henry Cohn, 2026, needs more optimization.
16 328 0.329380924677 Henry Cohn, 2026, needs more optimization.
16 329 0.329413775016 Henry Cohn, 2026, needs more optimization.
16 330 0.329584084754 Henry Cohn, 2026, needs more optimization.
16 331 0.329664350135 Henry Cohn, 2026, needs more optimization.
16 332 0.329772279703 Henry Cohn, 2026, needs more optimization.
16 333 0.329826551486 Henry Cohn, 2026, needs more optimization.
16 334 0.329942906015 Henry Cohn, 2026, needs more optimization.
16 335 0.330098906307 Henry Cohn, 2026, needs more optimization.
16 336 0.330206762954 Henry Cohn, 2026, needs more optimization.
16 337 0.330290899737 Henry Cohn, 2026, needs more optimization.
16 340 0.330298477294 Henry Cohn, 2026, needs more optimization.
16 341 0.330423664112 Henry Cohn, 2026, needs more optimization.
16 342 0.330503676608 Henry Cohn, 2026, needs more optimization.
16 343 0.330543467312 Henry Cohn, 2026, needs more optimization.
16 344 0.330711629888 Henry Cohn, 2026, needs more optimization.
16 345 0.330835460157 Henry Cohn, 2026, needs more optimization.
16 346 0.330871703513 Henry Cohn, 2026, needs more optimization.
16 347 0.331069372327 Henry Cohn, 2026, needs more optimization.
16 348 0.331088017959 Henry Cohn, 2026, needs more optimization.
16 349 0.331171629577 Henry Cohn, 2026, needs more optimization.
16 350 0.331208165889 Henry Cohn, 2026, needs more optimization.
16 351 0.331215787377 Henry Cohn, 2026, needs more optimization.
16 352 0.331418482484 Henry Cohn, 2026, needs more optimization.
16 353 0.331671922087 Henry Cohn, 2026, needs more optimization.
16 354 0.331829042044 Henry Cohn, 2026, needs more optimization.
16 356 0.331897422293 Henry Cohn, 2026, needs more optimization.
16 357 0.332231346446 Henry Cohn, 2026, needs more optimization.
16 358 0.332448195304 Henry Cohn, 2026, needs more optimization.
16 359 0.332517648208 Henry Cohn, 2026, needs more optimization.
16 360 0.332623189070 Henry Cohn, 2026, needs more optimization.
16 362 0.332764367566 Henry Cohn, 2026, needs more optimization.
16 364 0.332868796553 Henry Cohn, 2026, needs more optimization.
16 365 0.333031478858 Henry Cohn, 2026, needs more optimization.
16 366 0.333077203892 Henry Cohn, 2026, needs more optimization.
16 368 0.333167284029 Henry Cohn, 2026, needs more optimization.
16 369 0.333264193578 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 0.352002666954 Henry Cohn, 2026, needs more optimization.
16 514 0.391920906138 Henry Cohn, 2026, needs more optimization.
16 515 0.392184707636 Henry Cohn, 2025, needs more optimization.
16 516 0.392591412926 Henry Cohn, 2026, needs more optimization.
16 517 0.392634267266 Henry Cohn, 2025, needs more optimization.
16 518 0.392722410888 Henry Cohn, 2026, needs more optimization.
16 519 0.392822032060 Henry Cohn, 2025, needs more optimization.
16 520 0.392903207539 Henry Cohn, 2026, needs more optimization.
16 521 0.393133536522 Henry Cohn, 2025, needs more optimization.
16 522 0.393631271714 Henry Cohn, 2026, needs more optimization.
16 523 0.393642909640 Henry Cohn, 2025, needs more optimization.
16 524 0.394010879429 Henry Cohn, 2026, needs more optimization.
16 525 0.394048136884 Henry Cohn, 2025, needs more optimization.
16 526 0.394340397473 Henry Cohn, 2026, needs more optimization.
16 527 0.394364961294 Henry Cohn, 2025, needs more optimization.
16 528 0.394447496751 Henry Cohn, 2026, needs more optimization.
16 529 0.394734533399 Henry Cohn, 2025, needs more optimization.
16 530 0.394953167041 Henry Cohn, 2026, needs more optimization.
16 531 0.395372694593 Henry Cohn, 2025, needs more optimization.
16 532 0.395560759345 Henry Cohn, 2025, needs more optimization.
16 533 0.395856738708 Henry Cohn, 2025, needs more optimization.
16 534 0.395975147295 Henry Cohn, 2026, needs more optimization.
16 535 0.396176179232 Henry Cohn, 2025, needs more optimization.
16 536 0.396325004089 Henry Cohn, 2026, needs more optimization.
16 537 0.396383621089 Henry Cohn, 2025, needs more optimization.
16 538 0.396676412432 Henry Cohn, 2026, needs more optimization.
16 539 0.396705747724 Henry Cohn, 2025, needs more optimization.
16 540 0.397312657536 Henry Cohn, 2026, needs more optimization.
16 541 0.397369983799 Henry Cohn, 2025, needs more optimization.
16 542 0.397412311252 Henry Cohn, 2026, needs more optimization.
16 543 0.397713318899 Henry Cohn, 2025, needs more optimization.
16 544 0.397775330468 Henry Cohn, 2026, needs more optimization.
16 546 0.398403683960 Henry Cohn, 2026, needs more optimization.
16 547 0.398553798594 Henry Cohn, 2025, needs more optimization.
16 548 0.398573298565 Henry Cohn, 2026, needs more optimization.
16 549 0.399020449360 Henry Cohn, 2026, needs more optimization.
16 550 0.399260114052 Henry Cohn, 2026, needs more optimization.
16 551 0.399689431569 Henry Cohn, 2026, needs more optimization.
16 552 0.399865738888 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
16 770 0.404117037748 Henry Cohn, 2026, needs more optimization.
16 771 0.409607335639 Henry Cohn, 2026, needs more optimization.
16 772 0.410786270069 Henry Cohn, 2026, needs more optimization.
16 773 0.411184784141 Henry Cohn, 2026, needs more optimization.
16 774 0.411715171639 Henry Cohn, 2026, needs more optimization.
16 775 0.411994574508 Henry Cohn, 2026, needs more optimization.
16 776 0.412312443470 Henry Cohn, 2026, needs more optimization.
16 777 0.412904735648 Henry Cohn, 2026, needs more optimization.
16 778 0.413121119341 Henry Cohn, 2026, needs more optimization.
16 779 0.413220591400 Henry Cohn, 2026, needs more optimization.
16 780 0.413374577904 Henry Cohn, 2026, needs more optimization.
16 781 0.413503911545 Henry Cohn, 2026, needs more optimization.
16 782 0.413541561313 Henry Cohn, 2026, needs more optimization.
16 783 0.413578827126 Henry Cohn, 2026, needs more optimization.
16 784 0.413632571081 Henry Cohn, 2026, needs more optimization.
16 785 0.413692643002 Henry Cohn, 2026, needs more optimization.
16 786 0.413758592707 Henry Cohn, 2026, needs more optimization.
16 787 0.413885124462 Henry Cohn, 2026, needs more optimization.
16 788 0.414013277634 Henry Cohn, 2026, needs more optimization.
16 789 0.414226828160 Henry Cohn, 2026, needs more optimization.
16 791 0.414325446843 Henry Cohn, 2026, needs more optimization.
16 792 0.414519439331 Henry Cohn, 2026, needs more optimization.
16 793 0.414750765376 Henry Cohn, 2026, needs more optimization.
16 794 0.414951680147 Henry Cohn, 2026, needs more optimization.
16 795 0.415303098512 Henry Cohn, 2026, needs more optimization.
16 796 0.415534994474 Henry Cohn, 2026, needs more optimization.
16 797 0.415675152921 Henry Cohn, 2026, needs more optimization.
16 798 0.415950809324 Henry Cohn, 2026, needs more optimization.
16 799 0.416036370609 Henry Cohn, 2026, needs more optimization.
16 800 0.416324875949 Henry Cohn, 2026, needs more optimization.
16 801 0.416546039277 Henry Cohn, 2026, needs more optimization.
16 802 0.416867849576 Henry Cohn, 2026, needs more optimization.
16 803 0.417126499368 Henry Cohn, 2026, needs more optimization.
16 804 0.417377130296 Henry Cohn, 2026, needs more optimization.
16 805 0.417518229880 Henry Cohn, 2026, needs more optimization.
16 806 0.417562589464 Henry Cohn, 2026, needs more optimization.
16 807 0.418014441358 Henry Cohn, 2026, needs more optimization.
16 808 0.418178664220 Henry Cohn, 2026, needs more optimization.
16 809 0.418294970299 Henry Cohn, 2026, needs more optimization.
16 810 0.418408567834 Henry Cohn, 2026, needs more optimization.
16 811 0.418576278048 Henry Cohn, 2026, needs more optimization.
16 812 0.418997345576 Henry Cohn, 2026, needs more optimization.
16 813 0.419186978231 Henry Cohn, 2026, needs more optimization.
16 814 0.419360669795 Henry Cohn, 2026, needs more optimization.
16 815 0.419883165595 Henry Cohn, 2026, needs more optimization.
16 816 0.420199919152 Henry Cohn, 2026, needs more optimization.
16 817 0.420529477540 Henry Cohn, 2026, needs more optimization.
16 818 0.420660187211 Henry Cohn, 2026, needs more optimization.
16 819 0.420999653592 Henry Cohn, 2026, needs more optimization.
16 820 0.421226482730 Henry Cohn, 2026, needs more optimization.
16 821 0.421472832686 Henry Cohn, 2026, needs more optimization.
16 822 0.421704802166 Henry Cohn, 2026, needs more optimization.
16 823 0.421858323775 Henry Cohn, 2026, needs more optimization.
16 824 0.421996896677 Henry Cohn, 2026, needs more optimization.
16 825 0.422152060695 Henry Cohn, 2026, needs more optimization.
16 826 0.422217704566 Henry Cohn, 2026, needs more optimization.
16 827 0.422351680673 Henry Cohn, 2026, needs more optimization.
16 828 0.422469810782 Henry Cohn, 2026, needs more optimization.
16 829 0.422617561920 Henry Cohn, 2026, needs more optimization.
16 830 0.422779259053 Henry Cohn, 2026, needs more optimization.
16 831 0.422930323346 Henry Cohn, 2026, needs more optimization.
16 832 0.423020959138 Henry Cohn, 2026, needs more optimization.
16 833 0.423238600760 Henry Cohn, 2026, needs more optimization.
16 834 0.423364055104 Henry Cohn, 2026, needs more optimization.
16 835 0.423514527454 Henry Cohn, 2026, needs more optimization.
16 836 0.423667141649 Henry Cohn, 2026, needs more optimization.
16 837 0.423815238368 Henry Cohn, 2026, needs more optimization.
16 838 0.423911745316 Henry Cohn, 2026, needs more optimization.
16 839 0.424086754429 Henry Cohn, 2026, needs more optimization.
16 840 0.424335234261 Henry Cohn, 2026, needs more optimization.
16 841 0.424488797480 Henry Cohn, 2026, needs more optimization.
16 842 0.424712544393 Henry Cohn, 2026, needs more optimization.
16 843 0.424980000946 Henry Cohn, 2026, needs more optimization.
16 844 0.425184618543 Henry Cohn, 2026, needs more optimization.
16 845 0.425484588494 Henry Cohn, 2026, needs more optimization.
16 846 0.425657918297 Henry Cohn, 2026, needs more optimization.
16 847 0.425776121034 Henry Cohn, 2026, needs more optimization.
16 848 0.425965684282 Henry Cohn, 2026, needs more optimization.
16 849 0.426109901881 Henry Cohn, 2026, needs more optimization.
16 850 0.426265092928 Henry Cohn, 2026, needs more optimization.
16 851 0.426426286394 Henry Cohn, 2026, needs more optimization.
16 852 0.426651761890 Henry Cohn, 2026, needs more optimization.
16 853 0.426830686475 Henry Cohn, 2026, needs more optimization.
16 854 0.426972088979 Henry Cohn, 2026, needs more optimization.
16 855 0.427164705631 Henry Cohn, 2026, needs more optimization.
16 856 0.427358377350 Henry Cohn, 2026, needs more optimization.
16 857 0.427541302713 Henry Cohn, 2026, needs more optimization.
16 858 0.427704989820 Henry Cohn, 2026, needs more optimization.
16 859 0.427874367181 Henry Cohn, 2026, needs more optimization.
16 860 0.428167228936 Henry Cohn, 2026, needs more optimization.
16 861 0.428261953621 Henry Cohn, 2026, needs more optimization.
16 862 0.428427426976 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 0.055949336674 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 0.100854947492 Henry Cohn, 2026.
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 0.121403722185 Henry Cohn, 2026, needs more optimization.
17 66 0.124823812635 Henry Cohn, 2026, needs more optimization.
17 67 0.127103338533 Henry Cohn, 2026, needs more optimization.
17 68 0.127214004902 Henry Cohn, 2026, needs more optimization.
17 69 0.127247527905 Henry Cohn, 2026, needs more optimization.
17 71 0.127270310008 Henry Cohn, 2025.
17 74 0.127284404862 Henry Cohn, 2025.
17 76 0.127284594471 Henry Cohn, 2025.
17 77 0.127303652500 Henry Cohn, 2025, needs more optimization.
17 78 0.135257083416 Henry Cohn, 2026, needs more optimization.
17 79 0.142565732323 Henry Cohn, 2026, needs more optimization.
17 80 0.148027287454 Henry Cohn, 2026, needs more optimization.
17 81 0.152542230093 Henry Cohn, 2026, needs more optimization.
17 82 0.156555839847 Henry Cohn, 2026, needs more optimization.
17 83 0.160375445397 Henry Cohn, 2026, needs more optimization.
17 84 0.163972509407 Henry Cohn, 2026, needs more optimization.
17 85 0.164063426175 Henry Cohn, 2026, needs more optimization.
17 86 0.164532769717 Henry Cohn, 2026, needs more optimization.
17 87 0.165352418023 Henry Cohn, 2026, needs more optimization.
17 88 0.166742337226 Henry Cohn, 2026, needs more optimization.
17 89 0.166838473395 Henry Cohn, 2026, needs more optimization.
17 90 0.167172864860 Henry Cohn, 2026, needs more optimization.
17 91 0.167317201590 Henry Cohn, 2026, needs more optimization.
17 92 0.167374777330 Henry Cohn, 2026, needs more optimization.
17 93 0.167571607102 Henry Cohn, 2026, needs more optimization.
17 94 0.167898126758 Henry Cohn, 2026, needs more optimization.
17 95 0.168041892502 Henry Cohn, 2026, needs more optimization.
17 96 0.168431850103 Henry Cohn, 2026, needs more optimization.
17 97 0.168538303449 Henry Cohn, 2026, needs more optimization.
17 98 0.168637510209 Henry Cohn, 2026, needs more optimization.
17 99 0.168673108749 Henry Cohn, 2026, needs more optimization.
17 100 0.168683518721 Henry Cohn, 2026, needs more optimization.
17 101 0.168701480726 Henry Cohn, 2026, needs more optimization.
17 104 0.170753175474 Orthogonal union of 102 points in 16 dimensions and 2 points in 1 dimension.
128⁢x2−16⁢x−1
17 105 0.170753297094 Henry Cohn, 2026, needs more optimization.
17 106 0.170757033121 Henry Cohn, 2026, needs more optimization.
17 107 0.170761752904 Henry Cohn, 2026, needs more optimization.
17 108 0.175089260067 Henry Cohn, 2026, needs more optimization.
17 109 0.179937491931 Henry Cohn, 2026, needs more optimization.
17 110 0.180428573147 Henry Cohn, 2026, needs more optimization.
17 111 0.182624861378 Henry Cohn, 2026, needs more optimization.
17 112 0.184554439867 Henry Cohn, 2026, needs more optimization.
17 113 0.185921325349 Henry Cohn, 2026, needs more optimization.
17 114 0.188137075297 Henry Cohn, 2026, needs more optimization.
17 116 0.189009800326 Henry Cohn, 2026, needs more optimization.
17 117 0.189789203020 Henry Cohn, 2026, needs more optimization.
17 118 0.190935511409 Henry Cohn, 2026, needs more optimization.
17 119 0.191925830194 Henry Cohn, 2026, needs more optimization.
17 120 0.193947471168 Henry Cohn, 2026, needs more optimization.
17 121 0.195096735316 Henry Cohn, 2026, needs more optimization.
17 122 0.196705622342 Henry Cohn, 2026, needs more optimization.
17 123 0.196832010808 Henry Cohn, 2026, needs more optimization.
17 124 0.196936839321 Henry Cohn, 2026, needs more optimization.
17 125 0.197284770603 Henry Cohn, 2026, needs more optimization.
17 126 0.197443296154 Henry Cohn, 2026, needs more optimization.
17 127 0.197638499999 Henry Cohn, 2025, needs more optimization.
17 128 0.197717958736 Henry Cohn, 2026, needs more optimization.
17 129 0.198743969223 Henry Cohn, 2026, needs more optimization.
17 130 0.199288775085 Henry Cohn, 2026, needs more optimization.
17 131 0.199316164713 Henry Cohn, 2026, needs more optimization.
17 132 0.199447275271 Henry Cohn, 2026, needs more optimization.
17 133 0.199748114767 Henry Cohn, 2026, needs more optimization.
17 134 0.199868467610 Henry Cohn, 2026, needs more optimization.
17 135 0.199973248776 Henry Cohn, 2026, needs more optimization.
17 136 0.200008020169 Henry Cohn, 2026, needs more optimization.
17 137 0.200164723446 Henry Cohn, 2026, needs more optimization.
17 138 0.200570900932 Henry Cohn, 2026, needs more optimization.
17 139 0.202557910049 Henry Cohn, 2026, needs more optimization.
17 140 0.202779710231 Henry Cohn, 2026, needs more optimization.
17 141 0.202833496678 Henry Cohn, 2026, needs more optimization.
17 142 0.202860793984 Henry Cohn, 2026, needs more optimization.
17 143 0.202875947997 Henry Cohn, 2026, needs more optimization.
17 144 0.202892408977 Henry Cohn, 2026, needs more optimization.
17 145 0.202894675427 Henry Cohn, 2026, needs more optimization.
17 146 0.202901454831 Henry Cohn, 2026, needs more optimization.
17 147 0.202901454944 Henry Cohn, 2026, needs more optimization.
17 148 0.202901454950 Henry Cohn, 2026, needs more optimization.
17 149 0.202901454994 Henry Cohn, 2026, needs more optimization.
17 150 0.202904951835 Henry Cohn, 2026, needs more optimization.
17 151 0.202906541796 Henry Cohn, 2026, needs more optimization.
17 161 0.202913709779 Code with 159 points in 16 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.
44⁢x2−4⁢x−1
17 162 0.202913709779 Henry Cohn, 2026.
44⁢x2−4⁢x−1
17 163 0.202921362700 Henry Cohn, 2026, needs more optimization.
17 164 0.202921657844 Henry Cohn, 2026, needs more optimization.
17 165 0.203276668748 Henry Cohn, 2026, needs more optimization.
17 168 0.209702871391 Henry Cohn, 2026, needs more optimization.
17 177 0.214580576913 Henry Cohn, 2026.
59⁢x2−8⁢x−1
17 178 0.217257934501 Henry Cohn, 2026, needs more optimization.
17 179 0.223849272859 Henry Cohn, 2026, needs more optimization.
17 180 0.224792296027 Henry Cohn, 2026, needs more optimization.
17 181 0.227847629080 Henry Cohn, 2026, needs more optimization.
17 182 0.230369283205 Henry Cohn, 2026, needs more optimization.
17 183 0.234114985155 Henry Cohn, 2026, needs more optimization.
17 184 0.235598292528 Henry Cohn, 2026, needs more optimization.
17 185 0.237328881734 Henry Cohn, 2026, needs more optimization.
17 186 0.238579967843 Henry Cohn, 2026, needs more optimization.
17 187 0.239624435578 Henry Cohn, 2026, needs more optimization.
17 188 0.240418035351 Henry Cohn, 2026, needs more optimization.
17 189 0.240896059598 Henry Cohn, 2026, needs more optimization.
17 190 0.242055441258 Henry Cohn, 2026, needs more optimization.
17 191 0.242627942811 Henry Cohn, 2026, needs more optimization.
17 192 0.242641213459 Henry Cohn, 2026, needs more optimization.
17 193 0.242644758167 Henry Cohn, 2026, needs more optimization.
17 194 0.242673802932 Henry Cohn, 2026, needs more optimization.
17 195 0.242712856359 Henry Cohn, 2026, needs more optimization.
17 197 0.242774345576 Henry Cohn, 2026, needs more optimization.
17 198 0.242871544418 Henry Cohn, 2026, needs more optimization.
17 199 0.243146692912 Henry Cohn, 2026, needs more optimization.
17 200 0.243260188408 Henry Cohn, 2026, needs more optimization.
17 201 0.243571606974 Henry Cohn, 2026, needs more optimization.
17 202 0.244098300126 Henry Cohn, 2026, needs more optimization.
17 203 0.244218134006 Henry Cohn, 2026, needs more optimization.
17 204 0.244264049100 Henry Cohn, 2026, needs more optimization.
17 205 0.244550851376 Henry Cohn, 2026, needs more optimization.
17 206 0.244587539729 Henry Cohn, 2026, needs more optimization.
17 207 0.244863620509 Henry Cohn, 2026, needs more optimization.
17 208 0.244974586219 Henry Cohn, 2026, needs more optimization.
17 209 0.245664677278 Henry Cohn, 2026, needs more optimization.
17 210 0.245868779347 Henry Cohn, 2026, needs more optimization.
17 211 0.246211383269 Henry Cohn, 2026, needs more optimization.
17 212 0.246505927624 Henry Cohn, 2026, needs more optimization.
17 213 0.246758196851 Henry Cohn, 2026, needs more optimization.
17 214 0.246967720266 Henry Cohn, 2026, needs more optimization.
17 215 0.247294675656 Henry Cohn, 2026, needs more optimization.
17 216 0.247438750010 Henry Cohn, 2026, needs more optimization.
17 217 0.247595706105 Henry Cohn, 2026, needs more optimization.
17 218 0.247906954859 Henry Cohn, 2026, needs more optimization.
17 219 0.248198560454 Henry Cohn, 2026, needs more optimization.
17 220 0.248410345930 Henry Cohn, 2026, needs more optimization.
17 221 0.248752171340 Henry Cohn, 2026, needs more optimization.
17 222 0.248855755474 Henry Cohn, 2026, needs more optimization.
17 223 0.249074678149 Henry Cohn, 2026, needs more optimization.
17 224 0.249130943744 Henry Cohn, 2026, needs more optimization.
17 225 0.249221502010 Henry Cohn, 2026, needs more optimization.
17 226 0.249353162378 Henry Cohn, 2026, needs more optimization.
17 227 0.249397860027 Henry Cohn, 2026, needs more optimization.
17 228 0.249399903529 Henry Cohn, 2026, needs more optimization.
17 229 0.249459088365 Henry Cohn, 2026, needs more optimization.
17 230 0.249529611756 Henry Cohn, 2026, needs more optimization.
17 231 0.249647073895 Henry Cohn, 2026, needs more optimization.
17 232 0.249706333177 Henry Cohn, 2026, needs more optimization.
17 233 0.249707830965 Henry Cohn, 2026, needs more optimization.
17 235 0.249719810690 Henry Cohn, 2026, needs more optimization.
17 236 0.249743296207 Henry Cohn, 2026, needs more optimization.
17 237 0.249771680855 Henry Cohn, 2026, needs more optimization.
17 238 0.249787387204 Henry Cohn, 2026, needs more optimization.
17 239 0.249798033223 Henry Cohn, 2026, needs more optimization.
17 240 0.249806355424 Henry Cohn, 2026, needs more optimization.
17 241 0.249834690669 Henry Cohn, 2026, needs more optimization.
17 242 0.249865168826 Henry Cohn, 2026, needs more optimization.
17 243 0.249891858241 Henry Cohn, 2026, needs more optimization.
17 244 0.249892604863 Henry Cohn, 2026, needs more optimization.
17 245 0.249899032036 Henry Cohn, 2026, needs more optimization.
17 246 0.249901306085 Henry Cohn, 2026, needs more optimization.
17 250 0.249966738201 Henry Cohn, 2026, needs more optimization.
17 292 0.25 Henry Cohn, 2026.
4⁢x−1
17 293 0.250031951789 Henry Cohn, 2026, needs more optimization.
17 294 0.250110390953 Henry Cohn, 2026, needs more optimization.
17 295 0.251392939857 Henry Cohn, 2026, needs more optimization.
17 296 0.254746780272 Henry Cohn, 2026, needs more optimization.
17 297 0.257264751884 Henry Cohn, 2026, needs more optimization.
17 298 0.260151353066 Henry Cohn, 2026, needs more optimization.
17 299 0.261203102898 Henry Cohn, 2026, needs more optimization.
17 300 0.261203659160 Henry Cohn, 2026, needs more optimization.
17 314 0.261203876655 Henry Cohn, 2026, needs more optimization.
17 316 0.261203876715 Henry Cohn, 2026, needs more optimization.
17 318 0.261203876803 Henry Cohn, 2026, needs more optimization.
17 320 0.261203876882 Henry Cohn, 2026, needs more optimization.
17 321 0.284194766727 Henry Cohn, 2026, needs more optimization.
17 322 0.295324251165 Henry Cohn, 2026, needs more optimization.
17 324 0.295918708986 Henry Cohn, 2026, needs more optimization.
17 326 0.300326773475 Henry Cohn, 2026, needs more optimization.
17 328 0.304222259662 Henry Cohn, 2026, needs more optimization.
17 330 0.304262510967 Henry Cohn, 2026, needs more optimization.
17 332 0.304553600103 Henry Cohn, 2026, needs more optimization.
17 334 0.304616719130 Henry Cohn, 2026, needs more optimization.
17 336 0.304638480718 Henry Cohn, 2026, needs more optimization.
17 338 0.304653673034 Henry Cohn, 2026, needs more optimization.
17 339 0.304749836304 Henry Cohn, 2026, needs more optimization.
17 340 0.312890155346 Henry Cohn, 2026, needs more optimization.
17 342 0.313344933575 Henry Cohn, 2026, needs more optimization.
17 343 0.314841630605 Henry Cohn, 2025, needs more optimization.
17 344 0.314899169141 Henry Cohn, 2026, needs more optimization.
17 345 0.316057223042 Henry Cohn, 2025, needs more optimization.
17 346 0.316108517923 Henry Cohn, 2026, needs more optimization.
17 347 0.317382420133 Henry Cohn, 2025, needs more optimization.
17 348 0.317410084006 Henry Cohn, 2026, needs more optimization.
17 349 0.318631480893 Henry Cohn, 2025, needs more optimization.
17 350 0.318679326175 Henry Cohn, 2026, needs more optimization.
17 351 0.318842570612 Henry Cohn, 2025, needs more optimization.
17 352 0.320276065763 Henry Cohn, 2026, needs more optimization.
17 353 0.320358004020 Henry Cohn, 2025, needs more optimization.
17 354 0.322917349307 Henry Cohn, 2026, needs more optimization.
17 355 0.323240622037 Henry Cohn, 2025, needs more optimization.
17 356 0.324599002081 Henry Cohn, 2026, needs more optimization.
17 358 0.324671337732 Henry Cohn, 2026, needs more optimization.
17 359 0.325570396391 Henry Cohn, 2025, needs more optimization.
17 360 0.325675052905 Henry Cohn, 2026, needs more optimization.
17 361 0.326299331409 Henry Cohn, 2025, needs more optimization.
17 362 0.326416705972 Henry Cohn, 2026, needs more optimization.
17 364 0.327607843411 Henry Cohn, 2026, needs more optimization.
17 365 0.327661166414 Henry Cohn, 2025, needs more optimization.
17 366 0.328558424077 Henry Cohn, 2026, needs more optimization.
17 367 0.329725269071 Henry Cohn, 2025, needs more optimization.
17 368 0.330432271058 Henry Cohn, 2026, needs more optimization.
17 369 0.331390095815 Henry Cohn, 2026, needs more optimization.
17 370 0.331773912836 Henry Cohn, 2026, needs more optimization.
17 371 0.332190295833 Henry Cohn, 2026, needs more optimization.
17 372 0.332953507255 Henry Cohn, 2026, needs more optimization.
17 373 0.333263513216 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. T. Zhaowei, 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 0.355045606116 Henry Cohn, 2026, needs more optimization.
17 580 0.384489580965 Henry Cohn, 2026, needs more optimization.
17 581 0.384499164779 Henry Cohn, 2025, needs more optimization.
17 582 0.384681859624 Henry Cohn, 2026, needs more optimization.
17 583 0.384901400690 Henry Cohn, 2025, needs more optimization.
17 584 0.384949959725 Henry Cohn, 2026, needs more optimization.
17 585 0.384966903624 Henry Cohn, 2025, needs more optimization.
17 586 0.385530858075 Henry Cohn, 2026, needs more optimization.
17 587 0.385541637903 Henry Cohn, 2025, needs more optimization.
17 588 0.385564523673 Henry Cohn, 2026, needs more optimization.
17 589 0.385951190150 Henry Cohn, 2025, needs more optimization.
17 590 0.386009198276 Henry Cohn, 2026, needs more optimization.
17 591 0.386020831990 Henry Cohn, 2025, needs more optimization.
17 592 0.386570929069 Henry Cohn, 2026, needs more optimization.
17 593 0.386655880734 Henry Cohn, 2025, needs more optimization.
17 594 0.386661734516 Henry Cohn, 2026, needs more optimization.
17 595 0.386764215489 Henry Cohn, 2025, needs more optimization.
17 596 0.387207370810 Henry Cohn, 2026, needs more optimization.
17 597 0.387277927498 Henry Cohn, 2025, needs more optimization.
17 598 0.387343058446 Henry Cohn, 2026, needs more optimization.
17 599 0.387399697539 Henry Cohn, 2025, needs more optimization.
17 600 0.387673206849 Henry Cohn, 2026, needs more optimization.
17 601 0.387717207601 Henry Cohn, 2025, needs more optimization.
17 602 0.387885410672 Henry Cohn, 2026, needs more optimization.
17 603 0.388274213435 Henry Cohn, 2025, needs more optimization.
17 604 0.388275605376 Henry Cohn, 2026, needs more optimization.
17 605 0.388352213522 Henry Cohn, 2025, needs more optimization.
17 606 0.388628247728 Henry Cohn, 2026, needs more optimization.
17 607 0.388865235140 Henry Cohn, 2025, needs more optimization.
17 608 0.388896952533 Henry Cohn, 2026, needs more optimization.
17 609 0.389131916372 Henry Cohn, 2025, needs more optimization.
17 610 0.389142993867 Henry Cohn, 2026, needs more optimization.
17 611 0.389517822003 Henry Cohn, 2025, needs more optimization.
17 612 0.389542958746 Henry Cohn, 2026, needs more optimization.
17 613 0.389589334878 Henry Cohn, 2025, needs more optimization.
17 614 0.389849795797 Henry Cohn, 2026, needs more optimization.
17 615 0.389911542351 Henry Cohn, 2025, needs more optimization.
17 616 0.390341304547 Henry Cohn, 2026, needs more optimization.
17 617 0.390365724717 Henry Cohn, 2025, needs more optimization.
17 618 0.390474067427 Henry Cohn, 2026, needs more optimization.
17 619 0.390490728552 Henry Cohn, 2025, needs more optimization.
17 620 0.390690214187 Henry Cohn, 2026, needs more optimization.
17 621 0.390847575705 Henry Cohn, 2025, needs more optimization.
17 622 0.390848273759 Henry Cohn, 2026, needs more optimization.
17 624 0.391228368680 Henry Cohn, 2026, needs more optimization.
17 625 0.391368332007 Henry Cohn, 2025, needs more optimization.
17 626 0.391429947071 Henry Cohn, 2026, needs more optimization.
17 628 0.391878103269 Henry Cohn, 2025, needs more optimization.
17 629 0.391929328039 Henry Cohn, 2025, needs more optimization.
17 630 0.392001556934 Henry Cohn, 2026, needs more optimization.
17 631 0.392605304895 Henry Cohn, 2025, needs more optimization.
17 632 0.392625871423 Henry Cohn, 2026, needs more optimization.
17 633 0.392644325274 Henry Cohn, 2025, needs more optimization.
17 634 0.392985775995 Henry Cohn, 2026, needs more optimization.
17 635 0.393018103881 Henry Cohn, 2025, needs more optimization.
17 636 0.393036322130 Henry Cohn, 2026, needs more optimization.
17 637 0.393225216195 Henry Cohn, 2025, needs more optimization.
17 638 0.393595469493 Henry Cohn, 2025, needs more optimization.
17 639 0.393615961966 Henry Cohn, 2025, needs more optimization.
17 640 0.393850893355 Henry Cohn, 2026, needs more optimization.
17 641 0.393861933375 Henry Cohn, 2025, needs more optimization.
17 642 0.394138723952 Henry Cohn, 2026, needs more optimization.
17 643 0.394162888867 Henry Cohn, 2025, needs more optimization.
17 644 0.394217615501 Henry Cohn, 2026, needs more optimization.
17 645 0.394374143224 Henry Cohn, 2025, needs more optimization.
17 646 0.394728219863 Henry Cohn, 2026, needs more optimization.
17 647 0.394865721173 Henry Cohn, 2025, needs more optimization.
17 648 0.394885748828 Henry Cohn, 2026, needs more optimization.
17 649 0.395122837140 Henry Cohn, 2025, needs more optimization.
17 650 0.395176785937 Henry Cohn, 2026, needs more optimization.
17 651 0.395207336902 Henry Cohn, 2025, needs more optimization.
17 652 0.395686916140 Henry Cohn, 2026, needs more optimization.
17 653 0.395761077950 Henry Cohn, 2025, needs more optimization.
17 654 0.395806214541 Henry Cohn, 2026, needs more optimization.
17 655 0.395835524001 Henry Cohn, 2025, needs more optimization.
17 656 0.396208971634 Henry Cohn, 2026, needs more optimization.
17 657 0.396236676884 Henry Cohn, 2025, needs more optimization.
17 658 0.396240514766 Henry Cohn, 2026, needs more optimization.
17 659 0.396393049348 Henry Cohn, 2025, needs more optimization.
17 660 0.396650867275 Henry Cohn, 2026, needs more optimization.
17 661 0.396741644621 Henry Cohn, 2025, needs more optimization.
17 662 0.396991460866 Henry Cohn, 2026, needs more optimization.
17 663 0.397022110102 Henry Cohn, 2025, needs more optimization.
17 664 0.397062837170 Henry Cohn, 2026, needs more optimization.
17 665 0.397074844999 Henry Cohn, 2025, needs more optimization.
17 666 0.397607336147 Henry Cohn, 2026, needs more optimization.
17 667 0.397922919863 Henry Cohn, 2025, needs more optimization.
17 668 0.397951526077 Henry Cohn, 2026, needs more optimization.
17 669 0.398232768001 Henry Cohn, 2025, needs more optimization.
17 670 0.398264201904 Henry Cohn, 2026, needs more optimization.
17 672 0.398532721303 Henry Cohn, 2026, needs more optimization.
17 673 0.398547114794 Henry Cohn, 2025, needs more optimization.
17 674 0.398831684744 Henry Cohn, 2026, needs more optimization.
17 675 0.399163265373 Henry Cohn, 2026, needs more optimization.
17 676 0.399460068930 Henry Cohn, 2026, needs more optimization.
17 677 0.399591565221 Henry Cohn, 2026, needs more optimization.
17 678 0.399823704584 Henry Cohn, 2026, needs more optimization.
17 771 0.4 Orthogonal union of 769 points in 16 dimensions and 2 points in 1 dimension.
5⁢x−2
17 772 0.400015816743 Henry Cohn, 2026, needs more optimization.
17 773 0.400016162906 Henry Cohn, 2026, needs more optimization.
17 774 0.410786270069 Orthogonal union of 772 points in 16 dimensions and 2 points in 1 dimension.
17 775 0.411078243325 Henry Cohn, 2026, needs more optimization.
17 776 0.411377744053 Henry Cohn, 2026, needs more optimization.
17 777 0.411417241293 Henry Cohn, 2026, needs more optimization.
17 778 0.411456142080 Henry Cohn, 2026, needs more optimization.
17 779 0.411773764395 Henry Cohn, 2026, needs more optimization.
17 780 0.411785311602 Henry Cohn, 2026, needs more optimization.
17 781 0.411844710455 Henry Cohn, 2026, needs more optimization.
17 782 0.412060685354 Henry Cohn, 2026, needs more optimization.
17 783 0.412072656071 Henry Cohn, 2026, needs more optimization.
17 784 0.412301978580 Henry Cohn, 2026, needs more optimization.
17 785 0.412308647870 Henry Cohn, 2026, needs more optimization.
17 786 0.412394157061 Henry Cohn, 2026, needs more optimization.
17 787 0.412779426838 Henry Cohn, 2026, needs more optimization.
17 788 0.412790458138 Henry Cohn, 2026, needs more optimization.
17 789 0.412823329249 Henry Cohn, 2026, needs more optimization.
17 790 0.413138707314 Henry Cohn, 2026, needs more optimization.
17 791 0.413158776017 Henry Cohn, 2026, needs more optimization.
17 792 0.413166606292 Henry Cohn, 2026, needs more optimization.
17 793 0.413198572387 Henry Cohn, 2026, needs more optimization.
17 794 0.413526424265 Henry Cohn, 2026, needs more optimization.
17 795 0.413572258074 Henry Cohn, 2026, needs more optimization.
17 796 0.413607535542 Henry Cohn, 2026, needs more optimization.
17 797 0.413661931509 Henry Cohn, 2026, needs more optimization.
17 798 0.413780848941 Henry Cohn, 2026, needs more optimization.
17 799 0.414133704062 Henry Cohn, 2026, needs more optimization.
17 800 0.414143155809 Henry Cohn, 2026, needs more optimization.
17 801 0.414151872679 Henry Cohn, 2026, needs more optimization.
17 802 0.414198331515 Henry Cohn, 2026, needs more optimization.
17 803 0.414461010431 Henry Cohn, 2026, needs more optimization.
17 804 0.414473289276 Henry Cohn, 2026, needs more optimization.
17 805 0.414489110205 Henry Cohn, 2026, needs more optimization.
17 806 0.414838427665 Henry Cohn, 2026, needs more optimization.
17 807 0.414845641946 Henry Cohn, 2026, needs more optimization.
17 808 0.414867129605 Henry Cohn, 2026, needs more optimization.
17 809 0.414988438343 Henry Cohn, 2026, needs more optimization.
17 810 0.415034375897 Henry Cohn, 2026, needs more optimization.
17 811 0.415044174152 Henry Cohn, 2026, needs more optimization.
17 812 0.415442015846 Henry Cohn, 2026, needs more optimization.
17 813 0.415459415907 Henry Cohn, 2026, needs more optimization.
17 814 0.415493032647 Henry Cohn, 2026, needs more optimization.
17 815 0.415869911595 Henry Cohn, 2026, needs more optimization.
17 816 0.415887573019 Henry Cohn, 2026, needs more optimization.
17 817 0.415902819973 Henry Cohn, 2026, needs more optimization.
17 818 0.416094474108 Henry Cohn, 2026, needs more optimization.
17 819 0.416116289131 Henry Cohn, 2026, needs more optimization.
17 820 0.416336035615 Henry Cohn, 2026, needs more optimization.
17 821 0.416347977565 Henry Cohn, 2026, needs more optimization.
17 822 0.416635361342 Henry Cohn, 2026, needs more optimization.
17 823 0.416650214534 Henry Cohn, 2026, needs more optimization.
17 824 0.416650604132 Henry Cohn, 2026, needs more optimization.
17 825 0.416668308282 Henry Cohn, 2026, needs more optimization.
17 826 0.416675441463 Henry Cohn, 2026, needs more optimization.
17 827 0.416903720299 Henry Cohn, 2026, needs more optimization.
17 828 0.416907328036 Henry Cohn, 2026, needs more optimization.
17 829 0.417298255226 Henry Cohn, 2026, needs more optimization.
17 830 0.417338360099 Henry Cohn, 2026, needs more optimization.
17 831 0.417400879024 Henry Cohn, 2026, needs more optimization.
17 832 0.417550908223 Henry Cohn, 2026, needs more optimization.
17 833 0.417555945582 Henry Cohn, 2026, needs more optimization.
17 834 0.417564498196 Henry Cohn, 2026, needs more optimization.
17 835 0.417615191436 Henry Cohn, 2026, needs more optimization.
17 836 0.418054361132 Henry Cohn, 2026, needs more optimization.
17 837 0.418072818553 Henry Cohn, 2026, needs more optimization.
17 838 0.418088762005 Henry Cohn, 2026, needs more optimization.
17 839 0.418319448116 Henry Cohn, 2026, needs more optimization.
17 840 0.418326928163 Henry Cohn, 2026, needs more optimization.
17 841 0.418382157539 Henry Cohn, 2026, needs more optimization.
17 842 0.418637388893 Henry Cohn, 2026, needs more optimization.
17 843 0.418642674721 Henry Cohn, 2026, needs more optimization.
17 844 0.418653519023 Henry Cohn, 2026, needs more optimization.
17 845 0.418953037932 Henry Cohn, 2026, needs more optimization.
17 846 0.418961244591 Henry Cohn, 2026, needs more optimization.
17 847 0.419295113996 Henry Cohn, 2026, needs more optimization.
17 848 0.419467135138 Henry Cohn, 2026, needs more optimization.
17 849 0.419481879708 Henry Cohn, 2026, needs more optimization.
17 850 0.419488840831 Henry Cohn, 2026, needs more optimization.
17 851 0.419531595711 Henry Cohn, 2026, needs more optimization.
17 852 0.419783382270 Henry Cohn, 2026, needs more optimization.
17 853 0.419792728421 Henry Cohn, 2026, needs more optimization.
17 854 0.420101143691 Henry Cohn, 2026, needs more optimization.
17 855 0.420166716969 Henry Cohn, 2026, needs more optimization.
17 856 0.420198134879 Henry Cohn, 2026, needs more optimization.
17 857 0.420212200096 Henry Cohn, 2026, needs more optimization.
17 858 0.420221329202 Henry Cohn, 2026, needs more optimization.
17 859 0.420402654116 Henry Cohn, 2026, needs more optimization.
17 860 0.420435622319 Henry Cohn, 2026, needs more optimization.
17 861 0.420687065036 Henry Cohn, 2026, needs more optimization.
17 862 0.420720566373 Henry Cohn, 2026, needs more optimization.
17 863 0.420789908136 Henry Cohn, 2026, needs more optimization.
17 864 0.420800233866 Henry Cohn, 2026, needs more optimization.
17 865 0.420819986864 Henry Cohn, 2026, needs more optimization.
17 866 0.420893057165 Henry Cohn, 2026, needs more optimization.
17 867 0.421182253443 Henry Cohn, 2026, needs more optimization.
17 868 0.421196600618 Henry Cohn, 2026, needs more optimization.
17 869 0.421217278867 Henry Cohn, 2026, needs more optimization.
17 870 0.421304794457 Henry Cohn, 2026, needs more optimization.
17 871 0.421701090912 Henry Cohn, 2026, needs more optimization.
17 872 0.421730751141 Henry Cohn, 2026, needs more optimization.
17 873 0.421869623046 Henry Cohn, 2026, needs more optimization.
17 874 0.421908097048 Henry Cohn, 2026, needs more optimization.
17 875 0.422070745141 Henry Cohn, 2026, needs more optimization.
17 876 0.422266429629 Henry Cohn, 2026, needs more optimization.
17 877 0.422273918479 Henry Cohn, 2026, needs more optimization.
17 878 0.422279298293 Henry Cohn, 2026, needs more optimization.
17 879 0.422659205673 Henry Cohn, 2026, needs more optimization.
17 881 0.422670364333 Henry Cohn, 2026, needs more optimization.
17 882 0.422675526014 Henry Cohn, 2026, needs more optimization.
17 883 0.422709414002 Henry Cohn, 2026, needs more optimization.
17 884 0.422816554663 Henry Cohn, 2026, needs more optimization.
17 885 0.422877307846 Henry Cohn, 2026, needs more optimization.
17 886 0.423205687570 Henry Cohn, 2026, needs more optimization.
17 887 0.423216369592 Henry Cohn, 2026, needs more optimization.
17 888 0.423271999218 Henry Cohn, 2026, needs more optimization.
17 889 0.423300485927 Henry Cohn, 2026, needs more optimization.
17 890 0.423307880857 Henry Cohn, 2026, needs more optimization.
17 891 0.423458546555 Henry Cohn, 2026, needs more optimization.
17 892 0.423679842703 Henry Cohn, 2026, needs more optimization.
17 893 0.423712740118 Henry Cohn, 2026, needs more optimization.
17 894 0.423749261584 Henry Cohn, 2026, needs more optimization.
17 895 0.423972435637 Henry Cohn, 2026, needs more optimization.
17 896 0.423981096147 Henry Cohn, 2026, needs more optimization.
17 897 0.423992805752 Henry Cohn, 2026, needs more optimization.
17 898 0.424162508087 Henry Cohn, 2026, needs more optimization.
17 899 0.424172759398 Henry Cohn, 2026, needs more optimization.
17 900 0.424179997347 Henry Cohn, 2026, needs more optimization.
17 901 0.424475974446 Henry Cohn, 2026, needs more optimization.
17 902 0.424494416529 Henry Cohn, 2026, needs more optimization.
17 903 0.424619121787 Henry Cohn, 2026, needs more optimization.
17 904 0.424867718417 Henry Cohn, 2026, needs more optimization.
17 905 0.424875090511 Henry Cohn, 2026, needs more optimization.
17 906 0.424933793269 Henry Cohn, 2026, needs more optimization.
17 907 0.425077778835 Henry Cohn, 2026, needs more optimization.
17 908 0.425218804645 Henry Cohn, 2026, needs more optimization.
17 909 0.425231066236 Henry Cohn, 2026, needs more optimization.
17 910 0.425244760355 Henry Cohn, 2026, needs more optimization.
17 911 0.425556864754 Henry Cohn, 2026, needs more optimization.
17 912 0.425567139226 Henry Cohn, 2026, needs more optimization.
17 913 0.425611486201 Henry Cohn, 2026, needs more optimization.
17 914 0.425935399453 Henry Cohn, 2026, needs more optimization.
17 915 0.425973004766 Henry Cohn, 2026, needs more optimization.
17 916 0.425974475974 Henry Cohn, 2026, needs more optimization.
17 917 0.426241778762 Henry Cohn, 2026, needs more optimization.
17 918 0.426256445493 Henry Cohn, 2026, needs more optimization.
17 919 0.426306246734 Henry Cohn, 2026, needs more optimization.
17 920 0.426533376500 Henry Cohn, 2026, needs more optimization.
17 921 0.426539517558 Henry Cohn, 2026, needs more optimization.
17 922 0.426717992115 Henry Cohn, 2026, needs more optimization.
17 923 0.426826125583 Henry Cohn, 2026, needs more optimization.
17 924 0.426827699525 Henry Cohn, 2026, needs more optimization.
17 925 0.426863095249 Henry Cohn, 2026, needs more optimization.
17 926 0.427227099531 Henry Cohn, 2026, needs more optimization.
17 927 0.427276094219 Henry Cohn, 2026, needs more optimization.
17 928 0.427288884466 Henry Cohn, 2026, needs more optimization.
17 929 0.427299652259 Henry Cohn, 2026, needs more optimization.
17 930 0.427571604666 Henry Cohn, 2026, needs more optimization.
17 931 0.427776620955 Henry Cohn, 2026, needs more optimization.
17 932 0.427914716054 Henry Cohn, 2026, needs more optimization.
17 933 0.428114230167 Henry Cohn, 2026, needs more optimization.
17 934 0.428171578908 Henry Cohn, 2026, needs more optimization.
17 935 0.428275870185 Henry Cohn, 2026, needs more optimization.
17 936 0.428403360651 Henry Cohn, 2026, needs more optimization.
17 937 0.428510749809 Henry Cohn, 2026, needs more optimization.
17 1024 0.428571428572 Subcode of a code of size 1570 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
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.
18 48 0.074706792917 Henry Cohn, 2024.
18 50 0.078219048073 Henry Cohn, 2025.
368⁢x2−16⁢x−1
18 51 0.084340252912 Henry Cohn, 2025.
18 52 0.084342002724 Henry Cohn, 2025.
18 53 0.084342450321 Henry Cohn, 2025.
18 54 0.084342552633 Henry Cohn, 2025.
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.
18 69 0.101456854890 Henry Cohn, 2024.
176⁢x2−8⁢x−1
18 71 0.107360417204 Henry Cohn, 2026, needs more optimization.
18 72 0.109540130291 Henry Cohn, 2026, needs more optimization.
18 73 0.117134464852 Henry Cohn, 2026, needs more optimization.
18 74 0.121825115439 Henry Cohn, 2026, needs more optimization.
18 76 0.122045963410 Henry Cohn, 2026, needs more optimization.
18 77 0.123493846411 Henry Cohn, 2026, needs more optimization.
18 78 0.125826683534 Henry Cohn, 2026, needs more optimization.
18 80 0.126224060074 Henry Cohn, 2026, needs more optimization.
18 81 0.126904281674 Henry Cohn, 2026, needs more optimization.
18 82 0.127626718186 Henry Cohn, 2026, needs more optimization.
18 83 0.129098755680 Henry Cohn, 2026, needs more optimization.
18 84 0.130581918400 Henry Cohn, 2026, needs more optimization.
18 85 0.132295645173 Henry Cohn, 2026, needs more optimization.
18 86 0.132700084117 Henry Cohn, 2026, needs more optimization.
18 87 0.133675592670 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 0.155249851797 Henry Cohn, 2026, needs more optimization.
18 99 0.165211710795 Henry Cohn, 2026, needs more optimization.
18 100 0.167512152817 Henry Cohn, 2026, needs more optimization.
18 101 0.167585262307 Henry Cohn, 2026, needs more optimization.
18 102 0.168091410139 Henry Cohn, 2026, needs more optimization.
18 103 0.168582537376 Henry Cohn, 2026, needs more optimization.
18 104 0.169042218512 Henry Cohn, 2026, needs more optimization.
18 105 0.169059474211 Henry Cohn, 2026, needs more optimization.
18 106 0.169231003773 Henry Cohn, 2026, needs more optimization.
18 107 0.169525752017 Henry Cohn, 2026, needs more optimization.
18 108 0.170156210108 Henry Cohn, 2026, needs more optimization.
18 109 0.170449701157 Henry Cohn, 2026, needs more optimization.
18 110 0.170631915683 Henry Cohn, 2026, needs more optimization.
18 111 0.170820554204 Henry Cohn, 2026, needs more optimization.
18 112 0.171617847784 Henry Cohn, 2026, needs more optimization.
18 113 0.172991187581 Henry Cohn, 2026, needs more optimization.
18 114 0.175540853941 Henry Cohn, 2026, needs more optimization.
18 115 0.177482210568 Henry Cohn, 2026, needs more optimization.
18 116 0.179458482342 Henry Cohn, 2026, needs more optimization.
18 117 0.181388785750 Henry Cohn, 2026, needs more optimization.
18 118 0.183022569146 Henry Cohn, 2026, needs more optimization.
18 119 0.185088015247 Henry Cohn, 2026, needs more optimization.
18 120 0.185217299571 Henry Cohn, 2026, needs more optimization.
18 121 0.186200976847 Henry Cohn, 2026, needs more optimization.
18 122 0.187309346802 Henry Cohn, 2026, needs more optimization.
18 123 0.188916059509 Henry Cohn, 2026, needs more optimization.
18 130 0.189193290536 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 0.193070622517 Henry Cohn, 2026, needs more optimization.
18 134 0.193721012395 Henry Cohn, 2026, needs more optimization.
18 135 0.194298495175 Henry Cohn, 2026, needs more optimization.
18 136 0.194623026013 Henry Cohn, 2026, needs more optimization.
18 137 0.194954693374 Henry Cohn, 2026, needs more optimization.
18 138 0.195230197730 Henry Cohn, 2026, needs more optimization.
18 140 0.195281232520 Henry Cohn, 2026, needs more optimization.
18 144 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
18 146 0.200557378588 Henry Cohn, 2026, needs more optimization.
18 148 0.200690607331 Henry Cohn, 2026, needs more optimization.
18 149 0.200733793965 Henry Cohn, 2026, needs more optimization.
18 150 0.200749455424 Henry Cohn, 2026, needs more optimization.
18 151 0.200894664280 Henry Cohn, 2026, needs more optimization.
18 152 0.200984408985 Henry Cohn, 2026, needs more optimization.
18 153 0.201189772934 Henry Cohn, 2026, needs more optimization.
18 154 0.201422256036 Henry Cohn, 2026, needs more optimization.
18 155 0.201456188190 Henry Cohn, 2026, needs more optimization.
18 156 0.201493543981 Henry Cohn, 2026, needs more optimization.
18 157 0.201636336544 Henry Cohn, 2026, needs more optimization.
18 158 0.201636416606 Henry Cohn, 2026, needs more optimization.
18 159 0.201636416635 Henry Cohn, 2026, needs more optimization.
18 160 0.201667601119 Henry Cohn, 2026, needs more optimization.
18 161 0.202268705448 Henry Cohn, 2026, needs more optimization.
18 162 0.202319513045 Henry Cohn, 2026, needs more optimization.
18 163 0.202373950270 Henry Cohn, 2026, needs more optimization.
18 164 0.202537532522 Henry Cohn, 2026, needs more optimization.
18 165 0.202761305477 Henry Cohn, 2026, needs more optimization.
18 166 0.202859143239 Henry Cohn, 2026, needs more optimization.
18 167 0.202898281394 Henry Cohn, 2026, needs more optimization.
18 170 0.202919972291 Henry Cohn, 2026, needs more optimization.
18 171 0.203077459771 Henry Cohn, 2026, needs more optimization.
18 172 0.204258591876 Henry Cohn, 2026, needs more optimization.
18 173 0.206309769903 Henry Cohn, 2026, needs more optimization.
18 174 0.208717702340 Henry Cohn, 2026, needs more optimization.
18 175 0.212115733210 Henry Cohn, 2026, needs more optimization.
18 179 0.214580576913 Orthogonal union of 177 points in 17 dimensions and 2 points in 1 dimension.
59⁢x2−8⁢x−1
18 180 0.214589190956 Henry Cohn, 2026, needs more optimization.
18 181 0.214589440531 Henry Cohn, 2026, needs more optimization.
18 184 0.214589972894 Henry Cohn, 2026, needs more optimization.
18 186 0.214591279608 Henry Cohn, 2026, needs more optimization.
18 187 0.214759469336 Henry Cohn, 2026, needs more optimization.
18 188 0.217804567641 Henry Cohn, 2026, needs more optimization.
18 189 0.219048677183 Henry Cohn, 2026, needs more optimization.
18 190 0.220407550116 Henry Cohn, 2026, needs more optimization.
18 191 0.221444644041 Henry Cohn, 2026, needs more optimization.
18 192 0.223220570809 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 0.227401909859 Henry Cohn, 2026, needs more optimization.
18 207 0.228476633845 Henry Cohn, 2026, needs more optimization.
18 208 0.229747226174 Henry Cohn, 2026, needs more optimization.
18 209 0.230552070313 Henry Cohn, 2026, needs more optimization.
18 210 0.230996747457 Henry Cohn, 2026, needs more optimization.
18 211 0.231265700970 Henry Cohn, 2026, needs more optimization.
18 212 0.232483258340 Henry Cohn, 2026, needs more optimization.
18 213 0.233085738434 Henry Cohn, 2026, needs more optimization.
18 214 0.235292169367 Henry Cohn, 2026, needs more optimization.
18 215 0.235346614153 Henry Cohn, 2026, needs more optimization.
18 216 0.235429195596 Henry Cohn, 2026, needs more optimization.
18 217 0.236294260796 Henry Cohn, 2026, needs more optimization.
18 218 0.237012300297 Henry Cohn, 2026, needs more optimization.
18 219 0.237605250102 Henry Cohn, 2026, needs more optimization.
18 220 0.238606578304 Henry Cohn, 2026, needs more optimization.
18 221 0.239743970082 Henry Cohn, 2026, needs more optimization.
18 222 0.240340160087 Henry Cohn, 2026, needs more optimization.
18 223 0.241313211634 Henry Cohn, 2026, needs more optimization.
18 224 0.241541396334 Henry Cohn, 2026, needs more optimization.
18 225 0.241648239190 Henry Cohn, 2026, needs more optimization.
18 226 0.241769195292 Henry Cohn, 2026, needs more optimization.
18 227 0.241906082162 Henry Cohn, 2026, needs more optimization.
18 228 0.242082871691 Henry Cohn, 2026, needs more optimization.
18 229 0.242323952679 Henry Cohn, 2026, needs more optimization.
18 230 0.242430685838 Henry Cohn, 2026, needs more optimization.
18 231 0.242554696581 Henry Cohn, 2026, needs more optimization.
18 232 0.242827916920 Henry Cohn, 2026, needs more optimization.
18 233 0.243062705800 Henry Cohn, 2026, needs more optimization.
18 234 0.243545068020 Henry Cohn, 2026, needs more optimization.
18 235 0.243865080052 Henry Cohn, 2026, needs more optimization.
18 236 0.244001560079 Henry Cohn, 2026, needs more optimization.
18 237 0.244152457829 Henry Cohn, 2026, needs more optimization.
18 238 0.244367177008 Henry Cohn, 2026, needs more optimization.
18 239 0.245072328001 Henry Cohn, 2026, needs more optimization.
18 240 0.245614937980 Henry Cohn, 2026, needs more optimization.
18 241 0.245708674105 Henry Cohn, 2026, needs more optimization.
18 242 0.246301324956 Henry Cohn, 2026, needs more optimization.
18 256 0.246437043968 Henry Cohn, 2026, needs more optimization.
18 257 0.246750426289 Henry Cohn, 2026, needs more optimization.
18 259 0.247040525268 Henry Cohn, 2026, needs more optimization.
18 260 0.247075617158 Henry Cohn, 2026, needs more optimization.
18 261 0.247126454539 Henry Cohn, 2026, needs more optimization.
18 262 0.247149816983 Henry Cohn, 2026, needs more optimization.
18 263 0.247191335203 Henry Cohn, 2025, needs more optimization.
18 264 0.247202561970 Henry Cohn, 2026, needs more optimization.
18 265 0.247271444470 Henry Cohn, 2026, needs more optimization.
18 266 0.247341828640 Henry Cohn, 2026, needs more optimization.
18 267 0.247376892723 Henry Cohn, 2026, needs more optimization.
18 268 0.247467619966 Henry Cohn, 2026, needs more optimization.
18 269 0.247474143844 Henry Cohn, 2026, needs more optimization.
18 270 0.247485367186 Henry Cohn, 2026, needs more optimization.
18 271 0.247527104243 Henry Cohn, 2026, needs more optimization.
18 272 0.247574181497 Henry Cohn, 2026, needs more optimization.
18 273 0.247582007336 Henry Cohn, 2026, needs more optimization.
18 274 0.247594186795 Henry Cohn, 2026, needs more optimization.
18 275 0.247626131779 Henry Cohn, 2026, needs more optimization.
18 276 0.247646419114 Henry Cohn, 2026, needs more optimization.
18 277 0.247700629221 Henry Cohn, 2026, needs more optimization.
18 278 0.247719852045 Henry Cohn, 2026, needs more optimization.
18 279 0.247739692075 Henry Cohn, 2026, needs more optimization.
18 280 0.247741668987 Henry Cohn, 2026, needs more optimization.
18 281 0.247790624512 Henry Cohn, 2026, needs more optimization.
18 282 0.247800395602 Henry Cohn, 2026, needs more optimization.
18 284 0.247855356408 Henry Cohn, 2026, needs more optimization.
18 285 0.247856117220 Henry Cohn, 2026, needs more optimization.
18 286 0.247856125800 Henry Cohn, 2026, needs more optimization.
18 287 0.248699121494 Henry Cohn, 2026, needs more optimization.
18 288 0.248891333185 Henry Cohn, 2026, needs more optimization.
18 289 0.248943124800 Henry Cohn, 2025, needs more optimization.
18 290 0.249341399134 Henry Cohn, 2026, needs more optimization.
18 291 0.249401342871 Henry Cohn, 2026, needs more optimization.
18 292 0.249419613218 Henry Cohn, 2026, needs more optimization.
18 293 0.249730971240 Henry Cohn, 2026, needs more optimization.
18 295 0.249926483618 Henry Cohn, 2026, needs more optimization.
18 296 0.249940691576 Henry Cohn, 2026, needs more optimization.
18 298 0.250014119647 Henry Cohn, 2026, needs more optimization.
18 299 0.250015429068 Henry Cohn, 2026, needs more optimization.
18 300 0.250031618168 Henry Cohn, 2026, needs more optimization.
18 301 0.250080438662 Henry Cohn, 2026, needs more optimization.
18 302 0.250123060329 Henry Cohn, 2025, needs more optimization.
18 303 0.251311867492 Henry Cohn, 2026, needs more optimization.
18 304 0.259265953487 Henry Cohn, 2026, needs more optimization.
18 306 0.259283709399 Henry Cohn, 2026, needs more optimization.
18 307 0.259439567247 Henry Cohn, 2025, needs more optimization.
18 310 0.259898926815 Henry Cohn, 2026, needs more optimization.
18 314 0.259998414706 Henry Cohn, 2026, needs more optimization.
18 316 0.260117731035 Henry Cohn, 2026, needs more optimization.
18 318 0.260396288060 Henry Cohn, 2026, needs more optimization.
18 319 0.260531286407 Henry Cohn, 2025, needs more optimization.
18 327 0.260706937223 Henry Cohn, 2026, needs more optimization.
18 329 0.260861316083 Henry Cohn, 2026, needs more optimization.
18 330 0.261044900338 Henry Cohn, 2026, needs more optimization.
18 331 0.263139724570 Henry Cohn, 2026, needs more optimization.
18 332 0.266388611451 Henry Cohn, 2026, needs more optimization.
18 333 0.268752675585 Henry Cohn, 2026, needs more optimization.
18 334 0.270858069141 Henry Cohn, 2026, needs more optimization.
18 335 0.272981703608 Henry Cohn, 2026, needs more optimization.
18 336 0.275340786473 Henry Cohn, 2026, needs more optimization.
18 337 0.276990960047 Henry Cohn, 2026, needs more optimization.
18 338 0.278722560151 Henry Cohn, 2026, needs more optimization.
18 339 0.280342616422 Henry Cohn, 2026, needs more optimization.
18 340 0.281938777624 Henry Cohn, 2026, needs more optimization.
18 341 0.283134176940 Henry Cohn, 2026, needs more optimization.
18 342 0.284489040622 Henry Cohn, 2026, needs more optimization.
18 343 0.285661779661 Henry Cohn, 2026, needs more optimization.
18 344 0.286914263267 Henry Cohn, 2026, needs more optimization.
18 345 0.287471614384 Henry Cohn, 2026, needs more optimization.
18 346 0.288462265456 Henry Cohn, 2026, needs more optimization.
18 347 0.289658062885 Henry Cohn, 2026, needs more optimization.
18 348 0.290410132963 Henry Cohn, 2026, needs more optimization.
18 349 0.291094357677 Henry Cohn, 2026, needs more optimization.
18 350 0.291926308647 Henry Cohn, 2026, needs more optimization.
18 351 0.292114053573 Henry Cohn, 2026, needs more optimization.
18 352 0.292809310146 Henry Cohn, 2026, needs more optimization.
18 354 0.293446937045 Henry Cohn, 2026, needs more optimization.
18 355 0.294453168181 Henry Cohn, 2026, needs more optimization.
18 356 0.295984286969 Henry Cohn, 2026, needs more optimization.
18 364 0.296296296297 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
27⁢x−8
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 0.298406463245 Henry Cohn, 2026, needs more optimization.
18 482 0.300432687087 Henry Cohn, 2026, needs more optimization.
18 483 0.301586559090 Henry Cohn, 2025, needs more optimization.
18 484 0.302698728360 Henry Cohn, 2026, needs more optimization.
18 485 0.303492336125 Henry Cohn, 2026, needs more optimization.
18 486 0.305670494825 Henry Cohn, 2026, needs more optimization.
18 487 0.307369667820 Henry Cohn, 2026, needs more optimization.
18 488 0.309530402887 Henry Cohn, 2026, needs more optimization.
18 489 0.310112888442 Henry Cohn, 2026, needs more optimization.
18 490 0.310993334262 Henry Cohn, 2026, needs more optimization.
18 491 0.311812614330 Henry Cohn, 2026, needs more optimization.
18 492 0.312612893753 Henry Cohn, 2026, needs more optimization.
18 493 0.313337380762 Henry Cohn, 2026, needs more optimization.
18 494 0.313852212877 Henry Cohn, 2026, needs more optimization.
18 496 0.314178945346 Henry Cohn, 2026, needs more optimization.
18 497 0.314793963679 Henry Cohn, 2026, needs more optimization.
18 499 0.314998303095 Henry Cohn, 2026, needs more optimization.
18 500 0.315538618959 Henry Cohn, 2026, needs more optimization.
18 501 0.315975648206 Henry Cohn, 2026, needs more optimization.
18 502 0.316392482619 Henry Cohn, 2026, needs more optimization.
18 504 0.316745631627 Henry Cohn, 2026, needs more optimization.
18 505 0.317129590380 Henry Cohn, 2026, needs more optimization.
18 506 0.317460421992 Henry Cohn, 2026, needs more optimization.
18 507 0.317887716958 Henry Cohn, 2026, needs more optimization.
18 508 0.318381397317 Henry Cohn, 2026, needs more optimization.
18 509 0.318780917681 Henry Cohn, 2026, needs more optimization.
18 510 0.319037496663 Henry Cohn, 2026, needs more optimization.
18 511 0.319457922822 Henry Cohn, 2026, needs more optimization.
18 512 0.319755300869 Henry Cohn, 2026, needs more optimization.
18 513 0.319844210416 Henry Cohn, 2026, needs more optimization.
18 514 0.319862169028 Henry Cohn, 2026, needs more optimization.
18 515 0.320345298437 Henry Cohn, 2026, needs more optimization.
18 516 0.320822578864 Henry Cohn, 2026, needs more optimization.
18 517 0.321239103639 Henry Cohn, 2026, needs more optimization.
18 518 0.322128900086 Henry Cohn, 2026, needs more optimization.
18 519 0.322570835876 Henry Cohn, 2026, needs more optimization.
18 520 0.323062032308 Henry Cohn, 2026, needs more optimization.
18 521 0.323364821749 Henry Cohn, 2026, needs more optimization.
18 522 0.323557998308 Henry Cohn, 2026, needs more optimization.
18 523 0.323702392653 Henry Cohn, 2026, needs more optimization.
18 525 0.323765574864 Henry Cohn, 2026, needs more optimization.
18 526 0.324003639897 Henry Cohn, 2026, needs more optimization.
18 527 0.324489463147 Henry Cohn, 2026, needs more optimization.
18 528 0.324729223788 Henry Cohn, 2026, needs more optimization.
18 529 0.324972717106 Henry Cohn, 2026, needs more optimization.
18 530 0.324983910484 Henry Cohn, 2026, needs more optimization.
18 531 0.325313277730 Henry Cohn, 2026, needs more optimization.
18 532 0.325738926232 Henry Cohn, 2026, needs more optimization.
18 533 0.326066524535 Henry Cohn, 2026, needs more optimization.
18 534 0.326345869617 Henry Cohn, 2026, needs more optimization.
18 535 0.326617881817 Henry Cohn, 2026, needs more optimization.
18 536 0.326887366802 Henry Cohn, 2026, needs more optimization.
18 537 0.327162454673 Henry Cohn, 2026, needs more optimization.
18 538 0.327736844213 Henry Cohn, 2026, needs more optimization.
18 539 0.328024753797 Henry Cohn, 2026, needs more optimization.
18 540 0.328375261689 Henry Cohn, 2026, needs more optimization.
18 541 0.328777784877 Henry Cohn, 2026, needs more optimization.
18 542 0.329073656037 Henry Cohn, 2026, needs more optimization.
18 543 0.329362948056 Henry Cohn, 2026, needs more optimization.
18 544 0.329711350022 Henry Cohn, 2026, needs more optimization.
18 545 0.329772216735 Henry Cohn, 2026, needs more optimization.
18 546 0.330084116749 Henry Cohn, 2026, needs more optimization.
18 547 0.330410144935 Henry Cohn, 2026, needs more optimization.
18 548 0.330642963018 Henry Cohn, 2026, needs more optimization.
18 549 0.331026304759 Henry Cohn, 2026, needs more optimization.
18 550 0.331423146253 Henry Cohn, 2026, needs more optimization.
18 551 0.331708018565 Henry Cohn, 2026, needs more optimization.
18 552 0.332032026602 Henry Cohn, 2026, needs more optimization.
18 553 0.332412630375 Henry Cohn, 2026, needs more optimization.
18 555 0.332628474499 Henry Cohn, 2026, needs more optimization.
18 556 0.332960618658 Henry Cohn, 2026, needs more optimization.
18 557 0.333133939967 Henry Cohn, 2026, needs more optimization.
18 558 0.333262568883 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
18 674 0.349502823526 Henry Cohn, 2026, needs more optimization.
18 675 0.349949852156 Henry Cohn, 2026, needs more optimization.
18 676 0.351009172868 Henry Cohn, 2026, needs more optimization.
18 677 0.351704124079 Henry Cohn, 2026, needs more optimization.
18 678 0.352354278169 Henry Cohn, 2026, needs more optimization.
18 679 0.353289410670 Henry Cohn, 2026, needs more optimization.
18 680 0.354053162074 Henry Cohn, 2026, needs more optimization.
18 681 0.354649512578 Henry Cohn, 2026, needs more optimization.
18 682 0.355135513900 Henry Cohn, 2026, needs more optimization.
18 683 0.355830309292 Henry Cohn, 2026, needs more optimization.
18 684 0.356318085777 Henry Cohn, 2026, needs more optimization.
18 685 0.357017817351 Henry Cohn, 2026, needs more optimization.
18 867 0.357142857143 Henry Cohn, 2025, by modifying a construction from C. Ma, T. T. Zhaowei, 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 0.373325363819 Henry Cohn, 2026, needs more optimization.
18 869 0.385023846323 Henry Cohn, 2026, needs more optimization.
18 871 0.385062345878 Henry Cohn, 2026, needs more optimization.
18 873 0.385101566633 Henry Cohn, 2026, needs more optimization.
18 875 0.385134293592 Henry Cohn, 2026, needs more optimization.
18 877 0.385161571630 Henry Cohn, 2026, needs more optimization.
18 879 0.385205952734 Henry Cohn, 2026, needs more optimization.
18 881 0.385280428435 Henry Cohn, 2026, needs more optimization.
18 883 0.385355732553 Henry Cohn, 2026, needs more optimization.
18 885 0.385427371890 Henry Cohn, 2026, needs more optimization.
18 887 0.385534795837 Henry Cohn, 2026, needs more optimization.
18 889 0.385668488553 Henry Cohn, 2026, needs more optimization.
18 891 0.385779387614 Henry Cohn, 2026, needs more optimization.
18 893 0.386031902108 Henry Cohn, 2026, needs more optimization.
18 895 0.386108012278 Henry Cohn, 2026, needs more optimization.
18 897 0.386354945250 Henry Cohn, 2026, needs more optimization.
18 899 0.386431098274 Henry Cohn, 2026, needs more optimization.
18 901 0.386523851531 Henry Cohn, 2026, needs more optimization.
18 903 0.386640957206 Henry Cohn, 2026, needs more optimization.
18 905 0.386843211911 Henry Cohn, 2026, needs more optimization.
18 907 0.386898678207 Henry Cohn, 2026, needs more optimization.
18 909 0.386966427057 Henry Cohn, 2026, needs more optimization.
18 911 0.387025624212 Henry Cohn, 2026, needs more optimization.
18 913 0.387091610527 Henry Cohn, 2026, needs more optimization.
18 915 0.387155047039 Henry Cohn, 2026, needs more optimization.
18 917 0.387238909721 Henry Cohn, 2026, needs more optimization.
18 918 0.387406140266 Henry Cohn, 2026, needs more optimization.
18 919 0.387406141066 Henry Cohn, 2026, needs more optimization.
18 921 0.387492179865 Henry Cohn, 2026, needs more optimization.
18 923 0.387575991764 Henry Cohn, 2026, needs more optimization.
18 925 0.387644628190 Henry Cohn, 2026, needs more optimization.
18 927 0.387715762416 Henry Cohn, 2026, needs more optimization.
18 929 0.387833365722 Henry Cohn, 2026, needs more optimization.
18 931 0.387997122604 Henry Cohn, 2026, needs more optimization.
18 933 0.388248228039 Henry Cohn, 2026, needs more optimization.
18 935 0.388360604888 Henry Cohn, 2026, needs more optimization.
18 937 0.388468732119 Henry Cohn, 2026, needs more optimization.
18 939 0.388633660716 Henry Cohn, 2026, needs more optimization.
18 941 0.388767998692 Henry Cohn, 2026, needs more optimization.
18 943 0.388894604489 Henry Cohn, 2026, needs more optimization.
18 945 0.389027497452 Henry Cohn, 2026, needs more optimization.
18 947 0.389222141539 Henry Cohn, 2026, needs more optimization.
18 1024 0.389316299391 Henry Cohn, 2026, needs more optimization.
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 0.077608632538 Henry Cohn, 2026, needs more optimization.
19 53 0.080493593475 Henry Cohn, 2026.
19 54 0.081692292171 Henry Cohn, 2025.
19 55 0.082178889828 Henry Cohn, 2025.
19 56 0.083233613341 Henry Cohn, 2026, needs more optimization.
19 57 0.084818962260 Henry Cohn, 2025.
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 0.101319957448 Henry Cohn, 2026, needs more optimization.
19 70 0.101392647883 Henry Cohn, 2025, needs more optimization.
19 71 0.101456853396 Henry Cohn, 2025, needs more optimization.
19 72 0.102183669714 Henry Cohn, 2026, needs more optimization.
19 73 0.102201317334 Henry Cohn, 2026.
311⁢x2−22⁢x−1
19 74 0.104261643108 Henry Cohn, 2026, needs more optimization.
19 75 0.107816370365 Henry Cohn, 2026, needs more optimization.
19 76 0.111554533333 Henry Cohn, 2026, needs more optimization.
19 77 0.112842766161 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 0.132272376899 Henry Cohn, 2026, needs more optimization.
19 92 0.134685336705 Henry Cohn, 2026, needs more optimization.
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 0.153836524069 Henry Cohn, 2026, needs more optimization.
19 105 0.155558023691 Henry Cohn, 2026, needs more optimization.
19 106 0.155560107315 Henry Cohn, 2026, needs more optimization.
19 107 0.155579742659 Henry Cohn, 2026, needs more optimization.
19 108 0.156363614995 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 0.168802199662 Henry Cohn, 2026, needs more optimization.
19 134 0.174620105378 Henry Cohn, 2026, needs more optimization.
19 135 0.177865608406 Henry Cohn, 2026, needs more optimization.
19 136 0.177874933072 Henry Cohn, 2026, needs more optimization.
19 137 0.177881864651 Henry Cohn, 2026, needs more optimization.
19 138 0.177905918343 Henry Cohn, 2026, needs more optimization.
19 139 0.178029612350 Henry Cohn, 2026, needs more optimization.
19 140 0.178176574810 Henry Cohn, 2026, needs more optimization.
19 141 0.178377857361 Henry Cohn, 2026, needs more optimization.
19 142 0.178808740741 Henry Cohn, 2026, needs more optimization.
19 143 0.179227947477 Henry Cohn, 2026, needs more optimization.
19 144 0.179753657203 Henry Cohn, 2026, needs more optimization.
19 145 0.180760614320 Henry Cohn, 2026, needs more optimization.
19 146 0.181639807298 Henry Cohn, 2026, needs more optimization.
19 147 0.182386343675 Henry Cohn, 2026, needs more optimization.
19 148 0.183369175231 Henry Cohn, 2026, needs more optimization.
19 149 0.183926699205 Henry Cohn, 2026, needs more optimization.
19 150 0.184646543856 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 0.193637369265 Henry Cohn, 2026, needs more optimization.
19 178 0.194663251791 Henry Cohn, 2026, needs more optimization.
19 179 0.195476922962 Henry Cohn, 2026, needs more optimization.
19 180 0.195821119728 Henry Cohn, 2026, needs more optimization.
19 181 0.198089979723 Henry Cohn, 2026, needs more optimization.
19 182 0.198331862688 Henry Cohn, 2026, needs more optimization.
19 183 0.199879957966 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 0.203357314608 Henry Cohn, 2026, needs more optimization.
19 194 0.205905415946 Henry Cohn, 2026, needs more optimization.
19 195 0.207110998407 Henry Cohn, 2026, needs more optimization.
19 196 0.208040899820 Henry Cohn, 2026, needs more optimization.
19 197 0.208693183226 Henry Cohn, 2026, needs more optimization.
19 198 0.209395701920 Henry Cohn, 2026, needs more optimization.
19 199 0.209808492233 Henry Cohn, 2026, needs more optimization.
19 200 0.210590899380 Henry Cohn, 2026, needs more optimization.
19 201 0.211119357950 Henry Cohn, 2026, needs more optimization.
19 202 0.211607234808 Henry Cohn, 2026, needs more optimization.
19 203 0.212023097503 Henry Cohn, 2026, needs more optimization.
19 204 0.212310394009 Henry Cohn, 2026, needs more optimization.
19 205 0.212685452342 Henry Cohn, 2026, needs more optimization.
19 206 0.212895489767 Henry Cohn, 2026, needs more optimization.
19 207 0.213597081075 Henry Cohn, 2026, needs more optimization.
19 208 0.214239462357 Henry Cohn, 2026, needs more optimization.
19 209 0.214710942014 Henry Cohn, 2026, needs more optimization.
19 210 0.215123194194 Henry Cohn, 2026, needs more optimization.
19 211 0.215406311165 Henry Cohn, 2026, needs more optimization.
19 212 0.215588826572 Henry Cohn, 2026, needs more optimization.
19 213 0.216096289422 Henry Cohn, 2026, needs more optimization.
19 214 0.216351820623 Henry Cohn, 2026, needs more optimization.
19 215 0.218058358300 Henry Cohn, 2026, needs more optimization.
19 216 0.219013599466 Henry Cohn, 2026, needs more optimization.
19 217 0.219774129472 Henry Cohn, 2026, needs more optimization.
19 218 0.220505258820 Henry Cohn, 2026, needs more optimization.
19 219 0.221099258988 Henry Cohn, 2026, needs more optimization.
19 220 0.221717719018 Henry Cohn, 2026, needs more optimization.
19 221 0.222111004394 Henry Cohn, 2026, needs more optimization.
19 222 0.222589744621 Henry Cohn, 2026, needs more optimization.
19 223 0.222957926060 Henry Cohn, 2026, needs more optimization.
19 224 0.223241220314 Henry Cohn, 2026, needs more optimization.
19 225 0.223444973639 Henry Cohn, 2026, needs more optimization.
19 226 0.223667461875 Henry Cohn, 2026, needs more optimization.
19 227 0.223958619178 Henry Cohn, 2026, needs more optimization.
19 228 0.224163595155 Henry Cohn, 2026, needs more optimization.
19 229 0.224246339244 Henry Cohn, 2026, needs more optimization.
19 230 0.224318648869 Henry Cohn, 2026, needs more optimization.
19 231 0.224476277057 Henry Cohn, 2026, needs more optimization.
19 232 0.224536830260 Henry Cohn, 2026, needs more optimization.
19 233 0.224695407708 Henry Cohn, 2026, needs more optimization.
19 234 0.224766491944 Henry Cohn, 2026, needs more optimization.
19 236 0.225944062777 Henry Cohn, 2026, needs more optimization.
19 239 0.226002036617 Henry Cohn, 2026, needs more optimization.
19 240 0.226595376690 Henry Cohn, 2026, needs more optimization.
19 241 0.226739646462 Henry Cohn, 2026, needs more optimization.
19 242 0.226882297331 Henry Cohn, 2026, needs more optimization.
19 243 0.227174016747 Henry Cohn, 2026, needs more optimization.
19 244 0.228153538045 Henry Cohn, 2026, needs more optimization.
19 245 0.229078456458 Henry Cohn, 2026, needs more optimization.
19 246 0.229616956759 Henry Cohn, 2026, needs more optimization.
19 247 0.230104093250 Henry Cohn, 2026, needs more optimization.
19 277 0.230769230770 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13⁢x−3
19 278 0.235894248880 Henry Cohn, 2026, needs more optimization.
19 279 0.237144208068 Henry Cohn, 2026, needs more optimization.
19 280 0.238264872696 Henry Cohn, 2026, needs more optimization.
19 288 0.238519273263 Henry Cohn, 2026, needs more optimization.
19 291 0.238519273264 Henry Cohn, 2026, needs more optimization.
19 292 0.240889101961 Henry Cohn, 2026, needs more optimization.
19 294 0.244077353464 Henry Cohn, 2026, needs more optimization.
19 295 0.245551351184 Henry Cohn, 2026, needs more optimization.
19 296 0.246081683994 Henry Cohn, 2026, needs more optimization.
19 297 0.246485620890 Henry Cohn, 2026, needs more optimization.
19 298 0.246623291101 Henry Cohn, 2026, needs more optimization.
19 299 0.246853279526 Henry Cohn, 2026, needs more optimization.
19 300 0.248250982684 Henry Cohn, 2026, needs more optimization.
19 301 0.248749255732 Henry Cohn, 2026, needs more optimization.
19 302 0.249987633441 Henry Cohn, 2026, needs more optimization.
19 306 0.249989763672 Henry Cohn, 2026, needs more optimization.
19 307 0.249994992895 Henry Cohn, 2026, needs more optimization.
19 308 0.249995703148 Henry Cohn, 2026, needs more optimization.
19 310 0.250004560196 Henry Cohn, 2026, needs more optimization.
19 312 0.250025250933 Henry Cohn, 2026, needs more optimization.
19 314 0.250026538741 Henry Cohn, 2026, needs more optimization.
19 316 0.250040452200 Henry Cohn, 2026, needs more optimization.
19 318 0.250041457295 Henry Cohn, 2026, needs more optimization.
19 321 0.250043209609 Henry Cohn, 2026, needs more optimization.
19 322 0.250091163552 Henry Cohn, 2026, needs more optimization.
19 323 0.250124054478 Henry Cohn, 2026, needs more optimization.
19 324 0.250729997305 Henry Cohn, 2026, needs more optimization.
19 325 0.251181376933 Henry Cohn, 2026, needs more optimization.
19 326 0.259414860162 Henry Cohn, 2026, needs more optimization.
19 329 0.260706937223 Orthogonal union of 327 points in 18 dimensions and 2 points in 1 dimension.
19 331 0.260861316083 Orthogonal union of 329 points in 18 dimensions and 2 points in 1 dimension.
19 332 0.261044900338 Orthogonal union of 330 points in 18 dimensions and 2 points in 1 dimension.
19 333 0.263139724570 Orthogonal union of 331 points in 18 dimensions and 2 points in 1 dimension.
19 334 0.266388611451 Orthogonal union of 332 points in 18 dimensions and 2 points in 1 dimension.
19 335 0.268752675585 Orthogonal union of 333 points in 18 dimensions and 2 points in 1 dimension.
19 336 0.270858069141 Orthogonal union of 334 points in 18 dimensions and 2 points in 1 dimension.
19 337 0.272981703608 Orthogonal union of 335 points in 18 dimensions and 2 points in 1 dimension.
19 338 0.275340786473 Orthogonal union of 336 points in 18 dimensions and 2 points in 1 dimension.
19 339 0.276990960047 Orthogonal union of 337 points in 18 dimensions and 2 points in 1 dimension.
19 340 0.278722560151 Orthogonal union of 338 points in 18 dimensions and 2 points in 1 dimension.
19 341 0.280342616422 Orthogonal union of 339 points in 18 dimensions and 2 points in 1 dimension.
19 342 0.281938777624 Orthogonal union of 340 points in 18 dimensions and 2 points in 1 dimension.
19 343 0.283134176940 Orthogonal union of 341 points in 18 dimensions and 2 points in 1 dimension.
19 344 0.284489040622 Orthogonal union of 342 points in 18 dimensions and 2 points in 1 dimension.
19 345 0.285661779661 Orthogonal union of 343 points in 18 dimensions and 2 points in 1 dimension.
19 346 0.286914263267 Orthogonal union of 344 points in 18 dimensions and 2 points in 1 dimension.
19 350 0.287442992528 Henry Cohn, 2026, needs more optimization.
19 354 0.287475567571 Henry Cohn, 2026, needs more optimization.
19 358 0.287501332031 Henry Cohn, 2026, needs more optimization.
19 362 0.287559867284 Henry Cohn, 2026, needs more optimization.
19 366 0.287618805203 Henry Cohn, 2026, needs more optimization.
19 370 0.287698615603 Henry Cohn, 2026, needs more optimization.
19 372 0.287798049757 Henry Cohn, 2026, needs more optimization.
19 374 0.287918453343 Henry Cohn, 2026, needs more optimization.
19 378 0.288021238606 Henry Cohn, 2026, needs more optimization.
19 382 0.288113676701 Henry Cohn, 2026, needs more optimization.
19 386 0.288296847353 Henry Cohn, 2026, needs more optimization.
19 390 0.288447589533 Henry Cohn, 2026, needs more optimization.
19 394 0.288577485372 Henry Cohn, 2026, needs more optimization.
19 398 0.288770883243 Henry Cohn, 2026, needs more optimization.
19 419 0.288874173483 Henry Cohn, 2026, needs more optimization.
19 420 0.289521139730 Henry Cohn, 2026, needs more optimization.
19 421 0.289916082464 Henry Cohn, 2026, needs more optimization.
19 422 0.290957768272 Henry Cohn, 2026, needs more optimization.
19 485 0.296296296297 Henry Cohn, 2025.
27⁢x−8
19 489 0.296309401438 Henry Cohn, 2026, needs more optimization.
19 502 0.296316392024 Henry Cohn, 2026, needs more optimization.
19 504 0.296323077374 Henry Cohn, 2026, needs more optimization.
19 505 0.296492459732 Henry Cohn, 2026, needs more optimization.
19 506 0.296573838126 Henry Cohn, 2026, needs more optimization.
19 507 0.296594539460 Henry Cohn, 2026, needs more optimization.
19 508 0.296596627063 Henry Cohn, 2026, needs more optimization.
19 511 0.296671297876 Henry Cohn, 2026, needs more optimization.
19 512 0.296768209839 Henry Cohn, 2026, needs more optimization.
19 513 0.296776441951 Henry Cohn, 2026, needs more optimization.
19 523 0.296824849258 Henry Cohn, 2026, needs more optimization.
19 524 0.297004089192 Henry Cohn, 2026, needs more optimization.
19 525 0.297126277116 Henry Cohn, 2026, needs more optimization.
19 526 0.297336180345 Henry Cohn, 2026, needs more optimization.
19 527 0.297840233969 Henry Cohn, 2026, needs more optimization.
19 528 0.297891911775 Henry Cohn, 2026, needs more optimization.
19 529 0.297976220472 Henry Cohn, 2026, needs more optimization.
19 530 0.298090152463 Henry Cohn, 2026, needs more optimization.
19 534 0.298245204316 Henry Cohn, 2026, needs more optimization.
19 535 0.298251553457 Henry Cohn, 2026, needs more optimization.
19 536 0.298297853355 Henry Cohn, 2026, needs more optimization.
19 537 0.298348778203 Henry Cohn, 2026, needs more optimization.
19 538 0.298414203161 Henry Cohn, 2026, needs more optimization.
19 539 0.298466924201 Henry Cohn, 2026, needs more optimization.
19 540 0.298552011887 Henry Cohn, 2026, needs more optimization.
19 541 0.299330765051 Henry Cohn, 2026, needs more optimization.
19 552 0.299537160845 Henry Cohn, 2026, needs more optimization.
19 553 0.299574443095 Henry Cohn, 2026, needs more optimization.
19 554 0.299748664614 Henry Cohn, 2026, needs more optimization.
19 555 0.299921386768 Henry Cohn, 2026, needs more optimization.
19 556 0.301144455781 Henry Cohn, 2026, needs more optimization.
19 557 0.301890209568 Henry Cohn, 2026, needs more optimization.
19 560 0.304347826087 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
23⁢x−7
19 576 0.304347826087 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.
23⁢x−7
19 577 0.304506955116 Henry Cohn, 2026, needs more optimization.
19 578 0.304544966779 Henry Cohn, 2026, needs more optimization.
19 579 0.304610478353 Henry Cohn, 2026, needs more optimization.
19 580 0.304616094668 Henry Cohn, 2026, needs more optimization.
19 581 0.304638247229 Henry Cohn, 2026, needs more optimization.
19 582 0.304655240406 Henry Cohn, 2026, needs more optimization.
19 584 0.304688572506 Henry Cohn, 2026, needs more optimization.
19 585 0.304712559975 Henry Cohn, 2026, needs more optimization.
19 586 0.304718530445 Henry Cohn, 2026, needs more optimization.
19 588 0.304747554025 Henry Cohn, 2026, needs more optimization.
19 589 0.304768584912 Henry Cohn, 2026, needs more optimization.
19 590 0.304780871345 Henry Cohn, 2026, needs more optimization.
19 591 0.304807267890 Henry Cohn, 2026, needs more optimization.
19 592 0.304816887679 Henry Cohn, 2026, needs more optimization.
19 593 0.304850036313 Henry Cohn, 2025, needs more optimization.
19 594 0.304853512798 Henry Cohn, 2026, needs more optimization.
19 596 0.304882572546 Henry Cohn, 2026, needs more optimization.
19 598 0.304902665313 Henry Cohn, 2026, needs more optimization.
19 600 0.304924768823 Henry Cohn, 2026, needs more optimization.
19 602 0.304950732102 Henry Cohn, 2026, needs more optimization.
19 604 0.304954995080 Henry Cohn, 2026, needs more optimization.
19 606 0.304985964567 Henry Cohn, 2026, needs more optimization.
19 607 0.305008902041 Henry Cohn, 2025, needs more optimization.
19 608 0.305013451984 Henry Cohn, 2026, needs more optimization.
19 610 0.305019653088 Henry Cohn, 2026, needs more optimization.
19 612 0.305031675525 Henry Cohn, 2026, needs more optimization.
19 614 0.305038932744 Henry Cohn, 2026, needs more optimization.
19 616 0.305050192359 Henry Cohn, 2026, needs more optimization.
19 617 0.305068555187 Henry Cohn, 2025, needs more optimization.
19 618 0.305073545762 Henry Cohn, 2026, needs more optimization.
19 620 0.305081347021 Henry Cohn, 2026, needs more optimization.
19 622 0.305091844753 Henry Cohn, 2026, needs more optimization.
19 624 0.305097417134 Henry Cohn, 2026, needs more optimization.
19 626 0.305108073829 Henry Cohn, 2026, needs more optimization.
19 628 0.305119407750 Henry Cohn, 2026, needs more optimization.
19 630 0.305130483578 Henry Cohn, 2026, needs more optimization.
19 632 0.305145919737 Henry Cohn, 2026, needs more optimization.
19 634 0.305153759069 Henry Cohn, 2026, needs more optimization.
19 636 0.305161817320 Henry Cohn, 2026, needs more optimization.
19 638 0.305169608242 Henry Cohn, 2026, needs more optimization.
19 640 0.305175574270 Henry Cohn, 2026, needs more optimization.
19 642 0.308376875243 Henry Cohn, 2026, needs more optimization.
19 644 0.309227966944 Henry Cohn, 2026, needs more optimization.
19 646 0.309834682035 Henry Cohn, 2026, needs more optimization.
19 648 0.311072646970 Henry Cohn, 2026, needs more optimization.
19 650 0.311559395328 Henry Cohn, 2026, needs more optimization.
19 651 0.312098563747 Henry Cohn, 2025, needs more optimization.
19 652 0.312302448986 Henry Cohn, 2026, needs more optimization.
19 654 0.312821688736 Henry Cohn, 2026, needs more optimization.
19 656 0.313222186607 Henry Cohn, 2026, needs more optimization.
19 658 0.313880124979 Henry Cohn, 2026, needs more optimization.
19 660 0.314243955461 Henry Cohn, 2026, needs more optimization.
19 662 0.314619817608 Henry Cohn, 2026, needs more optimization.
19 664 0.315048124686 Henry Cohn, 2026, needs more optimization.
19 667 0.315402562394 Henry Cohn, 2026, needs more optimization.
19 668 0.315684776770 Henry Cohn, 2026, needs more optimization.
19 669 0.315861329434 Henry Cohn, 2026, needs more optimization.
19 670 0.316113371793 Henry Cohn, 2026, needs more optimization.
19 671 0.316460716831 Henry Cohn, 2026, needs more optimization.
19 672 0.316552154553 Henry Cohn, 2026, needs more optimization.
19 673 0.316709688688 Henry Cohn, 2026, needs more optimization.
19 674 0.316970919284 Henry Cohn, 2026, needs more optimization.
19 675 0.317125724600 Henry Cohn, 2026, needs more optimization.
19 676 0.317255027426 Henry Cohn, 2026, needs more optimization.
19 677 0.317326407835 Henry Cohn, 2026, needs more optimization.
19 678 0.317582486040 Henry Cohn, 2026, needs more optimization.
19 679 0.317936218241 Henry Cohn, 2026, needs more optimization.
19 680 0.318241372602 Henry Cohn, 2026, needs more optimization.
19 681 0.318374623822 Henry Cohn, 2026, needs more optimization.
19 682 0.318729714032 Henry Cohn, 2026, needs more optimization.
19 683 0.318993417172 Henry Cohn, 2026, needs more optimization.
19 684 0.319323576048 Henry Cohn, 2026, needs more optimization.
19 685 0.319458288432 Henry Cohn, 2026, needs more optimization.
19 686 0.319683383616 Henry Cohn, 2026, needs more optimization.
19 687 0.319794638488 Henry Cohn, 2026, needs more optimization.
19 688 0.320181355472 Henry Cohn, 2026, needs more optimization.
19 689 0.320289303214 Henry Cohn, 2026, needs more optimization.
19 690 0.320496326185 Henry Cohn, 2026, needs more optimization.
19 691 0.320742150948 Henry Cohn, 2026, needs more optimization.
19 692 0.321076234352 Henry Cohn, 2026, needs more optimization.
19 693 0.321294002098 Henry Cohn, 2026, needs more optimization.
19 694 0.321413561327 Henry Cohn, 2026, needs more optimization.
19 695 0.321763469567 Henry Cohn, 2026, needs more optimization.
19 696 0.321909466818 Henry Cohn, 2026, needs more optimization.
19 697 0.322140611100 Henry Cohn, 2026, needs more optimization.
19 698 0.322376706977 Henry Cohn, 2026, needs more optimization.
19 699 0.322549398083 Henry Cohn, 2026, needs more optimization.
19 700 0.322615590549 Henry Cohn, 2026, needs more optimization.
19 701 0.322692088616 Henry Cohn, 2026, needs more optimization.
19 702 0.322927338340 Henry Cohn, 2026, needs more optimization.
19 703 0.323196667968 Henry Cohn, 2026, needs more optimization.
19 704 0.323571375925 Henry Cohn, 2026, needs more optimization.
19 705 0.323715390002 Henry Cohn, 2026, needs more optimization.
19 706 0.323808952153 Henry Cohn, 2026, needs more optimization.
19 707 0.323995174823 Henry Cohn, 2026, needs more optimization.
19 708 0.324138944647 Henry Cohn, 2026, needs more optimization.
19 709 0.324312415631 Henry Cohn, 2026, needs more optimization.
19 710 0.324386551957 Henry Cohn, 2026, needs more optimization.
19 711 0.324476865332 Henry Cohn, 2026, needs more optimization.
19 712 0.324556577872 Henry Cohn, 2026, needs more optimization.
19 713 0.324828612538 Henry Cohn, 2026, needs more optimization.
19 714 0.324924730227 Henry Cohn, 2026, needs more optimization.
19 715 0.325146068062 Henry Cohn, 2026, needs more optimization.
19 716 0.325368556730 Henry Cohn, 2026, needs more optimization.
19 717 0.325619558049 Henry Cohn, 2026, needs more optimization.
19 718 0.325810181197 Henry Cohn, 2026, needs more optimization.
19 719 0.326042953422 Henry Cohn, 2026, needs more optimization.
19 720 0.326211035165 Henry Cohn, 2026, needs more optimization.
19 721 0.326328548917 Henry Cohn, 2026, needs more optimization.
19 722 0.326532725714 Henry Cohn, 2026, needs more optimization.
19 723 0.326641336668 Henry Cohn, 2026, needs more optimization.
19 724 0.326717068046 Henry Cohn, 2026, needs more optimization.
19 725 0.326822964839 Henry Cohn, 2026, needs more optimization.
19 726 0.326991237955 Henry Cohn, 2026, needs more optimization.
19 727 0.327099335394 Henry Cohn, 2026, needs more optimization.
19 728 0.327271095558 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 0.328269967781 Henry Cohn, 2026, needs more optimization.
19 735 0.328432786393 Henry Cohn, 2026, needs more optimization.
19 736 0.328576155202 Henry Cohn, 2026, needs more optimization.
19 737 0.328766789775 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 0.329462125371 Henry Cohn, 2026, needs more optimization.
19 741 0.329766890135 Henry Cohn, 2026, needs more optimization.
19 742 0.329881696117 Henry Cohn, 2026, needs more optimization.
19 743 0.330141426222 Henry Cohn, 2026, needs more optimization.
19 744 0.330406524597 Henry Cohn, 2026, needs more optimization.
19 745 0.330494421354 Henry Cohn, 2026, needs more optimization.
19 746 0.330749455350 Henry Cohn, 2026, needs more optimization.
19 747 0.330842623287 Henry Cohn, 2026, needs more optimization.
19 748 0.331096336913 Henry Cohn, 2026, needs more optimization.
19 749 0.331230916365 Henry Cohn, 2026, needs more optimization.
19 750 0.331425839333 Henry Cohn, 2026, needs more optimization.
19 751 0.331655460493 Henry Cohn, 2026, needs more optimization.
19 752 0.331888526360 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 0.332697360835 Henry Cohn, 2026, needs more optimization.
19 756 0.332869897609 Henry Cohn, 2026, needs more optimization.
19 757 0.333098580732 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 0.339564247470 Henry Cohn, 2026, needs more optimization.
19 898 0.341321382896 Henry Cohn, 2026, needs more optimization.
19 899 0.342710736514 Henry Cohn, 2026, needs more optimization.
19 900 0.344190688570 Henry Cohn, 2026, needs more optimization.
19 901 0.345708892182 Henry Cohn, 2026, needs more optimization.
19 902 0.346196560527 Henry Cohn, 2026, needs more optimization.
19 903 0.346989316677 Henry Cohn, 2026, needs more optimization.
19 904 0.347511723865 Henry Cohn, 2026, needs more optimization.
19 905 0.348046584459 Henry Cohn, 2026, needs more optimization.
19 906 0.348488327193 Henry Cohn, 2026, needs more optimization.
19 907 0.349125653486 Henry Cohn, 2025, needs more optimization.
19 908 0.349379233183 Henry Cohn, 2026, needs more optimization.
19 909 0.349790733491 Henry Cohn, 2026, needs more optimization.
19 910 0.350078486751 Henry Cohn, 2026, needs more optimization.
19 911 0.350179397445 Henry Cohn, 2026, needs more optimization.
19 912 0.350921071750 Henry Cohn, 2026, needs more optimization.
19 913 0.351034600979 Henry Cohn, 2025, needs more optimization.
19 914 0.351442708251 Henry Cohn, 2025, needs more optimization.
19 916 0.351531037932 Henry Cohn, 2026, needs more optimization.
19 917 0.351619501189 Henry Cohn, 2026, needs more optimization.
19 918 0.351664590736 Henry Cohn, 2026, needs more optimization.
19 919 0.351800276326 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 0.353230420678 Henry Cohn, 2026, needs more optimization.
19 930 0.353435076089 Henry Cohn, 2026, needs more optimization.
19 931 0.353686706140 Henry Cohn, 2026, needs more optimization.
19 932 0.353783146162 Henry Cohn, 2026, needs more optimization.
19 933 0.353871222440 Henry Cohn, 2026, needs more optimization.
19 934 0.354038520919 Henry Cohn, 2026, needs more optimization.
19 935 0.354198532308 Henry Cohn, 2026, needs more optimization.
19 936 0.354343602758 Henry Cohn, 2026, needs more optimization.
19 937 0.354523625015 Henry Cohn, 2026, needs more optimization.
19 938 0.354688802817 Henry Cohn, 2026, needs more optimization.
19 939 0.354886585323 Henry Cohn, 2026, needs more optimization.
19 940 0.355005957626 Henry Cohn, 2026, needs more optimization.
19 941 0.355059940145 Henry Cohn, 2026, needs more optimization.
19 942 0.355211834162 Henry Cohn, 2026, needs more optimization.
19 943 0.355244036315 Henry Cohn, 2026, needs more optimization.
19 944 0.355326813564 Henry Cohn, 2026, needs more optimization.
19 945 0.355500732302 Henry Cohn, 2026, needs more optimization.
19 946 0.355643803647 Henry Cohn, 2026, needs more optimization.
19 947 0.355784191448 Henry Cohn, 2026, needs more optimization.
19 948 0.355849931902 Henry Cohn, 2026, needs more optimization.
19 949 0.355977153894 Henry Cohn, 2026, needs more optimization.
19 950 0.356099911486 Henry Cohn, 2026, needs more optimization.
19 951 0.356367981526 Henry Cohn, 2026, needs more optimization.
19 952 0.356550451106 Henry Cohn, 2026, needs more optimization.
19 953 0.356684442666 Henry Cohn, 2026, needs more optimization.
19 954 0.356879197978 Henry Cohn, 2026, needs more optimization.
19 955 0.357036028866 Henry Cohn, 2026, needs more optimization.
19 956 0.357138832250 Henry Cohn, 2026, needs more optimization.
19 957 0.357202343294 Henry Cohn, 2026, needs more optimization.
19 958 0.357275403324 Henry Cohn, 2026, needs more optimization.
19 959 0.357357959901 Henry Cohn, 2026, needs more optimization.
19 960 0.357422078118 Henry Cohn, 2026, needs more optimization.
19 961 0.357595622760 Henry Cohn, 2026, needs more optimization.
19 962 0.357661198571 Henry Cohn, 2026, needs more optimization.
19 963 0.357861785710 Henry Cohn, 2026, needs more optimization.
19 964 0.357995597474 Henry Cohn, 2026, needs more optimization.
19 965 0.358125579662 Henry Cohn, 2026, needs more optimization.
19 966 0.358366884977 Henry Cohn, 2026, needs more optimization.
19 967 0.358479252127 Henry Cohn, 2026, needs more optimization.
19 968 0.358662197983 Henry Cohn, 2026, needs more optimization.
19 969 0.358717387403 Henry Cohn, 2026, needs more optimization.
19 970 0.358885174907 Henry Cohn, 2026, needs more optimization.
19 971 0.359014058617 Henry Cohn, 2026, needs more optimization.
19 972 0.359117295675 Henry Cohn, 2026, needs more optimization.
19 973 0.359288348361 Henry Cohn, 2026, needs more optimization.
19 974 0.359378978134 Henry Cohn, 2026, needs more optimization.
19 975 0.359493105987 Henry Cohn, 2026, needs more optimization.
19 976 0.359646606414 Henry Cohn, 2026, needs more optimization.
19 977 0.359741870072 Henry Cohn, 2026, needs more optimization.
19 978 0.359883109968 Henry Cohn, 2026, needs more optimization.
19 979 0.360020739593 Henry Cohn, 2026, needs more optimization.
19 980 0.360186197052 Henry Cohn, 2026, needs more optimization.
19 981 0.360378264310 Henry Cohn, 2026, needs more optimization.
19 982 0.360509918338 Henry Cohn, 2026, needs more optimization.
19 983 0.360592065068 Henry Cohn, 2026, needs more optimization.
19 984 0.360759934182 Henry Cohn, 2026, needs more optimization.
19 985 0.360906557866 Henry Cohn, 2026, needs more optimization.
19 986 0.361093810219 Henry Cohn, 2026, needs more optimization.
19 987 0.361163237306 Henry Cohn, 2026, needs more optimization.
19 988 0.361298345642 Henry Cohn, 2026, needs more optimization.
19 989 0.361363809010 Henry Cohn, 2026, needs more optimization.
19 990 0.361504779834 Henry Cohn, 2026, needs more optimization.
19 991 0.361566613290 Henry Cohn, 2026, needs more optimization.
19 992 0.361661238550 Henry Cohn, 2026, needs more optimization.
19 993 0.361773223203 Henry Cohn, 2026, needs more optimization.
19 994 0.361874887030 Henry Cohn, 2026, needs more optimization.
19 995 0.362029935741 Henry Cohn, 2026, needs more optimization.
19 996 0.362146092991 Henry Cohn, 2026, needs more optimization.
19 997 0.362230462707 Henry Cohn, 2026, needs more optimization.
19 998 0.362297503610 Henry Cohn, 2026, needs more optimization.
19 999 0.362428938782 Henry Cohn, 2026, needs more optimization.
19 1000 0.362472322179 Henry Cohn, 2026, needs more optimization.
19 1001 0.362545021760 Henry Cohn, 2026, needs more optimization.
19 1002 0.362690916017 Henry Cohn, 2026, needs more optimization.
19 1003 0.362881276916 Henry Cohn, 2026, needs more optimization.
19 1004 0.363037023767 Henry Cohn, 2026, needs more optimization.
19 1005 0.363190813313 Henry Cohn, 2026, needs more optimization.
19 1006 0.363297374771 Henry Cohn, 2026, needs more optimization.
19 1007 0.363410354095 Henry Cohn, 2026, needs more optimization.
19 1008 0.363542414576 Henry Cohn, 2026, needs more optimization.
19 1009 0.363638619799 Henry Cohn, 2026, needs more optimization.
19 1010 0.363670050139 Henry Cohn, 2026, needs more optimization.
19 1011 0.363868636482 Henry Cohn, 2026, needs more optimization.
19 1012 0.363970777661 Henry Cohn, 2026, needs more optimization.
19 1013 0.364012135912 Henry Cohn, 2026, needs more optimization.
19 1014 0.364120104446 Henry Cohn, 2026, needs more optimization.
19 1015 0.364306719502 Henry Cohn, 2026, needs more optimization.
19 1016 0.364466650168 Henry Cohn, 2026, needs more optimization.
19 1017 0.364533417054 Henry Cohn, 2026, needs more optimization.
19 1018 0.364688383422 Henry Cohn, 2026, needs more optimization.
19 1019 0.364782760152 Henry Cohn, 2026, needs more optimization.
19 1020 0.364886620939 Henry Cohn, 2026, needs more optimization.
19 1021 0.364974901544 Henry Cohn, 2026, needs more optimization.
19 1022 0.365051553159 Henry Cohn, 2026, needs more optimization.
19 1023 0.365156837284 Henry Cohn, 2026, needs more optimization.
19 1024 0.365288510168 Henry Cohn, 2026, needs more optimization.
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 0.087640553690 Henry Cohn, 2026, needs more optimization.
20 66 0.089602007877 Henry Cohn, 2026, needs more optimization.
20 67 0.095918257385 Henry Cohn, 2026, needs more optimization.
20 68 0.097744099611 Henry Cohn, 2025, needs more optimization.
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 84 0.112895349963 Henry Cohn, 2025, needs more optimization.
20 85 0.112902505500 Henry Cohn, 2025, 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 0.121893957808 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 0.136915269073 Henry Cohn, 2026, needs more optimization.
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 0.145853791081 Henry Cohn, 2026, needs more optimization.
20 125 0.147670835579 Henry Cohn, 2026, needs more optimization.
20 126 0.149831609589 Henry Cohn, 2026, needs more optimization.
20 127 0.150090306704 Henry Cohn, 2026, needs more optimization.
20 128 0.150091864275 Henry Cohn, 2026, needs more optimization.
20 129 0.150493364755 Henry Cohn, 2026, needs more optimization.
20 130 0.150610322438 Henry Cohn, 2026, needs more optimization.
20 131 0.150690485887 Henry Cohn, 2026, needs more optimization.
20 132 0.150697836381 Henry Cohn, 2026, needs more optimization.
20 133 0.151453018405 Henry Cohn, 2026, needs more optimization.
20 136 0.151505609414 Henry Cohn, 2026, needs more optimization.
20 137 0.153202651097 Henry Cohn, 2026, needs more optimization.
20 138 0.154440405466 Henry Cohn, 2026, needs more optimization.
20 139 0.155171111570 Henry Cohn, 2026, needs more optimization.
20 140 0.156027125137 Henry Cohn, 2026, needs more optimization.
20 141 0.157502608513 Henry Cohn, 2025, needs more optimization.
20 142 0.161809087535 Henry Cohn, 2026, needs more optimization.
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 0.181540268775 Henry Cohn, 2026, needs more optimization.
20 172 0.189109200344 Henry Cohn, 2026, needs more optimization.
20 186 0.189193017535 Henry Cohn, 2026, needs more optimization.
20 188 0.189193024805 Henry Cohn, 2026, needs more optimization.
20 190 0.189194686505 Henry Cohn, 2026, needs more optimization.
20 191 0.189889704811 Henry Cohn, 2026, needs more optimization.
20 192 0.192020186626 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 0.203357314605 Henry Cohn, 2026, needs more optimization.
20 258 0.205920911966 Henry Cohn, 2026, needs more optimization.
20 259 0.207516721316 Henry Cohn, 2026, needs more optimization.
20 262 0.208386799893 Henry Cohn, 2026, needs more optimization.
20 263 0.208834164018 Henry Cohn, 2026, needs more optimization.
20 264 0.208834342511 Henry Cohn, 2026, needs more optimization.
20 265 0.215284193597 Henry Cohn, 2026, needs more optimization.
20 266 0.215288075765 Henry Cohn, 2026, needs more optimization.
20 267 0.215294779807 Henry Cohn, 2026, needs more optimization.
20 268 0.215304977006 Henry Cohn, 2026, needs more optimization.
20 269 0.215306595769 Henry Cohn, 2026, needs more optimization.
20 270 0.215314819670 Henry Cohn, 2026, needs more optimization.
20 271 0.215378206300 Henry Cohn, 2026, needs more optimization.
20 272 0.215402378840 Henry Cohn, 2026, needs more optimization.
20 273 0.215516364673 Henry Cohn, 2026, needs more optimization.
20 274 0.215594811782 Henry Cohn, 2026, needs more optimization.
20 275 0.215832398236 Henry Cohn, 2026, needs more optimization.
20 276 0.215931933903 Henry Cohn, 2026, needs more optimization.
20 277 0.215984540920 Henry Cohn, 2026, needs more optimization.
20 278 0.216163024638 Henry Cohn, 2026, needs more optimization.
20 279 0.216315570354 Henry Cohn, 2026, needs more optimization.
20 280 0.216553453454 Henry Cohn, 2026, needs more optimization.
20 281 0.216765236665 Henry Cohn, 2026, needs more optimization.
20 282 0.217059844998 Henry Cohn, 2026, needs more optimization.
20 283 0.217450543075 Henry Cohn, 2026, needs more optimization.
20 284 0.217951284559 Henry Cohn, 2026, needs more optimization.
20 285 0.218278186402 Henry Cohn, 2026, needs more optimization.
20 286 0.218626305408 Henry Cohn, 2026, needs more optimization.
20 287 0.218962735117 Henry Cohn, 2026, needs more optimization.
20 288 0.219759812258 Henry Cohn, 2026, needs more optimization.
20 289 0.220562087361 Henry Cohn, 2026, needs more optimization.
20 291 0.220669218828 Henry Cohn, 2026, needs more optimization.
20 293 0.220694934244 Henry Cohn, 2026, needs more optimization.
20 294 0.220694934336 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
20 378 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 0.242774565706 Henry Cohn, 2026, needs more optimization.
20 380 0.244554859588 Henry Cohn, 2026, needs more optimization.
20 381 0.245519481047 Henry Cohn, 2026, needs more optimization.
20 382 0.246813032829 Henry Cohn, 2026, needs more optimization.
20 383 0.247244744742 Henry Cohn, 2026, needs more optimization.
20 384 0.248185461312 Henry Cohn, 2026, needs more optimization.
20 385 0.249239307392 Henry Cohn, 2026, needs more optimization.
20 386 0.249997598252 Henry Cohn, 2026, needs more optimization.
20 405 0.25 C. Ma, T. T. Zhaowei, 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 0.262180653313 Henry Cohn, 2026, needs more optimization.
20 407 0.265017918205 Henry Cohn, 2026, needs more optimization.
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 474 0.269878874139 Henry Cohn, 2026, needs more optimization.
20 475 0.271304137415 Henry Cohn, 2025, needs more optimization.
20 476 0.272622512553 Henry Cohn, 2026, needs more optimization.
20 477 0.273459280230 Henry Cohn, 2025, needs more optimization.
20 478 0.274374315395 Henry Cohn, 2026, needs more optimization.
20 479 0.275200367871 Henry Cohn, 2025, needs more optimization.
20 482 0.275413246016 Henry Cohn, 2026, needs more optimization.
20 486 0.275456496021 Henry Cohn, 2026, needs more optimization.
20 490 0.275473677208 Henry Cohn, 2026, needs more optimization.
20 494 0.275491698811 Henry Cohn, 2026, needs more optimization.
20 498 0.275508380878 Henry Cohn, 2026, needs more optimization.
20 499 0.281346754647 Henry Cohn, 2025, needs more optimization.
20 500 0.281348261555 Henry Cohn, 2025, needs more optimization.
20 502 0.281390049027 Henry Cohn, 2026, needs more optimization.
20 503 0.281393107933 Henry Cohn, 2025, needs more optimization.
20 504 0.283650277827 Henry Cohn, 2026, needs more optimization.
20 506 0.285040555584 Henry Cohn, 2026, needs more optimization.
20 508 0.285343377207 Henry Cohn, 2026, needs more optimization.
20 510 0.285380590851 Henry Cohn, 2026, needs more optimization.
20 511 0.285651857828 Henry Cohn, 2025, needs more optimization.
20 514 0.288329200750 Henry Cohn, 2026, needs more optimization.
20 518 0.288362613655 Henry Cohn, 2026, needs more optimization.
20 520 0.288372970609 Henry Cohn, 2026, needs more optimization.
20 521 0.289404389705 Henry Cohn, 2026, needs more optimization.
20 544 0.289726812929 Henry Cohn, 2026, needs more optimization.
20 550 0.289726813054 Henry Cohn, 2026, needs more optimization.
20 552 0.289765170476 Henry Cohn, 2026, needs more optimization.
20 553 0.291238887058 Henry Cohn, 2026, needs more optimization.
20 554 0.292502856930 Henry Cohn, 2026, needs more optimization.
20 555 0.293226095400 Henry Cohn, 2026, needs more optimization.
20 556 0.293631654635 Henry Cohn, 2026, needs more optimization.
20 557 0.293820806860 Henry Cohn, 2026, needs more optimization.
20 558 0.300252411116 Henry Cohn, 2026, needs more optimization.
20 559 0.300434461878 Henry Cohn, 2026, needs more optimization.
20 560 0.300614733784 Henry Cohn, 2026, needs more optimization.
20 561 0.300693071866 Henry Cohn, 2026, needs more optimization.
20 562 0.300715651851 Henry Cohn, 2026, needs more optimization.
20 563 0.300717837539 Henry Cohn, 2026, needs more optimization.
20 564 0.302921680231 Henry Cohn, 2026, needs more optimization.
20 565 0.303059573853 Henry Cohn, 2026, needs more optimization.
20 566 0.303212079289 Henry Cohn, 2026, needs more optimization.
20 567 0.303452799377 Henry Cohn, 2026, needs more optimization.
20 568 0.303678227232 Henry Cohn, 2026, needs more optimization.
20 673 0.304347826087 Henry Cohn, 2025.
23⁢x−7
20 674 0.304358208645 Henry Cohn, 2026, needs more optimization.
20 680 0.304367528966 Henry Cohn, 2026, needs more optimization.
20 896 0.311475409837 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
61⁢x−19
20 897 0.312148003960 Henry Cohn, 2026, needs more optimization.
20 898 0.312346245971 Henry Cohn, 2026, needs more optimization.
20 899 0.312507637820 Henry Cohn, 2026, needs more optimization.
20 900 0.312540011762 Henry Cohn, 2026, needs more optimization.
20 901 0.312685802827 Henry Cohn, 2026, needs more optimization.
20 902 0.312829711046 Henry Cohn, 2026, needs more optimization.
20 903 0.312931194467 Henry Cohn, 2026, needs more optimization.
20 904 0.312985013976 Henry Cohn, 2026, needs more optimization.
20 905 0.312997834828 Henry Cohn, 2026, needs more optimization.
20 906 0.313124201212 Henry Cohn, 2026, needs more optimization.
20 907 0.313158571886 Henry Cohn, 2026, needs more optimization.
20 908 0.313269275702 Henry Cohn, 2026, needs more optimization.
20 909 0.313292757873 Henry Cohn, 2026, needs more optimization.
20 910 0.313362748697 Henry Cohn, 2026, needs more optimization.
20 911 0.313412018689 Henry Cohn, 2026, needs more optimization.
20 912 0.313458851296 Henry Cohn, 2026, needs more optimization.
20 913 0.313483525835 Henry Cohn, 2026, needs more optimization.
20 914 0.313570152004 Henry Cohn, 2026, needs more optimization.
20 915 0.313657877166 Henry Cohn, 2026, needs more optimization.
20 916 0.313689185245 Henry Cohn, 2026, needs more optimization.
20 917 0.313704303330 Henry Cohn, 2026, needs more optimization.
20 918 0.313767938376 Henry Cohn, 2026, needs more optimization.
20 919 0.313810339009 Henry Cohn, 2026, needs more optimization.
20 920 0.313821753717 Henry Cohn, 2026, needs more optimization.
20 921 0.313849399729 Henry Cohn, 2026, needs more optimization.
20 922 0.313884239983 Henry Cohn, 2026, needs more optimization.
20 923 0.313891791134 Henry Cohn, 2026, needs more optimization.
20 924 0.313896470232 Henry Cohn, 2026, needs more optimization.
20 925 0.313903877161 Henry Cohn, 2026, needs more optimization.
20 926 0.313932743468 Henry Cohn, 2026, needs more optimization.
20 927 0.313976126651 Henry Cohn, 2026, needs more optimization.
20 928 0.313987096650 Henry Cohn, 2026, needs more optimization.
20 929 0.314019415126 Henry Cohn, 2026, needs more optimization.
20 930 0.314060382132 Henry Cohn, 2026, needs more optimization.
20 931 0.314095401116 Henry Cohn, 2026, needs more optimization.
20 932 0.314105414716 Henry Cohn, 2026, needs more optimization.
20 933 0.314130815788 Henry Cohn, 2026, needs more optimization.
20 934 0.314138377266 Henry Cohn, 2026, needs more optimization.
20 935 0.314146139557 Henry Cohn, 2026, needs more optimization.
20 936 0.314148192896 Henry Cohn, 2026, needs more optimization.
20 937 0.314162408472 Henry Cohn, 2026, needs more optimization.
20 938 0.314173973895 Henry Cohn, 2026, needs more optimization.
20 939 0.314188494789 Henry Cohn, 2026, needs more optimization.
20 940 0.314247841153 Henry Cohn, 2026, needs more optimization.
20 941 0.314268150111 Henry Cohn, 2026, needs more optimization.
20 942 0.314280076412 Henry Cohn, 2026, needs more optimization.
20 943 0.314302896893 Henry Cohn, 2026, needs more optimization.
20 944 0.314310558267 Henry Cohn, 2026, needs more optimization.
20 945 0.314323784116 Henry Cohn, 2026, needs more optimization.
20 946 0.314337699210 Henry Cohn, 2026, needs more optimization.
20 947 0.314358056623 Henry Cohn, 2026, needs more optimization.
20 948 0.314389395166 Henry Cohn, 2026, needs more optimization.
20 949 0.314405870312 Henry Cohn, 2026, needs more optimization.
20 950 0.314426869619 Henry Cohn, 2026, needs more optimization.
20 951 0.314452221534 Henry Cohn, 2026, needs more optimization.
20 952 0.314458294723 Henry Cohn, 2026, needs more optimization.
20 953 0.314464350616 Henry Cohn, 2026, needs more optimization.
20 954 0.314500912913 Henry Cohn, 2026, needs more optimization.
20 955 0.314528896989 Henry Cohn, 2026, needs more optimization.
20 956 0.314553955096 Henry Cohn, 2026, needs more optimization.
20 957 0.314566553688 Henry Cohn, 2026, needs more optimization.
20 958 0.314580635862 Henry Cohn, 2026, needs more optimization.
20 959 0.314596423130 Henry Cohn, 2026, needs more optimization.
20 960 0.314608007053 Henry Cohn, 2026, needs more optimization.
20 961 0.314621584946 Henry Cohn, 2026, needs more optimization.
20 962 0.314640337377 Henry Cohn, 2026, needs more optimization.
20 963 0.314645939956 Henry Cohn, 2026, needs more optimization.
20 964 0.314653666340 Henry Cohn, 2026, needs more optimization.
20 965 0.314661749999 Henry Cohn, 2026, needs more optimization.
20 966 0.314668360655 Henry Cohn, 2026, needs more optimization.
20 967 0.314678438983 Henry Cohn, 2026, needs more optimization.
20 968 0.314691494481 Henry Cohn, 2026, needs more optimization.
20 969 0.314696548049 Henry Cohn, 2026, needs more optimization.
20 970 0.314701383628 Henry Cohn, 2026, needs more optimization.
20 972 0.316635841942 Henry Cohn, 2026, needs more optimization.
20 973 0.316636394688 Henry Cohn, 2026, needs more optimization.
20 974 0.316637012300 Henry Cohn, 2026, needs more optimization.
20 975 0.316637066106 Henry Cohn, 2026, needs more optimization.
20 977 0.316637151012 Henry Cohn, 2026, needs more optimization.
20 978 0.317291630840 Henry Cohn, 2026, needs more optimization.
20 979 0.318163705596 Henry Cohn, 2026, needs more optimization.
20 980 0.318163805803 Henry Cohn, 2026, needs more optimization.
20 981 0.318163888728 Henry Cohn, 2026, needs more optimization.
20 982 0.318175051037 Henry Cohn, 2026, needs more optimization.
20 984 0.318183545207 Henry Cohn, 2026, needs more optimization.
20 985 0.318198468145 Henry Cohn, 2026, needs more optimization.
20 988 0.318200273204 Henry Cohn, 2026, needs more optimization.
20 989 0.318200705316 Henry Cohn, 2026, needs more optimization.
20 990 0.318498649335 Henry Cohn, 2026, needs more optimization.
20 991 0.319298996742 Henry Cohn, 2026, needs more optimization.
20 992 0.319662706947 Henry Cohn, 2026, needs more optimization.
20 994 0.320421726048 Henry Cohn, 2026, needs more optimization.
20 996 0.321277826314 Henry Cohn, 2026, needs more optimization.
20 998 0.321868831705 Henry Cohn, 2026, needs more optimization.
20 999 0.322169041077 Henry Cohn, 2026, needs more optimization.
20 1001 0.322169852446 Henry Cohn, 2026, needs more optimization.
20 1002 0.322170877535 Henry Cohn, 2026, needs more optimization.
20 1005 0.323142074763 Henry Cohn, 2026, needs more optimization.
20 1006 0.323142292848 Henry Cohn, 2026, needs more optimization.
20 1007 0.323233655634 Henry Cohn, 2026, needs more optimization.
20 1008 0.323233914732 Henry Cohn, 2026, needs more optimization.
20 1010 0.323535144301 Henry Cohn, 2026, needs more optimization.
20 1011 0.323930812970 Henry Cohn, 2026, needs more optimization.
20 1012 0.323933408162 Henry Cohn, 2026, needs more optimization.
20 1015 0.323934860617 Henry Cohn, 2026, needs more optimization.
20 1016 0.324031372969 Henry Cohn, 2026, needs more optimization.
20 1017 0.324031585086 Henry Cohn, 2026, needs more optimization.
20 1018 0.324162313124 Henry Cohn, 2026, needs more optimization.
20 1020 0.324162583394 Henry Cohn, 2026, needs more optimization.
20 1021 0.324252552106 Henry Cohn, 2026, needs more optimization.
20 1022 0.324253213675 Henry Cohn, 2026, needs more optimization.
20 1023 0.324776449183 Henry Cohn, 2026, needs more optimization.
20 1024 0.324776552083 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 0.062636651896 Ilmari Vahteristo, 2026.
21 53 0.066665620363 Henry Cohn, 2025.
21 54 0.066665850459 Henry Cohn, 2025.
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 0.066666666337 Henry Cohn, 2025, 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.
21 65 0.081966984796 Henry Cohn, 2025, needs more optimization.
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 0.093247656079 Henry Cohn, 2026, needs more optimization.
21 82 0.093297851019 Henry Cohn, 2026, needs more optimization.
21 83 0.095616261103 Henry Cohn, 2026, needs more optimization.
21 84 0.096120290871 Henry Cohn, 2026, needs more optimization.
21 85 0.097702080335 Henry Cohn, 2026, needs more optimization.
21 86 0.104649382377 Henry Cohn, 2026, needs more optimization.
21 87 0.107536752898 Henry Cohn, 2026, needs more optimization.
21 88 0.108040226878 Henry Cohn, 2026, needs more optimization.
21 89 0.108846463758 Henry Cohn, 2026, needs more optimization.
21 90 0.110085419958 Henry Cohn, 2026, needs more optimization.
21 91 0.110089945291 Henry Cohn, 2026, needs more optimization.
21 92 0.110758056129 Henry Cohn, 2026, needs more optimization.
21 93 0.110771839137 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 0.127363959721 Henry Cohn, 2026, needs more optimization.
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 0.139350238132 Henry Cohn, 2026, needs more optimization.
21 122 0.139354052717 Henry Cohn, 2026, needs more optimization.
21 123 0.139434781082 Henry Cohn, 2026, needs more optimization.
21 124 0.140535785430 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 0.153926281049 Henry Cohn, 2026, needs more optimization.
21 164 0.160794343007 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 0.172187000257 Henry Cohn, 2026, needs more optimization.
21 200 0.179136495953 Henry Cohn, 2026, needs more optimization.
21 201 0.183755880676 Henry Cohn, 2026, needs more optimization.
21 202 0.185633668172 Henry Cohn, 2026, needs more optimization.
21 203 0.186149971253 Henry Cohn, 2026, needs more optimization.
21 204 0.186524056152 Henry Cohn, 2026, needs more optimization.
21 205 0.188124406252 Henry Cohn, 2026, needs more optimization.
21 206 0.188766063918 Henry Cohn, 2026, needs more optimization.
21 207 0.188942886779 Henry Cohn, 2026, needs more optimization.
21 208 0.189175863014 Henry Cohn, 2026, needs more optimization.
21 210 0.189189189190 Kissing configuration of 529 points in 22 dimensions from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−7
21 225 0.189189189190 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.
37⁢x−7
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 0.192317869874 Henry Cohn, 2026, needs more optimization.
21 235 0.192350103281 Henry Cohn, 2026, needs more optimization.
21 236 0.195041257186 Henry Cohn, 2026, needs more optimization.
21 237 0.195512085707 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
21 337 0.222410623729 Henry Cohn, 2026, needs more optimization.
21 338 0.226065312242 Henry Cohn, 2026, needs more optimization.
21 339 0.226801656895 Henry Cohn, 2026, needs more optimization.
21 340 0.229010772641 Henry Cohn, 2026, needs more optimization.
21 341 0.230666540405 Henry Cohn, 2026, needs more optimization.
21 355 0.230776052977 Henry Cohn, 2026, needs more optimization.
21 380 0.230776052998 Henry Cohn, 2026, needs more optimization.
21 383 0.230778233220 Henry Cohn, 2026, needs more optimization.
21 392 0.230778503671 Henry Cohn, 2026, needs more optimization.
21 393 0.230778723395 Henry Cohn, 2026, needs more optimization.
21 394 0.230779278356 Henry Cohn, 2026, needs more optimization.
21 395 0.230785122357 Henry Cohn, 2026, needs more optimization.
21 396 0.233252642308 Henry Cohn, 2026, needs more optimization.
21 397 0.237338318539 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. T. Zhaowei, 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 0.253544079801 Henry Cohn, 2026, needs more optimization.
21 569 0.254518958933 Henry Cohn, 2026, needs more optimization.
21 570 0.255078958935 Henry Cohn, 2026, needs more optimization.
21 571 0.255486007922 Henry Cohn, 2026, needs more optimization.
21 572 0.255809179132 Henry Cohn, 2026, needs more optimization.
21 573 0.256128287087 Henry Cohn, 2026, needs more optimization.
21 574 0.256388377104 Henry Cohn, 2026, needs more optimization.
21 575 0.256604672130 Henry Cohn, 2026, needs more optimization.
21 576 0.256821106708 Henry Cohn, 2026, needs more optimization.
21 577 0.257069372139 Henry Cohn, 2026, needs more optimization.
21 578 0.257283085853 Henry Cohn, 2026, needs more optimization.
21 579 0.257427093904 Henry Cohn, 2026, needs more optimization.
21 580 0.257579055482 Henry Cohn, 2026, needs more optimization.
21 581 0.257698840678 Henry Cohn, 2026, needs more optimization.
21 582 0.257818088655 Henry Cohn, 2026, needs more optimization.
21 583 0.257904639732 Henry Cohn, 2026, needs more optimization.
21 584 0.258019171368 Henry Cohn, 2026, needs more optimization.
21 585 0.258110395006 Henry Cohn, 2026, needs more optimization.
21 586 0.258238572087 Henry Cohn, 2026, needs more optimization.
21 587 0.258304372639 Henry Cohn, 2026, needs more optimization.
21 588 0.258376583729 Henry Cohn, 2026, needs more optimization.
21 589 0.258447057823 Henry Cohn, 2026, needs more optimization.
21 590 0.258602690804 Henry Cohn, 2026, needs more optimization.
21 591 0.258704948063 Henry Cohn, 2026, needs more optimization.
21 592 0.258738330937 Henry Cohn, 2026, needs more optimization.
21 593 0.258981632142 Henry Cohn, 2026, needs more optimization.
21 594 0.259216106261 Henry Cohn, 2026, needs more optimization.
21 595 0.259325996493 Henry Cohn, 2026, needs more optimization.
21 596 0.259401890986 Henry Cohn, 2026, needs more optimization.
21 597 0.259468365642 Henry Cohn, 2026, needs more optimization.
21 598 0.259604772219 Henry Cohn, 2026, needs more optimization.
21 599 0.259678786436 Henry Cohn, 2026, needs more optimization.
21 600 0.259744160698 Henry Cohn, 2026, needs more optimization.
21 601 0.259794948773 Henry Cohn, 2026, needs more optimization.
21 602 0.259832968258 Henry Cohn, 2026, needs more optimization.
21 603 0.259910050461 Henry Cohn, 2026, needs more optimization.
21 604 0.259942866467 Henry Cohn, 2026, needs more optimization.
21 605 0.260047911770 Henry Cohn, 2026, needs more optimization.
21 606 0.260137372111 Henry Cohn, 2026, needs more optimization.
21 607 0.260231589473 Henry Cohn, 2026, needs more optimization.
21 608 0.260276841083 Henry Cohn, 2026, needs more optimization.
21 609 0.260317334373 Henry Cohn, 2026, needs more optimization.
21 610 0.260501644801 Henry Cohn, 2026, needs more optimization.
21 611 0.260607010610 Henry Cohn, 2026, needs more optimization.
21 612 0.260671159142 Henry Cohn, 2026, needs more optimization.
21 613 0.260793310314 Henry Cohn, 2026, needs more optimization.
21 614 0.260884602399 Henry Cohn, 2026, needs more optimization.
21 615 0.260942913346 Henry Cohn, 2026, needs more optimization.
21 616 0.261033758999 Henry Cohn, 2026, needs more optimization.
21 617 0.261091651409 Henry Cohn, 2026, needs more optimization.
21 618 0.261168714761 Henry Cohn, 2026, needs more optimization.
21 619 0.261235573960 Henry Cohn, 2026, needs more optimization.
21 620 0.261276087150 Henry Cohn, 2026, needs more optimization.
21 621 0.261313693881 Henry Cohn, 2026, needs more optimization.
21 622 0.261352587672 Henry Cohn, 2026, needs more optimization.
21 623 0.261397044948 Henry Cohn, 2026, needs more optimization.
21 624 0.261431765856 Henry Cohn, 2026, needs more optimization.
21 625 0.261465918519 Henry Cohn, 2026, needs more optimization.
21 626 0.261507297148 Henry Cohn, 2026, needs more optimization.
21 627 0.261580950357 Henry Cohn, 2026, needs more optimization.
21 628 0.261639501785 Henry Cohn, 2026, needs more optimization.
21 629 0.261695907394 Henry Cohn, 2026, needs more optimization.
21 630 0.262085092058 Henry Cohn, 2026, needs more optimization.
21 631 0.262331352506 Henry Cohn, 2026, needs more optimization.
21 632 0.262520358703 Henry Cohn, 2026, needs more optimization.
21 633 0.262619110606 Henry Cohn, 2026, needs more optimization.
21 634 0.262690011262 Henry Cohn, 2026, needs more optimization.
21 635 0.262741425041 Henry Cohn, 2026, needs more optimization.
21 636 0.262892286027 Henry Cohn, 2026, needs more optimization.
21 637 0.263012215755 Henry Cohn, 2026, needs more optimization.
21 638 0.263142657662 Henry Cohn, 2026, needs more optimization.
21 639 0.263232057098 Henry Cohn, 2026, needs more optimization.
21 640 0.263331634796 Henry Cohn, 2026, needs more optimization.
21 641 0.263419001088 Henry Cohn, 2026, needs more optimization.
21 642 0.263581973257 Henry Cohn, 2026, needs more optimization.
21 643 0.263706273103 Henry Cohn, 2026, needs more optimization.
21 644 0.263829002308 Henry Cohn, 2026, needs more optimization.
21 645 0.263936658558 Henry Cohn, 2026, needs more optimization.
21 646 0.263975183288 Henry Cohn, 2026, needs more optimization.
21 647 0.264052005386 Henry Cohn, 2026, needs more optimization.
21 648 0.264128250796 Henry Cohn, 2026, needs more optimization.
21 649 0.264189550788 Henry Cohn, 2026, needs more optimization.
21 650 0.264295841804 Henry Cohn, 2026, needs more optimization.
21 651 0.264369605346 Henry Cohn, 2026, needs more optimization.
21 652 0.264440804304 Henry Cohn, 2026, needs more optimization.
21 653 0.264507969563 Henry Cohn, 2026, needs more optimization.
21 654 0.264561035994 Henry Cohn, 2026, needs more optimization.
21 655 0.264636921169 Henry Cohn, 2026, needs more optimization.
21 656 0.264735844722 Henry Cohn, 2026, needs more optimization.
21 657 0.264805016235 Henry Cohn, 2026, needs more optimization.
21 658 0.264897276443 Henry Cohn, 2026, needs more optimization.
21 659 0.264991043315 Henry Cohn, 2026, needs more optimization.
21 660 0.265126313906 Henry Cohn, 2026, needs more optimization.
21 661 0.265181054985 Henry Cohn, 2026, needs more optimization.
21 662 0.265233482766 Henry Cohn, 2026, needs more optimization.
21 663 0.265297895344 Henry Cohn, 2026, needs more optimization.
21 664 0.265376890979 Henry Cohn, 2026, needs more optimization.
21 665 0.265449359904 Henry Cohn, 2026, needs more optimization.
21 666 0.265523035272 Henry Cohn, 2026, needs more optimization.
21 667 0.265560591041 Henry Cohn, 2026, needs more optimization.
21 668 0.265605810210 Henry Cohn, 2026, needs more optimization.
21 669 0.265633862434 Henry Cohn, 2026, needs more optimization.
21 670 0.265669567586 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 0.266081244822 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.
21 685 0.266668455446 Henry Cohn, 2026, needs more optimization.
21 686 0.266720185134 Henry Cohn, 2026, needs more optimization.
21 687 0.266775357376 Henry Cohn, 2026, needs more optimization.
21 688 0.266841018277 Henry Cohn, 2026, needs more optimization.
21 689 0.266878055093 Henry Cohn, 2026, needs more optimization.
21 690 0.266947222145 Henry Cohn, 2026, needs more optimization.
21 691 0.266967859251 Henry Cohn, 2026, needs more optimization.
21 692 0.267003078311 Henry Cohn, 2026, needs more optimization.
21 693 0.267031902117 Henry Cohn, 2026, needs more optimization.
21 694 0.267057776235 Henry Cohn, 2026, needs more optimization.
21 695 0.267074284294 Henry Cohn, 2026, needs more optimization.
21 696 0.267090184879 Henry Cohn, 2026, needs more optimization.
21 697 0.267100676094 Henry Cohn, 2026, needs more optimization.
21 698 0.267110400534 Henry Cohn, 2026, needs more optimization.
21 699 0.267115463147 Henry Cohn, 2026, needs more optimization.
21 703 0.267116157137 Henry Cohn, 2026, needs more optimization.
21 728 0.267171850614 Henry Cohn, 2026, needs more optimization.
21 729 0.267261241913 Henry Cohn, 2026.
14⁢x2−1
21 730 0.277258763745 Henry Cohn, 2026, needs more optimization.
21 731 0.282540168905 Henry Cohn, 2026, needs more optimization.
21 732 0.284836262599 Henry Cohn, 2026, needs more optimization.
21 850 0.285714285715 Henry Cohn, 2026.
7⁢x−2
21 851 0.290306188578 Henry Cohn, 2026, needs more optimization.
21 1024 0.307692307693 Henry Cohn, 2026.
13⁢x−4
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 0.041709010751 Henry Cohn, 2026.
22 47 0.046962270332 Henry Cohn, 2026.
22 48 0.047524915294 Henry Cohn, 2025, continuous family of codes without rattlers.
64⁢x2+18⁢x−1
22 49 0.047603596837 Henry Cohn, 2025, needs more optimization.
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 0.064358164597 Henry Cohn, 2026, needs more optimization.
22 56 0.066598164965 Henry Cohn, 2026, needs more optimization.
22 57 0.066630471300 Henry Cohn, 2026, needs more optimization.
22 58 0.066656227158 Henry Cohn, 2026, needs more optimization.
22 59 0.066662119049 Henry Cohn, 2026, needs more optimization.
22 60 0.066664720886 Henry Cohn, 2026, needs more optimization.
22 61 0.069653549396 Henry Cohn, 2026, needs more optimization.
22 62 0.071702992839 Henry Cohn, 2026, needs more optimization.
22 64 0.076920313892 Henry Cohn, 2026, needs more optimization.
22 65 0.076924075556 Henry Cohn, 2026, needs more optimization.
22 66 0.078243584927 Henry Cohn, 2026, needs more optimization.
22 67 0.079295799194 Henry Cohn, 2026, needs more optimization.
22 68 0.080927905685 Henry Cohn, 2026, needs more optimization.
22 69 0.083023892084 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 0.083333305431 Henry Cohn, 2025, 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 0.086876541533 Henry Cohn, 2026, needs more optimization.
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 0.109433688341 Henry Cohn, 2026, needs more optimization.
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 0.121319631005 Henry Cohn, 2026, needs more optimization.
22 117 0.122811460180 Henry Cohn, 2026, needs more optimization.
22 118 0.130035496536 Henry Cohn, 2026, needs more optimization.
22 121 0.131782945737 Code with 119 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.
129⁢x−17
22 126 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 0.135538651570 Henry Cohn, 2026, needs more optimization.
22 143 0.138390129411 Henry Cohn, 2026, needs more optimization.
22 144 0.139626978555 Henry Cohn, 2026, needs more optimization.
22 164 0.142857142858 Code with 162 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.
7⁢x−1
22 166 0.142857142858 Henry Cohn, 2026.
7⁢x−1
22 167 0.150688296302 Henry Cohn, 2026, needs more optimization.
22 168 0.155185167736 Henry Cohn, 2026, needs more optimization.
22 169 0.159348015193 Henry Cohn, 2026, needs more optimization.
22 171 0.160003450226 Henry Cohn, 2026, needs more optimization.
22 172 0.160015338708 Henry Cohn, 2026, needs more optimization.
22 173 0.160444282801 Henry Cohn, 2026, needs more optimization.
22 174 0.161564286462 Henry Cohn, 2026, needs more optimization.
22 200 0.161904761905 Code with 198 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.
105⁢x−17
22 201 0.161904761905 Henry Cohn, 2026.
105⁢x−17
22 202 0.161908900522 Henry Cohn, 2026, needs more optimization.
22 203 0.165621275741 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 0.179128778933 Henry Cohn, 2026, needs more optimization.
22 277 0.187499926617 Henry Cohn, 2026, needs more optimization.
22 278 0.190126401549 Henry Cohn, 2026, needs more optimization.
22 279 0.191729170167 Henry Cohn, 2026, needs more optimization.
22 280 0.193449269881 Henry Cohn, 2026, needs more optimization.
22 281 0.194567949195 Henry Cohn, 2026, needs more optimization.
22 282 0.195748141099 Henry Cohn, 2026, needs more optimization.
22 283 0.196337952160 Henry Cohn, 2026, needs more optimization.
22 284 0.196354931953 Henry Cohn, 2026, needs more optimization.
22 285 0.196362023444 Henry Cohn, 2026, needs more optimization.
22 286 0.196362023445 Henry Cohn, 2026, needs more optimization.
22 287 0.199298166870 Henry Cohn, 2026, needs more optimization.
22 338 0.2 Code with 336 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.
5⁢x−1
22 352 0.2 C. Ma, T. T. Zhaowei, 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 0.201777989826 Henry Cohn, 2026, needs more optimization.
22 354 0.202842512270 Henry Cohn, 2026, needs more optimization.
22 355 0.203728568800 Henry Cohn, 2026, needs more optimization.
22 356 0.204034968655 Henry Cohn, 2026, needs more optimization.
22 357 0.204058374135 Henry Cohn, 2026, needs more optimization.
22 358 0.204059482334 Henry Cohn, 2026, needs more optimization.
22 359 0.204491312853 Henry Cohn, 2026, needs more optimization.
22 374 0.204624019942 Henry Cohn, 2026, needs more optimization.
22 375 0.205727533365 Henry Cohn, 2026, needs more optimization.
22 376 0.206395598603 Henry Cohn, 2026, needs more optimization.
22 377 0.206704072839 Henry Cohn, 2026, needs more optimization.
22 378 0.206884763860 Henry Cohn, 2026, needs more optimization.
22 379 0.207062386894 Henry Cohn, 2026, needs more optimization.
22 380 0.207123965729 Henry Cohn, 2026, needs more optimization.
22 381 0.207166893231 Henry Cohn, 2026, needs more optimization.
22 382 0.207174909140 Henry Cohn, 2026, needs more optimization.
22 383 0.207175839357 Henry Cohn, 2026, needs more optimization.
22 386 0.207175875042 Henry Cohn, 2026, needs more optimization.
22 387 0.207176114782 Henry Cohn, 2026, needs more optimization.
22 388 0.207176158995 Henry Cohn, 2026, needs more optimization.
22 390 0.207176159167 Henry Cohn, 2026, needs more optimization.
22 391 0.208469005766 Henry Cohn, 2026, needs more optimization.
22 392 0.208855075840 Henry Cohn, 2026, needs more optimization.
22 393 0.209069677977 Henry Cohn, 2026, needs more optimization.
22 394 0.209110265315 Henry Cohn, 2026, needs more optimization.
22 395 0.209435297058 Henry Cohn, 2026, needs more optimization.
22 396 0.209530996233 Henry Cohn, 2026, needs more optimization.
22 401 0.209602945641 Henry Cohn, 2026, needs more optimization.
22 402 0.209661978867 Henry Cohn, 2026, needs more optimization.
22 404 0.209689132896 Henry Cohn, 2026, needs more optimization.
22 405 0.209706921537 Henry Cohn, 2026, needs more optimization.
22 415 0.209711494422 Henry Cohn, 2026, needs more optimization.
22 416 0.209814770636 Henry Cohn, 2026, needs more optimization.
22 430 0.209817069798 Henry Cohn, 2026, needs more optimization.
22 431 0.210993089904 Henry Cohn, 2026, needs more optimization.
22 432 0.211663365424 Henry Cohn, 2026, needs more optimization.
22 433 0.212039942051 Henry Cohn, 2026, needs more optimization.
22 436 0.212148697335 Henry Cohn, 2026, needs more optimization.
22 437 0.212406691096 Henry Cohn, 2026, needs more optimization.
22 442 0.212505214885 Henry Cohn, 2026, needs more optimization.
22 451 0.212654836504 Henry Cohn, 2026, needs more optimization.
22 452 0.213200716356 Henry Cohn, 2026.
22⁢x2−1
22 484 0.229650348229 Henry Cohn, 2026, needs more optimization.
22 485 0.229651854557 Henry Cohn, 2026, needs more optimization.
22 504 0.229926564994 Henry Cohn, 2026, needs more optimization.
22 505 0.229927684818 Henry Cohn, 2025, needs more optimization.
22 506 0.231137105351 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 0.238101475164 Henry Cohn, 2026, needs more optimization.
22 558 0.239588529206 Henry Cohn, 2026, needs more optimization.
22 559 0.240037435785 Henry Cohn, 2026, needs more optimization.
22 560 0.240924637064 Henry Cohn, 2026, needs more optimization.
22 561 0.241399129596 Henry Cohn, 2026, needs more optimization.
22 562 0.244240377998 Henry Cohn, 2026, needs more optimization.
22 563 0.246336632156 Henry Cohn, 2026, needs more optimization.
22 564 0.248072455665 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 0.047343032480 Henry Cohn, 2026, needs more optimization.
23 52 0.047477902142 Henry Cohn, 2026, needs more optimization.
23 53 0.047609748527 Henry Cohn, 2024, needs more optimization.
23 54 0.047609798559 Henry Cohn, 2024, needs more optimization.
23 55 0.055366146929 Ilmari Vahteristo, 2026.
23 56 0.057275984127 Henry Cohn, 2025.
23 57 0.061654365426 Ilmari Vahteristo, 2026.
23 58 0.064515997905 Henry Cohn, 2026, needs more optimization.
23 59 0.066320745246 Henry Cohn, 2026, needs more optimization.
23 60 0.066528798193 Henry Cohn, 2026, needs more optimization.
23 61 0.066599568077 Henry Cohn, 2025, needs more optimization.
23 62 0.066599790838 Henry Cohn, 2025, needs more optimization.
23 63 0.067250816631 Henry Cohn, 2026, needs more optimization.
23 64 0.069716146304 Henry Cohn, 2026, needs more optimization.
23 65 0.073273148299 Henry Cohn, 2026, needs more optimization.
23 66 0.076375847388 Henry Cohn, 2026, needs more optimization.
23 67 0.076896812052 Henry Cohn, 2026, needs more optimization.
23 68 0.076898475206 Henry Cohn, 2026, needs more optimization.
23 69 0.077673811408 Henry Cohn, 2026, needs more optimization.
23 70 0.077985696760 Henry Cohn, 2026, needs more optimization.
23 71 0.079646217867 Henry Cohn, 2026, needs more optimization.
23 72 0.080065728343 Henry Cohn, 2026, needs more optimization.
23 73 0.082616150139 Henry Cohn, 2026, needs more optimization.
23 81 0.083333222004 Henry Cohn, 2025, needs more optimization.
23 82 0.083397112292 Henry Cohn, 2026, needs more optimization.
23 83 0.087449050695 Henry Cohn, 2026, needs more optimization.
23 84 0.090623839956 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 0.103889056804 Henry Cohn, 2026, needs more optimization.
23 105 0.111107997922 Henry Cohn, 2026, needs more optimization.
23 116 0.111111109788 Henry Cohn, 2025, needs more optimization.
23 117 0.111124745908 Henry Cohn, 2026, needs more optimization.
23 118 0.114667517866 Henry Cohn, 2026, needs more optimization.
23 119 0.118704727684 Henry Cohn, 2026, needs more optimization.
23 120 0.121176526071 Henry Cohn, 2026, needs more optimization.
23 121 0.127647601521 Henry Cohn, 2026, needs more optimization.
23 122 0.130971314321 Henry Cohn, 2026, needs more optimization.
23 123 0.131779371379 Henry Cohn, 2025, needs more optimization.
23 128 0.131782945737 Orthogonal union of 126 points in 22 dimensions and 2 points in 1 dimension.
129⁢x−17
23 129 0.131786541715 Henry Cohn, 2026, needs more optimization.
23 130 0.131807435199 Henry Cohn, 2026, needs more optimization.
23 131 0.132302116608 Henry Cohn, 2026, needs more optimization.
23 132 0.134434136145 Henry Cohn, 2026, needs more optimization.
23 133 0.134909146276 Henry Cohn, 2026, needs more optimization.
23 138 0.135135135136 Code with 136 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.
37⁢x−5
23 147 0.135135135136 Henry Cohn, 2026.
37⁢x−5
23 148 0.135957117352 Henry Cohn, 2026, needs more optimization.
23 149 0.141370933618 Henry Cohn, 2026, needs more optimization.
23 166 0.142857142858 Code with 164 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.
7⁢x−1
23 168 0.142857142858 Orthogonal union of 166 points in 22 dimensions and 2 points in 1 dimension.
7⁢x−1
23 170 0.142865346672 Henry Cohn, 2026, needs more optimization.
23 171 0.145114614792 Henry Cohn, 2026, needs more optimization.
23 172 0.146954878624 Henry Cohn, 2026, needs more optimization.
23 173 0.152684286153 Henry Cohn, 2026, needs more optimization.
23 174 0.153135950404 Henry Cohn, 2026, needs more optimization.
23 175 0.153452354811 Henry Cohn, 2026, needs more optimization.
23 176 0.155757905844 Henry Cohn, 2026, needs more optimization.
23 177 0.156428331757 Henry Cohn, 2026, needs more optimization.
23 178 0.157406042927 Henry Cohn, 2026, needs more optimization.
23 179 0.159171796567 Henry Cohn, 2026, needs more optimization.
23 180 0.159733749098 Henry Cohn, 2026, needs more optimization.
23 181 0.160348109733 Henry Cohn, 2026, needs more optimization.
23 182 0.161288004527 Henry Cohn, 2026, needs more optimization.
23 183 0.161674573835 Henry Cohn, 2026, needs more optimization.
23 202 0.161904761905 Code with 200 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.
105⁢x−17
23 203 0.161904761905 Orthogonal union of 201 points in 22 dimensions and 2 points in 1 dimension.
105⁢x−17
23 204 0.161908900522 Orthogonal union of 202 points in 22 dimensions and 2 points in 1 dimension.
23 205 0.161911665725 Henry Cohn, 2026, needs more optimization.
23 206 0.161913848782 Henry Cohn, 2026, needs more optimization.
23 207 0.161927731330 Henry Cohn, 2026, needs more optimization.
23 208 0.161983177469 Henry Cohn, 2026, needs more optimization.
23 209 0.164066353004 Henry Cohn, 2026, needs more optimization.
23 210 0.165127098241 Henry Cohn, 2026, needs more optimization.
23 211 0.165546772305 Henry Cohn, 2026, needs more optimization.
23 212 0.166177640812 Henry Cohn, 2026, needs more optimization.
23 213 0.166506808891 Henry Cohn, 2026, needs more optimization.
23 214 0.166625308605 Henry Cohn, 2026, needs more optimization.
23 277 0.166666666667 Code with 275 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.
6⁢x−1
23 278 0.166666666667 Henry Cohn, 2026.
6⁢x−1
23 279 0.168170314389 Henry Cohn, 2026, needs more optimization.
23 280 0.174327275431 Henry Cohn, 2026, needs more optimization.
23 281 0.178899860896 Henry Cohn, 2026, needs more optimization.
23 282 0.182014702714 Henry Cohn, 2026, needs more optimization.
23 283 0.183739003205 Henry Cohn, 2026, needs more optimization.
23 284 0.185789425679 Henry Cohn, 2026, needs more optimization.
23 285 0.186584196309 Henry Cohn, 2026, needs more optimization.
23 286 0.187998632475 Henry Cohn, 2026, needs more optimization.
23 287 0.188150424170 Henry Cohn, 2026, needs more optimization.
23 288 0.188412282482 Henry Cohn, 2026, needs more optimization.
23 289 0.189258717615 Henry Cohn, 2026, needs more optimization.
23 290 0.189441177608 Henry Cohn, 2026, needs more optimization.
23 291 0.189522185757 Henry Cohn, 2026, needs more optimization.
23 292 0.189608349864 Henry Cohn, 2026, needs more optimization.
23 293 0.189645890787 Henry Cohn, 2026, needs more optimization.
23 296 0.189665249264 Henry Cohn, 2026, needs more optimization.
23 300 0.189665249274 Henry Cohn, 2026, needs more optimization.
23 301 0.190679389695 Henry Cohn, 2026, needs more optimization.
23 302 0.193124020750 Henry Cohn, 2026, needs more optimization.
23 303 0.194215665408 Henry Cohn, 2026, needs more optimization.
23 304 0.196110334837 Henry Cohn, 2026, needs more optimization.
23 305 0.196890800571 Henry Cohn, 2026, needs more optimization.
23 306 0.197809481502 Henry Cohn, 2026, needs more optimization.
23 307 0.198676826660 Henry Cohn, 2026, needs more optimization.
23 308 0.199152065293 Henry Cohn, 2026, needs more optimization.
23 309 0.199336439460 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 0.232851959978 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 0.238101475164 Orthogonal union of 557 points in 22 dimensions and 2 points in 1 dimension.
23 560 0.239588529206 Orthogonal union of 558 points in 22 dimensions and 2 points in 1 dimension.
23 561 0.240037435785 Orthogonal union of 559 points in 22 dimensions and 2 points in 1 dimension.
23 562 0.240924637064 Orthogonal union of 560 points in 22 dimensions and 2 points in 1 dimension.
23 573 0.241022864393 Henry Cohn, 2026, needs more optimization.
23 574 0.241269120694 Henry Cohn, 2026, needs more optimization.
23 575 0.241535521140 Henry Cohn, 2026, needs more optimization.
23 576 0.242871058847 Henry Cohn, 2026, needs more optimization.
23 577 0.242963249821 Henry Cohn, 2026, needs more optimization.
23 578 0.243886703258 Henry Cohn, 2026, needs more optimization.
23 579 0.244078494688 Henry Cohn, 2026, needs more optimization.
23 580 0.244893064816 Henry Cohn, 2026, needs more optimization.
23 581 0.245573513517 Henry Cohn, 2026, needs more optimization.
23 582 0.245573513531 Henry Cohn, 2026, needs more optimization.
23 583 0.245894697454 Henry Cohn, 2026, needs more optimization.
23 584 0.246056395793 Henry Cohn, 2026, needs more optimization.
23 585 0.246563166729 Henry Cohn, 2026, needs more optimization.
23 586 0.246609631913 Henry Cohn, 2026, needs more optimization.
23 587 0.246690843106 Henry Cohn, 2026, needs more optimization.
23 592 0.246762031139 Henry Cohn, 2026, needs more optimization.
23 594 0.247311423978 Henry Cohn, 2026, needs more optimization.
23 595 0.247745067284 Henry Cohn, 2026, needs more optimization.
23 596 0.247834241925 Henry Cohn, 2026, needs more optimization.
23 597 0.248222979961 Henry Cohn, 2026, needs more optimization.
23 598 0.248614506431 Henry Cohn, 2026, needs more optimization.
23 599 0.248862090521 Henry Cohn, 2026, needs more optimization.
23 600 0.249039912656 Henry Cohn, 2026, needs more optimization.
23 601 0.249413931171 Henry Cohn, 2026, needs more optimization.
23 602 0.249676570512 Henry Cohn, 2026, needs more optimization.
23 604 0.249816024767 Henry Cohn, 2026, needs more optimization.
23 605 0.249930931112 Henry Cohn, 2026, needs more optimization.
23 894 0.25 Henry Cohn, 2026.
4⁢x−1
23 895 0.251929698830 Henry Cohn, 2026, needs more optimization.
23 896 0.254246971702 Henry Cohn, 2026, needs more optimization.
23 897 0.254397635336 Henry Cohn, 2026, needs more optimization.
23 898 0.255438886374 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 0.256938452771 Henry Cohn, 2026, needs more optimization.
23 903 0.258206534585 Henry Cohn, 2026, needs more optimization.
23 904 0.259223738467 Henry Cohn, 2026, needs more optimization.
23 906 0.259898659612 Henry Cohn, 2026, needs more optimization.
23 907 0.261595656694 Henry Cohn, 2026, needs more optimization.
23 908 0.264971928146 Henry Cohn, 2026, needs more optimization.
23 910 0.265493735158 Henry Cohn, 2026, needs more optimization.
23 911 0.266114548382 Henry Cohn, 2026, needs more optimization.
23 912 0.267368910073 Henry Cohn, 2026, needs more optimization.
23 913 0.268144738948 Henry Cohn, 2026, needs more optimization.
23 914 0.268802719680 Henry Cohn, 2026, needs more optimization.
23 915 0.268836540165 Henry Cohn, 2026, needs more optimization.
23 916 0.269663508977 Henry Cohn, 2026, needs more optimization.
23 917 0.270174895664 Henry Cohn, 2026, needs more optimization.
23 918 0.270910965697 Henry Cohn, 2026, needs more optimization.
23 919 0.271281877066 Henry Cohn, 2026, needs more optimization.
23 920 0.272118292082 Henry Cohn, 2026, needs more optimization.
23 921 0.272173315481 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 0.047563043071 Henry Cohn, 2024, needs more optimization.
24 57 0.053295300110 Ilmari Vahteristo, 2026.
24 58 0.054403503474 Henry Cohn, 2025.
24 59 0.057903810057 Henry Cohn, 2026.
24 60 0.061562313320 Henry Cohn, 2026, needs more optimization.
24 61 0.064594321353 Ilmari Vahteristo, 2026.
24 62 0.065853017142 Henry Cohn, 2026, needs more optimization.
24 63 0.065859031114 Henry Cohn, 2026, needs more optimization.
24 64 0.065897911729 Henry Cohn, 2026, needs more optimization.
24 65 0.066587691116 Henry Cohn, 2026, needs more optimization.
24 66 0.068180518582 Henry Cohn, 2026, needs more optimization.
24 67 0.070763242144 Henry Cohn, 2026, needs more optimization.
24 68 0.072116568748 Henry Cohn, 2026, needs more optimization.
24 69 0.073247208276 Henry Cohn, 2026, needs more optimization.
24 70 0.076553865233 Henry Cohn, 2026, needs more optimization.
24 71 0.076921821053 Henry Cohn, 2026, needs more optimization.
24 72 0.077496905631 Henry Cohn, 2026, needs more optimization.
24 73 0.077815782765 Henry Cohn, 2026, needs more optimization.
24 74 0.077908691268 Henry Cohn, 2026, needs more optimization.
24 75 0.078600390568 Henry Cohn, 2026, needs more optimization.
24 76 0.078850062000 Henry Cohn, 2026, needs more optimization.
24 77 0.081784626507 Henry Cohn, 2026, needs more optimization.
24 78 0.082774182084 Henry Cohn, 2026, needs more optimization.
24 79 0.083242252634 Henry Cohn, 2026, needs more optimization.
24 80 0.083289194550 Henry Cohn, 2026, needs more optimization.
24 81 0.083306459877 Henry Cohn, 2026, needs more optimization.
24 83 0.083320171859 Henry Cohn, 2025, needs more optimization.
24 84 0.083335156567 Henry Cohn, 2026, needs more optimization.
24 85 0.083335338109 Henry Cohn, 2026, needs more optimization.
24 86 0.086447948297 Henry Cohn, 2026, needs more optimization.
24 87 0.088166420236 Henry Cohn, 2026, needs more optimization.
24 88 0.089937149505 Henry Cohn, 2026, needs more optimization.
24 89 0.090286196348 Henry Cohn, 2026, needs more optimization.
24 90 0.090668443646 Henry Cohn, 2026, needs more optimization.
24 91 0.090834171392 Henry Cohn, 2026, needs more optimization.
24 92 0.090886623151 Henry Cohn, 2026, needs more optimization.
24 93 0.090908675164 Henry Cohn, 2026, needs more optimization.
24 104 0.090909090666 Henry Cohn, 2025, needs more optimization.
24 105 0.091535358779 Henry Cohn, 2026, needs more optimization.
24 106 0.095278625079 Henry Cohn, 2026, needs more optimization.
24 107 0.102478292355 Henry Cohn, 2026, needs more optimization.
24 108 0.105659351990 Henry Cohn, 2026, needs more optimization.
24 118 0.111099565428 Henry Cohn, 2025, needs more optimization.
24 119 0.111113332242 Henry Cohn, 2026, needs more optimization.
24 120 0.111113680879 Henry Cohn, 2026, needs more optimization.
24 121 0.111113986191 Henry Cohn, 2026, needs more optimization.
24 122 0.112368306160 Henry Cohn, 2026, needs more optimization.
24 123 0.116180792187 Henry Cohn, 2026, needs more optimization.
24 124 0.117906183525 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
24 130 0.131782945737 Orthogonal union of 126 points in 22 dimensions and 4 points in 2 dimensions.
129⁢x−17
24 131 0.131783805577 Henry Cohn, 2026, needs more optimization.
24 132 0.131784194380 Henry Cohn, 2026, needs more optimization.
24 133 0.131787574814 Henry Cohn, 2026, needs more optimization.
24 134 0.131788302178 Henry Cohn, 2026, needs more optimization.
24 135 0.131963230338 Henry Cohn, 2026, needs more optimization.
24 136 0.132226461738 Henry Cohn, 2026, needs more optimization.
24 137 0.132941116529 Henry Cohn, 2026, needs more optimization.
24 138 0.133282125518 Henry Cohn, 2026, needs more optimization.
24 139 0.134287652793 Henry Cohn, 2026, needs more optimization.
24 140 0.134691765315 Henry Cohn, 2026, needs more optimization.
24 141 0.134899508124 Henry Cohn, 2026, needs more optimization.
24 142 0.135004179249 Henry Cohn, 2026, needs more optimization.
24 143 0.135119503666 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
24 150 0.135136897422 Henry Cohn, 2026, needs more optimization.
24 151 0.135174343268 Henry Cohn, 2026, needs more optimization.
24 152 0.135430751946 Henry Cohn, 2026, needs more optimization.
24 153 0.136308737406 Henry Cohn, 2026, needs more optimization.
24 154 0.139284445872 Henry Cohn, 2026, needs more optimization.
24 155 0.141688477827 Henry Cohn, 2026, needs more optimization.
24 167 0.142857140433 Henry Cohn, 2026, needs more optimization.
24 172 0.142857140440 Henry Cohn, 2026, needs more optimization.
24 174 0.142857172719 Henry Cohn, 2026, needs more optimization.
24 175 0.143487682188 Henry Cohn, 2026, needs more optimization.
24 178 0.146069489746 Henry Cohn, 2026, needs more optimization.
24 179 0.146668846254 Henry Cohn, 2026, needs more optimization.
24 180 0.149030386280 Henry Cohn, 2026, needs more optimization.
24 181 0.151587910968 Henry Cohn, 2026, needs more optimization.
24 182 0.152665327695 Henry Cohn, 2026, needs more optimization.
24 183 0.153482574545 Henry Cohn, 2026, needs more optimization.
24 184 0.154898748694 Henry Cohn, 2026, needs more optimization.
24 185 0.155546081687 Henry Cohn, 2026, needs more optimization.
24 186 0.156465216512 Henry Cohn, 2026, needs more optimization.
24 187 0.157779778371 Henry Cohn, 2026, needs more optimization.
24 188 0.158909420824 Henry Cohn, 2026, needs more optimization.
24 189 0.159707270558 Henry Cohn, 2026, needs more optimization.
24 190 0.160152347561 Henry Cohn, 2026, needs more optimization.
24 191 0.160983432500 Henry Cohn, 2026, needs more optimization.
24 192 0.161222581731 Henry Cohn, 2026, needs more optimization.
24 204 0.161904761905 Code with 202 points in 23 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.
105⁢x−17
24 205 0.161904761905 Orthogonal union of 201 points in 22 dimensions and 4 points in 2 dimensions.
105⁢x−17
24 212 0.161905139997 Henry Cohn, 2026, needs more optimization.
24 213 0.161925381993 Henry Cohn, 2026, needs more optimization.
24 214 0.162020003411 Henry Cohn, 2026, needs more optimization.
24 215 0.162171553565 Henry Cohn, 2026, needs more optimization.
24 216 0.163090004918 Henry Cohn, 2026, needs more optimization.
24 217 0.163195051801 Henry Cohn, 2026, needs more optimization.
24 218 0.164221528941 Henry Cohn, 2026, needs more optimization.
24 219 0.164941471789 Henry Cohn, 2026, needs more optimization.
24 220 0.165098429101 Henry Cohn, 2026, needs more optimization.
24 221 0.165727475100 Henry Cohn, 2026, needs more optimization.
24 222 0.166047478937 Henry Cohn, 2026, needs more optimization.
24 223 0.166312270068 Henry Cohn, 2026, needs more optimization.
24 224 0.166572852550 Henry Cohn, 2026, needs more optimization.
24 279 0.166666666667 Code with 277 points in 23 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.
6⁢x−1
24 280 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 2 points in 1 dimension.
6⁢x−1
24 281 0.166676642845 Henry Cohn, 2026, needs more optimization.
24 282 0.166679189561 Henry Cohn, 2026, needs more optimization.
24 283 0.166690731113 Henry Cohn, 2026, needs more optimization.
24 284 0.168120941774 Henry Cohn, 2026, needs more optimization.
24 285 0.170164958123 Henry Cohn, 2026, needs more optimization.
24 286 0.172469362500 Henry Cohn, 2026, needs more optimization.
24 287 0.175049573935 Henry Cohn, 2026, needs more optimization.
24 288 0.177036869995 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 0.184915496078 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
24 554 0.2 Code with 552 points in 23 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.
5⁢x−1
24 555 0.232851959978 Orthogonal union of 553 points in 23 dimensions and 2 points in 1 dimension.
24 561 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 7 points in 3 dimensions.
21⁢x−5
24 562 0.238202129214 Henry Cohn, 2026, needs more optimization.
24 566 0.238234498849 Henry Cohn, 2026, needs more optimization.
24 570 0.238325649487 Henry Cohn, 2026, needs more optimization.
24 574 0.239143835786 Henry Cohn, 2026, needs more optimization.
24 575 0.241022864393 Orthogonal union of 573 points in 23 dimensions and 2 points in 1 dimension.
24 576 0.241269120694 Orthogonal union of 574 points in 23 dimensions and 2 points in 1 dimension.
24 577 0.241535521140 Orthogonal union of 575 points in 23 dimensions and 2 points in 1 dimension.
24 578 0.242871058847 Orthogonal union of 576 points in 23 dimensions and 2 points in 1 dimension.
24 579 0.242963249821 Orthogonal union of 577 points in 23 dimensions and 2 points in 1 dimension.
24 580 0.243886703258 Orthogonal union of 578 points in 23 dimensions and 2 points in 1 dimension.
24 581 0.244078494688 Orthogonal union of 579 points in 23 dimensions and 2 points in 1 dimension.
24 582 0.244893064816 Orthogonal union of 580 points in 23 dimensions and 2 points in 1 dimension.
24 583 0.245573513517 Orthogonal union of 581 points in 23 dimensions and 2 points in 1 dimension.
24 584 0.245573513531 Orthogonal union of 582 points in 23 dimensions and 2 points in 1 dimension.
24 609 0.245887136588 Henry Cohn, 2026, needs more optimization.
24 610 0.246006420038 Henry Cohn, 2026, needs more optimization.
24 611 0.246098523295 Henry Cohn, 2026, needs more optimization.
24 615 0.246323964522 Henry Cohn, 2026, needs more optimization.
24 616 0.246641944516 Henry Cohn, 2026, needs more optimization.
24 617 0.246964563693 Henry Cohn, 2026, needs more optimization.
24 618 0.247496699340 Henry Cohn, 2026, needs more optimization.
24 619 0.247931644505 Henry Cohn, 2026, needs more optimization.
24 620 0.247940624734 Henry Cohn, 2026, needs more optimization.
24 621 0.248318272931 Henry Cohn, 2026, needs more optimization.
24 623 0.248675404004 Henry Cohn, 2026, needs more optimization.
24 624 0.249080033754 Henry Cohn, 2026, needs more optimization.
24 625 0.249389823977 Henry Cohn, 2026, needs more optimization.
24 626 0.249646168474 Henry Cohn, 2026, needs more optimization.
24 627 0.249957008591 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 0.251929698830 Orthogonal union of 895 points in 23 dimensions and 2 points in 1 dimension.
24 898 0.254246971702 Orthogonal union of 896 points in 23 dimensions and 2 points in 1 dimension.
24 899 0.254397635336 Orthogonal union of 897 points in 23 dimensions and 2 points in 1 dimension.
24 900 0.255438886374 Orthogonal union of 898 points in 23 dimensions and 2 points in 1 dimension.
24 902 0.256477369157 Orthogonal union of 900 points in 23 dimensions and 2 points in 1 dimension.
24 903 0.256477369165 Orthogonal union of 901 points in 23 dimensions and 2 points in 1 dimension.
24 904 0.256938452771 Orthogonal union of 902 points in 23 dimensions and 2 points in 1 dimension.
24 905 0.258206534585 Orthogonal union of 903 points in 23 dimensions and 2 points in 1 dimension.
24 906 0.259223738467 Orthogonal union of 904 points in 23 dimensions and 2 points in 1 dimension.
24 908 0.259898659612 Orthogonal union of 906 points in 23 dimensions and 2 points in 1 dimension.
24 909 0.261595656694 Orthogonal union of 907 points in 23 dimensions and 2 points in 1 dimension.
24 910 0.264971928146 Orthogonal union of 908 points in 23 dimensions and 2 points in 1 dimension.
24 912 0.265493735158 Orthogonal union of 910 points in 23 dimensions and 2 points in 1 dimension.
24 913 0.266114548382 Orthogonal union of 911 points in 23 dimensions and 2 points in 1 dimension.
24 914 0.267368910073 Orthogonal union of 912 points in 23 dimensions and 2 points in 1 dimension.
24 915 0.268144738948 Orthogonal union of 913 points in 23 dimensions and 2 points in 1 dimension.
24 916 0.268802719680 Orthogonal union of 914 points in 23 dimensions and 2 points in 1 dimension.
24 917 0.268836540165 Orthogonal union of 915 points in 23 dimensions and 2 points in 1 dimension.
24 918 0.269663508977 Orthogonal union of 916 points in 23 dimensions and 2 points in 1 dimension.
24 919 0.270174895664 Orthogonal union of 917 points in 23 dimensions and 2 points in 1 dimension.
24 920 0.270910965697 Orthogonal union of 918 points in 23 dimensions and 2 points in 1 dimension.
24 921 0.271281877066 Orthogonal union of 919 points in 23 dimensions and 2 points in 1 dimension.
24 922 0.272118292082 Orthogonal union of 920 points in 23 dimensions and 2 points in 1 dimension.
24 923 0.272173315481 Orthogonal union of 921 points in 23 dimensions and 2 points in 1 dimension.
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 53 0.045305381447 Henry Cohn, 2025, needs more optimization.
25 54 0.045671054769 Henry Cohn, 2025.
25 55 0.046279562119 Henry Cohn, 2025.
25 56 0.046433703861 Henry Cohn, 2025, needs more optimization.
25 57 0.046863894921 Henry Cohn, 2025.
25 58 0.046863920964 Henry Cohn, 2025.
25 59 0.051394584232 Henry Cohn, 2024.
25 60 0.052967516574 Ilmari Vahteristo, 2026.
25 61 0.056074458886 Henry Cohn, 2026, needs more optimization.
25 62 0.060614048413 Ilmari Vahteristo, 2026.
25 63 0.062393204143 Henry Cohn, 2026, needs more optimization.
25 64 0.064224592914 Henry Cohn, 2026, needs more optimization.
25 65 0.065096075979 Henry Cohn, 2026, needs more optimization.
25 66 0.065382268725 Henry Cohn, 2024, needs more optimization.
25 67 0.066213051890 Henry Cohn, 2026, needs more optimization.
25 68 0.066469740511 Henry Cohn, 2026, needs more optimization.
25 69 0.068628304625 Henry Cohn, 2026, needs more optimization.
25 70 0.071056156548 Henry Cohn, 2026, needs more optimization.
25 71 0.071857004935 Henry Cohn, 2026, needs more optimization.
25 72 0.073521608209 Henry Cohn, 2026, needs more optimization.
25 73 0.076172581849 Henry Cohn, 2026, needs more optimization.
25 74 0.076878062267 Henry Cohn, 2026, needs more optimization.
25 75 0.076924227688 Henry Cohn, 2026, needs more optimization.
25 76 0.076924428273 Henry Cohn, 2026, needs more optimization.
25 77 0.077472989425 Henry Cohn, 2026, needs more optimization.
25 78 0.077922497456 Henry Cohn, 2026, needs more optimization.
25 79 0.078551974277 Henry Cohn, 2026, needs more optimization.
25 80 0.080840288189 Henry Cohn, 2026, needs more optimization.
25 81 0.082238876256 Henry Cohn, 2026, needs more optimization.
25 82 0.082621206381 Henry Cohn, 2026, needs more optimization.
25 83 0.083051068980 Henry Cohn, 2026, needs more optimization.
25 84 0.083128144684 Henry Cohn, 2026, needs more optimization.
25 85 0.083152918633 Henry Cohn, 2026, needs more optimization.
25 86 0.083298269280 Henry Cohn, 2026, needs more optimization.
25 87 0.083324459220 Henry Cohn, 2026, needs more optimization.
25 88 0.083331112248 Henry Cohn, 2026, needs more optimization.
25 89 0.085175115266 Henry Cohn, 2026, needs more optimization.
25 90 0.087176126131 Henry Cohn, 2026, needs more optimization.
25 91 0.087575631124 Henry Cohn, 2026, needs more optimization.
25 92 0.088985619981 Henry Cohn, 2026, needs more optimization.
25 93 0.089851970069 Henry Cohn, 2026, needs more optimization.
25 94 0.090214446736 Henry Cohn, 2026, needs more optimization.
25 95 0.090474815680 Henry Cohn, 2026, needs more optimization.
25 96 0.090647928346 Henry Cohn, 2026, needs more optimization.
25 97 0.090861831328 Henry Cohn, 2026, needs more optimization.
25 98 0.090881995848 Henry Cohn, 2026, needs more optimization.
25 99 0.090903638972 Henry Cohn, 2026, needs more optimization.
25 106 0.090909090666 Orthogonal union of 104 points in 24 dimensions and 2 points in 1 dimension.
25 107 0.090912729141 Henry Cohn, 2026, needs more optimization.
25 108 0.093005776844 Henry Cohn, 2026, needs more optimization.
25 109 0.095561053839 Henry Cohn, 2026, needs more optimization.
25 110 0.100477491701 Henry Cohn, 2026, needs more optimization.
25 111 0.102647690180 Henry Cohn, 2026, needs more optimization.
25 117 0.105319726475 Henry Cohn, 2026.
375⁢x2−30⁢x−1
25 118 0.107634943680 Henry Cohn, 2026, needs more optimization.
25 119 0.108659080050 Henry Cohn, 2026, needs more optimization.
25 120 0.108744060929 Henry Cohn, 2026, needs more optimization.
25 121 0.109313075610 Henry Cohn, 2026, needs more optimization.
25 122 0.110263305639 Henry Cohn, 2026, needs more optimization.
25 123 0.111109715013 Henry Cohn, 2026, needs more optimization.
25 124 0.111110673751 Henry Cohn, 2026, needs more optimization.
25 125 0.111112955319 Henry Cohn, 2026, needs more optimization.
25 126 0.111126208744 Henry Cohn, 2026, needs more optimization.
25 127 0.111229347419 Henry Cohn, 2026, needs more optimization.
25 128 0.111399349118 Henry Cohn, 2026, needs more optimization.
25 129 0.117119510913 Henry Cohn, 2026, needs more optimization.
25 130 0.120036186929 Henry Cohn, 2026, needs more optimization.
25 131 0.122027936770 Henry Cohn, 2026, needs more optimization.
25 132 0.123583659785 Henry Cohn, 2026, needs more optimization.
25 133 0.124985790400 Henry Cohn, 2026, needs more optimization.
25 134 0.126246752815 Henry Cohn, 2026, needs more optimization.
25 135 0.128192665814 Henry Cohn, 2026, needs more optimization.
25 136 0.129733344705 Henry Cohn, 2026, needs more optimization.
25 137 0.131718880118 Henry Cohn, 2026, needs more optimization.
25 138 0.131763228461 Henry Cohn, 2026, needs more optimization.
25 139 0.131778135429 Henry Cohn, 2026, needs more optimization.
25 140 0.131785394229 Henry Cohn, 2026, needs more optimization.
25 141 0.131919356278 Henry Cohn, 2026, needs more optimization.
25 142 0.132978926648 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 0.135174273058 Henry Cohn, 2026, needs more optimization.
25 158 0.137173809024 Henry Cohn, 2026, needs more optimization.
25 159 0.138823413098 Henry Cohn, 2026, needs more optimization.
25 160 0.140563869258 Henry Cohn, 2026, needs more optimization.
25 161 0.141385145626 Henry Cohn, 2026, needs more optimization.
25 169 0.142857140433 Orthogonal union of 167 points in 24 dimensions and 2 points in 1 dimension.
25 174 0.142857140440 Orthogonal union of 172 points in 24 dimensions and 2 points in 1 dimension.
25 176 0.142857172719 Orthogonal union of 174 points in 24 dimensions and 2 points in 1 dimension.
25 177 0.142861256645 Henry Cohn, 2026, needs more optimization.
25 178 0.142890511671 Henry Cohn, 2026, needs more optimization.
25 179 0.143147974455 Henry Cohn, 2026, needs more optimization.
25 180 0.143255116666 Henry Cohn, 2026, needs more optimization.
25 181 0.144736712200 Henry Cohn, 2026, needs more optimization.
25 182 0.144744445025 Henry Cohn, 2026, needs more optimization.
25 183 0.145949224180 Henry Cohn, 2026, needs more optimization.
25 184 0.147691671949 Henry Cohn, 2026, needs more optimization.
25 185 0.150226984875 Henry Cohn, 2026, needs more optimization.
25 186 0.150922221093 Henry Cohn, 2026, needs more optimization.
25 187 0.150980996869 Henry Cohn, 2026, needs more optimization.
25 188 0.151967418175 Henry Cohn, 2026, needs more optimization.
25 189 0.152567907252 Henry Cohn, 2026, needs more optimization.
25 190 0.152874039893 Henry Cohn, 2026, needs more optimization.
25 191 0.153285677043 Henry Cohn, 2026, needs more optimization.
25 192 0.153559681715 Henry Cohn, 2026, needs more optimization.
25 193 0.153647283163 Henry Cohn, 2026, needs more optimization.
25 194 0.154412241607 Henry Cohn, 2026, needs more optimization.
25 195 0.156289544376 Henry Cohn, 2026, needs more optimization.
25 196 0.157020846783 Henry Cohn, 2026, needs more optimization.
25 197 0.157275139721 Henry Cohn, 2026, needs more optimization.
25 198 0.158176469700 Henry Cohn, 2026, needs more optimization.
25 199 0.159020643429 Henry Cohn, 2026, needs more optimization.
25 200 0.159824426944 Henry Cohn, 2026, needs more optimization.
25 201 0.160740536610 Henry Cohn, 2026, needs more optimization.
25 202 0.161139763665 Henry Cohn, 2026, needs more optimization.
25 203 0.161831777467 Henry Cohn, 2026, needs more optimization.
25 204 0.161838667047 Henry Cohn, 2026, needs more optimization.
25 205 0.161876339520 Henry Cohn, 2026, needs more optimization.
25 206 0.161890055666 Henry Cohn, 2025, needs more optimization.
25 208 0.161891112345 Henry Cohn, 2026, needs more optimization.
25 209 0.161897264007 Henry Cohn, 2026, needs more optimization.
25 210 0.161900221645 Henry Cohn, 2026, needs more optimization.
25 211 0.161901326506 Henry Cohn, 2026, needs more optimization.
25 212 0.161903902009 Henry Cohn, 2026, needs more optimization.
25 214 0.161905139997 Orthogonal union of 212 points in 24 dimensions and 2 points in 1 dimension.
25 215 0.161906722349 Henry Cohn, 2026, needs more optimization.
25 216 0.161908025900 Henry Cohn, 2026, needs more optimization.
25 217 0.161914417567 Henry Cohn, 2026, needs more optimization.
25 218 0.161917997140 Henry Cohn, 2026, needs more optimization.
25 220 0.161927447829 Henry Cohn, 2026, needs more optimization.
25 221 0.161932082708 Henry Cohn, 2026, needs more optimization.
25 222 0.161950545720 Henry Cohn, 2026, needs more optimization.
25 223 0.162333176545 Henry Cohn, 2026, needs more optimization.
25 224 0.162666502047 Henry Cohn, 2026, needs more optimization.
25 225 0.162919250609 Henry Cohn, 2026, needs more optimization.
25 226 0.163646779165 Henry Cohn, 2026, needs more optimization.
25 227 0.164412775144 Henry Cohn, 2026, needs more optimization.
25 228 0.164902007487 Henry Cohn, 2026, needs more optimization.
25 229 0.165464173959 Henry Cohn, 2026, needs more optimization.
25 230 0.165804065341 Henry Cohn, 2026, needs more optimization.
25 231 0.165910752624 Henry Cohn, 2026, needs more optimization.
25 232 0.166107846699 Henry Cohn, 2026, needs more optimization.
25 233 0.166317099696 Henry Cohn, 2026, needs more optimization.
25 234 0.166439086792 Henry Cohn, 2026, needs more optimization.
25 235 0.166573833908 Henry Cohn, 2026, needs more optimization.
25 237 0.166626309624 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
25 284 0.166675855742 Henry Cohn, 2026, needs more optimization.
25 285 0.166678444752 Henry Cohn, 2026, needs more optimization.
25 286 0.166692150986 Henry Cohn, 2026, needs more optimization.
25 287 0.166718357538 Henry Cohn, 2026, needs more optimization.
25 288 0.166786075699 Henry Cohn, 2026, needs more optimization.
25 289 0.167223770137 Henry Cohn, 2026, needs more optimization.
25 290 0.167934991268 Henry Cohn, 2026, needs more optimization.
25 291 0.169284808705 Henry Cohn, 2026, needs more optimization.
25 292 0.170247288745 Henry Cohn, 2026, needs more optimization.
25 293 0.171035367187 Henry Cohn, 2026, needs more optimization.
25 294 0.174200607198 Henry Cohn, 2026, needs more optimization.
25 295 0.174856959174 Henry Cohn, 2026, needs more optimization.
25 296 0.176756146776 Henry Cohn, 2026, needs more optimization.
25 297 0.177370949473 Henry Cohn, 2026, needs more optimization.
25 298 0.178981284512 Henry Cohn, 2026, needs more optimization.
25 299 0.180728715314 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
25 316 0.184915496078 Orthogonal union of 314 points in 24 dimensions and 2 points in 1 dimension.
25 332 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 2 points in 1 dimension.
31⁢x−6
25 334 0.193558897113 Henry Cohn, 2026, needs more optimization.
25 335 0.194701625827 Henry Cohn, 2026, needs more optimization.
25 336 0.194789363361 Henry Cohn, 2026, needs more optimization.
25 337 0.197142335309 Henry Cohn, 2026, needs more optimization.
25 338 0.197382082247 Henry Cohn, 2026, needs more optimization.
25 339 0.198310610666 Henry Cohn, 2026, needs more optimization.
25 340 0.199041896149 Henry Cohn, 2026, needs more optimization.
25 556 0.2 Orthogonal union of 552 points in 23 dimensions and 4 points in 2 dimensions.
5⁢x−1
25 557 0.200003594574 Henry Cohn, 2026, needs more optimization.
25 558 0.200010840602 Henry Cohn, 2026, needs more optimization.
25 559 0.200025254385 Henry Cohn, 2026, needs more optimization.
25 560 0.200250213533 Henry Cohn, 2026, needs more optimization.
25 561 0.201101825344 Henry Cohn, 2026, needs more optimization.
25 562 0.202204858202 Henry Cohn, 2026, needs more optimization.
25 564 0.202222732698 Henry Cohn, 2026, needs more optimization.
25 565 0.204375144191 Henry Cohn, 2026, needs more optimization.
25 566 0.207492029650 Henry Cohn, 2026, needs more optimization.
25 567 0.210344730128 Henry Cohn, 2026, needs more optimization.
25 568 0.212620049203 Henry Cohn, 2026, needs more optimization.
25 569 0.214736726592 Henry Cohn, 2026, needs more optimization.
25 570 0.216986257841 Henry Cohn, 2026, needs more optimization.
25 571 0.218502985141 Henry Cohn, 2026, needs more optimization.
25 572 0.220268177141 Henry Cohn, 2026, needs more optimization.
25 573 0.221864283043 Henry Cohn, 2026, needs more optimization.
25 574 0.222944294027 Henry Cohn, 2026, needs more optimization.
25 575 0.224230577379 Henry Cohn, 2026, needs more optimization.
25 576 0.225327526755 Henry Cohn, 2026, needs more optimization.
25 577 0.226837055978 Henry Cohn, 2026, needs more optimization.
25 578 0.227891986078 Henry Cohn, 2026, needs more optimization.
25 579 0.228517196126 Henry Cohn, 2026, needs more optimization.
25 580 0.229079598080 Henry Cohn, 2026, needs more optimization.
25 581 0.229882834554 Henry Cohn, 2026, needs more optimization.
25 582 0.230043706448 Henry Cohn, 2026, needs more optimization.
25 583 0.231345472037 Henry Cohn, 2026, needs more optimization.
25 584 0.232207827229 Henry Cohn, 2026, needs more optimization.
25 585 0.232479376363 Henry Cohn, 2026, needs more optimization.
25 586 0.233414506364 Henry Cohn, 2026, needs more optimization.
25 587 0.234451135578 Henry Cohn, 2026, needs more optimization.
25 588 0.234601320648 Henry Cohn, 2026, needs more optimization.
25 589 0.235304794842 Henry Cohn, 2026, needs more optimization.
25 590 0.235970793319 Henry Cohn, 2026, needs more optimization.
25 591 0.236630001220 Henry Cohn, 2026, needs more optimization.
25 592 0.237526725225 Henry Cohn, 2026, needs more optimization.
25 593 0.237671063124 Henry Cohn, 2026, needs more optimization.
25 594 0.238058235503 Henry Cohn, 2026, needs more optimization.
25 595 0.238948008534 Henry Cohn, 2026, needs more optimization.
25 596 0.239511803067 Henry Cohn, 2026, needs more optimization.
25 597 0.240112868607 Henry Cohn, 2026, needs more optimization.
25 598 0.240693069986 Henry Cohn, 2026, needs more optimization.
25 599 0.241168217465 Henry Cohn, 2026, needs more optimization.
25 600 0.241823370934 Henry Cohn, 2026, needs more optimization.
25 601 0.242526225877 Henry Cohn, 2026, needs more optimization.
25 602 0.242871757120 Henry Cohn, 2026, needs more optimization.
25 603 0.243279547799 Henry Cohn, 2026, needs more optimization.
25 604 0.243610854905 Henry Cohn, 2026, needs more optimization.
25 605 0.244097702168 Henry Cohn, 2026, needs more optimization.
25 606 0.245069454852 Henry Cohn, 2026, needs more optimization.
25 607 0.245120758338 Henry Cohn, 2026, needs more optimization.
25 608 0.245346668370 Henry Cohn, 2026, needs more optimization.
25 611 0.245887136588 Orthogonal union of 609 points in 24 dimensions and 2 points in 1 dimension.
25 612 0.246006420038 Orthogonal union of 610 points in 24 dimensions and 2 points in 1 dimension.
25 613 0.246098523295 Orthogonal union of 611 points in 24 dimensions and 2 points in 1 dimension.
25 617 0.246323964522 Orthogonal union of 615 points in 24 dimensions and 2 points in 1 dimension.
25 618 0.246641944516 Orthogonal union of 616 points in 24 dimensions and 2 points in 1 dimension.
25 619 0.246964563693 Orthogonal union of 617 points in 24 dimensions and 2 points in 1 dimension.
25 620 0.247496699340 Orthogonal union of 618 points in 24 dimensions and 2 points in 1 dimension.
25 621 0.247931644505 Orthogonal union of 619 points in 24 dimensions and 2 points in 1 dimension.
25 622 0.247940624734 Orthogonal union of 620 points in 24 dimensions and 2 points in 1 dimension.
25 623 0.248318272931 Orthogonal union of 621 points in 24 dimensions and 2 points in 1 dimension.
25 625 0.248675404004 Orthogonal union of 623 points in 24 dimensions and 2 points in 1 dimension.
25 626 0.249080033754 Orthogonal union of 624 points in 24 dimensions and 2 points in 1 dimension.
25 648 0.249312976442 Henry Cohn, 2026, needs more optimization.
25 649 0.249323799709 Henry Cohn, 2026, needs more optimization.
25 650 0.249329953737 Henry Cohn, 2026, needs more optimization.
25 651 0.249401720663 Henry Cohn, 2026, needs more optimization.
25 654 0.249409739452 Henry Cohn, 2026, needs more optimization.
25 656 0.249440714832 Henry Cohn, 2026, needs more optimization.
25 657 0.249527919144 Henry Cohn, 2026, needs more optimization.
25 658 0.249552104205 Henry Cohn, 2026, needs more optimization.
25 659 0.249576913702 Henry Cohn, 2026, needs more optimization.
25 662 0.249605065733 Henry Cohn, 2026, needs more optimization.
25 663 0.249623120464 Henry Cohn, 2026, needs more optimization.
25 664 0.249675774473 Henry Cohn, 2026, needs more optimization.
25 665 0.249693891277 Henry Cohn, 2026, needs more optimization.
25 666 0.249752841763 Henry Cohn, 2026, needs more optimization.
25 667 0.249830848290 Henry Cohn, 2026, needs more optimization.
25 668 0.249834645072 Henry Cohn, 2026, needs more optimization.
25 669 0.249850469484 Henry Cohn, 2026, needs more optimization.
25 671 0.249866435979 Henry Cohn, 2026, needs more optimization.
25 672 0.249873689001 Henry Cohn, 2026, needs more optimization.
25 673 0.249985249377 Henry Cohn, 2026, needs more optimization.
25 674 0.249985750835 Henry Cohn, 2026, needs more optimization.
25 676 0.249987693396 Henry Cohn, 2026, needs more optimization.
25 677 0.249996682153 Henry Cohn, 2026, needs more optimization.
25 900 0.25 Henry Cohn, 2025.
4⁢x−1
25 901 0.250037345728 Henry Cohn, 2026, needs more optimization.
25 912 0.250104800224 Henry Cohn, 2026, needs more optimization.
25 914 0.250130232067 Henry Cohn, 2026, needs more optimization.
25 916 0.250136617581 Henry Cohn, 2026, needs more optimization.
25 917 0.250253724244 Henry Cohn, 2026, needs more optimization.
25 918 0.250288604194 Henry Cohn, 2026, needs more optimization.
25 919 0.250479263938 Henry Cohn, 2026, needs more optimization.
25 920 0.250625617692 Henry Cohn, 2026, needs more optimization.
25 921 0.251206789934 Henry Cohn, 2026, needs more optimization.
25 922 0.251382916040 Henry Cohn, 2026, needs more optimization.
25 923 0.251624149089 Henry Cohn, 2026, needs more optimization.
25 924 0.251918783626 Henry Cohn, 2026, needs more optimization.
25 925 0.252062322280 Henry Cohn, 2026, needs more optimization.
25 926 0.252482949757 Henry Cohn, 2026, needs more optimization.
25 927 0.252544722754 Henry Cohn, 2026, needs more optimization.
25 928 0.253070931814 Henry Cohn, 2026, needs more optimization.
25 929 0.253639768002 Henry Cohn, 2026, needs more optimization.
25 930 0.254155665662 Henry Cohn, 2026, needs more optimization.
25 931 0.254740549844 Henry Cohn, 2026, needs more optimization.
25 932 0.255019149547 Henry Cohn, 2026, needs more optimization.
25 933 0.255304176936 Henry Cohn, 2026, needs more optimization.
25 934 0.255967790196 Henry Cohn, 2026, needs more optimization.
25 935 0.256352157607 Henry Cohn, 2026, needs more optimization.
25 936 0.257031433270 Henry Cohn, 2026, needs more optimization.
25 937 0.257611324824 Henry Cohn, 2026, needs more optimization.
25 938 0.258243572885 Henry Cohn, 2026, needs more optimization.
25 939 0.258595037206 Henry Cohn, 2026, needs more optimization.
25 940 0.258776973263 Henry Cohn, 2026, needs more optimization.
25 941 0.259458565543 Henry Cohn, 2026, needs more optimization.
25 942 0.260030468419 Henry Cohn, 2026, needs more optimization.
25 943 0.260404260799 Henry Cohn, 2026, needs more optimization.
25 944 0.260656489719 Henry Cohn, 2026, needs more optimization.
25 945 0.261410381708 Henry Cohn, 2026, needs more optimization.
25 946 0.261850403922 Henry Cohn, 2026, needs more optimization.
25 947 0.262120601730 Henry Cohn, 2026, needs more optimization.
25 948 0.263025137617 Henry Cohn, 2026, needs more optimization.
25 949 0.263443170239 Henry Cohn, 2026, needs more optimization.
25 950 0.263770972564 Henry Cohn, 2026, needs more optimization.
25 951 0.264244859119 Henry Cohn, 2026, needs more optimization.
25 952 0.264631984213 Henry Cohn, 2026, needs more optimization.
25 953 0.265026669126 Henry Cohn, 2026, needs more optimization.
25 954 0.265586531574 Henry Cohn, 2026, needs more optimization.
25 955 0.266112204214 Henry Cohn, 2026, needs more optimization.
25 956 0.266828484457 Henry Cohn, 2026, needs more optimization.
25 957 0.266976480929 Henry Cohn, 2026, needs more optimization.
25 958 0.267168480431 Henry Cohn, 2026, needs more optimization.
25 959 0.267436195308 Henry Cohn, 2026, needs more optimization.
25 960 0.267546822985 Henry Cohn, 2026, needs more optimization.
25 961 0.267933281269 Henry Cohn, 2026, needs more optimization.
25 962 0.268252080774 Henry Cohn, 2026, needs more optimization.
25 963 0.268454773358 Henry Cohn, 2026, needs more optimization.
25 964 0.268650129729 Henry Cohn, 2026, needs more optimization.
25 965 0.269252806993 Henry Cohn, 2026, needs more optimization.
25 966 0.269594538019 Henry Cohn, 2026, needs more optimization.
25 967 0.269905364566 Henry Cohn, 2026, needs more optimization.
25 968 0.270238970568 Henry Cohn, 2026, needs more optimization.
25 969 0.270822271371 Henry Cohn, 2026, needs more optimization.
25 970 0.270822271372 Henry Cohn, 2026, needs more optimization.
25 971 0.271003040181 Henry Cohn, 2026, needs more optimization.
25 972 0.271500054157 Henry Cohn, 2026, needs more optimization.
25 973 0.271522310470 Henry Cohn, 2026, needs more optimization.
25 974 0.271648889423 Henry Cohn, 2026, needs more optimization.
25 975 0.271992635266 Henry Cohn, 2026, needs more optimization.
25 976 0.272305986896 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 0.035747894971 Henry Cohn, 2026, needs more optimization.
26 55 0.044558069283 Henry Cohn, 2026, needs more optimization.
26 56 0.044663560912 Henry Cohn, 2026, needs more optimization.
26 57 0.045162601400 Henry Cohn, 2026, needs more optimization.
26 58 0.045550434603 Henry Cohn, 2024.
26 59 0.046163974402 Henry Cohn, 2025.
26 60 0.046456376998 Henry Cohn, 2026, needs more optimization.
26 61 0.049243792051 Ilmari Vahteristo, 2026.
26 62 0.051910677056 Henry Cohn, 2026, needs more optimization.
26 63 0.054432495111 Henry Cohn, 2026, needs more optimization.
26 64 0.057479203623 Henry Cohn, 2026, needs more optimization.
26 65 0.060288207084 Ilmari Vahteristo, 2026.
26 66 0.062100657948 Ilmari Vahteristo, 2026.
26 67 0.063559236059 Henry Cohn, 2026, needs more optimization.
26 68 0.063600411345 Henry Cohn, 2026, needs more optimization.
26 69 0.064916629007 Henry Cohn, 2026, needs more optimization.
26 70 0.065400202147 Henry Cohn, 2026, needs more optimization.
26 71 0.067315893910 Henry Cohn, 2026, needs more optimization.
26 72 0.068297564169 Henry Cohn, 2026, needs more optimization.
26 73 0.070994630518 Henry Cohn, 2026, needs more optimization.
26 74 0.073191112187 Henry Cohn, 2026, needs more optimization.
26 75 0.074411709885 Henry Cohn, 2026, needs more optimization.
26 76 0.075418030224 Henry Cohn, 2026, needs more optimization.
26 77 0.076579497750 Henry Cohn, 2026, needs more optimization.
26 78 0.076864990301 Henry Cohn, 2026, needs more optimization.
26 79 0.076920089242 Henry Cohn, 2026, needs more optimization.
26 80 0.076967648257 Henry Cohn, 2026, needs more optimization.
26 81 0.077577286856 Henry Cohn, 2026, needs more optimization.
26 82 0.077924828167 Henry Cohn, 2026, needs more optimization.
26 83 0.079100881430 Henry Cohn, 2026, needs more optimization.
26 84 0.079410382251 Henry Cohn, 2026, needs more optimization.
26 85 0.081666142999 Henry Cohn, 2026, needs more optimization.
26 86 0.082512890261 Henry Cohn, 2026, needs more optimization.
26 87 0.082856208664 Henry Cohn, 2026, needs more optimization.
26 88 0.082947482818 Henry Cohn, 2026, needs more optimization.
26 89 0.083193324866 Henry Cohn, 2026, needs more optimization.
26 90 0.083304500874 Henry Cohn, 2026, needs more optimization.
26 91 0.083321489270 Henry Cohn, 2026, needs more optimization.
26 92 0.084415236972 Henry Cohn, 2026, needs more optimization.
26 93 0.085534564383 Henry Cohn, 2026, needs more optimization.
26 94 0.086904413922 Henry Cohn, 2026, needs more optimization.
26 95 0.088409155005 Henry Cohn, 2026, needs more optimization.
26 96 0.088785257959 Henry Cohn, 2026, needs more optimization.
26 97 0.089476909408 Henry Cohn, 2026, needs more optimization.
26 98 0.089870154125 Henry Cohn, 2026, needs more optimization.
26 99 0.090269132945 Henry Cohn, 2026, needs more optimization.
26 100 0.090364089552 Henry Cohn, 2026, needs more optimization.
26 101 0.090572460120 Henry Cohn, 2026, needs more optimization.
26 102 0.090760757619 Henry Cohn, 2026, needs more optimization.
26 103 0.090846454380 Henry Cohn, 2026, needs more optimization.
26 104 0.090890636960 Henry Cohn, 2026, needs more optimization.
26 105 0.090903868802 Henry Cohn, 2026, needs more optimization.
26 108 0.090909090666 Orthogonal union of 104 points in 24 dimensions and 4 points in 2 dimensions.
26 109 0.090910866552 Henry Cohn, 2026, needs more optimization.
26 110 0.090912497041 Henry Cohn, 2026, needs more optimization.
26 111 0.091921189353 Henry Cohn, 2026, needs more optimization.
26 112 0.094593478426 Henry Cohn, 2026, needs more optimization.
26 113 0.097432440644 Henry Cohn, 2026, needs more optimization.
26 114 0.100904545962 Henry Cohn, 2026, needs more optimization.
26 119 0.103125332235 Henry Cohn, 2026.
191⁢x2−10⁢x−1
26 120 0.103149900835 Henry Cohn, 2026, needs more optimization.
26 121 0.103945584755 Henry Cohn, 2026, needs more optimization.
26 122 0.105676620725 Henry Cohn, 2026, needs more optimization.
26 123 0.106265325565 Henry Cohn, 2026, needs more optimization.
26 124 0.107120809256 Henry Cohn, 2026, needs more optimization.
26 125 0.107687921378 Henry Cohn, 2026, needs more optimization.
26 126 0.108579423630 Henry Cohn, 2026, needs more optimization.
26 127 0.109127620313 Henry Cohn, 2026, needs more optimization.
26 128 0.111085523762 Henry Cohn, 2026, needs more optimization.
26 129 0.111099538419 Henry Cohn, 2026, needs more optimization.
26 130 0.111107456815 Henry Cohn, 2026, needs more optimization.
26 131 0.111118149731 Henry Cohn, 2026, needs more optimization.
26 132 0.112933808320 Henry Cohn, 2026, needs more optimization.
26 133 0.115162675930 Henry Cohn, 2026, needs more optimization.
26 134 0.116224309245 Henry Cohn, 2026, needs more optimization.
26 135 0.116309938419 Henry Cohn, 2026, needs more optimization.
26 136 0.116455216684 Henry Cohn, 2026, needs more optimization.
26 137 0.121421384805 Henry Cohn, 2026, needs more optimization.
26 138 0.122301886438 Henry Cohn, 2026, needs more optimization.
26 139 0.122355946938 Henry Cohn, 2026, needs more optimization.
26 140 0.127204785273 Henry Cohn, 2026, needs more optimization.
26 141 0.129201947598 Henry Cohn, 2026, needs more optimization.
26 143 0.131473144128 Henry Cohn, 2026, needs more optimization.
26 144 0.131692066683 Henry Cohn, 2026, needs more optimization.
26 145 0.131732748026 Henry Cohn, 2026, needs more optimization.
26 146 0.131788609213 Henry Cohn, 2026, needs more optimization.
26 147 0.131911831435 Henry Cohn, 2026, needs more optimization.
26 148 0.132500801236 Henry Cohn, 2026, needs more optimization.
26 149 0.133178978679 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 0.133341767968 Henry Cohn, 2026, needs more optimization.
26 160 0.134598515128 Henry Cohn, 2026, needs more optimization.
26 161 0.135140901809 Henry Cohn, 2026, needs more optimization.
26 162 0.135384609263 Henry Cohn, 2026, needs more optimization.
26 163 0.136053494519 Henry Cohn, 2026, needs more optimization.
26 164 0.136787994085 Henry Cohn, 2026, needs more optimization.
26 165 0.138337750989 Henry Cohn, 2026, needs more optimization.
26 166 0.138941425009 Henry Cohn, 2026, needs more optimization.
26 167 0.140493277028 Henry Cohn, 2026, needs more optimization.
26 168 0.141052193033 Henry Cohn, 2026, needs more optimization.
26 169 0.142717083291 Henry Cohn, 2026, needs more optimization.
26 170 0.142752962155 Henry Cohn, 2026, needs more optimization.
26 171 0.142761495589 Henry Cohn, 2026, needs more optimization.
26 172 0.142769121474 Henry Cohn, 2026, needs more optimization.
26 173 0.142786130046 Henry Cohn, 2026, needs more optimization.
26 174 0.142805795771 Henry Cohn, 2026, needs more optimization.
26 175 0.142821972208 Henry Cohn, 2026, needs more optimization.
26 176 0.142827056151 Henry Cohn, 2026, needs more optimization.
26 178 0.142829684486 Henry Cohn, 2026, needs more optimization.
26 180 0.142829848920 Henry Cohn, 2026, needs more optimization.
26 181 0.142839217540 Henry Cohn, 2026, needs more optimization.
26 182 0.142851600205 Henry Cohn, 2026, needs more optimization.
26 183 0.142856623245 Henry Cohn, 2026, needs more optimization.
26 184 0.142861713876 Henry Cohn, 2026, needs more optimization.
26 185 0.142903417497 Henry Cohn, 2026, needs more optimization.
26 186 0.143138099687 Henry Cohn, 2026, needs more optimization.
26 187 0.143817566266 Henry Cohn, 2026, needs more optimization.
26 188 0.145474458371 Henry Cohn, 2026, needs more optimization.
26 189 0.146619563673 Henry Cohn, 2026, needs more optimization.
26 191 0.147866256862 Henry Cohn, 2026, needs more optimization.
26 192 0.148235390619 Henry Cohn, 2026, needs more optimization.
26 193 0.149301571489 Henry Cohn, 2026, needs more optimization.
26 194 0.149793919566 Henry Cohn, 2026, needs more optimization.
26 195 0.150078743148 Henry Cohn, 2026, needs more optimization.
26 196 0.150169805818 Henry Cohn, 2026, needs more optimization.
26 197 0.151157222518 Henry Cohn, 2026, needs more optimization.
26 198 0.151413770252 Henry Cohn, 2026, needs more optimization.
26 199 0.152228035700 Henry Cohn, 2026, needs more optimization.
26 200 0.152756042888 Henry Cohn, 2026, needs more optimization.
26 201 0.153085907911 Henry Cohn, 2026, needs more optimization.
26 202 0.153892599261 Henry Cohn, 2026, needs more optimization.
26 203 0.154352049527 Henry Cohn, 2026, needs more optimization.
26 204 0.155099013773 Henry Cohn, 2026, needs more optimization.
26 205 0.155330689748 Henry Cohn, 2026, needs more optimization.
26 206 0.156545785563 Henry Cohn, 2026, needs more optimization.
26 207 0.157591952884 Henry Cohn, 2026, needs more optimization.
26 208 0.157797585477 Henry Cohn, 2026, needs more optimization.
26 209 0.158256742482 Henry Cohn, 2026, needs more optimization.
26 210 0.158755823215 Henry Cohn, 2026, needs more optimization.
26 211 0.159428810172 Henry Cohn, 2026, needs more optimization.
26 212 0.160038705855 Henry Cohn, 2026, needs more optimization.
26 213 0.160263030846 Henry Cohn, 2026, needs more optimization.
26 214 0.161294456422 Henry Cohn, 2026, needs more optimization.
26 216 0.161829884076 Henry Cohn, 2026, needs more optimization.
26 217 0.161831102106 Henry Cohn, 2026, needs more optimization.
26 218 0.161846552322 Henry Cohn, 2026, needs more optimization.
26 219 0.161848054252 Henry Cohn, 2026, needs more optimization.
26 220 0.161864572500 Henry Cohn, 2026, needs more optimization.
26 221 0.161873363124 Henry Cohn, 2026, needs more optimization.
26 222 0.161877339471 Henry Cohn, 2026, needs more optimization.
26 224 0.161893584746 Henry Cohn, 2026, needs more optimization.
26 225 0.161903485632 Henry Cohn, 2026, needs more optimization.
26 226 0.161905472441 Henry Cohn, 2026, needs more optimization.
26 227 0.161907879117 Henry Cohn, 2026, needs more optimization.
26 228 0.161910109497 Henry Cohn, 2026, needs more optimization.
26 230 0.161914729153 Henry Cohn, 2026, needs more optimization.
26 231 0.161942942215 Henry Cohn, 2026, needs more optimization.
26 232 0.161976554314 Henry Cohn, 2026, needs more optimization.
26 233 0.162068507810 Henry Cohn, 2026, needs more optimization.
26 234 0.163179851401 Henry Cohn, 2026, needs more optimization.
26 235 0.163457162014 Henry Cohn, 2026, needs more optimization.
26 236 0.163994924154 Henry Cohn, 2026, needs more optimization.
26 237 0.164269768475 Henry Cohn, 2026, needs more optimization.
26 238 0.164612057468 Henry Cohn, 2026, needs more optimization.
26 239 0.164867310245 Henry Cohn, 2026, needs more optimization.
26 240 0.165375352374 Henry Cohn, 2026, needs more optimization.
26 241 0.165623143988 Henry Cohn, 2026, needs more optimization.
26 242 0.165948264929 Henry Cohn, 2026, needs more optimization.
26 243 0.166051531747 Henry Cohn, 2026, needs more optimization.
26 244 0.166198692449 Henry Cohn, 2026, needs more optimization.
26 245 0.166253678507 Henry Cohn, 2026, needs more optimization.
26 246 0.166271799266 Henry Cohn, 2026, needs more optimization.
26 247 0.166444243927 Henry Cohn, 2026, needs more optimization.
26 249 0.166457713425 Henry Cohn, 2026, needs more optimization.
26 250 0.166640023145 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 0.166674753120 Henry Cohn, 2026, needs more optimization.
26 288 0.166676316080 Henry Cohn, 2026, needs more optimization.
26 289 0.166678675918 Henry Cohn, 2026, needs more optimization.
26 290 0.166678854746 Henry Cohn, 2026, needs more optimization.
26 291 0.166682355477 Henry Cohn, 2026, needs more optimization.
26 292 0.166722146160 Henry Cohn, 2026, needs more optimization.
26 293 0.166728195031 Henry Cohn, 2026, needs more optimization.
26 294 0.166766303550 Henry Cohn, 2026, needs more optimization.
26 295 0.166789269133 Henry Cohn, 2026, needs more optimization.
26 296 0.167044365266 Henry Cohn, 2026, needs more optimization.
26 297 0.167089004451 Henry Cohn, 2026, needs more optimization.
26 298 0.167435843496 Henry Cohn, 2026, needs more optimization.
26 299 0.168747029607 Henry Cohn, 2026, needs more optimization.
26 300 0.170818468627 Henry Cohn, 2026, needs more optimization.
26 301 0.171964316023 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 0.184915496078 Orthogonal union of 314 points in 24 dimensions and 4 points in 2 dimensions.
26 334 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 4 points in 2 dimensions.
31⁢x−6
26 336 0.193558897113 Orthogonal union of 334 points in 25 dimensions and 2 points in 1 dimension.
26 337 0.194701625827 Orthogonal union of 335 points in 25 dimensions and 2 points in 1 dimension.
26 338 0.194789363361 Orthogonal union of 336 points in 25 dimensions and 2 points in 1 dimension.
26 339 0.197142335309 Orthogonal union of 337 points in 25 dimensions and 2 points in 1 dimension.
26 340 0.197382082247 Orthogonal union of 338 points in 25 dimensions and 2 points in 1 dimension.
26 341 0.198310610666 Orthogonal union of 339 points in 25 dimensions and 2 points in 1 dimension.
26 342 0.199041896149 Orthogonal union of 340 points in 25 dimensions and 2 points in 1 dimension.
26 558 0.2 Orthogonal union of 552 points in 23 dimensions and 6 points in 3 dimensions.
5⁢x−1
26 559 0.200003594574 Orthogonal union of 557 points in 25 dimensions and 2 points in 1 dimension.
26 560 0.200010840602 Orthogonal union of 558 points in 25 dimensions and 2 points in 1 dimension.
26 561 0.200025254385 Orthogonal union of 559 points in 25 dimensions and 2 points in 1 dimension.
26 562 0.200092912683 Henry Cohn, 2026, needs more optimization.
26 563 0.200101611377 Henry Cohn, 2026, needs more optimization.
26 564 0.202204858202 Orthogonal union of 562 points in 25 dimensions and 2 points in 1 dimension.
26 566 0.202222732698 Orthogonal union of 564 points in 25 dimensions and 2 points in 1 dimension.
26 567 0.204375144191 Orthogonal union of 565 points in 25 dimensions and 2 points in 1 dimension.
26 568 0.207492029650 Orthogonal union of 566 points in 25 dimensions and 2 points in 1 dimension.
26 569 0.210344730128 Orthogonal union of 567 points in 25 dimensions and 2 points in 1 dimension.
26 570 0.212620049203 Orthogonal union of 568 points in 25 dimensions and 2 points in 1 dimension.
26 571 0.214736726592 Orthogonal union of 569 points in 25 dimensions and 2 points in 1 dimension.
26 572 0.216986257841 Orthogonal union of 570 points in 25 dimensions and 2 points in 1 dimension.
26 573 0.218502985141 Orthogonal union of 571 points in 25 dimensions and 2 points in 1 dimension.
26 574 0.220268177141 Orthogonal union of 572 points in 25 dimensions and 2 points in 1 dimension.
26 575 0.221864283043 Orthogonal union of 573 points in 25 dimensions and 2 points in 1 dimension.
26 576 0.222944294027 Orthogonal union of 574 points in 25 dimensions and 2 points in 1 dimension.
26 577 0.224230577379 Orthogonal union of 575 points in 25 dimensions and 2 points in 1 dimension.
26 578 0.225327526755 Orthogonal union of 576 points in 25 dimensions and 2 points in 1 dimension.
26 579 0.226837055978 Orthogonal union of 577 points in 25 dimensions and 2 points in 1 dimension.
26 580 0.227891986078 Orthogonal union of 578 points in 25 dimensions and 2 points in 1 dimension.
26 581 0.228517196126 Orthogonal union of 579 points in 25 dimensions and 2 points in 1 dimension.
26 582 0.229079598080 Orthogonal union of 580 points in 25 dimensions and 2 points in 1 dimension.
26 583 0.229882834554 Orthogonal union of 581 points in 25 dimensions and 2 points in 1 dimension.
26 584 0.230043706448 Orthogonal union of 582 points in 25 dimensions and 2 points in 1 dimension.
26 585 0.231345472037 Orthogonal union of 583 points in 25 dimensions and 2 points in 1 dimension.
26 586 0.232207827229 Orthogonal union of 584 points in 25 dimensions and 2 points in 1 dimension.
26 587 0.232479376363 Orthogonal union of 585 points in 25 dimensions and 2 points in 1 dimension.
26 588 0.233414506364 Orthogonal union of 586 points in 25 dimensions and 2 points in 1 dimension.
26 589 0.234451135578 Orthogonal union of 587 points in 25 dimensions and 2 points in 1 dimension.
26 590 0.234601320648 Orthogonal union of 588 points in 25 dimensions and 2 points in 1 dimension.
26 591 0.235304794842 Orthogonal union of 589 points in 25 dimensions and 2 points in 1 dimension.
26 592 0.235970793319 Orthogonal union of 590 points in 25 dimensions and 2 points in 1 dimension.
26 593 0.236630001220 Orthogonal union of 591 points in 25 dimensions and 2 points in 1 dimension.
26 594 0.237526725225 Orthogonal union of 592 points in 25 dimensions and 2 points in 1 dimension.
26 595 0.237671063124 Orthogonal union of 593 points in 25 dimensions and 2 points in 1 dimension.
26 596 0.238058235503 Orthogonal union of 594 points in 25 dimensions and 2 points in 1 dimension.
26 598 0.238580363055 Henry Cohn, 2026, needs more optimization.
26 602 0.239199552312 Henry Cohn, 2026, needs more optimization.
26 606 0.240347986335 Henry Cohn, 2026, needs more optimization.
26 610 0.241904503314 Henry Cohn, 2026, needs more optimization.
26 614 0.243428508628 Henry Cohn, 2026, needs more optimization.
26 618 0.244651756744 Henry Cohn, 2026, needs more optimization.
26 622 0.245756914472 Henry Cohn, 2026, needs more optimization.
26 626 0.246665595465 Henry Cohn, 2026, needs more optimization.
26 630 0.247357185475 Henry Cohn, 2026, needs more optimization.
26 634 0.248058881023 Henry Cohn, 2026, needs more optimization.
26 635 0.248714826490 Henry Cohn, 2026, needs more optimization.
26 638 0.248714826533 Henry Cohn, 2026, needs more optimization.
26 644 0.248901834813 Henry Cohn, 2026, needs more optimization.
26 675 0.248901834814 Henry Cohn, 2026, needs more optimization.
26 676 0.248935348986 Henry Cohn, 2026, needs more optimization.
26 677 0.248961748222 Henry Cohn, 2026, needs more optimization.
26 679 0.248992765238 Henry Cohn, 2026, needs more optimization.
26 680 0.248992765243 Henry Cohn, 2026, needs more optimization.
26 682 0.249042754918 Henry Cohn, 2026, needs more optimization.
26 683 0.249137735572 Henry Cohn, 2026, needs more optimization.
26 684 0.249237501568 Henry Cohn, 2026, needs more optimization.
26 685 0.249287763634 Henry Cohn, 2026, needs more optimization.
26 686 0.249300057763 Henry Cohn, 2026, needs more optimization.
26 687 0.249353909827 Henry Cohn, 2026, needs more optimization.
26 690 0.249378400273 Henry Cohn, 2026, needs more optimization.
26 691 0.249465780630 Henry Cohn, 2026, needs more optimization.
26 693 0.249520463405 Henry Cohn, 2026, needs more optimization.
26 694 0.249568655261 Henry Cohn, 2026, needs more optimization.
26 696 0.249568740696 Henry Cohn, 2026, needs more optimization.
26 697 0.249578866772 Henry Cohn, 2026, needs more optimization.
26 698 0.249678301398 Henry Cohn, 2026, needs more optimization.
26 699 0.249769494184 Henry Cohn, 2026, needs more optimization.
26 700 0.249795167525 Henry Cohn, 2026, needs more optimization.
26 701 0.249811587767 Henry Cohn, 2026, needs more optimization.
26 707 0.249895880546 Henry Cohn, 2026, needs more optimization.
26 708 0.249920287627 Henry Cohn, 2026, needs more optimization.
26 709 0.249922947727 Henry Cohn, 2026, needs more optimization.
26 710 0.249939436011 Henry Cohn, 2026, needs more optimization.
26 711 0.249941255336 Henry Cohn, 2026, needs more optimization.
26 712 0.249942680972 Henry Cohn, 2026, needs more optimization.
26 713 0.249956399823 Henry Cohn, 2026, needs more optimization.
26 714 0.249966952907 Henry Cohn, 2026, needs more optimization.
26 715 0.249966952908 Henry Cohn, 2026, needs more optimization.
26 716 0.249975319241 Henry Cohn, 2026, needs more optimization.
26 717 0.249981170222 Henry Cohn, 2026, needs more optimization.
26 723 0.249983667894 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
26 913 0.250046355276 Henry Cohn, 2026, needs more optimization.
26 914 0.250051754907 Henry Cohn, 2026, needs more optimization.
26 915 0.250057995122 Henry Cohn, 2026, needs more optimization.
26 917 0.250060920463 Henry Cohn, 2026, needs more optimization.
26 919 0.250078002603 Henry Cohn, 2026, needs more optimization.
26 920 0.250078052920 Henry Cohn, 2026, needs more optimization.
26 921 0.250080369764 Henry Cohn, 2026, needs more optimization.
26 922 0.250083025662 Henry Cohn, 2026, needs more optimization.
26 923 0.250097698431 Henry Cohn, 2026, needs more optimization.
26 924 0.250103148778 Henry Cohn, 2026, needs more optimization.
26 927 0.250117385527 Henry Cohn, 2026, needs more optimization.
26 928 0.250119874664 Henry Cohn, 2026, needs more optimization.
26 930 0.250184364358 Henry Cohn, 2026, needs more optimization.
26 932 0.250226029270 Henry Cohn, 2026, needs more optimization.
26 933 0.250263785397 Henry Cohn, 2026, needs more optimization.
26 934 0.250272199915 Henry Cohn, 2026, needs more optimization.
26 935 0.250345712835 Henry Cohn, 2026, needs more optimization.
26 936 0.250440191181 Henry Cohn, 2026, needs more optimization.
26 937 0.250484027890 Henry Cohn, 2026, needs more optimization.
26 938 0.250518418424 Henry Cohn, 2026, needs more optimization.
26 939 0.250630661054 Henry Cohn, 2026, needs more optimization.
26 940 0.250726069263 Henry Cohn, 2026, needs more optimization.
26 941 0.250989835025 Henry Cohn, 2026, needs more optimization.
26 942 0.251265333524 Henry Cohn, 2026, needs more optimization.
26 943 0.251610026071 Henry Cohn, 2026, needs more optimization.
26 944 0.251725946172 Henry Cohn, 2026, needs more optimization.
26 945 0.252019138646 Henry Cohn, 2026, needs more optimization.
26 946 0.252309108421 Henry Cohn, 2026, needs more optimization.
26 947 0.252581770553 Henry Cohn, 2026, needs more optimization.
26 948 0.252945728232 Henry Cohn, 2026, needs more optimization.
26 949 0.253454083787 Henry Cohn, 2026, needs more optimization.
26 950 0.253742212802 Henry Cohn, 2026, needs more optimization.
26 951 0.253945336917 Henry Cohn, 2026, needs more optimization.
26 952 0.254491192248 Henry Cohn, 2026, needs more optimization.
26 953 0.254824580369 Henry Cohn, 2026, needs more optimization.
26 954 0.255021751441 Henry Cohn, 2026, needs more optimization.
26 955 0.255389004129 Henry Cohn, 2026, needs more optimization.
26 956 0.256047515411 Henry Cohn, 2026, needs more optimization.
26 957 0.256375948278 Henry Cohn, 2026, needs more optimization.
26 958 0.256596728548 Henry Cohn, 2026, needs more optimization.
26 959 0.256882468687 Henry Cohn, 2026, needs more optimization.
26 960 0.257406422955 Henry Cohn, 2026, needs more optimization.
26 961 0.257718517152 Henry Cohn, 2026, needs more optimization.
26 962 0.258001301963 Henry Cohn, 2026, needs more optimization.
26 963 0.258501355147 Henry Cohn, 2026, needs more optimization.
26 964 0.258896772444 Henry Cohn, 2026, needs more optimization.
26 965 0.259169752041 Henry Cohn, 2026, needs more optimization.
26 966 0.259431971968 Henry Cohn, 2026, needs more optimization.
26 967 0.260010414330 Henry Cohn, 2026, needs more optimization.
26 968 0.260181049638 Henry Cohn, 2026, needs more optimization.
26 969 0.261007215523 Henry Cohn, 2026, needs more optimization.
26 970 0.261114148970 Henry Cohn, 2026, needs more optimization.
26 971 0.261484984724 Henry Cohn, 2026, needs more optimization.
26 972 0.261764032122 Henry Cohn, 2026, needs more optimization.
26 973 0.261826427503 Henry Cohn, 2026, needs more optimization.
26 974 0.262151867523 Henry Cohn, 2026, needs more optimization.
26 975 0.262540546816 Henry Cohn, 2026, needs more optimization.
26 976 0.263200481174 Henry Cohn, 2026, needs more optimization.
26 977 0.263814734277 Henry Cohn, 2026, needs more optimization.
26 978 0.264216115103 Henry Cohn, 2026, needs more optimization.
26 979 0.264392603894 Henry Cohn, 2026, needs more optimization.
26 980 0.264706559331 Henry Cohn, 2026, needs more optimization.
26 981 0.265218781393 Henry Cohn, 2026, needs more optimization.
26 982 0.265747362577 Henry Cohn, 2026, needs more optimization.
26 983 0.265978714579 Henry Cohn, 2026, needs more optimization.
26 984 0.266115491341 Henry Cohn, 2026, needs more optimization.
26 985 0.266447092359 Henry Cohn, 2026, needs more optimization.
26 986 0.266781625132 Henry Cohn, 2026, needs more optimization.
26 987 0.267126940942 Henry Cohn, 2026, needs more optimization.
26 988 0.267464050002 Henry Cohn, 2026, needs more optimization.
26 989 0.267700552717 Henry Cohn, 2026, needs more optimization.
26 990 0.267789875326 Henry Cohn, 2026, needs more optimization.
26 991 0.267893634826 Henry Cohn, 2026, needs more optimization.
26 992 0.268286734067 Henry Cohn, 2026, needs more optimization.
26 993 0.268406948087 Henry Cohn, 2026, needs more optimization.
26 994 0.268560455383 Henry Cohn, 2026, needs more optimization.
26 995 0.268699784584 Henry Cohn, 2026, needs more optimization.
26 996 0.268798469361 Henry Cohn, 2026, needs more optimization.
26 997 0.269147135778 Henry Cohn, 2026, needs more optimization.
26 998 0.269635123967 Henry Cohn, 2026, needs more optimization.
26 999 0.269886066635 Henry Cohn, 2026, needs more optimization.
26 1000 0.270026229118 Henry Cohn, 2026, needs more optimization.
26 1002 0.270607726975 Henry Cohn, 2026, needs more optimization.
26 1003 0.270963873594 Henry Cohn, 2026, needs more optimization.
26 1004 0.271130216561 Henry Cohn, 2026, needs more optimization.
26 1005 0.271480818860 Henry Cohn, 2026, needs more optimization.
26 1007 0.271739105478 Henry Cohn, 2026, needs more optimization.
26 1008 0.271752485788 Henry Cohn, 2026, needs more optimization.
26 1009 0.271902777785 Henry Cohn, 2026, needs more optimization.
26 1010 0.272300003831 Henry Cohn, 2026, needs more optimization.
26 1011 0.272485107857 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 57 0.043679995742 Henry Cohn, 2024.
27 58 0.044384904811 Henry Cohn, 2026, needs more optimization.
27 59 0.044780194273 Henry Cohn, 2026, needs more optimization.
27 60 0.045477973897 Henry Cohn, 2024, needs more optimization.
27 61 0.045484387668 Henry Cohn, 2024, needs more optimization.
27 62 0.046198040189 Henry Cohn, 2025.
27 63 0.047653467851 Ilmari Vahteristo, 2026.
27 64 0.050114573766 Ilmari Vahteristo, 2026.
27 65 0.054278580194 Ilmari Vahteristo, 2026.
27 66 0.056204126432 Ilmari Vahteristo, 2026.
27 67 0.058358887805 Ilmari Vahteristo, 2026.
27 68 0.060151159919 Ilmari Vahteristo, 2026.
27 69 0.061647483492 Ilmari Vahteristo, 2026.
27 70 0.062922671894 Henry Cohn, 2026, needs more optimization.
27 71 0.064107549690 Henry Cohn, 2026, needs more optimization.
27 72 0.064938703566 Henry Cohn, 2026, needs more optimization.
27 73 0.065805542879 Henry Cohn, 2026, needs more optimization.
27 74 0.066383272572 Henry Cohn, 2026, needs more optimization.
27 75 0.068128633261 Henry Cohn, 2026, needs more optimization.
27 76 0.070113017465 Henry Cohn, 2026, needs more optimization.
27 77 0.072327221285 Henry Cohn, 2026, needs more optimization.
27 78 0.074624795276 Henry Cohn, 2026, needs more optimization.
27 79 0.075331327438 Henry Cohn, 2026, needs more optimization.
27 80 0.076122276909 Henry Cohn, 2026, needs more optimization.
27 81 0.076640303489 Henry Cohn, 2026, needs more optimization.
27 82 0.076894452895 Henry Cohn, 2026, needs more optimization.
27 83 0.076959451300 Henry Cohn, 2026, needs more optimization.
27 84 0.077059848801 Henry Cohn, 2026, needs more optimization.
27 85 0.077375337867 Henry Cohn, 2026, needs more optimization.
27 86 0.077717939174 Henry Cohn, 2026, needs more optimization.
27 87 0.078411575925 Henry Cohn, 2026, needs more optimization.
27 88 0.078632181819 Henry Cohn, 2026, needs more optimization.
27 89 0.079858580896 Henry Cohn, 2026, needs more optimization.
27 90 0.079979745309 Henry Cohn, 2026, needs more optimization.
27 91 0.080292300100 Henry Cohn, 2026, needs more optimization.
27 92 0.080556966106 Henry Cohn, 2026, needs more optimization.
27 94 0.080683331300 Henry Cohn, 2026, needs more optimization.
27 95 0.080685560105 Henry Cohn, 2026, needs more optimization.
27 96 0.080686096040 Henry Cohn, 2026, needs more optimization.
27 98 0.080688337004 Henry Cohn, 2026, needs more optimization.
27 99 0.084251301208 Henry Cohn, 2026, needs more optimization.
27 100 0.087396843564 Henry Cohn, 2026, needs more optimization.
27 101 0.088632575068 Henry Cohn, 2026, needs more optimization.
27 102 0.089495202410 Henry Cohn, 2026, needs more optimization.
27 103 0.089993255161 Henry Cohn, 2026, needs more optimization.
27 104 0.090258381350 Henry Cohn, 2026, needs more optimization.
27 105 0.090493853844 Henry Cohn, 2026, needs more optimization.
27 106 0.090611631487 Henry Cohn, 2026, needs more optimization.
27 107 0.090667795332 Henry Cohn, 2026, needs more optimization.
27 108 0.090773036350 Henry Cohn, 2026, needs more optimization.
27 109 0.090814020245 Henry Cohn, 2026, needs more optimization.
27 110 0.090815383917 Henry Cohn, 2026, needs more optimization.
27 111 0.090861513599 Henry Cohn, 2026, needs more optimization.
27 112 0.090895235257 Henry Cohn, 2026, needs more optimization.
27 113 0.090909413844 Henry Cohn, 2026, needs more optimization.
27 114 0.091267483454 Henry Cohn, 2026, needs more optimization.
27 115 0.093244658984 Henry Cohn, 2026, needs more optimization.
27 116 0.095893983551 Henry Cohn, 2026, needs more optimization.
27 117 0.098845836777 Henry Cohn, 2026, needs more optimization.
27 118 0.101376692034 Henry Cohn, 2026, needs more optimization.
27 120 0.103122419447 Henry Cohn, 2026, needs more optimization.
27 121 0.103125332235 Orthogonal union of 119 points in 26 dimensions and 2 points in 1 dimension.
191⁢x2−10⁢x−1
27 123 0.103125332798 Henry Cohn, 2026, needs more optimization.
27 125 0.103125336303 Henry Cohn, 2026, needs more optimization.
27 126 0.104794837256 Henry Cohn, 2026, needs more optimization.
27 127 0.106317064180 Henry Cohn, 2026, needs more optimization.
27 128 0.106622060495 Henry Cohn, 2026, needs more optimization.
27 129 0.107240835781 Henry Cohn, 2026, needs more optimization.
27 130 0.107692441329 Henry Cohn, 2026, needs more optimization.
27 131 0.108500531865 Henry Cohn, 2026, needs more optimization.
27 132 0.109625680083 Henry Cohn, 2026, needs more optimization.
27 133 0.110569214799 Henry Cohn, 2026, needs more optimization.
27 134 0.111032493963 Henry Cohn, 2026, needs more optimization.
27 135 0.111034840474 Henry Cohn, 2026, needs more optimization.
27 136 0.111797816791 Henry Cohn, 2026, needs more optimization.
27 137 0.113456485785 Henry Cohn, 2026, needs more optimization.
27 138 0.114536637641 Henry Cohn, 2026, needs more optimization.
27 139 0.114844732298 Henry Cohn, 2026, needs more optimization.
27 140 0.116042872472 Henry Cohn, 2026, needs more optimization.
27 141 0.116318048118 Henry Cohn, 2026, needs more optimization.
27 142 0.117570362120 Henry Cohn, 2026, needs more optimization.
27 143 0.120407933403 Henry Cohn, 2026, needs more optimization.
27 144 0.121001772639 Henry Cohn, 2026, needs more optimization.
27 145 0.123136128169 Henry Cohn, 2026, needs more optimization.
27 146 0.125388443993 Henry Cohn, 2026, needs more optimization.
27 147 0.127237443108 Henry Cohn, 2026, needs more optimization.
27 148 0.129864440947 Henry Cohn, 2026, needs more optimization.
27 149 0.131294176852 Henry Cohn, 2026, needs more optimization.
27 150 0.131466516067 Henry Cohn, 2026, needs more optimization.
27 151 0.132806808217 Henry Cohn, 2026, needs more optimization.
27 152 0.132866170261 Henry Cohn, 2026, needs more optimization.
27 153 0.132933263726 Henry Cohn, 2026, needs more optimization.
27 154 0.132988279042 Henry Cohn, 2026, needs more optimization.
27 155 0.133180973332 Henry Cohn, 2026, needs more optimization.
27 156 0.133234201816 Henry Cohn, 2026, needs more optimization.
27 157 0.133259876548 Henry Cohn, 2026, needs more optimization.
27 160 0.133281675069 Henry Cohn, 2026, needs more optimization.
27 161 0.133306800091 Henry Cohn, 2026, needs more optimization.
27 162 0.133328342255 Henry Cohn, 2026, needs more optimization.
27 163 0.133332016249 Henry Cohn, 2026, needs more optimization.
27 164 0.133500761754 Henry Cohn, 2026, needs more optimization.
27 166 0.135091594904 Henry Cohn, 2026, needs more optimization.
27 167 0.135116296886 Henry Cohn, 2026, needs more optimization.
27 168 0.135150499509 Henry Cohn, 2026, needs more optimization.
27 169 0.135342983092 Henry Cohn, 2026, needs more optimization.
27 170 0.135944002630 Henry Cohn, 2026, needs more optimization.
27 171 0.136384005468 Henry Cohn, 2026, needs more optimization.
27 172 0.137281177808 Henry Cohn, 2026, needs more optimization.
27 173 0.138904481193 Henry Cohn, 2026, needs more optimization.
27 174 0.139555738549 Henry Cohn, 2026, needs more optimization.
27 175 0.140952152391 Henry Cohn, 2026, needs more optimization.
27 177 0.142310280058 Henry Cohn, 2026, needs more optimization.
27 179 0.142477464630 Henry Cohn, 2026, needs more optimization.
27 180 0.142533324153 Henry Cohn, 2026, needs more optimization.
27 181 0.142570880766 Henry Cohn, 2026, needs more optimization.
27 183 0.142588299534 Henry Cohn, 2026, needs more optimization.
27 184 0.142715432218 Henry Cohn, 2026, needs more optimization.
27 185 0.142731394289 Henry Cohn, 2026, needs more optimization.
27 187 0.142770904266 Henry Cohn, 2026, needs more optimization.
27 190 0.142801324990 Henry Cohn, 2026, needs more optimization.
27 191 0.142841964586 Henry Cohn, 2026, needs more optimization.
27 192 0.142974740216 Henry Cohn, 2026, needs more optimization.
27 193 0.142979721029 Henry Cohn, 2026, needs more optimization.
27 194 0.143908234802 Henry Cohn, 2026, needs more optimization.
27 195 0.144426448557 Henry Cohn, 2026, needs more optimization.
27 196 0.146036588998 Henry Cohn, 2026, needs more optimization.
27 197 0.146650328936 Henry Cohn, 2026, needs more optimization.
27 198 0.147562525499 Henry Cohn, 2026, needs more optimization.
27 199 0.148384094301 Henry Cohn, 2026, needs more optimization.
27 200 0.148964106509 Henry Cohn, 2026, needs more optimization.
27 201 0.149750034631 Henry Cohn, 2026, needs more optimization.
27 202 0.150200413591 Henry Cohn, 2026, needs more optimization.
27 203 0.150857763187 Henry Cohn, 2026, needs more optimization.
27 204 0.151142255731 Henry Cohn, 2026, needs more optimization.
27 205 0.151181567093 Henry Cohn, 2026, needs more optimization.
27 206 0.152076278665 Henry Cohn, 2026, needs more optimization.
27 207 0.152627136700 Henry Cohn, 2026, needs more optimization.
27 208 0.153623117561 Henry Cohn, 2026, needs more optimization.
27 209 0.153816990269 Henry Cohn, 2026, needs more optimization.
27 210 0.154297963992 Henry Cohn, 2026, needs more optimization.
27 211 0.154781149177 Henry Cohn, 2026, needs more optimization.
27 212 0.155022717761 Henry Cohn, 2026, needs more optimization.
27 213 0.155204237398 Henry Cohn, 2026, needs more optimization.
27 214 0.155646656222 Henry Cohn, 2026, needs more optimization.
27 215 0.157311087467 Henry Cohn, 2026, needs more optimization.
27 216 0.157505010338 Henry Cohn, 2026, needs more optimization.
27 217 0.157993625051 Henry Cohn, 2026, needs more optimization.
27 218 0.158832153121 Henry Cohn, 2026, needs more optimization.
27 219 0.159309906388 Henry Cohn, 2026, needs more optimization.
27 220 0.159917439765 Henry Cohn, 2026, needs more optimization.
27 221 0.160631293261 Henry Cohn, 2026, needs more optimization.
27 223 0.161451197703 Henry Cohn, 2026, needs more optimization.
27 224 0.161585332738 Henry Cohn, 2026, needs more optimization.
27 225 0.161608785875 Henry Cohn, 2026, needs more optimization.
27 227 0.161610985581 Henry Cohn, 2026, needs more optimization.
27 230 0.161669445660 Henry Cohn, 2026, needs more optimization.
27 231 0.161810810640 Henry Cohn, 2026, needs more optimization.
27 232 0.161817972035 Henry Cohn, 2026, needs more optimization.
27 234 0.161827786628 Henry Cohn, 2026, needs more optimization.
27 235 0.161842192267 Henry Cohn, 2026, needs more optimization.
27 236 0.161914914189 Henry Cohn, 2026, needs more optimization.
27 237 0.161916549194 Henry Cohn, 2026, needs more optimization.
27 238 0.161919136554 Henry Cohn, 2026, needs more optimization.
27 239 0.161924078600 Henry Cohn, 2026, needs more optimization.
27 241 0.161924787392 Henry Cohn, 2026, needs more optimization.
27 242 0.161948379813 Henry Cohn, 2026, needs more optimization.
27 243 0.162249930333 Henry Cohn, 2026, needs more optimization.
27 244 0.162278814997 Henry Cohn, 2026, needs more optimization.
27 245 0.162454846995 Henry Cohn, 2026, needs more optimization.
27 246 0.162563983251 Henry Cohn, 2026, needs more optimization.
27 247 0.162693340716 Henry Cohn, 2026, needs more optimization.
27 248 0.162750973195 Henry Cohn, 2026, needs more optimization.
27 249 0.162915306064 Henry Cohn, 2026, needs more optimization.
27 250 0.163025751303 Henry Cohn, 2026, needs more optimization.
27 251 0.163661922454 Henry Cohn, 2026, needs more optimization.
27 252 0.163925810632 Henry Cohn, 2026, needs more optimization.
27 253 0.164157351933 Henry Cohn, 2026, needs more optimization.
27 254 0.164351064642 Henry Cohn, 2026, needs more optimization.
27 255 0.164518422426 Henry Cohn, 2026, needs more optimization.
27 256 0.164658062786 Henry Cohn, 2026, needs more optimization.
27 257 0.165009210593 Henry Cohn, 2026, needs more optimization.
27 258 0.165054449534 Henry Cohn, 2026, needs more optimization.
27 259 0.165400510633 Henry Cohn, 2026, needs more optimization.
27 260 0.165521717377 Henry Cohn, 2026, needs more optimization.
27 261 0.165755681377 Henry Cohn, 2026, needs more optimization.
27 262 0.165815600836 Henry Cohn, 2026, needs more optimization.
27 263 0.166054823929 Henry Cohn, 2026, needs more optimization.
27 264 0.166164957674 Henry Cohn, 2026, needs more optimization.
27 265 0.166346251022 Henry Cohn, 2026, needs more optimization.
27 266 0.166391044334 Henry Cohn, 2026, needs more optimization.
27 267 0.166483414122 Henry Cohn, 2026, needs more optimization.
27 268 0.166505903824 Henry Cohn, 2026, needs more optimization.
27 269 0.166522201536 Henry Cohn, 2026, needs more optimization.
27 270 0.166562908371 Henry Cohn, 2026, needs more optimization.
27 272 0.166573714396 Henry Cohn, 2026, needs more optimization.
27 273 0.166640041370 Henry Cohn, 2026, needs more optimization.
27 274 0.166657070678 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
27 291 0.166672027288 Henry Cohn, 2026, needs more optimization.
27 292 0.166673229182 Henry Cohn, 2026, needs more optimization.
27 295 0.166674552060 Henry Cohn, 2026, needs more optimization.
27 296 0.166674786954 Henry Cohn, 2026, needs more optimization.
27 297 0.166681434880 Henry Cohn, 2026, needs more optimization.
27 299 0.166686188122 Henry Cohn, 2026, needs more optimization.
27 300 0.166696298850 Henry Cohn, 2026, needs more optimization.
27 301 0.166799257665 Henry Cohn, 2026, needs more optimization.
27 302 0.170818468627 Orthogonal union of 300 points in 26 dimensions and 2 points in 1 dimension.
27 303 0.171964316023 Orthogonal union of 301 points in 26 dimensions and 2 points in 1 dimension.
27 319 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 6 points in 3 dimensions.
11⁢x−2
27 320 0.184915496078 Orthogonal union of 314 points in 24 dimensions and 6 points in 3 dimensions.
27 336 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 6 points in 3 dimensions.
31⁢x−6
27 343 0.193549910392 Henry Cohn, 2026, needs more optimization.
27 344 0.193550638256 Henry Cohn, 2026, needs more optimization.
27 345 0.193552755251 Henry Cohn, 2026, needs more optimization.
27 346 0.193557604838 Henry Cohn, 2026, needs more optimization.
27 349 0.193576397709 Henry Cohn, 2026, needs more optimization.
27 350 0.193601068636 Henry Cohn, 2026, needs more optimization.
27 351 0.193815246094 Henry Cohn, 2026, needs more optimization.
27 352 0.193853051880 Henry Cohn, 2026, needs more optimization.
27 353 0.194729014138 Henry Cohn, 2026, needs more optimization.
27 354 0.194739934636 Henry Cohn, 2026, needs more optimization.
27 355 0.194908466941 Henry Cohn, 2026, needs more optimization.
27 356 0.195385293071 Henry Cohn, 2026, needs more optimization.
27 357 0.195606076090 Henry Cohn, 2026, needs more optimization.
27 358 0.195810642033 Henry Cohn, 2026, needs more optimization.
27 359 0.196064725305 Henry Cohn, 2026, needs more optimization.
27 360 0.196194963092 Henry Cohn, 2026, needs more optimization.
27 361 0.196394857824 Henry Cohn, 2026, needs more optimization.
27 362 0.196835218063 Henry Cohn, 2026, needs more optimization.
27 363 0.197373329586 Henry Cohn, 2026, needs more optimization.
27 364 0.197972411287 Henry Cohn, 2026, needs more optimization.
27 365 0.198194078298 Henry Cohn, 2026, needs more optimization.
27 366 0.198617123903 Henry Cohn, 2026, needs more optimization.
27 367 0.199017756464 Henry Cohn, 2026, needs more optimization.
27 368 0.199336475356 Henry Cohn, 2026, needs more optimization.
27 369 0.199488428072 Henry Cohn, 2026, needs more optimization.
27 370 0.199572761227 Henry Cohn, 2026, needs more optimization.
27 371 0.199836934896 Henry Cohn, 2026, needs more optimization.
27 372 0.199836934897 Henry Cohn, 2026, needs more optimization.
27 373 0.199840532607 Henry Cohn, 2026, needs more optimization.
27 374 0.199923361743 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 0.200025254385 Orthogonal union of 559 points in 25 dimensions and 4 points in 2 dimensions.
27 564 0.200071739851 Henry Cohn, 2025, needs more optimization.
27 566 0.200076155705 Henry Cohn, 2025, needs more optimization.
27 568 0.200135182099 Henry Cohn, 2026, needs more optimization.
27 569 0.204375144191 Orthogonal union of 565 points in 25 dimensions and 4 points in 2 dimensions.
27 570 0.207492029650 Orthogonal union of 566 points in 25 dimensions and 4 points in 2 dimensions.
27 571 0.210344730128 Orthogonal union of 567 points in 25 dimensions and 4 points in 2 dimensions.
27 572 0.212620049203 Orthogonal union of 568 points in 25 dimensions and 4 points in 2 dimensions.
27 573 0.214736726592 Orthogonal union of 569 points in 25 dimensions and 4 points in 2 dimensions.
27 574 0.216986257841 Orthogonal union of 570 points in 25 dimensions and 4 points in 2 dimensions.
27 575 0.218502985141 Henry Cohn, 2026, needs more optimization.
27 576 0.220268177141 Orthogonal union of 572 points in 25 dimensions and 4 points in 2 dimensions.
27 577 0.221864283043 Orthogonal union of 573 points in 25 dimensions and 4 points in 2 dimensions.
27 578 0.222944294027 Orthogonal union of 574 points in 25 dimensions and 4 points in 2 dimensions.
27 579 0.224230577379 Orthogonal union of 575 points in 25 dimensions and 4 points in 2 dimensions.
27 580 0.225327526755 Orthogonal union of 576 points in 25 dimensions and 4 points in 2 dimensions.
27 581 0.226837055978 Orthogonal union of 577 points in 25 dimensions and 4 points in 2 dimensions.
27 582 0.227891986078 Orthogonal union of 578 points in 25 dimensions and 4 points in 2 dimensions.
27 583 0.228517196126 Orthogonal union of 579 points in 25 dimensions and 4 points in 2 dimensions.
27 584 0.229079598080 Orthogonal union of 580 points in 25 dimensions and 4 points in 2 dimensions.
27 585 0.229882834554 Orthogonal union of 581 points in 25 dimensions and 4 points in 2 dimensions.
27 586 0.230043706448 Orthogonal union of 582 points in 25 dimensions and 4 points in 2 dimensions.
27 587 0.231345472037 Orthogonal union of 583 points in 25 dimensions and 4 points in 2 dimensions.
27 588 0.232207827229 Orthogonal union of 584 points in 25 dimensions and 4 points in 2 dimensions.
27 589 0.232479376363 Orthogonal union of 585 points in 25 dimensions and 4 points in 2 dimensions.
27 590 0.233414506364 Orthogonal union of 586 points in 25 dimensions and 4 points in 2 dimensions.
27 591 0.234451135578 Orthogonal union of 587 points in 25 dimensions and 4 points in 2 dimensions.
27 592 0.234601320648 Orthogonal union of 588 points in 25 dimensions and 4 points in 2 dimensions.
27 593 0.235304794842 Orthogonal union of 589 points in 25 dimensions and 4 points in 2 dimensions.
27 594 0.235970793319 Orthogonal union of 590 points in 25 dimensions and 4 points in 2 dimensions.
27 595 0.236630001220 Orthogonal union of 591 points in 25 dimensions and 4 points in 2 dimensions.
27 596 0.237526725225 Orthogonal union of 592 points in 25 dimensions and 4 points in 2 dimensions.
27 597 0.237671063124 Orthogonal union of 593 points in 25 dimensions and 4 points in 2 dimensions.
27 598 0.238058235503 Orthogonal union of 594 points in 25 dimensions and 4 points in 2 dimensions.
27 602 0.238151490905 Henry Cohn, 2026, needs more optimization.
27 606 0.238174171959 Henry Cohn, 2026, needs more optimization.
27 610 0.238220872289 Henry Cohn, 2026, needs more optimization.
27 614 0.238329901415 Henry Cohn, 2026, needs more optimization.
27 618 0.238532697917 Henry Cohn, 2026, needs more optimization.
27 622 0.239084078461 Henry Cohn, 2026, needs more optimization.
27 626 0.240102535925 Henry Cohn, 2026, needs more optimization.
27 630 0.241358812394 Henry Cohn, 2026, needs more optimization.
27 634 0.242594432858 Henry Cohn, 2026, needs more optimization.
27 638 0.243831565826 Henry Cohn, 2026, needs more optimization.
27 642 0.244872620175 Henry Cohn, 2026, needs more optimization.
27 646 0.245772796248 Henry Cohn, 2026, needs more optimization.
27 650 0.246466192069 Henry Cohn, 2026, needs more optimization.
27 694 0.246684744996 Henry Cohn, 2026, needs more optimization.
27 695 0.246685816578 Henry Cohn, 2026, needs more optimization.
27 696 0.246700029016 Henry Cohn, 2026, needs more optimization.
27 697 0.246790396031 Henry Cohn, 2026, needs more optimization.
27 698 0.246815307977 Henry Cohn, 2026, needs more optimization.
27 701 0.246952142463 Henry Cohn, 2026, needs more optimization.
27 702 0.246984696932 Henry Cohn, 2026, needs more optimization.
27 703 0.247102940611 Henry Cohn, 2026, needs more optimization.
27 704 0.247218502510 Henry Cohn, 2026, needs more optimization.
27 705 0.247230707629 Henry Cohn, 2026, needs more optimization.
27 706 0.247358977487 Henry Cohn, 2026, needs more optimization.
27 707 0.247489855139 Henry Cohn, 2026, needs more optimization.
27 708 0.247622921785 Henry Cohn, 2026, needs more optimization.
27 709 0.247688868613 Henry Cohn, 2026, needs more optimization.
27 710 0.247789938139 Henry Cohn, 2026, needs more optimization.
27 711 0.247963187538 Henry Cohn, 2026, needs more optimization.
27 712 0.248081709114 Henry Cohn, 2026, needs more optimization.
27 713 0.248157835289 Henry Cohn, 2026, needs more optimization.
27 714 0.248223338146 Henry Cohn, 2026, needs more optimization.
27 715 0.248307566366 Henry Cohn, 2026, needs more optimization.
27 716 0.248408090853 Henry Cohn, 2026, needs more optimization.
27 717 0.248463139710 Henry Cohn, 2026, needs more optimization.
27 718 0.248533752348 Henry Cohn, 2026, needs more optimization.
27 719 0.248571931797 Henry Cohn, 2026, needs more optimization.
27 720 0.248572837404 Henry Cohn, 2026, needs more optimization.
27 721 0.248592764453 Henry Cohn, 2026, needs more optimization.
27 722 0.248726590660 Henry Cohn, 2026, needs more optimization.
27 724 0.248810840428 Henry Cohn, 2026, needs more optimization.
27 725 0.248817293524 Henry Cohn, 2026, needs more optimization.
27 726 0.248853025677 Henry Cohn, 2026, needs more optimization.
27 727 0.248891168282 Henry Cohn, 2026, needs more optimization.
27 728 0.248918985293 Henry Cohn, 2026, needs more optimization.
27 729 0.248949541174 Henry Cohn, 2026, needs more optimization.
27 730 0.248983037310 Henry Cohn, 2026, needs more optimization.
27 731 0.249050630557 Henry Cohn, 2026, needs more optimization.
27 732 0.249126896300 Henry Cohn, 2026, needs more optimization.
27 735 0.249242205772 Henry Cohn, 2026, needs more optimization.
27 736 0.249307906438 Henry Cohn, 2026, needs more optimization.
27 737 0.249376604234 Henry Cohn, 2026, needs more optimization.
27 738 0.249426011837 Henry Cohn, 2026, needs more optimization.
27 739 0.249432637492 Henry Cohn, 2026, needs more optimization.
27 740 0.249525463989 Henry Cohn, 2026, needs more optimization.
27 741 0.249549204752 Henry Cohn, 2026, needs more optimization.
27 742 0.249581565222 Henry Cohn, 2026, needs more optimization.
27 743 0.249611832505 Henry Cohn, 2026, needs more optimization.
27 744 0.249634575361 Henry Cohn, 2026, needs more optimization.
27 746 0.249702535539 Henry Cohn, 2026, needs more optimization.
27 747 0.249743064488 Henry Cohn, 2026, needs more optimization.
27 748 0.249754659118 Henry Cohn, 2026, needs more optimization.
27 749 0.249778132962 Henry Cohn, 2026, needs more optimization.
27 750 0.249797262784 Henry Cohn, 2026, needs more optimization.
27 751 0.249810215581 Henry Cohn, 2026, needs more optimization.
27 752 0.249813063743 Henry Cohn, 2026, needs more optimization.
27 753 0.249831343142 Henry Cohn, 2026, needs more optimization.
27 755 0.249868252216 Henry Cohn, 2026, needs more optimization.
27 756 0.249878834551 Henry Cohn, 2026, needs more optimization.
27 758 0.249884931712 Henry Cohn, 2026, needs more optimization.
27 759 0.249916577426 Henry Cohn, 2026, needs more optimization.
27 760 0.249922653363 Henry Cohn, 2026, needs more optimization.
27 761 0.249934004934 Henry Cohn, 2026, needs more optimization.
27 762 0.249955331133 Henry Cohn, 2026, needs more optimization.
27 763 0.249965272544 Henry Cohn, 2026, needs more optimization.
27 764 0.249983889053 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
27 915 0.250046355276 Orthogonal union of 913 points in 26 dimensions and 2 points in 1 dimension.
27 916 0.250051754907 Orthogonal union of 914 points in 26 dimensions and 2 points in 1 dimension.
27 917 0.250057995122 Orthogonal union of 915 points in 26 dimensions and 2 points in 1 dimension.
27 919 0.250060920463 Orthogonal union of 917 points in 26 dimensions and 2 points in 1 dimension.
27 921 0.250078002603 Orthogonal union of 919 points in 26 dimensions and 2 points in 1 dimension.
27 922 0.250078052920 Orthogonal union of 920 points in 26 dimensions and 2 points in 1 dimension.
27 923 0.250080369764 Orthogonal union of 921 points in 26 dimensions and 2 points in 1 dimension.
27 924 0.250083025662 Orthogonal union of 922 points in 26 dimensions and 2 points in 1 dimension.
27 925 0.250097698431 Orthogonal union of 923 points in 26 dimensions and 2 points in 1 dimension.
27 926 0.250103148778 Orthogonal union of 924 points in 26 dimensions and 2 points in 1 dimension.
27 929 0.250117385527 Orthogonal union of 927 points in 26 dimensions and 2 points in 1 dimension.
27 930 0.250119874664 Orthogonal union of 928 points in 26 dimensions and 2 points in 1 dimension.
27 932 0.250184364358 Orthogonal union of 930 points in 26 dimensions and 2 points in 1 dimension.
27 934 0.250226029270 Orthogonal union of 932 points in 26 dimensions and 2 points in 1 dimension.
27 935 0.250263785397 Orthogonal union of 933 points in 26 dimensions and 2 points in 1 dimension.
27 936 0.250272199915 Orthogonal union of 934 points in 26 dimensions and 2 points in 1 dimension.
27 937 0.250345712835 Orthogonal union of 935 points in 26 dimensions and 2 points in 1 dimension.
27 938 0.250440191181 Orthogonal union of 936 points in 26 dimensions and 2 points in 1 dimension.
27 939 0.250484027890 Orthogonal union of 937 points in 26 dimensions and 2 points in 1 dimension.
27 940 0.250518418424 Orthogonal union of 938 points in 26 dimensions and 2 points in 1 dimension.
27 941 0.250630661054 Orthogonal union of 939 points in 26 dimensions and 2 points in 1 dimension.
27 942 0.250726069263 Orthogonal union of 940 points in 26 dimensions and 2 points in 1 dimension.
27 943 0.250989835025 Orthogonal union of 941 points in 26 dimensions and 2 points in 1 dimension.
27 944 0.251265333524 Orthogonal union of 942 points in 26 dimensions and 2 points in 1 dimension.
27 945 0.251610026071 Orthogonal union of 943 points in 26 dimensions and 2 points in 1 dimension.
27 946 0.251725946172 Orthogonal union of 944 points in 26 dimensions and 2 points in 1 dimension.
27 947 0.252019138646 Orthogonal union of 945 points in 26 dimensions and 2 points in 1 dimension.
27 948 0.252309108421 Orthogonal union of 946 points in 26 dimensions and 2 points in 1 dimension.
27 949 0.252581770553 Orthogonal union of 947 points in 26 dimensions and 2 points in 1 dimension.
27 950 0.252945728232 Orthogonal union of 948 points in 26 dimensions and 2 points in 1 dimension.
27 951 0.253454083787 Orthogonal union of 949 points in 26 dimensions and 2 points in 1 dimension.
27 952 0.253742212802 Orthogonal union of 950 points in 26 dimensions and 2 points in 1 dimension.
27 953 0.253945336917 Henry Cohn, 2026, needs more optimization.
27 954 0.254491192248 Henry Cohn, 2026, needs more optimization.
27 955 0.254824580369 Orthogonal union of 953 points in 26 dimensions and 2 points in 1 dimension.
27 956 0.255021751441 Orthogonal union of 954 points in 26 dimensions and 2 points in 1 dimension.
27 957 0.255389004129 Orthogonal union of 955 points in 26 dimensions and 2 points in 1 dimension.
27 958 0.256047515411 Orthogonal union of 956 points in 26 dimensions and 2 points in 1 dimension.
27 959 0.256375948278 Orthogonal union of 957 points in 26 dimensions and 2 points in 1 dimension.
27 960 0.256596728548 Orthogonal union of 958 points in 26 dimensions and 2 points in 1 dimension.
27 961 0.256882468687 Orthogonal union of 959 points in 26 dimensions and 2 points in 1 dimension.
27 962 0.257406422955 Orthogonal union of 960 points in 26 dimensions and 2 points in 1 dimension.
27 963 0.257718517152 Orthogonal union of 961 points in 26 dimensions and 2 points in 1 dimension.
27 964 0.258001301963 Orthogonal union of 962 points in 26 dimensions and 2 points in 1 dimension.
27 965 0.258501355147 Orthogonal union of 963 points in 26 dimensions and 2 points in 1 dimension.
27 966 0.258896772444 Orthogonal union of 964 points in 26 dimensions and 2 points in 1 dimension.
27 967 0.259169752041 Orthogonal union of 965 points in 26 dimensions and 2 points in 1 dimension.
27 968 0.259431971968 Orthogonal union of 966 points in 26 dimensions and 2 points in 1 dimension.
27 969 0.260010414330 Orthogonal union of 967 points in 26 dimensions and 2 points in 1 dimension.
27 970 0.260181049638 Orthogonal union of 968 points in 26 dimensions and 2 points in 1 dimension.
27 971 0.261007215523 Orthogonal union of 969 points in 26 dimensions and 2 points in 1 dimension.
27 972 0.261114148970 Orthogonal union of 970 points in 26 dimensions and 2 points in 1 dimension.
27 973 0.261484984724 Orthogonal union of 971 points in 26 dimensions and 2 points in 1 dimension.
27 974 0.261764032122 Orthogonal union of 972 points in 26 dimensions and 2 points in 1 dimension.
27 975 0.261826427503 Orthogonal union of 973 points in 26 dimensions and 2 points in 1 dimension.
27 976 0.262151867523 Orthogonal union of 974 points in 26 dimensions and 2 points in 1 dimension.
27 977 0.262540546816 Orthogonal union of 975 points in 26 dimensions and 2 points in 1 dimension.
27 978 0.263200481174 Orthogonal union of 976 points in 26 dimensions and 2 points in 1 dimension.
27 979 0.263814734277 Orthogonal union of 977 points in 26 dimensions and 2 points in 1 dimension.
27 980 0.264216115103 Orthogonal union of 978 points in 26 dimensions and 2 points in 1 dimension.
27 981 0.264392603894 Orthogonal union of 979 points in 26 dimensions and 2 points in 1 dimension.
27 982 0.264706559331 Orthogonal union of 980 points in 26 dimensions and 2 points in 1 dimension.
27 983 0.265218781393 Orthogonal union of 981 points in 26 dimensions and 2 points in 1 dimension.
27 984 0.265747362577 Orthogonal union of 982 points in 26 dimensions and 2 points in 1 dimension.
27 985 0.265978714579 Orthogonal union of 983 points in 26 dimensions and 2 points in 1 dimension.
27 986 0.266115491341 Orthogonal union of 984 points in 26 dimensions and 2 points in 1 dimension.
27 987 0.266447092359 Orthogonal union of 985 points in 26 dimensions and 2 points in 1 dimension.
27 988 0.266781625132 Orthogonal union of 986 points in 26 dimensions and 2 points in 1 dimension.
27 989 0.267126940942 Orthogonal union of 987 points in 26 dimensions and 2 points in 1 dimension.
27 990 0.267464050002 Orthogonal union of 988 points in 26 dimensions and 2 points in 1 dimension.
27 991 0.267700552717 Orthogonal union of 989 points in 26 dimensions and 2 points in 1 dimension.
27 992 0.267789875326 Orthogonal union of 990 points in 26 dimensions and 2 points in 1 dimension.
27 993 0.267893634826 Orthogonal union of 991 points in 26 dimensions and 2 points in 1 dimension.
27 994 0.268286734067 Orthogonal union of 992 points in 26 dimensions and 2 points in 1 dimension.
27 995 0.268406948087 Orthogonal union of 993 points in 26 dimensions and 2 points in 1 dimension.
27 996 0.268560455383 Orthogonal union of 994 points in 26 dimensions and 2 points in 1 dimension.
27 997 0.268699784584 Orthogonal union of 995 points in 26 dimensions and 2 points in 1 dimension.
27 998 0.268798469361 Orthogonal union of 996 points in 26 dimensions and 2 points in 1 dimension.
27 999 0.269147135778 Orthogonal union of 997 points in 26 dimensions and 2 points in 1 dimension.
27 1000 0.269635123967 Orthogonal union of 998 points in 26 dimensions and 2 points in 1 dimension.
27 1001 0.269886066635 Orthogonal union of 999 points in 26 dimensions and 2 points in 1 dimension.
27 1002 0.270026229118 Orthogonal union of 1000 points in 26 dimensions and 2 points in 1 dimension.
27 1004 0.270607726975 Orthogonal union of 1002 points in 26 dimensions and 2 points in 1 dimension.
27 1005 0.270963873594 Orthogonal union of 1003 points in 26 dimensions and 2 points in 1 dimension.
27 1006 0.271130216561 Orthogonal union of 1004 points in 26 dimensions and 2 points in 1 dimension.
27 1007 0.271480818860 Orthogonal union of 1005 points in 26 dimensions and 2 points in 1 dimension.
27 1009 0.271739105478 Orthogonal union of 1007 points in 26 dimensions and 2 points in 1 dimension.
27 1010 0.271752485788 Orthogonal union of 1008 points in 26 dimensions and 2 points in 1 dimension.
27 1011 0.271902777785 Orthogonal union of 1009 points in 26 dimensions and 2 points in 1 dimension.
27 1012 0.272300003831 Orthogonal union of 1010 points in 26 dimensions and 2 points in 1 dimension.
27 1013 0.272485107857 Orthogonal union of 1011 points in 26 dimensions and 2 points in 1 dimension.
27 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
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 Henry Cohn, 2025.
30⁢x−1
28 59 0.042123224895 Henry Cohn, 2026, needs more optimization.
28 60 0.044207083554 Henry Cohn, 2026, needs more optimization.
28 61 0.044427604359 Henry Cohn, 2024, needs more optimization.
28 62 0.044625901428 Henry Cohn, 2024, needs more optimization.
28 63 0.045182176447 Henry Cohn, 2025.
28 64 0.045901657151 Henry Cohn, 2024, needs more optimization.
28 65 0.046144688998 Ilmari Vahteristo, 2026.
28 66 0.047459655819 Henry Cohn, 2026, needs more optimization.
28 67 0.052297853928 Henry Cohn, 2026, needs more optimization.
28 68 0.054257777968 Henry Cohn, 2026, needs more optimization.
28 69 0.055902314494 Ilmari Vahteristo, 2026.
28 70 0.058160876266 Henry Cohn, 2026, needs more optimization.
28 71 0.059630876408 Ilmari Vahteristo, 2026.
28 72 0.061425534645 Ilmari Vahteristo, 2026.
28 73 0.063231032281 Ilmari Vahteristo, 2026.
28 74 0.064088659114 Henry Cohn, 2026, needs more optimization.
28 75 0.064460441711 Henry Cohn, 2026, needs more optimization.
28 76 0.065107470611 Henry Cohn, 2026, needs more optimization.
28 77 0.065929172700 Henry Cohn, 2026, needs more optimization.
28 78 0.067571589868 Henry Cohn, 2026, needs more optimization.
28 79 0.069484887075 Henry Cohn, 2026, needs more optimization.
28 80 0.070912616840 Henry Cohn, 2026, needs more optimization.
28 81 0.072937949431 Henry Cohn, 2026, needs more optimization.
28 82 0.074536648447 Henry Cohn, 2026, needs more optimization.
28 83 0.075107286780 Henry Cohn, 2026, needs more optimization.
28 84 0.075994545746 Henry Cohn, 2026, needs more optimization.
28 85 0.076728639671 Henry Cohn, 2026, needs more optimization.
28 86 0.076884539205 Henry Cohn, 2026, needs more optimization.
28 87 0.076915260604 Henry Cohn, 2026, needs more optimization.
28 88 0.076926982972 Henry Cohn, 2026, needs more optimization.
28 89 0.077241411225 Henry Cohn, 2026, needs more optimization.
28 90 0.077537204186 Henry Cohn, 2026, needs more optimization.
28 91 0.078294914190 Henry Cohn, 2026, needs more optimization.
28 92 0.078682990685 Henry Cohn, 2026, needs more optimization.
28 93 0.079255326328 Henry Cohn, 2026, needs more optimization.
28 94 0.079399741202 Henry Cohn, 2026, needs more optimization.
28 95 0.079800755584 Henry Cohn, 2026, needs more optimization.
28 96 0.080121381462 Henry Cohn, 2026, needs more optimization.
28 97 0.080284248950 Henry Cohn, 2026, needs more optimization.
28 98 0.080499449614 Henry Cohn, 2026, needs more optimization.
28 99 0.080650684358 Henry Cohn, 2026, needs more optimization.
28 100 0.080687070828 Henry Cohn, 2026, needs more optimization.
28 101 0.080687266281 Henry Cohn, 2026, needs more optimization.
28 102 0.083360350094 Henry Cohn, 2026, needs more optimization.
28 103 0.083873264391 Henry Cohn, 2026, needs more optimization.
28 104 0.086800995039 Henry Cohn, 2026, needs more optimization.
28 105 0.087840861269 Henry Cohn, 2026, needs more optimization.
28 106 0.088357351815 Henry Cohn, 2026, needs more optimization.
28 107 0.089042600663 Henry Cohn, 2026, needs more optimization.
28 108 0.089298537653 Henry Cohn, 2026, needs more optimization.
28 109 0.089614249411 Henry Cohn, 2026, needs more optimization.
28 110 0.090176565566 Henry Cohn, 2026, needs more optimization.
28 111 0.090382410672 Henry Cohn, 2026, needs more optimization.
28 112 0.090398986837 Henry Cohn, 2026, needs more optimization.
28 113 0.090476452523 Henry Cohn, 2026, needs more optimization.
28 114 0.090596463104 Henry Cohn, 2026, needs more optimization.
28 115 0.090770852827 Henry Cohn, 2026, needs more optimization.
28 116 0.090884944236 Henry Cohn, 2026, needs more optimization.
28 117 0.090909736756 Henry Cohn, 2026, needs more optimization.
28 118 0.091675659728 Henry Cohn, 2026, needs more optimization.
28 119 0.094363233771 Henry Cohn, 2026, needs more optimization.
28 120 0.096255191733 Henry Cohn, 2026, needs more optimization.
28 121 0.098148937279 Henry Cohn, 2026, needs more optimization.
28 122 0.099654964286 Henry Cohn, 2026, needs more optimization.
28 123 0.101805947778 Henry Cohn, 2026, needs more optimization.
28 124 0.102878763691 Henry Cohn, 2026, needs more optimization.
28 125 0.103068782625 Henry Cohn, 2026, needs more optimization.
28 129 0.103114200786 Henry Cohn, 2026, needs more optimization.
28 130 0.103165192771 Henry Cohn, 2026, needs more optimization.
28 131 0.104419960229 Henry Cohn, 2026, needs more optimization.
28 132 0.105713309364 Henry Cohn, 2026, needs more optimization.
28 133 0.106279459263 Henry Cohn, 2026, needs more optimization.
28 134 0.108139525644 Henry Cohn, 2026, needs more optimization.
28 135 0.108634810438 Henry Cohn, 2026, needs more optimization.
28 136 0.109592328265 Henry Cohn, 2026, needs more optimization.
28 137 0.110291432201 Henry Cohn, 2026, needs more optimization.
28 138 0.110916127060 Henry Cohn, 2026, needs more optimization.
28 139 0.110935533256 Henry Cohn, 2026, needs more optimization.
28 140 0.111583613607 Henry Cohn, 2026, needs more optimization.
28 141 0.112429224658 Henry Cohn, 2026, needs more optimization.
28 142 0.113895832004 Henry Cohn, 2026, needs more optimization.
28 143 0.115284246218 Henry Cohn, 2026, needs more optimization.
28 144 0.116151767313 Henry Cohn, 2026, needs more optimization.
28 145 0.117183850175 Henry Cohn, 2026, needs more optimization.
28 146 0.117979608661 Henry Cohn, 2026, needs more optimization.
28 147 0.119198839866 Henry Cohn, 2026, needs more optimization.
28 148 0.120739405837 Henry Cohn, 2026, needs more optimization.
28 149 0.121669146845 Henry Cohn, 2026, needs more optimization.
28 150 0.122936589991 Henry Cohn, 2026, needs more optimization.
28 151 0.124444828254 Henry Cohn, 2026, needs more optimization.
28 152 0.125864134494 Henry Cohn, 2026, needs more optimization.
28 153 0.126664383231 Henry Cohn, 2026, needs more optimization.
28 154 0.127884687069 Henry Cohn, 2026, needs more optimization.
28 155 0.129192610893 Henry Cohn, 2026, needs more optimization.
28 156 0.131004770279 Henry Cohn, 2026, needs more optimization.
28 157 0.131490147907 Henry Cohn, 2026, needs more optimization.
28 158 0.131591590046 Henry Cohn, 2026, needs more optimization.
28 159 0.131926839997 Henry Cohn, 2026, needs more optimization.
28 160 0.132062786160 Henry Cohn, 2026, needs more optimization.
28 161 0.132297650228 Henry Cohn, 2026, needs more optimization.
28 162 0.132517743322 Henry Cohn, 2026, needs more optimization.
28 163 0.132722182838 Henry Cohn, 2026, needs more optimization.
28 164 0.132815247590 Henry Cohn, 2026, needs more optimization.
28 165 0.133021234764 Henry Cohn, 2026, needs more optimization.
28 166 0.133093972923 Henry Cohn, 2026, needs more optimization.
28 167 0.133200804972 Henry Cohn, 2026, needs more optimization.
28 168 0.133252804086 Henry Cohn, 2026, needs more optimization.
28 169 0.133307200648 Henry Cohn, 2026, needs more optimization.
28 170 0.133812055331 Henry Cohn, 2026, needs more optimization.
28 171 0.134701709174 Henry Cohn, 2026, needs more optimization.
28 172 0.134873519262 Henry Cohn, 2026, needs more optimization.
28 173 0.134937577808 Henry Cohn, 2026, needs more optimization.
28 174 0.135045063235 Henry Cohn, 2026, needs more optimization.
28 175 0.135072074922 Henry Cohn, 2026, needs more optimization.
28 176 0.135152495403 Henry Cohn, 2026, needs more optimization.
28 177 0.135601006083 Henry Cohn, 2026, needs more optimization.
28 178 0.135982070288 Henry Cohn, 2026, needs more optimization.
28 179 0.137069453176 Henry Cohn, 2026, needs more optimization.
28 180 0.137983723433 Henry Cohn, 2026, needs more optimization.
28 181 0.138863563567 Henry Cohn, 2026, needs more optimization.
28 182 0.139692826627 Henry Cohn, 2026, needs more optimization.
28 183 0.140545523088 Henry Cohn, 2026, needs more optimization.
28 184 0.142150458967 Henry Cohn, 2026, needs more optimization.
28 185 0.142185847151 Henry Cohn, 2026, needs more optimization.
28 186 0.142206487744 Henry Cohn, 2026, needs more optimization.
28 187 0.142215634073 Henry Cohn, 2026, needs more optimization.
28 188 0.142226861247 Henry Cohn, 2026, needs more optimization.
28 191 0.142278879891 Henry Cohn, 2026, needs more optimization.
28 193 0.142524101481 Henry Cohn, 2026, needs more optimization.
28 194 0.142565021022 Henry Cohn, 2026, needs more optimization.
28 195 0.142635255285 Henry Cohn, 2026, needs more optimization.
28 196 0.142728312258 Henry Cohn, 2026, needs more optimization.
28 197 0.142775219338 Henry Cohn, 2026, needs more optimization.
28 198 0.142822346217 Henry Cohn, 2026, needs more optimization.
28 199 0.142881415253 Henry Cohn, 2026, needs more optimization.
28 200 0.143371737297 Henry Cohn, 2026, needs more optimization.
28 201 0.143698799416 Henry Cohn, 2026, needs more optimization.
28 202 0.144188611857 Henry Cohn, 2026, needs more optimization.
28 203 0.145069379362 Henry Cohn, 2026, needs more optimization.
28 204 0.145915089778 Henry Cohn, 2026, needs more optimization.
28 205 0.146229579153 Henry Cohn, 2026, needs more optimization.
28 206 0.147132765558 Henry Cohn, 2026, needs more optimization.
28 207 0.147473270040 Henry Cohn, 2026, needs more optimization.
28 208 0.148537146917 Henry Cohn, 2026, needs more optimization.
28 209 0.148542972096 Henry Cohn, 2026, needs more optimization.
28 210 0.148581010416 Henry Cohn, 2026, needs more optimization.
28 211 0.148722857994 Henry Cohn, 2026, needs more optimization.
28 212 0.148854094656 Henry Cohn, 2026, needs more optimization.
28 213 0.148969973795 Henry Cohn, 2026, needs more optimization.
28 214 0.149194605674 Henry Cohn, 2026, needs more optimization.
28 215 0.149657552584 Henry Cohn, 2026, needs more optimization.
28 216 0.150543257110 Henry Cohn, 2026, needs more optimization.
28 217 0.151230206357 Henry Cohn, 2026, needs more optimization.
28 218 0.151397557275 Henry Cohn, 2026, needs more optimization.
28 219 0.151435250250 Henry Cohn, 2026, needs more optimization.
28 220 0.151774275772 Henry Cohn, 2026, needs more optimization.
28 221 0.152071550830 Henry Cohn, 2026, needs more optimization.
28 222 0.152188761521 Henry Cohn, 2026, needs more optimization.
28 223 0.152351469051 Henry Cohn, 2026, needs more optimization.
28 224 0.153522558072 Henry Cohn, 2026, needs more optimization.
28 225 0.154565732765 Henry Cohn, 2026, needs more optimization.
28 226 0.155343041020 Henry Cohn, 2026, needs more optimization.
28 227 0.155689011688 Henry Cohn, 2026, needs more optimization.
28 228 0.155956629848 Henry Cohn, 2026, needs more optimization.
28 229 0.156139285403 Henry Cohn, 2026, needs more optimization.
28 230 0.156365626379 Henry Cohn, 2026, needs more optimization.
28 231 0.156967065794 Henry Cohn, 2026, needs more optimization.
28 232 0.157325696716 Henry Cohn, 2026, needs more optimization.
28 233 0.157967046675 Henry Cohn, 2026, needs more optimization.
28 234 0.158810973842 Henry Cohn, 2026, needs more optimization.
28 235 0.158962213006 Henry Cohn, 2026, needs more optimization.
28 236 0.159603179152 Henry Cohn, 2026, needs more optimization.
28 237 0.159905147014 Henry Cohn, 2026, needs more optimization.
28 238 0.161492416581 Henry Cohn, 2026, needs more optimization.
28 239 0.161494365578 Henry Cohn, 2026, needs more optimization.
28 240 0.161533054934 Henry Cohn, 2026, needs more optimization.
28 241 0.161549815518 Henry Cohn, 2026, needs more optimization.
28 242 0.161597176768 Henry Cohn, 2026, needs more optimization.
28 243 0.161651226401 Henry Cohn, 2026, needs more optimization.
28 244 0.161665921739 Henry Cohn, 2026, needs more optimization.
28 245 0.161693828072 Henry Cohn, 2026, needs more optimization.
28 247 0.161731013986 Henry Cohn, 2026, needs more optimization.
28 248 0.161753478711 Henry Cohn, 2026, needs more optimization.
28 250 0.161801587313 Henry Cohn, 2026, needs more optimization.
28 251 0.161874507989 Henry Cohn, 2026, needs more optimization.
28 252 0.162039631218 Henry Cohn, 2026, needs more optimization.
28 253 0.162058282828 Henry Cohn, 2026, needs more optimization.
28 254 0.162142335094 Henry Cohn, 2026, needs more optimization.
28 255 0.162162308081 Henry Cohn, 2026, needs more optimization.
28 256 0.162592148589 Henry Cohn, 2026, needs more optimization.
28 257 0.162665553564 Henry Cohn, 2026, needs more optimization.
28 258 0.162871905288 Henry Cohn, 2026, needs more optimization.
28 259 0.163037246905 Henry Cohn, 2026, needs more optimization.
28 260 0.163404738621 Henry Cohn, 2026, needs more optimization.
28 261 0.163587791159 Henry Cohn, 2026, needs more optimization.
28 262 0.163954541597 Henry Cohn, 2026, needs more optimization.
28 263 0.164185740941 Henry Cohn, 2026, needs more optimization.
28 264 0.164360035142 Henry Cohn, 2026, needs more optimization.
28 265 0.164478913625 Henry Cohn, 2026, needs more optimization.
28 266 0.164673246665 Henry Cohn, 2026, needs more optimization.
28 267 0.164750156373 Henry Cohn, 2026, needs more optimization.
28 268 0.164862652756 Henry Cohn, 2026, needs more optimization.
28 269 0.165068326254 Henry Cohn, 2026, needs more optimization.
28 270 0.165098211976 Henry Cohn, 2026, needs more optimization.
28 271 0.165237584012 Henry Cohn, 2026, needs more optimization.
28 272 0.165388025678 Henry Cohn, 2026, needs more optimization.
28 273 0.165647692862 Henry Cohn, 2026, needs more optimization.
28 274 0.165708957558 Henry Cohn, 2026, needs more optimization.
28 275 0.165795984975 Henry Cohn, 2026, needs more optimization.
28 276 0.165976000200 Henry Cohn, 2026, needs more optimization.
28 277 0.166107838308 Henry Cohn, 2026, needs more optimization.
28 278 0.166267393697 Henry Cohn, 2026, needs more optimization.
28 279 0.166349377681 Henry Cohn, 2026, needs more optimization.
28 280 0.166357392094 Henry Cohn, 2026, needs more optimization.
28 281 0.166373033535 Henry Cohn, 2026, needs more optimization.
28 282 0.166397990170 Henry Cohn, 2026, needs more optimization.
28 283 0.166460052990 Henry Cohn, 2026, needs more optimization.
28 286 0.166470451772 Henry Cohn, 2026, needs more optimization.
28 287 0.166514145328 Henry Cohn, 2026, needs more optimization.
28 288 0.166532762200 Henry Cohn, 2026, needs more optimization.
28 289 0.166579406563 Henry Cohn, 2026, needs more optimization.
28 290 0.166604249118 Henry Cohn, 2026, needs more optimization.
28 291 0.166639743126 Henry Cohn, 2026, needs more optimization.
28 293 0.166652071652 Henry Cohn, 2026, needs more optimization.
28 294 0.166661905904 Henry Cohn, 2026, needs more optimization.
28 297 0.166664602186 Henry Cohn, 2026, needs more optimization.
28 298 0.166669540014 Henry Cohn, 2026, needs more optimization.
28 301 0.166671357086 Henry Cohn, 2026, needs more optimization.
28 302 0.166696298850 Orthogonal union of 300 points in 27 dimensions and 2 points in 1 dimension.
28 303 0.166799257665 Orthogonal union of 301 points in 27 dimensions and 2 points in 1 dimension.
28 304 0.170818468627 Orthogonal union of 300 points in 26 dimensions and 4 points in 2 dimensions.
28 305 0.171964316023 Orthogonal union of 301 points in 26 dimensions and 4 points in 2 dimensions.
28 306 0.179682601621 Henry Cohn, 2026, needs more optimization.
28 323 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 10 points in 4 dimensions.
11⁢x−2
28 324 0.184915496078 Orthogonal union of 314 points in 24 dimensions and 10 points in 4 dimensions.
28 326 0.190674770384 Henry Cohn, 2026, needs more optimization.
28 330 0.191141747941 Henry Cohn, 2026, needs more optimization.
28 334 0.191519289235 Henry Cohn, 2026, needs more optimization.
28 338 0.192042192413 Henry Cohn, 2026, needs more optimization.
28 342 0.192561925054 Henry Cohn, 2026, needs more optimization.
28 361 0.193107880848 Henry Cohn, 2026, needs more optimization.
28 362 0.193107880849 Henry Cohn, 2026, needs more optimization.
28 364 0.193273102693 Henry Cohn, 2026, needs more optimization.
28 365 0.193430286411 Henry Cohn, 2026, needs more optimization.
28 366 0.193468753933 Henry Cohn, 2026, needs more optimization.
28 367 0.193695378614 Henry Cohn, 2026, needs more optimization.
28 368 0.194056100256 Henry Cohn, 2026, needs more optimization.
28 369 0.194149649657 Henry Cohn, 2026, needs more optimization.
28 370 0.194366081625 Henry Cohn, 2026, needs more optimization.
28 371 0.194806409106 Henry Cohn, 2026, needs more optimization.
28 372 0.194919033660 Henry Cohn, 2026, needs more optimization.
28 373 0.195131963750 Henry Cohn, 2026, needs more optimization.
28 374 0.195551472227 Henry Cohn, 2026, needs more optimization.
28 375 0.195920115465 Henry Cohn, 2026, needs more optimization.
28 376 0.195930031233 Henry Cohn, 2026, needs more optimization.
28 378 0.196147956336 Henry Cohn, 2026, needs more optimization.
28 379 0.196299849938 Henry Cohn, 2026, needs more optimization.
28 380 0.196553594232 Henry Cohn, 2026, needs more optimization.
28 382 0.196621219842 Henry Cohn, 2026, needs more optimization.
28 383 0.197030012294 Henry Cohn, 2026, needs more optimization.
28 384 0.197217603987 Henry Cohn, 2026, needs more optimization.
28 385 0.197506654731 Henry Cohn, 2026, needs more optimization.
28 386 0.197507449401 Henry Cohn, 2026, needs more optimization.
28 387 0.197742737925 Henry Cohn, 2026, needs more optimization.
28 388 0.197889860761 Henry Cohn, 2026, needs more optimization.
28 390 0.198040743560 Henry Cohn, 2026, needs more optimization.
28 391 0.198417703040 Henry Cohn, 2026, needs more optimization.
28 393 0.198532674323 Henry Cohn, 2026, needs more optimization.
28 398 0.198647092193 Henry Cohn, 2026, needs more optimization.
28 399 0.198693826414 Henry Cohn, 2026, needs more optimization.
28 402 0.198810576072 Henry Cohn, 2026, needs more optimization.
28 404 0.198996536954 Henry Cohn, 2026, needs more optimization.
28 405 0.199008975929 Henry Cohn, 2026, needs more optimization.
28 406 0.199226649491 Henry Cohn, 2026, needs more optimization.
28 407 0.199253900704 Henry Cohn, 2026, needs more optimization.
28 412 0.199270158717 Henry Cohn, 2026, needs more optimization.
28 413 0.199307923111 Henry Cohn, 2026, needs more optimization.
28 414 0.199416958797 Henry Cohn, 2026, needs more optimization.
28 416 0.199500614244 Henry Cohn, 2026, needs more optimization.
28 418 0.199600796826 Henry Cohn, 2026, needs more optimization.
28 419 0.199600796827 Henry Cohn, 2026, needs more optimization.
28 422 0.199626876843 Henry Cohn, 2026, needs more optimization.
28 423 0.199639549115 Henry Cohn, 2026, needs more optimization.
28 424 0.199645024159 Henry Cohn, 2026, needs more optimization.
28 426 0.199744108800 Henry Cohn, 2026, needs more optimization.
28 427 0.199764409660 Henry Cohn, 2026, needs more optimization.
28 432 0.199770241912 Henry Cohn, 2026, needs more optimization.
28 433 0.199796125221 Henry Cohn, 2026, needs more optimization.
28 434 0.199824512214 Henry Cohn, 2026, needs more optimization.
28 444 0.199834492294 Henry Cohn, 2026, needs more optimization.
28 445 0.199855845514 Henry Cohn, 2026, needs more optimization.
28 446 0.199861398320 Henry Cohn, 2026, needs more optimization.
28 447 0.199880061985 Henry Cohn, 2026, needs more optimization.
28 448 0.199889742404 Henry Cohn, 2026, needs more optimization.
28 449 0.199907047043 Henry Cohn, 2026, needs more optimization.
28 450 0.199927391720 Henry Cohn, 2026, needs more optimization.
28 451 0.199940798371 Henry Cohn, 2026, needs more optimization.
28 452 0.199940798378 Henry Cohn, 2026, needs more optimization.
28 453 0.199943345675 Henry Cohn, 2026, needs more optimization.
28 454 0.199969565410 Henry Cohn, 2026, needs more optimization.
28 457 0.199977643450 Henry Cohn, 2026, needs more optimization.
28 460 0.199977692418 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
28 570 0.200113880481 Henry Cohn, 2026, needs more optimization.
28 571 0.204375144191 Orthogonal union of 565 points in 25 dimensions and 6 points in 3 dimensions.
28 572 0.207492029650 Orthogonal union of 566 points in 25 dimensions and 6 points in 3 dimensions.
28 573 0.210138312731 Orthogonal union of 566 points in 25 dimensions and 7 points in 3 dimensions.
3⁢x3−9⁢x2−3⁢x+1
28 574 0.210344730128 Orthogonal union of 567 points in 25 dimensions and 7 points in 3 dimensions.
28 575 0.212620049203 Orthogonal union of 568 points in 25 dimensions and 7 points in 3 dimensions.
28 576 0.214736726592 Orthogonal union of 569 points in 25 dimensions and 7 points in 3 dimensions.
28 577 0.216986257841 Orthogonal union of 570 points in 25 dimensions and 7 points in 3 dimensions.
28 578 0.218502985141 Orthogonal union of 571 points in 25 dimensions and 7 points in 3 dimensions.
28 579 0.220268177141 Orthogonal union of 572 points in 25 dimensions and 7 points in 3 dimensions.
28 580 0.221864283043 Orthogonal union of 573 points in 25 dimensions and 7 points in 3 dimensions.
28 581 0.222944294027 Orthogonal union of 574 points in 25 dimensions and 7 points in 3 dimensions.
28 582 0.224230577379 Orthogonal union of 575 points in 25 dimensions and 7 points in 3 dimensions.
28 583 0.225327526755 Orthogonal union of 576 points in 25 dimensions and 7 points in 3 dimensions.
28 584 0.226837055978 Orthogonal union of 577 points in 25 dimensions and 7 points in 3 dimensions.
28 585 0.227891986078 Orthogonal union of 578 points in 25 dimensions and 7 points in 3 dimensions.
28 586 0.228517196126 Orthogonal union of 579 points in 25 dimensions and 7 points in 3 dimensions.
28 587 0.229079598080 Orthogonal union of 580 points in 25 dimensions and 7 points in 3 dimensions.
28 588 0.229882834554 Orthogonal union of 581 points in 25 dimensions and 7 points in 3 dimensions.
28 589 0.230043706448 Orthogonal union of 582 points in 25 dimensions and 7 points in 3 dimensions.
28 590 0.231345472037 Orthogonal union of 583 points in 25 dimensions and 7 points in 3 dimensions.
28 591 0.232207827229 Orthogonal union of 584 points in 25 dimensions and 7 points in 3 dimensions.
28 592 0.232479376363 Orthogonal union of 585 points in 25 dimensions and 7 points in 3 dimensions.
28 593 0.233414506364 Orthogonal union of 586 points in 25 dimensions and 7 points in 3 dimensions.
28 594 0.234451135578 Orthogonal union of 587 points in 25 dimensions and 7 points in 3 dimensions.
28 595 0.234601320648 Orthogonal union of 588 points in 25 dimensions and 7 points in 3 dimensions.
28 596 0.235304794842 Orthogonal union of 589 points in 25 dimensions and 7 points in 3 dimensions.
28 597 0.235970793319 Orthogonal union of 590 points in 25 dimensions and 7 points in 3 dimensions.
28 598 0.236630001220 Orthogonal union of 591 points in 25 dimensions and 7 points in 3 dimensions.
28 599 0.237526725225 Orthogonal union of 592 points in 25 dimensions and 7 points in 3 dimensions.
28 600 0.237671063124 Orthogonal union of 593 points in 25 dimensions and 7 points in 3 dimensions.
28 602 0.238052789456 Henry Cohn, 2026, needs more optimization.
28 606 0.238071482182 Henry Cohn, 2026, needs more optimization.
28 610 0.238090788354 Henry Cohn, 2026, needs more optimization.
28 614 0.238113406545 Henry Cohn, 2026, needs more optimization.
28 618 0.238145216565 Henry Cohn, 2026, needs more optimization.
28 622 0.238200908420 Henry Cohn, 2026, needs more optimization.
28 626 0.238310571052 Henry Cohn, 2026, needs more optimization.
28 630 0.238633709579 Henry Cohn, 2026, needs more optimization.
28 634 0.239543540704 Henry Cohn, 2026, needs more optimization.
28 636 0.241508043760 Henry Cohn, 2026, needs more optimization.
28 638 0.242106374983 Henry Cohn, 2026, needs more optimization.
28 642 0.243034668397 Henry Cohn, 2026, needs more optimization.
28 644 0.243924637617 Henry Cohn, 2026, needs more optimization.
28 646 0.243924638252 Henry Cohn, 2026, needs more optimization.
28 650 0.244551208487 Henry Cohn, 2026, needs more optimization.
28 654 0.245010789094 Henry Cohn, 2026, needs more optimization.
28 658 0.245451833013 Henry Cohn, 2026, needs more optimization.
28 662 0.245869790263 Henry Cohn, 2026, needs more optimization.
28 666 0.246193830607 Henry Cohn, 2026, needs more optimization.
28 670 0.246546529490 Henry Cohn, 2026, needs more optimization.
28 696 0.246684744996 Orthogonal union of 694 points in 27 dimensions and 2 points in 1 dimension.
28 697 0.246685816578 Orthogonal union of 695 points in 27 dimensions and 2 points in 1 dimension.
28 698 0.246700029016 Orthogonal union of 696 points in 27 dimensions and 2 points in 1 dimension.
28 699 0.246790396031 Orthogonal union of 697 points in 27 dimensions and 2 points in 1 dimension.
28 700 0.246815307977 Orthogonal union of 698 points in 27 dimensions and 2 points in 1 dimension.
28 703 0.246952142463 Orthogonal union of 701 points in 27 dimensions and 2 points in 1 dimension.
28 704 0.246984696932 Orthogonal union of 702 points in 27 dimensions and 2 points in 1 dimension.
28 705 0.247102940611 Orthogonal union of 703 points in 27 dimensions and 2 points in 1 dimension.
28 706 0.247218502510 Orthogonal union of 704 points in 27 dimensions and 2 points in 1 dimension.
28 707 0.247230707629 Orthogonal union of 705 points in 27 dimensions and 2 points in 1 dimension.
28 708 0.247358977487 Orthogonal union of 706 points in 27 dimensions and 2 points in 1 dimension.
28 709 0.247489855139 Orthogonal union of 707 points in 27 dimensions and 2 points in 1 dimension.
28 710 0.247622921785 Orthogonal union of 708 points in 27 dimensions and 2 points in 1 dimension.
28 711 0.247688868613 Orthogonal union of 709 points in 27 dimensions and 2 points in 1 dimension.
28 712 0.247789938139 Orthogonal union of 710 points in 27 dimensions and 2 points in 1 dimension.
28 713 0.247963187538 Orthogonal union of 711 points in 27 dimensions and 2 points in 1 dimension.
28 714 0.248081709114 Orthogonal union of 712 points in 27 dimensions and 2 points in 1 dimension.
28 731 0.248138557111 Henry Cohn, 2026, needs more optimization.
28 732 0.248138557112 Henry Cohn, 2026, needs more optimization.
28 733 0.248175410594 Henry Cohn, 2026, needs more optimization.
28 734 0.248176318526 Henry Cohn, 2026, needs more optimization.
28 735 0.248211406930 Henry Cohn, 2026, needs more optimization.
28 736 0.248230539667 Henry Cohn, 2026, needs more optimization.
28 737 0.248244394913 Henry Cohn, 2026, needs more optimization.
28 738 0.248261013864 Henry Cohn, 2026, needs more optimization.
28 739 0.248297041059 Henry Cohn, 2026, needs more optimization.
28 740 0.248305032703 Henry Cohn, 2026, needs more optimization.
28 741 0.248385249843 Henry Cohn, 2026, needs more optimization.
28 742 0.248409215399 Henry Cohn, 2026, needs more optimization.
28 743 0.248466386939 Henry Cohn, 2026, needs more optimization.
28 744 0.248522142586 Henry Cohn, 2026, needs more optimization.
28 746 0.248581018491 Henry Cohn, 2026, needs more optimization.
28 747 0.248628150913 Henry Cohn, 2026, needs more optimization.
28 748 0.248633261299 Henry Cohn, 2026, needs more optimization.
28 749 0.248652410237 Henry Cohn, 2026, needs more optimization.
28 750 0.248703383612 Henry Cohn, 2026, needs more optimization.
28 751 0.248729848896 Henry Cohn, 2026, needs more optimization.
28 752 0.248798747581 Henry Cohn, 2026, needs more optimization.
28 753 0.248825987209 Henry Cohn, 2026, needs more optimization.
28 755 0.248888348712 Henry Cohn, 2026, needs more optimization.
28 756 0.248943550346 Henry Cohn, 2026, needs more optimization.
28 757 0.248990170270 Henry Cohn, 2026, needs more optimization.
28 758 0.249047417253 Henry Cohn, 2026, needs more optimization.
28 759 0.249071257261 Henry Cohn, 2026, needs more optimization.
28 760 0.249083548517 Henry Cohn, 2026, needs more optimization.
28 761 0.249128706305 Henry Cohn, 2026, needs more optimization.
28 762 0.249147355543 Henry Cohn, 2026, needs more optimization.
28 763 0.249159205575 Henry Cohn, 2026, needs more optimization.
28 764 0.249196579266 Henry Cohn, 2026, needs more optimization.
28 765 0.249225102550 Henry Cohn, 2026, needs more optimization.
28 766 0.249268914729 Henry Cohn, 2026, needs more optimization.
28 767 0.249283280428 Henry Cohn, 2026, needs more optimization.
28 768 0.249305082519 Henry Cohn, 2026, needs more optimization.
28 769 0.249324064809 Henry Cohn, 2026, needs more optimization.
28 770 0.249329733101 Henry Cohn, 2026, needs more optimization.
28 771 0.249358463071 Henry Cohn, 2026, needs more optimization.
28 773 0.249386514808 Henry Cohn, 2026, needs more optimization.
28 774 0.249402617118 Henry Cohn, 2026, needs more optimization.
28 775 0.249431386140 Henry Cohn, 2026, needs more optimization.
28 776 0.249464276089 Henry Cohn, 2026, needs more optimization.
28 777 0.249494402577 Henry Cohn, 2026, needs more optimization.
28 778 0.249525666187 Henry Cohn, 2026, needs more optimization.
28 779 0.249545377096 Henry Cohn, 2026, needs more optimization.
28 780 0.249553712585 Henry Cohn, 2026, needs more optimization.
28 781 0.249575751114 Henry Cohn, 2026, needs more optimization.
28 782 0.249583984969 Henry Cohn, 2026, needs more optimization.
28 783 0.249596256226 Henry Cohn, 2026, needs more optimization.
28 784 0.249608882110 Henry Cohn, 2026, needs more optimization.
28 785 0.249624833010 Henry Cohn, 2026, needs more optimization.
28 786 0.249651573913 Henry Cohn, 2026, needs more optimization.
28 787 0.249680871508 Henry Cohn, 2026, needs more optimization.
28 788 0.249685620341 Henry Cohn, 2026, needs more optimization.
28 789 0.249705264375 Henry Cohn, 2026, needs more optimization.
28 790 0.249726788299 Henry Cohn, 2026, needs more optimization.
28 791 0.249743472472 Henry Cohn, 2026, needs more optimization.
28 792 0.249743709491 Henry Cohn, 2026, needs more optimization.
28 793 0.249765126150 Henry Cohn, 2026, needs more optimization.
28 799 0.249787894470 Henry Cohn, 2026, needs more optimization.
28 801 0.249792105509 Henry Cohn, 2026, needs more optimization.
28 802 0.249794397658 Henry Cohn, 2026, needs more optimization.
28 803 0.249810649214 Henry Cohn, 2026, needs more optimization.
28 804 0.249819646033 Henry Cohn, 2026, needs more optimization.
28 805 0.249838987911 Henry Cohn, 2026, needs more optimization.
28 806 0.249846007864 Henry Cohn, 2026, needs more optimization.
28 808 0.249849141117 Henry Cohn, 2026, needs more optimization.
28 810 0.249869349549 Henry Cohn, 2026, needs more optimization.
28 811 0.249882852813 Henry Cohn, 2026, needs more optimization.
28 812 0.249886643610 Henry Cohn, 2026, needs more optimization.
28 813 0.249890532675 Henry Cohn, 2026, needs more optimization.
28 816 0.249925560149 Henry Cohn, 2026, needs more optimization.
28 817 0.249947877686 Henry Cohn, 2026, needs more optimization.
28 820 0.249968402765 Henry Cohn, 2026, needs more optimization.
28 821 0.249973197588 Henry Cohn, 2026, needs more optimization.
28 822 0.249978720343 Henry Cohn, 2026, needs more optimization.
28 823 0.249993421912 Henry Cohn, 2026, needs more optimization.
28 824 0.249995980853 Henry Cohn, 2026, needs more optimization.
28 825 0.249998720572 Henry Cohn, 2026, needs more optimization.
28 976 0.25 Henry Cohn, 2026.
4⁢x−1
28 977 0.250024248965 Henry Cohn, 2026, needs more optimization.
28 978 0.250025658596 Henry Cohn, 2026, needs more optimization.
28 979 0.250035791685 Henry Cohn, 2026, needs more optimization.
28 980 0.250038995579 Henry Cohn, 2026, needs more optimization.
28 981 0.250044974668 Henry Cohn, 2026, needs more optimization.
28 982 0.250045856531 Henry Cohn, 2026, needs more optimization.
28 984 0.250053881403 Henry Cohn, 2026, needs more optimization.
28 985 0.250062489010 Henry Cohn, 2026, needs more optimization.
28 986 0.250062814470 Henry Cohn, 2026, needs more optimization.
28 987 0.250067178715 Henry Cohn, 2026, needs more optimization.
28 989 0.250078896727 Henry Cohn, 2026, needs more optimization.
28 991 0.250083588040 Henry Cohn, 2026, needs more optimization.
28 993 0.250090299409 Henry Cohn, 2026, needs more optimization.
28 994 0.250119877695 Henry Cohn, 2026, needs more optimization.
28 995 0.250146208769 Henry Cohn, 2026, needs more optimization.
28 997 0.250174971682 Henry Cohn, 2026, needs more optimization.
28 998 0.250188533594 Henry Cohn, 2026, needs more optimization.
28 1002 0.250207873663 Henry Cohn, 2026, needs more optimization.
28 1004 0.250224113381 Henry Cohn, 2026, needs more optimization.
28 1005 0.250271756223 Henry Cohn, 2026, needs more optimization.
28 1006 0.250355533485 Henry Cohn, 2026, needs more optimization.
28 1007 0.250492703909 Henry Cohn, 2026, needs more optimization.
28 1008 0.250556650226 Henry Cohn, 2026, needs more optimization.
28 1009 0.250649183935 Henry Cohn, 2026, needs more optimization.
28 1010 0.250829126356 Henry Cohn, 2026, needs more optimization.
28 1011 0.251011141085 Henry Cohn, 2026, needs more optimization.
28 1012 0.251210508745 Henry Cohn, 2026, needs more optimization.
28 1013 0.251444377413 Henry Cohn, 2026, needs more optimization.
28 1014 0.251656820376 Henry Cohn, 2026, needs more optimization.
28 1015 0.251818239135 Henry Cohn, 2026, needs more optimization.
28 1016 0.252008986578 Henry Cohn, 2026, needs more optimization.
28 1017 0.252293705511 Henry Cohn, 2026, needs more optimization.
28 1018 0.252596418108 Henry Cohn, 2026, needs more optimization.
28 1019 0.252819793214 Henry Cohn, 2026, needs more optimization.
28 1020 0.253020846429 Henry Cohn, 2026, needs more optimization.
28 1021 0.253164780370 Henry Cohn, 2026, needs more optimization.
28 1022 0.253256808194 Henry Cohn, 2026, needs more optimization.
28 1023 0.253588872453 Henry Cohn, 2026, needs more optimization.
28 1024 0.253916577770 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 0.040901763915 Ilmari Vahteristo, 2026.
29 62 0.043321650170 Henry Cohn, 2026, needs more optimization.
29 63 0.043679238443 Henry Cohn, 2026, needs more optimization.
29 64 0.044358604455 Henry Cohn, 2026, needs more optimization.
29 65 0.044606014654 Henry Cohn, 2026, needs more optimization.
29 66 0.044624560381 Henry Cohn, 2026, needs more optimization.
29 67 0.044634959655 Ilmari Vahteristo, 2026.
29 68 0.046023775799 Henry Cohn, 2026, needs more optimization.
29 69 0.050838211862 Henry Cohn, 2026, needs more optimization.
29 70 0.052604081662 Ilmari Vahteristo, 2026.
29 71 0.054294848325 Henry Cohn, 2026, needs more optimization.
29 72 0.056160785158 Ilmari Vahteristo, 2026.
29 73 0.057724695261 Henry Cohn, 2026, needs more optimization.
29 74 0.059425484827 Ilmari Vahteristo, 2026.
29 75 0.061018195925 Ilmari Vahteristo, 2026.
29 76 0.062593921318 Ilmari Vahteristo, 2026.
29 77 0.063118781133 Henry Cohn, 2026, needs more optimization.
29 78 0.063579419253 Henry Cohn, 2026, needs more optimization.
29 79 0.064149508910 Henry Cohn, 2026, needs more optimization.
29 80 0.065731224072 Henry Cohn, 2026, needs more optimization.
29 81 0.066916771118 Henry Cohn, 2026, needs more optimization.
29 82 0.068551141001 Henry Cohn, 2026, needs more optimization.
29 83 0.070359470518 Henry Cohn, 2026, needs more optimization.
29 84 0.072182192822 Henry Cohn, 2026, needs more optimization.
29 85 0.073571723209 Henry Cohn, 2026, needs more optimization.
29 86 0.074839660492 Henry Cohn, 2026, needs more optimization.
29 87 0.075744746100 Henry Cohn, 2026, needs more optimization.
29 88 0.076067748082 Henry Cohn, 2026, needs more optimization.
29 89 0.076456235217 Henry Cohn, 2026, needs more optimization.
29 90 0.076802878012 Henry Cohn, 2026, needs more optimization.
29 91 0.076986014503 Henry Cohn, 2026, needs more optimization.
29 92 0.077171106453 Henry Cohn, 2026, needs more optimization.
29 93 0.077401578944 Henry Cohn, 2026, needs more optimization.
29 94 0.077820000724 Henry Cohn, 2026, needs more optimization.
29 95 0.078080044562 Henry Cohn, 2026, needs more optimization.
29 96 0.078171353380 Henry Cohn, 2026, needs more optimization.
29 97 0.078819540834 Henry Cohn, 2026, needs more optimization.
29 98 0.078879347224 Henry Cohn, 2026, needs more optimization.
29 99 0.079122379005 Henry Cohn, 2026, needs more optimization.
29 100 0.079421808113 Henry Cohn, 2026, needs more optimization.
29 101 0.080120971957 Henry Cohn, 2026, needs more optimization.
29 102 0.080455160854 Henry Cohn, 2026, needs more optimization.
29 103 0.080679349826 Henry Cohn, 2026, needs more optimization.
29 104 0.080687183639 Henry Cohn, 2026, needs more optimization.
29 105 0.080736412433 Henry Cohn, 2026, needs more optimization.
29 106 0.083545885732 Henry Cohn, 2026, needs more optimization.
29 107 0.084055404834 Henry Cohn, 2026, needs more optimization.
29 108 0.085738500867 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 0.089757553696 Henry Cohn, 2026, needs more optimization.
29 114 0.089843804795 Henry Cohn, 2026, needs more optimization.
29 115 0.089940094957 Henry Cohn, 2026, needs more optimization.
29 116 0.090082242897 Henry Cohn, 2026, needs more optimization.
29 117 0.090304375906 Henry Cohn, 2026, needs more optimization.
29 118 0.090583603889 Henry Cohn, 2026, needs more optimization.
29 119 0.090787470282 Henry Cohn, 2026, needs more optimization.
29 120 0.090870157470 Henry Cohn, 2026, needs more optimization.
29 121 0.091123624631 Henry Cohn, 2026, needs more optimization.
29 122 0.091985338205 Henry Cohn, 2026, needs more optimization.
29 123 0.093254360085 Henry Cohn, 2026, needs more optimization.
29 124 0.094254725843 Henry Cohn, 2026, needs more optimization.
29 125 0.096614678626 Henry Cohn, 2026, needs more optimization.
29 126 0.098458673212 Henry Cohn, 2026, needs more optimization.
29 127 0.100092681919 Henry Cohn, 2026, needs more optimization.
29 128 0.101514436646 Henry Cohn, 2026, needs more optimization.
29 130 0.102457215480 Henry Cohn, 2026, needs more optimization.
29 131 0.102540926031 Henry Cohn, 2026, needs more optimization.
29 132 0.102592999546 Henry Cohn, 2026, needs more optimization.
29 133 0.102982107446 Henry Cohn, 2026, needs more optimization.
29 134 0.103022646978 Henry Cohn, 2026, needs more optimization.
29 135 0.103129995114 Henry Cohn, 2026, needs more optimization.
29 136 0.103853518140 Henry Cohn, 2026, needs more optimization.
29 137 0.105576868033 Henry Cohn, 2026, needs more optimization.
29 138 0.106936076895 Henry Cohn, 2026, needs more optimization.
29 139 0.107580998731 Henry Cohn, 2026, needs more optimization.
29 140 0.108487734788 Henry Cohn, 2026, needs more optimization.
29 141 0.109326411502 Henry Cohn, 2026, needs more optimization.
29 142 0.109816910319 Henry Cohn, 2026, needs more optimization.
29 143 0.110516659226 Henry Cohn, 2026, needs more optimization.
29 144 0.110745679049 Henry Cohn, 2026, needs more optimization.
29 145 0.110906904805 Henry Cohn, 2026, needs more optimization.
29 146 0.111264292591 Henry Cohn, 2026, needs more optimization.
29 147 0.111390686249 Henry Cohn, 2026, needs more optimization.
29 148 0.112364223551 Henry Cohn, 2026, needs more optimization.
29 149 0.114442084961 Henry Cohn, 2026, needs more optimization.
29 150 0.115378760583 Henry Cohn, 2026, needs more optimization.
29 151 0.116263608053 Henry Cohn, 2026, needs more optimization.
29 152 0.116962974033 Henry Cohn, 2026, needs more optimization.
29 153 0.118402654499 Henry Cohn, 2026, needs more optimization.
29 154 0.119134678965 Henry Cohn, 2026, needs more optimization.
29 155 0.120125980611 Henry Cohn, 2026, needs more optimization.
29 156 0.121120865439 Henry Cohn, 2026, needs more optimization.
29 157 0.122326161149 Henry Cohn, 2026, needs more optimization.
29 158 0.123124288777 Henry Cohn, 2026, needs more optimization.
29 159 0.124379562441 Henry Cohn, 2026, needs more optimization.
29 160 0.125449501241 Henry Cohn, 2026, needs more optimization.
29 162 0.127297587558 Henry Cohn, 2026, needs more optimization.
29 163 0.127941576577 Henry Cohn, 2026, needs more optimization.
29 164 0.128083991332 Henry Cohn, 2026, needs more optimization.
29 165 0.128153898965 Henry Cohn, 2026, needs more optimization.
29 166 0.128304719170 Henry Cohn, 2026, needs more optimization.
29 167 0.128422786138 Henry Cohn, 2026, needs more optimization.
29 168 0.129230989963 Henry Cohn, 2026, needs more optimization.
29 169 0.129869344342 Henry Cohn, 2026, needs more optimization.
29 170 0.131579856642 Henry Cohn, 2026, needs more optimization.
29 171 0.131871254641 Henry Cohn, 2026, needs more optimization.
29 172 0.132220854534 Henry Cohn, 2026, needs more optimization.
29 173 0.132679858343 Henry Cohn, 2026, needs more optimization.
29 174 0.132976041513 Henry Cohn, 2026, needs more optimization.
29 175 0.133135792314 Henry Cohn, 2026, needs more optimization.
29 176 0.133283966974 Henry Cohn, 2026, needs more optimization.
29 177 0.133530617011 Henry Cohn, 2026, needs more optimization.
29 178 0.134484001952 Henry Cohn, 2026, needs more optimization.
29 179 0.134619419973 Henry Cohn, 2026, needs more optimization.
29 180 0.134786983879 Henry Cohn, 2026, needs more optimization.
29 181 0.135019987080 Henry Cohn, 2026, needs more optimization.
29 182 0.135094578811 Henry Cohn, 2026, needs more optimization.
29 183 0.135400325666 Henry Cohn, 2026, needs more optimization.
29 184 0.135628048600 Henry Cohn, 2026, needs more optimization.
29 185 0.135987316461 Henry Cohn, 2026, needs more optimization.
29 186 0.136346491587 Henry Cohn, 2026, needs more optimization.
29 187 0.137216070243 Henry Cohn, 2026, needs more optimization.
29 188 0.137966039989 Henry Cohn, 2026, needs more optimization.
29 189 0.138336938541 Henry Cohn, 2026, needs more optimization.
29 190 0.139158736242 Henry Cohn, 2026, needs more optimization.
29 191 0.139947916621 Henry Cohn, 2026, needs more optimization.
29 192 0.140859553997 Henry Cohn, 2026, needs more optimization.
29 193 0.141751391176 Henry Cohn, 2026, needs more optimization.
29 194 0.141868054120 Henry Cohn, 2026, needs more optimization.
29 195 0.141873900002 Henry Cohn, 2026, needs more optimization.
29 196 0.142057894855 Henry Cohn, 2026, needs more optimization.
29 197 0.142095655447 Henry Cohn, 2026, needs more optimization.
29 198 0.142170561097 Henry Cohn, 2026, needs more optimization.
29 199 0.142205580863 Henry Cohn, 2026, needs more optimization.
29 200 0.142286573054 Henry Cohn, 2026, needs more optimization.
29 201 0.142348972185 Henry Cohn, 2026, needs more optimization.
29 202 0.142400311311 Henry Cohn, 2026, needs more optimization.
29 203 0.142422963125 Henry Cohn, 2026, needs more optimization.
29 204 0.142451070989 Henry Cohn, 2026, needs more optimization.
29 205 0.142558049154 Henry Cohn, 2026, needs more optimization.
29 206 0.142703156212 Henry Cohn, 2026, needs more optimization.
29 207 0.142865554803 Henry Cohn, 2026, needs more optimization.
29 208 0.142994666735 Henry Cohn, 2026, needs more optimization.
29 209 0.143548836600 Henry Cohn, 2026, needs more optimization.
29 210 0.143761526150 Henry Cohn, 2026, needs more optimization.
29 211 0.144242298143 Henry Cohn, 2026, needs more optimization.
29 212 0.144978931605 Henry Cohn, 2026, needs more optimization.
29 213 0.145546804337 Henry Cohn, 2026, needs more optimization.
29 214 0.145856276494 Henry Cohn, 2026, needs more optimization.
29 215 0.145880058658 Henry Cohn, 2026, needs more optimization.
29 217 0.146017136431 Henry Cohn, 2026, needs more optimization.
29 219 0.146522718212 Henry Cohn, 2026, needs more optimization.
29 220 0.146732076499 Henry Cohn, 2026, needs more optimization.
29 221 0.146771782182 Henry Cohn, 2026, needs more optimization.
29 222 0.146865745890 Henry Cohn, 2026, needs more optimization.
29 223 0.147032789703 Henry Cohn, 2026, needs more optimization.
29 224 0.147107806807 Henry Cohn, 2026, needs more optimization.
29 225 0.147195159698 Henry Cohn, 2026, needs more optimization.
29 226 0.147369631763 Henry Cohn, 2026, needs more optimization.
29 227 0.148008661914 Henry Cohn, 2026, needs more optimization.
29 228 0.148053206179 Henry Cohn, 2026, needs more optimization.
29 229 0.148341096877 Henry Cohn, 2026, needs more optimization.
29 230 0.148490860419 Henry Cohn, 2026, needs more optimization.
29 231 0.149985294741 Henry Cohn, 2026, needs more optimization.
29 232 0.150002807051 Henry Cohn, 2026, needs more optimization.
29 233 0.150393225915 Henry Cohn, 2026, needs more optimization.
29 234 0.150445633110 Henry Cohn, 2026, needs more optimization.
29 235 0.150562298821 Henry Cohn, 2026, needs more optimization.
29 236 0.150574010409 Henry Cohn, 2026, needs more optimization.
29 237 0.150733704006 Henry Cohn, 2026, needs more optimization.
29 238 0.152152057729 Henry Cohn, 2026, needs more optimization.
29 239 0.152277197851 Henry Cohn, 2026, needs more optimization.
29 240 0.152360721520 Henry Cohn, 2026, needs more optimization.
29 241 0.152785172920 Henry Cohn, 2026, needs more optimization.
29 242 0.153100759410 Henry Cohn, 2026, needs more optimization.
29 243 0.154976697889 Henry Cohn, 2026, needs more optimization.
29 244 0.155425653812 Henry Cohn, 2026, needs more optimization.
29 245 0.155679159775 Henry Cohn, 2026, needs more optimization.
29 246 0.158252210430 Henry Cohn, 2026, needs more optimization.
29 247 0.158502455413 Henry Cohn, 2026, needs more optimization.
29 248 0.159680808458 Henry Cohn, 2026, needs more optimization.
29 249 0.159850175859 Henry Cohn, 2026, needs more optimization.
29 250 0.159914448115 Henry Cohn, 2026, needs more optimization.
29 251 0.160532721707 Henry Cohn, 2026, needs more optimization.
29 252 0.161346508412 Henry Cohn, 2026, needs more optimization.
29 253 0.161404688085 Henry Cohn, 2026, needs more optimization.
29 254 0.161480856859 Henry Cohn, 2026, needs more optimization.
29 255 0.161704555449 Henry Cohn, 2026, needs more optimization.
29 256 0.161724101905 Henry Cohn, 2026, needs more optimization.
29 257 0.161788126528 Henry Cohn, 2026, needs more optimization.
29 261 0.162194665177 Henry Cohn, 2026, needs more optimization.
29 262 0.162274561231 Henry Cohn, 2026, needs more optimization.
29 263 0.162276709808 Henry Cohn, 2026, needs more optimization.
29 264 0.162351990416 Henry Cohn, 2026, needs more optimization.
29 265 0.162362235186 Henry Cohn, 2026, needs more optimization.
29 267 0.162366923628 Henry Cohn, 2026, needs more optimization.
29 268 0.162440235784 Henry Cohn, 2026, needs more optimization.
29 269 0.162826795289 Henry Cohn, 2026, needs more optimization.
29 270 0.162940064215 Henry Cohn, 2026, needs more optimization.
29 271 0.163174880831 Henry Cohn, 2026, needs more optimization.
29 272 0.163181208905 Henry Cohn, 2026, needs more optimization.
29 273 0.163378114518 Henry Cohn, 2026, needs more optimization.
29 274 0.163440176860 Henry Cohn, 2026, needs more optimization.
29 275 0.163521350820 Henry Cohn, 2026, needs more optimization.
29 276 0.163583764560 Henry Cohn, 2026, needs more optimization.
29 277 0.163665940105 Henry Cohn, 2026, needs more optimization.
29 278 0.163816137644 Henry Cohn, 2026, needs more optimization.
29 279 0.163890032977 Henry Cohn, 2026, needs more optimization.
29 280 0.163968313386 Henry Cohn, 2026, needs more optimization.
29 281 0.164222409569 Henry Cohn, 2026, needs more optimization.
29 282 0.164312398972 Henry Cohn, 2026, needs more optimization.
29 283 0.164462026743 Henry Cohn, 2026, needs more optimization.
29 284 0.164572133566 Henry Cohn, 2026, needs more optimization.
29 285 0.164977216437 Henry Cohn, 2026, needs more optimization.
29 286 0.164989405848 Henry Cohn, 2026, needs more optimization.
29 287 0.165129731733 Henry Cohn, 2026, needs more optimization.
29 288 0.165258606105 Henry Cohn, 2026, needs more optimization.
29 289 0.165302173185 Henry Cohn, 2026, needs more optimization.
29 290 0.165497537371 Henry Cohn, 2026, needs more optimization.
29 291 0.165615974165 Henry Cohn, 2026, needs more optimization.
29 293 0.165681550538 Henry Cohn, 2026, needs more optimization.
29 294 0.165786537059 Henry Cohn, 2026, needs more optimization.
29 295 0.165845521002 Henry Cohn, 2026, needs more optimization.
29 296 0.165873066578 Henry Cohn, 2026, needs more optimization.
29 297 0.165933666821 Henry Cohn, 2026, needs more optimization.
29 298 0.165949733346 Henry Cohn, 2026, needs more optimization.
29 299 0.165978675204 Henry Cohn, 2026, needs more optimization.
29 300 0.166031763235 Henry Cohn, 2026, needs more optimization.
29 301 0.166056916771 Henry Cohn, 2026, needs more optimization.
29 303 0.166671357086 Orthogonal union of 301 points in 28 dimensions and 2 points in 1 dimension.
29 304 0.166696298850 Orthogonal union of 300 points in 27 dimensions and 4 points in 2 dimensions.
29 305 0.166799257665 Orthogonal union of 301 points in 27 dimensions and 4 points in 2 dimensions.
29 306 0.170818468627 Orthogonal union of 300 points in 26 dimensions and 6 points in 3 dimensions.
29 307 0.171964316023 Orthogonal union of 301 points in 26 dimensions and 6 points in 3 dimensions.
29 308 0.177158896376 Henry Cohn, 2026, needs more optimization.
29 309 0.178795972454 Henry Cohn, 2025, needs more optimization.
29 310 0.179391364267 Henry Cohn, 2025, needs more optimization.
29 325 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 12 points in 5 dimensions.
11⁢x−2
29 326 0.184915496078 Orthogonal union of 314 points in 24 dimensions and 12 points in 5 dimensions.
29 330 0.186646573954 Henry Cohn, 2026, needs more optimization.
29 334 0.187712766832 Henry Cohn, 2026, needs more optimization.
29 338 0.188829551887 Henry Cohn, 2026, needs more optimization.
29 342 0.189799877117 Henry Cohn, 2026, needs more optimization.
29 346 0.190596888923 Henry Cohn, 2026, needs more optimization.
29 350 0.191269161501 Henry Cohn, 2026, needs more optimization.
29 354 0.191899840111 Henry Cohn, 2026, needs more optimization.
29 382 0.192160835297 Henry Cohn, 2026, needs more optimization.
29 383 0.192236929795 Henry Cohn, 2026, needs more optimization.
29 384 0.192465635806 Henry Cohn, 2026, needs more optimization.
29 385 0.192643236817 Henry Cohn, 2026, needs more optimization.
29 386 0.192890405531 Henry Cohn, 2026, needs more optimization.
29 387 0.193121620258 Henry Cohn, 2026, needs more optimization.
29 388 0.193320595414 Henry Cohn, 2026, needs more optimization.
29 389 0.193681233756 Henry Cohn, 2026, needs more optimization.
29 390 0.193807237371 Henry Cohn, 2026, needs more optimization.
29 391 0.193965098847 Henry Cohn, 2026, needs more optimization.
29 392 0.194068799336 Henry Cohn, 2026, needs more optimization.
29 393 0.194215319547 Henry Cohn, 2026, needs more optimization.
29 394 0.194422333954 Henry Cohn, 2026, needs more optimization.
29 395 0.194637623576 Henry Cohn, 2026, needs more optimization.
29 396 0.194963256434 Henry Cohn, 2026, needs more optimization.
29 397 0.195031346389 Henry Cohn, 2026, needs more optimization.
29 398 0.195097973315 Henry Cohn, 2026, needs more optimization.
29 399 0.195097973318 Henry Cohn, 2026, needs more optimization.
29 400 0.195191676138 Henry Cohn, 2026, needs more optimization.
29 401 0.195536181188 Henry Cohn, 2026, needs more optimization.
29 402 0.195641121706 Henry Cohn, 2026, needs more optimization.
29 403 0.195786111905 Henry Cohn, 2026, needs more optimization.
29 404 0.195823598692 Henry Cohn, 2026, needs more optimization.
29 405 0.196050666460 Henry Cohn, 2026, needs more optimization.
29 406 0.196361171181 Henry Cohn, 2026, needs more optimization.
29 407 0.196474020245 Henry Cohn, 2026, needs more optimization.
29 408 0.196596875649 Henry Cohn, 2026, needs more optimization.
29 409 0.196870438325 Henry Cohn, 2026, needs more optimization.
29 410 0.196962359012 Henry Cohn, 2026, needs more optimization.
29 411 0.197247611804 Henry Cohn, 2026, needs more optimization.
29 412 0.197548146148 Henry Cohn, 2026, needs more optimization.
29 414 0.197687677619 Henry Cohn, 2026, needs more optimization.
29 415 0.197841880146 Henry Cohn, 2026, needs more optimization.
29 417 0.197897228633 Henry Cohn, 2026, needs more optimization.
29 418 0.198176112252 Henry Cohn, 2026, needs more optimization.
29 420 0.198176112253 Henry Cohn, 2026, needs more optimization.
29 422 0.198271368636 Henry Cohn, 2026, needs more optimization.
29 423 0.198442837728 Henry Cohn, 2026, needs more optimization.
29 426 0.198699645599 Henry Cohn, 2026, needs more optimization.
29 427 0.198735333905 Henry Cohn, 2026, needs more optimization.
29 428 0.198843822179 Henry Cohn, 2026, needs more optimization.
29 429 0.198857152909 Henry Cohn, 2026, needs more optimization.
29 430 0.199002838433 Henry Cohn, 2026, needs more optimization.
29 435 0.199074838031 Henry Cohn, 2026, needs more optimization.
29 436 0.199074838032 Henry Cohn, 2026, needs more optimization.
29 437 0.199074838034 Henry Cohn, 2026, needs more optimization.
29 438 0.199097779596 Henry Cohn, 2026, needs more optimization.
29 439 0.199101779195 Henry Cohn, 2026, needs more optimization.
29 440 0.199101779196 Henry Cohn, 2026, needs more optimization.
29 442 0.199107368371 Henry Cohn, 2026, needs more optimization.
29 445 0.199222400444 Henry Cohn, 2026, needs more optimization.
29 446 0.199374252729 Henry Cohn, 2026, needs more optimization.
29 447 0.199379267783 Henry Cohn, 2026, needs more optimization.
29 449 0.199379267785 Henry Cohn, 2026, needs more optimization.
29 450 0.199383117578 Henry Cohn, 2026, needs more optimization.
29 451 0.199455180134 Henry Cohn, 2026, needs more optimization.
29 452 0.199463665415 Henry Cohn, 2026, needs more optimization.
29 454 0.199501051705 Henry Cohn, 2026, needs more optimization.
29 455 0.199510185241 Henry Cohn, 2026, needs more optimization.
29 456 0.199512982277 Henry Cohn, 2026, needs more optimization.
29 457 0.199530954281 Henry Cohn, 2026, needs more optimization.
29 458 0.199553806237 Henry Cohn, 2026, needs more optimization.
29 461 0.199573857392 Henry Cohn, 2026, needs more optimization.
29 462 0.199663098537 Henry Cohn, 2026, needs more optimization.
29 463 0.199819982190 Henry Cohn, 2026, needs more optimization.
29 468 0.199829303554 Henry Cohn, 2026, needs more optimization.
29 469 0.199842221150 Henry Cohn, 2026, needs more optimization.
29 470 0.199859424319 Henry Cohn, 2026, needs more optimization.
29 471 0.199874049881 Henry Cohn, 2026, needs more optimization.
29 472 0.199874049882 Henry Cohn, 2026, needs more optimization.
29 474 0.199877454041 Henry Cohn, 2026, needs more optimization.
29 478 0.199879757200 Henry Cohn, 2026, needs more optimization.
29 479 0.199901306775 Henry Cohn, 2026, needs more optimization.
29 483 0.199913661596 Henry Cohn, 2026, needs more optimization.
29 485 0.199918267269 Henry Cohn, 2026, needs more optimization.
29 486 0.199921573666 Henry Cohn, 2026, needs more optimization.
29 488 0.199939750700 Henry Cohn, 2026, needs more optimization.
29 489 0.199953138307 Henry Cohn, 2026, needs more optimization.
29 491 0.199957454795 Henry Cohn, 2026, needs more optimization.
29 492 0.199970330760 Henry Cohn, 2026, needs more optimization.
29 493 0.199978809802 Henry Cohn, 2026, needs more optimization.
29 494 0.199979340513 Henry Cohn, 2026, needs more optimization.
29 495 0.199989563756 Henry Cohn, 2026, needs more optimization.
29 570 0.2 Orthogonal union of 552 points in 23 dimensions and 18 points in 6 dimensions.
5⁢x−1
29 585 0.200046648867 Henry Cohn, 2026, needs more optimization.
29 586 0.225327526755 Orthogonal union of 576 points in 25 dimensions and 10 points in 4 dimensions.
29 587 0.226837055978 Orthogonal union of 577 points in 25 dimensions and 10 points in 4 dimensions.
29 588 0.227891986078 Orthogonal union of 578 points in 25 dimensions and 10 points in 4 dimensions.
29 589 0.228517196126 Orthogonal union of 579 points in 25 dimensions and 10 points in 4 dimensions.
29 590 0.229079598080 Orthogonal union of 580 points in 25 dimensions and 10 points in 4 dimensions.
29 591 0.229882834554 Orthogonal union of 581 points in 25 dimensions and 10 points in 4 dimensions.
29 592 0.230043706448 Orthogonal union of 582 points in 25 dimensions and 10 points in 4 dimensions.
29 593 0.230404267943 Henry Cohn, 2026, needs more optimization.
29 594 0.231345472037 Orthogonal union of 583 points in 25 dimensions and 11 points in 4 dimensions.
29 595 0.232207827229 Orthogonal union of 584 points in 25 dimensions and 11 points in 4 dimensions.
29 596 0.232479376363 Orthogonal union of 585 points in 25 dimensions and 11 points in 4 dimensions.
29 597 0.233414506364 Orthogonal union of 586 points in 25 dimensions and 11 points in 4 dimensions.
29 598 0.234451135578 Orthogonal union of 587 points in 25 dimensions and 11 points in 4 dimensions.
29 599 0.234601320648 Orthogonal union of 588 points in 25 dimensions and 11 points in 4 dimensions.
29 600 0.235304794842 Orthogonal union of 589 points in 25 dimensions and 11 points in 4 dimensions.
29 601 0.235970793319 Orthogonal union of 590 points in 25 dimensions and 11 points in 4 dimensions.
29 602 0.236630001220 Orthogonal union of 591 points in 25 dimensions and 11 points in 4 dimensions.
29 603 0.236746113239 Henry Cohn, 2026, needs more optimization.
29 604 0.236755244569 Henry Cohn, 2026, needs more optimization.
29 605 0.236792082737 Henry Cohn, 2026, needs more optimization.
29 606 0.236866667916 Henry Cohn, 2026, needs more optimization.
29 607 0.237573215381 Henry Cohn, 2026, needs more optimization.
29 608 0.237579102548 Henry Cohn, 2026, needs more optimization.
29 610 0.237739863755 Henry Cohn, 2026, needs more optimization.
29 614 0.237821281448 Henry Cohn, 2026, needs more optimization.
29 618 0.237903058886 Henry Cohn, 2026, needs more optimization.
29 622 0.237969504979 Henry Cohn, 2026, needs more optimization.
29 626 0.238027035787 Henry Cohn, 2026, needs more optimization.
29 630 0.238073782076 Henry Cohn, 2026, needs more optimization.
29 634 0.238131581561 Henry Cohn, 2026, needs more optimization.
29 636 0.238294864888 Henry Cohn, 2026, needs more optimization.
29 638 0.238302101833 Henry Cohn, 2026, needs more optimization.
29 640 0.239119677104 Henry Cohn, 2026, needs more optimization.
29 642 0.239393404822 Henry Cohn, 2026, needs more optimization.
29 646 0.240214185602 Henry Cohn, 2026, needs more optimization.
29 650 0.241064041064 Henry Cohn, 2026, needs more optimization.
29 654 0.241869130256 Henry Cohn, 2026, needs more optimization.
29 658 0.242706888439 Henry Cohn, 2026, needs more optimization.
29 662 0.243369083187 Henry Cohn, 2026, needs more optimization.
29 666 0.243904471183 Henry Cohn, 2026, needs more optimization.
29 735 0.244127674175 Henry Cohn, 2026, needs more optimization.
29 736 0.244127674176 Henry Cohn, 2026, needs more optimization.
29 737 0.244127674182 Henry Cohn, 2026, needs more optimization.
29 744 0.244148420077 Henry Cohn, 2026, needs more optimization.
29 745 0.244194768101 Henry Cohn, 2026, needs more optimization.
29 748 0.244207232625 Henry Cohn, 2026, needs more optimization.
29 749 0.244226798418 Henry Cohn, 2026, needs more optimization.
29 750 0.244367127937 Henry Cohn, 2026, needs more optimization.
29 751 0.244375901991 Henry Cohn, 2026, needs more optimization.
29 752 0.244494126518 Henry Cohn, 2026, needs more optimization.
29 753 0.244537766968 Henry Cohn, 2026, needs more optimization.
29 754 0.244572811765 Henry Cohn, 2026, needs more optimization.
29 755 0.244665651649 Henry Cohn, 2026, needs more optimization.
29 756 0.244801397987 Henry Cohn, 2026, needs more optimization.
29 757 0.244868721158 Henry Cohn, 2026, needs more optimization.
29 758 0.244902084255 Henry Cohn, 2026, needs more optimization.
29 759 0.245010599490 Henry Cohn, 2026, needs more optimization.
29 760 0.245050337556 Henry Cohn, 2026, needs more optimization.
29 761 0.245195296745 Henry Cohn, 2026, needs more optimization.
29 762 0.245352075845 Henry Cohn, 2026, needs more optimization.
29 764 0.245415702472 Henry Cohn, 2026, needs more optimization.
29 765 0.245415702473 Henry Cohn, 2026, needs more optimization.
29 766 0.245517869964 Henry Cohn, 2026, needs more optimization.
29 767 0.245532950304 Henry Cohn, 2026, needs more optimization.
29 768 0.245590855874 Henry Cohn, 2026, needs more optimization.
29 769 0.245699280781 Henry Cohn, 2026, needs more optimization.
29 770 0.245825209985 Henry Cohn, 2026, needs more optimization.
29 771 0.245825209987 Henry Cohn, 2026, needs more optimization.
29 772 0.245875160644 Henry Cohn, 2026, needs more optimization.
29 773 0.246000964467 Henry Cohn, 2026, needs more optimization.
29 774 0.246115119735 Henry Cohn, 2026, needs more optimization.
29 775 0.246173868938 Henry Cohn, 2026, needs more optimization.
29 776 0.246273317827 Henry Cohn, 2026, needs more optimization.
29 777 0.246536812921 Henry Cohn, 2026, needs more optimization.
29 778 0.246554521164 Henry Cohn, 2026, needs more optimization.
29 779 0.246584747051 Henry Cohn, 2026, needs more optimization.
29 780 0.246639576819 Henry Cohn, 2026, needs more optimization.
29 781 0.246692917920 Henry Cohn, 2026, needs more optimization.
29 782 0.246714811658 Henry Cohn, 2026, needs more optimization.
29 783 0.246751916511 Henry Cohn, 2026, needs more optimization.
29 784 0.246889769789 Henry Cohn, 2026, needs more optimization.
29 785 0.247012390772 Henry Cohn, 2026, needs more optimization.
29 786 0.247030049186 Henry Cohn, 2026, needs more optimization.
29 787 0.247049742618 Henry Cohn, 2026, needs more optimization.
29 788 0.247105749153 Henry Cohn, 2026, needs more optimization.
29 789 0.247143077982 Henry Cohn, 2026, needs more optimization.
29 790 0.247261092801 Henry Cohn, 2026, needs more optimization.
29 791 0.247404385436 Henry Cohn, 2026, needs more optimization.
29 792 0.247425593664 Henry Cohn, 2026, needs more optimization.
29 795 0.247491213913 Henry Cohn, 2026, needs more optimization.
29 796 0.247537972080 Henry Cohn, 2026, needs more optimization.
29 797 0.247663732294 Henry Cohn, 2026, needs more optimization.
29 799 0.247763192992 Henry Cohn, 2026, needs more optimization.
29 800 0.247763192993 Henry Cohn, 2026, needs more optimization.
29 801 0.247825308882 Henry Cohn, 2026, needs more optimization.
29 802 0.247847918775 Henry Cohn, 2026, needs more optimization.
29 803 0.247855582865 Henry Cohn, 2026, needs more optimization.
29 804 0.247912841035 Henry Cohn, 2026, needs more optimization.
29 805 0.248146611231 Henry Cohn, 2026, needs more optimization.
29 806 0.248216200705 Henry Cohn, 2026, needs more optimization.
29 807 0.248216200709 Henry Cohn, 2026, needs more optimization.
29 808 0.248253933148 Henry Cohn, 2026, needs more optimization.
29 810 0.248318097625 Henry Cohn, 2026, needs more optimization.
29 811 0.248354912762 Henry Cohn, 2026, needs more optimization.
29 812 0.248482252499 Henry Cohn, 2026, needs more optimization.
29 813 0.248510773389 Henry Cohn, 2026, needs more optimization.
29 814 0.248542571756 Henry Cohn, 2026, needs more optimization.
29 815 0.248616428309 Henry Cohn, 2026, needs more optimization.
29 816 0.248644002665 Henry Cohn, 2026, needs more optimization.
29 818 0.248689512754 Henry Cohn, 2026, needs more optimization.
29 819 0.248805311320 Henry Cohn, 2026, needs more optimization.
29 820 0.248809247931 Henry Cohn, 2026, needs more optimization.
29 821 0.248819341201 Henry Cohn, 2026, needs more optimization.
29 822 0.248836776037 Henry Cohn, 2026, needs more optimization.
29 823 0.248918078859 Henry Cohn, 2026, needs more optimization.
29 824 0.249114296442 Henry Cohn, 2026, needs more optimization.
29 826 0.249132882280 Henry Cohn, 2026, needs more optimization.
29 828 0.249132882285 Henry Cohn, 2026, needs more optimization.
29 829 0.249206903245 Henry Cohn, 2026, needs more optimization.
29 838 0.249347288537 Henry Cohn, 2026, needs more optimization.
29 839 0.249386973680 Henry Cohn, 2026, needs more optimization.
29 840 0.249386973683 Henry Cohn, 2026, needs more optimization.
29 845 0.249391499956 Henry Cohn, 2026, needs more optimization.
29 847 0.249405616630 Henry Cohn, 2026, needs more optimization.
29 848 0.249445754308 Henry Cohn, 2026, needs more optimization.
29 849 0.249489047942 Henry Cohn, 2026, needs more optimization.
29 850 0.249520530946 Henry Cohn, 2026, needs more optimization.
29 851 0.249567953508 Henry Cohn, 2026, needs more optimization.
29 855 0.249643129945 Henry Cohn, 2026, needs more optimization.
29 856 0.249669261083 Henry Cohn, 2026, needs more optimization.
29 857 0.249684272419 Henry Cohn, 2026, needs more optimization.
29 858 0.249689505496 Henry Cohn, 2026, needs more optimization.
29 859 0.249696576419 Henry Cohn, 2026, needs more optimization.
29 861 0.249723633426 Henry Cohn, 2026, needs more optimization.
29 862 0.249735982409 Henry Cohn, 2026, needs more optimization.
29 863 0.249737610467 Henry Cohn, 2026, needs more optimization.
29 866 0.249756328700 Henry Cohn, 2026, needs more optimization.
29 867 0.249759244632 Henry Cohn, 2026, needs more optimization.
29 868 0.249768379693 Henry Cohn, 2026, needs more optimization.
29 869 0.249787523058 Henry Cohn, 2026, needs more optimization.
29 870 0.249811652871 Henry Cohn, 2026, needs more optimization.
29 871 0.249819270141 Henry Cohn, 2026, needs more optimization.
29 872 0.249829994034 Henry Cohn, 2026, needs more optimization.
29 876 0.249859502574 Henry Cohn, 2026, needs more optimization.
29 877 0.249863492518 Henry Cohn, 2026, needs more optimization.
29 886 0.249868416795 Henry Cohn, 2026, needs more optimization.
29 887 0.249879607397 Henry Cohn, 2026, needs more optimization.
29 889 0.249883006358 Henry Cohn, 2026, needs more optimization.
29 890 0.249896800131 Henry Cohn, 2026, needs more optimization.
29 891 0.249906882841 Henry Cohn, 2026, needs more optimization.
29 895 0.249917760496 Henry Cohn, 2026, needs more optimization.
29 896 0.249921791083 Henry Cohn, 2026, needs more optimization.
29 897 0.249925934380 Henry Cohn, 2026, needs more optimization.
29 898 0.249929397181 Henry Cohn, 2026, needs more optimization.
29 900 0.249952660254 Henry Cohn, 2026, needs more optimization.
29 902 0.249958432063 Henry Cohn, 2026, needs more optimization.
29 903 0.249960947518 Henry Cohn, 2026, needs more optimization.
29 904 0.249972984397 Henry Cohn, 2026, needs more optimization.
29 905 0.249989697608 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 0.250024248965 Orthogonal union of 977 points in 28 dimensions and 2 points in 1 dimension.
29 980 0.250025658596 Orthogonal union of 978 points in 28 dimensions and 2 points in 1 dimension.
29 981 0.250035791685 Orthogonal union of 979 points in 28 dimensions and 2 points in 1 dimension.
29 982 0.250038995579 Orthogonal union of 980 points in 28 dimensions and 2 points in 1 dimension.
29 983 0.250044974668 Orthogonal union of 981 points in 28 dimensions and 2 points in 1 dimension.
29 984 0.250045856531 Orthogonal union of 982 points in 28 dimensions and 2 points in 1 dimension.
29 986 0.250053881403 Orthogonal union of 984 points in 28 dimensions and 2 points in 1 dimension.
29 987 0.250062489010 Orthogonal union of 985 points in 28 dimensions and 2 points in 1 dimension.
29 988 0.250062814470 Orthogonal union of 986 points in 28 dimensions and 2 points in 1 dimension.
29 989 0.250067178715 Orthogonal union of 987 points in 28 dimensions and 2 points in 1 dimension.
29 991 0.250078896727 Henry Cohn, 2026, needs more optimization.
29 993 0.250083588040 Orthogonal union of 991 points in 28 dimensions and 2 points in 1 dimension.
29 995 0.250090299409 Orthogonal union of 993 points in 28 dimensions and 2 points in 1 dimension.
29 996 0.250119877695 Orthogonal union of 994 points in 28 dimensions and 2 points in 1 dimension.
29 997 0.250146208769 Orthogonal union of 995 points in 28 dimensions and 2 points in 1 dimension.
29 999 0.250174971682 Orthogonal union of 997 points in 28 dimensions and 2 points in 1 dimension.
29 1000 0.250188533594 Orthogonal union of 998 points in 28 dimensions and 2 points in 1 dimension.
29 1004 0.250207873663 Orthogonal union of 1002 points in 28 dimensions and 2 points in 1 dimension.
29 1006 0.250224113381 Orthogonal union of 1004 points in 28 dimensions and 2 points in 1 dimension.
29 1007 0.250271756223 Orthogonal union of 1005 points in 28 dimensions and 2 points in 1 dimension.
29 1008 0.250355533485 Orthogonal union of 1006 points in 28 dimensions and 2 points in 1 dimension.
29 1009 0.250492703909 Orthogonal union of 1007 points in 28 dimensions and 2 points in 1 dimension.
29 1010 0.250556650226 Orthogonal union of 1008 points in 28 dimensions and 2 points in 1 dimension.
29 1011 0.250649183935 Orthogonal union of 1009 points in 28 dimensions and 2 points in 1 dimension.
29 1012 0.250829126356 Orthogonal union of 1010 points in 28 dimensions and 2 points in 1 dimension.
29 1013 0.251011141085 Orthogonal union of 1011 points in 28 dimensions and 2 points in 1 dimension.
29 1014 0.251210508745 Orthogonal union of 1012 points in 28 dimensions and 2 points in 1 dimension.
29 1015 0.251444377413 Orthogonal union of 1013 points in 28 dimensions and 2 points in 1 dimension.
29 1016 0.251656820376 Orthogonal union of 1014 points in 28 dimensions and 2 points in 1 dimension.
29 1017 0.251818239135 Orthogonal union of 1015 points in 28 dimensions and 2 points in 1 dimension.
29 1018 0.252008986578 Orthogonal union of 1016 points in 28 dimensions and 2 points in 1 dimension.
29 1019 0.252293705511 Orthogonal union of 1017 points in 28 dimensions and 2 points in 1 dimension.
29 1020 0.252596418108 Orthogonal union of 1018 points in 28 dimensions and 2 points in 1 dimension.
29 1021 0.252819793214 Orthogonal union of 1019 points in 28 dimensions and 2 points in 1 dimension.
29 1022 0.253020846429 Orthogonal union of 1020 points in 28 dimensions and 2 points in 1 dimension.
29 1023 0.253164780370 Orthogonal union of 1021 points in 28 dimensions and 2 points in 1 dimension.
29 1024 0.253256808194 Orthogonal union of 1022 points in 28 dimensions and 2 points in 1 dimension.
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 0.031274722522 Henry Cohn, 2026, needs more optimization.
30 63 0.039846497808 Ilmari Vahteristo, 2026.
30 64 0.041979616323 Henry Cohn, 2026, needs more optimization.
30 65 0.043476230860 Henry Cohn, 2026, needs more optimization.
30 66 0.044301112855 Henry Cohn, 2026, needs more optimization.
30 67 0.044456014538 Henry Cohn, 2026, needs more optimization.
30 68 0.044556632084 Henry Cohn, 2026, needs more optimization.
30 69 0.044563869603 Ilmari Vahteristo, 2026.
30 70 0.044757477298 Henry Cohn, 2026, needs more optimization.
30 71 0.049847240264 Ilmari Vahteristo, 2026.
30 72 0.051259526107 Ilmari Vahteristo, 2026.
30 73 0.052492486450 Ilmari Vahteristo, 2026.
30 74 0.054354656515 Henry Cohn, 2026, needs more optimization.
30 75 0.056244486017 Ilmari Vahteristo, 2026.
30 76 0.057567970062 Ilmari Vahteristo, 2026.
30 77 0.059053763774 Ilmari Vahteristo, 2026.
30 78 0.060514438100 Henry Cohn, 2026, needs more optimization.
30 79 0.062144623806 Henry Cohn, 2026, needs more optimization.
30 80 0.062598281110 Henry Cohn, 2026, needs more optimization.
30 81 0.062840662877 Henry Cohn, 2026, needs more optimization.
30 82 0.064290493137 Henry Cohn, 2026, needs more optimization.
30 83 0.065112988256 Henry Cohn, 2026, needs more optimization.
30 84 0.066460260232 Henry Cohn, 2026, needs more optimization.
30 85 0.068034028230 Henry Cohn, 2026, needs more optimization.
30 86 0.069489198859 Henry Cohn, 2026, needs more optimization.
30 87 0.071181183894 Henry Cohn, 2026, needs more optimization.
30 88 0.072751549117 Henry Cohn, 2026, needs more optimization.
30 89 0.074132286982 Henry Cohn, 2026, needs more optimization.
30 90 0.074431580852 Henry Cohn, 2026, needs more optimization.
30 91 0.075429100149 Henry Cohn, 2026, needs more optimization.
30 92 0.076299924411 Henry Cohn, 2026, needs more optimization.
30 93 0.076899900336 Henry Cohn, 2026, needs more optimization.
30 94 0.076905071341 Henry Cohn, 2026, needs more optimization.
30 95 0.076937705910 Henry Cohn, 2026, needs more optimization.
30 96 0.077028880437 Henry Cohn, 2026, needs more optimization.
30 97 0.077180879266 Henry Cohn, 2026, needs more optimization.
30 98 0.077277068756 Henry Cohn, 2026, needs more optimization.
30 99 0.077386849218 Henry Cohn, 2026, needs more optimization.
30 100 0.077770052793 Henry Cohn, 2026, needs more optimization.
30 101 0.077962740977 Henry Cohn, 2026, needs more optimization.
30 102 0.078263656873 Henry Cohn, 2026, needs more optimization.
30 103 0.078825215956 Henry Cohn, 2026, needs more optimization.
30 104 0.079148122194 Henry Cohn, 2026, needs more optimization.
30 105 0.079852427106 Henry Cohn, 2026, needs more optimization.
30 106 0.080644846690 Henry Cohn, 2026, needs more optimization.
30 107 0.080679879223 Henry Cohn, 2026, needs more optimization.
30 108 0.080814373456 Henry Cohn, 2026, needs more optimization.
30 109 0.081524428663 Henry Cohn, 2026, needs more optimization.
30 110 0.082137985698 Henry Cohn, 2026, needs more optimization.
30 111 0.082309251353 Henry Cohn, 2026, needs more optimization.
30 112 0.084409892382 Henry Cohn, 2026, needs more optimization.
30 113 0.085914924219 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 0.088247867930 Henry Cohn, 2026, needs more optimization.
30 116 0.088509865765 Henry Cohn, 2026, needs more optimization.
30 117 0.088766957745 Henry Cohn, 2026, needs more optimization.
30 118 0.089132966543 Henry Cohn, 2026, needs more optimization.
30 119 0.089423437146 Henry Cohn, 2026, needs more optimization.
30 120 0.089961754455 Henry Cohn, 2026, needs more optimization.
30 121 0.090189988171 Henry Cohn, 2026, needs more optimization.
30 122 0.090368152418 Henry Cohn, 2026, needs more optimization.
30 123 0.090688812771 Henry Cohn, 2026, needs more optimization.
30 124 0.090790944141 Henry Cohn, 2026, needs more optimization.
30 125 0.091219578568 Henry Cohn, 2026, needs more optimization.
30 126 0.091624817213 Henry Cohn, 2026, needs more optimization.
30 127 0.092702729559 Henry Cohn, 2026, needs more optimization.
30 128 0.094163220916 Henry Cohn, 2026, needs more optimization.
30 129 0.095345362316 Henry Cohn, 2026, needs more optimization.
30 130 0.097375496169 Henry Cohn, 2026, needs more optimization.
30 131 0.098512388174 Henry Cohn, 2026, needs more optimization.
30 132 0.099549075151 Henry Cohn, 2026, needs more optimization.
30 133 0.100627373656 Henry Cohn, 2026, needs more optimization.
30 134 0.102005780801 Henry Cohn, 2026, needs more optimization.
30 135 0.102542682072 Henry Cohn, 2026, needs more optimization.
30 136 0.102554222725 Henry Cohn, 2026, needs more optimization.
30 137 0.102576170203 Henry Cohn, 2026, needs more optimization.
30 138 0.102587610501 Henry Cohn, 2026, needs more optimization.
30 139 0.102619157643 Henry Cohn, 2026, needs more optimization.
30 140 0.102945356927 Henry Cohn, 2026, needs more optimization.
30 141 0.103465733046 Henry Cohn, 2026, needs more optimization.
30 142 0.104553086218 Henry Cohn, 2026, needs more optimization.
30 143 0.105327319283 Henry Cohn, 2026, needs more optimization.
30 144 0.106168230867 Henry Cohn, 2026, needs more optimization.
30 145 0.107203617626 Henry Cohn, 2026, needs more optimization.
30 146 0.108228518729 Henry Cohn, 2026, needs more optimization.
30 147 0.108928258546 Henry Cohn, 2026, needs more optimization.
30 148 0.109291334803 Henry Cohn, 2026, needs more optimization.
30 149 0.109890878864 Henry Cohn, 2026, needs more optimization.
30 150 0.110412128587 Henry Cohn, 2026, needs more optimization.
30 151 0.110744160793 Henry Cohn, 2026, needs more optimization.
30 152 0.111404547627 Henry Cohn, 2026, needs more optimization.
30 153 0.112199756927 Henry Cohn, 2026, needs more optimization.
30 154 0.112752829909 Henry Cohn, 2026, needs more optimization.
30 155 0.112821542063 Henry Cohn, 2026, needs more optimization.
30 156 0.114168982083 Henry Cohn, 2026, needs more optimization.
30 157 0.115172511136 Henry Cohn, 2026, needs more optimization.
30 158 0.116193573730 Henry Cohn, 2026, needs more optimization.
30 159 0.117143959882 Henry Cohn, 2026, needs more optimization.
30 160 0.118118645618 Henry Cohn, 2026, needs more optimization.
30 161 0.118698421180 Henry Cohn, 2026, needs more optimization.
30 162 0.119883308300 Henry Cohn, 2026, needs more optimization.
30 163 0.120528256439 Henry Cohn, 2026, needs more optimization.
30 164 0.121560008636 Henry Cohn, 2026, needs more optimization.
30 165 0.122518921145 Henry Cohn, 2026, needs more optimization.
30 166 0.123252063669 Henry Cohn, 2026, needs more optimization.
30 167 0.124276530343 Henry Cohn, 2026, needs more optimization.
30 168 0.125310611651 Henry Cohn, 2026, needs more optimization.
30 169 0.126468094249 Henry Cohn, 2026, needs more optimization.
30 170 0.127109070005 Henry Cohn, 2026, needs more optimization.
30 171 0.127785020271 Henry Cohn, 2026, needs more optimization.
30 172 0.128621408783 Henry Cohn, 2026, needs more optimization.
30 173 0.129539904936 Henry Cohn, 2026, needs more optimization.
30 174 0.129913472158 Henry Cohn, 2026, needs more optimization.
30 175 0.130357927001 Henry Cohn, 2026, needs more optimization.
30 176 0.131695930663 Henry Cohn, 2026, needs more optimization.
30 177 0.131825972288 Henry Cohn, 2026, needs more optimization.
30 178 0.131920308690 Henry Cohn, 2026, needs more optimization.
30 179 0.132220741449 Henry Cohn, 2026, needs more optimization.
30 180 0.132519026472 Henry Cohn, 2026, needs more optimization.
30 181 0.132631712261 Henry Cohn, 2026, needs more optimization.
30 182 0.132844818897 Henry Cohn, 2026, needs more optimization.
30 183 0.133173143663 Henry Cohn, 2026, needs more optimization.
30 184 0.133573840471 Henry Cohn, 2026, needs more optimization.
30 185 0.134154119600 Henry Cohn, 2026, needs more optimization.
30 186 0.134200106882 Henry Cohn, 2026, needs more optimization.
30 187 0.134306686445 Henry Cohn, 2026, needs more optimization.
30 188 0.134366788071 Henry Cohn, 2026, needs more optimization.
30 189 0.134549378482 Henry Cohn, 2026, needs more optimization.
30 190 0.134739802457 Henry Cohn, 2026, needs more optimization.
30 191 0.134967378396 Henry Cohn, 2026, needs more optimization.
30 192 0.135182951893 Henry Cohn, 2026, needs more optimization.
30 193 0.135698685078 Henry Cohn, 2026, needs more optimization.
30 194 0.136212268674 Henry Cohn, 2026, needs more optimization.
30 195 0.136991613127 Henry Cohn, 2026, needs more optimization.
30 196 0.137592707381 Henry Cohn, 2026, needs more optimization.
30 197 0.137965894927 Henry Cohn, 2026, needs more optimization.
30 198 0.138517739499 Henry Cohn, 2026, needs more optimization.
30 199 0.139406147392 Henry Cohn, 2026, needs more optimization.
30 200 0.140310314370 Henry Cohn, 2026, needs more optimization.
30 201 0.141158134127 Henry Cohn, 2026, needs more optimization.
30 202 0.141185164430 Henry Cohn, 2026, needs more optimization.
30 203 0.141280718487 Henry Cohn, 2026, needs more optimization.
30 204 0.141306236357 Henry Cohn, 2026, needs more optimization.
30 205 0.141407420457 Henry Cohn, 2026, needs more optimization.
30 206 0.141523595719 Henry Cohn, 2026, needs more optimization.
30 207 0.141571886214 Henry Cohn, 2026, needs more optimization.
30 208 0.141645557929 Henry Cohn, 2026, needs more optimization.
30 209 0.141837663518 Henry Cohn, 2026, needs more optimization.
30 210 0.141994338725 Henry Cohn, 2026, needs more optimization.
30 212 0.142298905793 Henry Cohn, 2026, needs more optimization.
30 213 0.142299935452 Henry Cohn, 2026, needs more optimization.
30 214 0.142370716382 Henry Cohn, 2026, needs more optimization.
30 215 0.142512670381 Henry Cohn, 2026, needs more optimization.
30 216 0.142827785283 Henry Cohn, 2026, needs more optimization.
30 217 0.142871445180 Henry Cohn, 2026, needs more optimization.
30 218 0.143128476636 Henry Cohn, 2026, needs more optimization.
30 219 0.143711246791 Henry Cohn, 2026, needs more optimization.
30 220 0.143960995081 Henry Cohn, 2026, needs more optimization.
30 221 0.144389951347 Henry Cohn, 2026, needs more optimization.
30 222 0.144505717471 Henry Cohn, 2026, needs more optimization.
30 223 0.144863504998 Henry Cohn, 2026, needs more optimization.
30 224 0.144985254493 Henry Cohn, 2026, needs more optimization.
30 225 0.145294651263 Henry Cohn, 2026, needs more optimization.
30 226 0.145732715531 Henry Cohn, 2026, needs more optimization.
30 227 0.146514903414 Henry Cohn, 2026, needs more optimization.
30 228 0.146701527836 Henry Cohn, 2026, needs more optimization.
30 229 0.146749645761 Henry Cohn, 2026, needs more optimization.
30 230 0.147226183273 Henry Cohn, 2026, needs more optimization.
30 231 0.147320317004 Henry Cohn, 2026, needs more optimization.
30 232 0.147434498095 Henry Cohn, 2026, needs more optimization.
30 233 0.147498746887 Henry Cohn, 2026, needs more optimization.
30 234 0.148093540160 Henry Cohn, 2026, needs more optimization.
30 235 0.148990210943 Henry Cohn, 2026, needs more optimization.
30 236 0.149041990548 Henry Cohn, 2026, needs more optimization.
30 237 0.149286781769 Henry Cohn, 2026, needs more optimization.
30 238 0.149572348388 Henry Cohn, 2026, needs more optimization.
30 239 0.149628300940 Henry Cohn, 2026, needs more optimization.
30 240 0.149794752387 Henry Cohn, 2026, needs more optimization.
30 241 0.149935566404 Henry Cohn, 2026, needs more optimization.
30 242 0.150338100742 Henry Cohn, 2026, needs more optimization.
30 243 0.151278695834 Henry Cohn, 2026, needs more optimization.
30 244 0.151724721484 Henry Cohn, 2026, needs more optimization.
30 245 0.152092711808 Henry Cohn, 2026, needs more optimization.
30 246 0.152151745645 Henry Cohn, 2026, needs more optimization.
30 247 0.152301238021 Henry Cohn, 2026, needs more optimization.
30 248 0.152585958852 Henry Cohn, 2026, needs more optimization.
30 249 0.152706107415 Henry Cohn, 2026, needs more optimization.
30 250 0.153028363951 Henry Cohn, 2026, needs more optimization.
30 251 0.153948806667 Henry Cohn, 2026, needs more optimization.
30 252 0.154042507903 Henry Cohn, 2026, needs more optimization.
30 253 0.155270781947 Henry Cohn, 2026, needs more optimization.
30 254 0.155497987535 Henry Cohn, 2026, needs more optimization.
30 255 0.155572938676 Henry Cohn, 2026, needs more optimization.
30 256 0.155727123023 Henry Cohn, 2026, needs more optimization.
30 257 0.155818472897 Henry Cohn, 2026, needs more optimization.
30 258 0.156887374400 Henry Cohn, 2026, needs more optimization.
30 259 0.157826667852 Henry Cohn, 2026, needs more optimization.
30 260 0.158203485385 Henry Cohn, 2026, needs more optimization.
30 261 0.158636444209 Henry Cohn, 2026, needs more optimization.
30 262 0.159276435674 Henry Cohn, 2026, needs more optimization.
30 263 0.159816745177 Henry Cohn, 2026, needs more optimization.
30 264 0.160626899204 Henry Cohn, 2026, needs more optimization.
30 265 0.160811240159 Henry Cohn, 2026, needs more optimization.
30 266 0.160814178838 Henry Cohn, 2026, needs more optimization.
30 267 0.161020539930 Henry Cohn, 2026, needs more optimization.
30 268 0.161261622102 Henry Cohn, 2026, needs more optimization.
30 269 0.161445912952 Henry Cohn, 2026, needs more optimization.
30 270 0.161731055562 Henry Cohn, 2026, needs more optimization.
30 271 0.161738482599 Henry Cohn, 2026, needs more optimization.
30 272 0.161776753953 Henry Cohn, 2026, needs more optimization.
30 273 0.161795344914 Henry Cohn, 2026, needs more optimization.
30 274 0.161795470940 Henry Cohn, 2026, needs more optimization.
30 275 0.161798402149 Henry Cohn, 2026, needs more optimization.
30 276 0.161841937743 Henry Cohn, 2026, needs more optimization.
30 277 0.161855028810 Henry Cohn, 2026, needs more optimization.
30 278 0.161894767803 Henry Cohn, 2026, needs more optimization.
30 279 0.161901468783 Henry Cohn, 2026, needs more optimization.
30 280 0.161917199996 Henry Cohn, 2026, needs more optimization.
30 281 0.161985161430 Henry Cohn, 2026, needs more optimization.
30 282 0.162021576390 Henry Cohn, 2026, needs more optimization.
30 283 0.162125276964 Henry Cohn, 2026, needs more optimization.
30 284 0.162334979805 Henry Cohn, 2026, needs more optimization.
30 285 0.162391884350 Henry Cohn, 2026, needs more optimization.
30 286 0.162531986447 Henry Cohn, 2026, needs more optimization.
30 287 0.162788069560 Henry Cohn, 2026, needs more optimization.
30 288 0.162895208289 Henry Cohn, 2026, needs more optimization.
30 289 0.163012696912 Henry Cohn, 2026, needs more optimization.
30 290 0.163071982693 Henry Cohn, 2026, needs more optimization.
30 291 0.163201019349 Henry Cohn, 2026, needs more optimization.
30 292 0.163381662724 Henry Cohn, 2026, needs more optimization.
30 293 0.163495793710 Henry Cohn, 2026, needs more optimization.
30 294 0.163713380132 Henry Cohn, 2026, needs more optimization.
30 295 0.163808458633 Henry Cohn, 2026, needs more optimization.
30 296 0.163988611632 Henry Cohn, 2026, needs more optimization.
30 297 0.164159666070 Henry Cohn, 2026, needs more optimization.
30 298 0.164251360504 Henry Cohn, 2026, needs more optimization.
30 299 0.164480393113 Henry Cohn, 2026, needs more optimization.
30 300 0.164605063582 Henry Cohn, 2026, needs more optimization.
30 301 0.164747688579 Henry Cohn, 2026, needs more optimization.
30 302 0.166031763235 Orthogonal union of 300 points in 29 dimensions and 2 points in 1 dimension.
30 303 0.166056916771 Orthogonal union of 301 points in 29 dimensions and 2 points in 1 dimension.
30 305 0.166671357086 Orthogonal union of 301 points in 28 dimensions and 4 points in 2 dimensions.
30 306 0.166696298850 Orthogonal union of 300 points in 27 dimensions and 6 points in 3 dimensions.
30 307 0.166799257665 Orthogonal union of 301 points in 27 dimensions and 6 points in 3 dimensions.
30 308 0.167435843496 Orthogonal union of 298 points in 26 dimensions and 10 points in 4 dimensions.
30 309 0.168747029607 Orthogonal union of 299 points in 26 dimensions and 10 points in 4 dimensions.
30 310 0.170818468627 Orthogonal union of 300 points in 26 dimensions and 10 points in 4 dimensions.
30 311 0.171964316023 Orthogonal union of 301 points in 26 dimensions and 10 points in 4 dimensions.
30 312 0.176297427668 Henry Cohn, 2026, needs more optimization.
30 313 0.176309067334 Henry Cohn, 2025, needs more optimization.
30 314 0.176348608760 Henry Cohn, 2026, needs more optimization.
30 329 0.181818181819 Orthogonal union of 313 points in 24 dimensions and 16 points in 6 dimensions.
11⁢x−2
30 330 0.183274239530 Henry Cohn, 2026, needs more optimization.
30 334 0.184866927165 Henry Cohn, 2026, needs more optimization.
30 338 0.185452224918 Henry Cohn, 2026, needs more optimization.
30 342 0.186184943951 Henry Cohn, 2026, needs more optimization.
30 346 0.186869724716 Henry Cohn, 2026, needs more optimization.
30 350 0.187245197605 Henry Cohn, 2026, needs more optimization.
30 354 0.187787088964 Henry Cohn, 2026, needs more optimization.
30 358 0.188490482893 Henry Cohn, 2026, needs more optimization.
30 362 0.189071934975 Henry Cohn, 2026, needs more optimization.
30 366 0.189848087593 Henry Cohn, 2026, needs more optimization.
30 370 0.190727243662 Henry Cohn, 2026, needs more optimization.
30 374 0.191620472840 Henry Cohn, 2026, needs more optimization.
30 384 0.192160835297 Orthogonal union of 382 points in 29 dimensions and 2 points in 1 dimension.
30 385 0.192236929795 Orthogonal union of 383 points in 29 dimensions and 2 points in 1 dimension.
30 398 0.192370002309 Henry Cohn, 2026, needs more optimization.
30 399 0.192370002312 Henry Cohn, 2026, needs more optimization.
30 400 0.192378805877 Henry Cohn, 2026, needs more optimization.
30 401 0.192778231382 Henry Cohn, 2026, needs more optimization.
30 402 0.193028722940 Henry Cohn, 2026, needs more optimization.
30 403 0.193227065722 Henry Cohn, 2026, needs more optimization.
30 404 0.193271892399 Henry Cohn, 2026, needs more optimization.
30 405 0.193493885444 Henry Cohn, 2026, needs more optimization.
30 407 0.193585433501 Henry Cohn, 2026, needs more optimization.
30 408 0.194035224959 Henry Cohn, 2026, needs more optimization.
30 409 0.194283123357 Henry Cohn, 2026, needs more optimization.
30 410 0.194462983546 Henry Cohn, 2026, needs more optimization.
30 411 0.194524642001 Henry Cohn, 2026, needs more optimization.
30 412 0.194746750314 Henry Cohn, 2026, needs more optimization.
30 415 0.194892155633 Henry Cohn, 2026, needs more optimization.
30 416 0.195335017150 Henry Cohn, 2026, needs more optimization.
30 417 0.195632864688 Henry Cohn, 2026, needs more optimization.
30 418 0.195632864690 Henry Cohn, 2026, needs more optimization.
30 419 0.195691239526 Henry Cohn, 2026, needs more optimization.
30 420 0.195926683544 Henry Cohn, 2026, needs more optimization.
30 421 0.196188164891 Henry Cohn, 2026, needs more optimization.
30 422 0.196360338373 Henry Cohn, 2026, needs more optimization.
30 423 0.196623226294 Henry Cohn, 2026, needs more optimization.
30 424 0.196647647178 Henry Cohn, 2026, needs more optimization.
30 425 0.196653540221 Henry Cohn, 2026, needs more optimization.
30 426 0.196757961493 Henry Cohn, 2026, needs more optimization.
30 428 0.196773247804 Henry Cohn, 2026, needs more optimization.
30 429 0.196837650631 Henry Cohn, 2026, needs more optimization.
30 430 0.197090224360 Henry Cohn, 2026, needs more optimization.
30 431 0.197267979532 Henry Cohn, 2026, needs more optimization.
30 432 0.197297142542 Henry Cohn, 2026, needs more optimization.
30 434 0.197471364113 Henry Cohn, 2026, needs more optimization.
30 435 0.197569926355 Henry Cohn, 2026, needs more optimization.
30 436 0.197726552263 Henry Cohn, 2026, needs more optimization.
30 438 0.197817479204 Henry Cohn, 2026, needs more optimization.
30 439 0.197856383505 Henry Cohn, 2026, needs more optimization.
30 441 0.198207350313 Henry Cohn, 2026, needs more optimization.
30 442 0.198421348793 Henry Cohn, 2026, needs more optimization.
30 443 0.198425018437 Henry Cohn, 2026, needs more optimization.
30 444 0.198440945832 Henry Cohn, 2026, needs more optimization.
30 447 0.198487391592 Henry Cohn, 2026, needs more optimization.
30 448 0.198546999628 Henry Cohn, 2026, needs more optimization.
30 451 0.198687566226 Henry Cohn, 2026, needs more optimization.
30 452 0.198687566229 Henry Cohn, 2026, needs more optimization.
30 453 0.198790020093 Henry Cohn, 2026, needs more optimization.
30 454 0.198913925670 Henry Cohn, 2026, needs more optimization.
30 455 0.199030437566 Henry Cohn, 2026, needs more optimization.
30 457 0.199063110983 Henry Cohn, 2026, needs more optimization.
30 459 0.199128296654 Henry Cohn, 2026, needs more optimization.
30 460 0.199154565772 Henry Cohn, 2026, needs more optimization.
30 467 0.199180471335 Henry Cohn, 2026, needs more optimization.
30 468 0.199251858638 Henry Cohn, 2026, needs more optimization.
30 470 0.199254239267 Henry Cohn, 2026, needs more optimization.
30 472 0.199310586858 Henry Cohn, 2026, needs more optimization.
30 474 0.199325970830 Henry Cohn, 2026, needs more optimization.
30 481 0.199417349379 Henry Cohn, 2026, needs more optimization.
30 483 0.199441215742 Henry Cohn, 2026, needs more optimization.
30 484 0.199461439848 Henry Cohn, 2026, needs more optimization.
30 485 0.199478230902 Henry Cohn, 2026, needs more optimization.
30 486 0.199493769705 Henry Cohn, 2026, needs more optimization.
30 487 0.199510497427 Henry Cohn, 2026, needs more optimization.
30 488 0.199518207090 Henry Cohn, 2026, needs more optimization.
30 489 0.199560588003 Henry Cohn, 2026, needs more optimization.
30 490 0.199608497139 Henry Cohn, 2026, needs more optimization.
30 491 0.199622871469 Henry Cohn, 2026, needs more optimization.
30 493 0.199641723121 Henry Cohn, 2026, needs more optimization.
30 494 0.199649964423 Henry Cohn, 2026, needs more optimization.
30 495 0.199666231918 Henry Cohn, 2026, needs more optimization.
30 496 0.199677912699 Henry Cohn, 2026, needs more optimization.
30 499 0.199748248606 Henry Cohn, 2026, needs more optimization.
30 502 0.199749072147 Henry Cohn, 2026, needs more optimization.
30 504 0.199782526584 Henry Cohn, 2026, needs more optimization.
30 505 0.199829547762 Henry Cohn, 2026, needs more optimization.
30 513 0.199846702179 Henry Cohn, 2026, needs more optimization.
30 514 0.199851507286 Henry Cohn, 2026, needs more optimization.
30 515 0.199872070025 Henry Cohn, 2026, needs more optimization.
30 516 0.199880982503 Henry Cohn, 2026, needs more optimization.
30 517 0.199885587968 Henry Cohn, 2026, needs more optimization.
30 518 0.199887395551 Henry Cohn, 2026, needs more optimization.
30 519 0.199897372419 Henry Cohn, 2026, needs more optimization.
30 523 0.199903226968 Henry Cohn, 2026, needs more optimization.
30 524 0.199915656523 Henry Cohn, 2026, needs more optimization.
30 525 0.199932713400 Henry Cohn, 2026, needs more optimization.
30 527 0.199955526945 Henry Cohn, 2026, needs more optimization.
30 528 0.199958555022 Henry Cohn, 2026, needs more optimization.
30 529 0.199968684387 Henry Cohn, 2026, needs more optimization.
30 530 0.199975416646 Henry Cohn, 2026, needs more optimization.
30 533 0.199979781811 Henry Cohn, 2026, needs more optimization.
30 534 0.199983080632 Henry Cohn, 2026, needs more optimization.
30 537 0.199990818973 Henry Cohn, 2026, needs more optimization.
30 538 0.199991104660 Henry Cohn, 2026, needs more optimization.
30 539 0.199991644743 Henry Cohn, 2026, needs more optimization.
30 540 0.199998684088 Henry Cohn, 2026, needs more optimization.
30 576 0.2 Orthogonal union of 552 points in 23 dimensions and 24 points in 7 dimensions.
5⁢x−1
30 577 0.200040738021 Henry Cohn, 2025, needs more optimization.
30 584 0.200044686574 Henry Cohn, 2026, needs more optimization.
30 585 0.200045798599 Henry Cohn, 2025, needs more optimization.
30 587 0.200046648867 Orthogonal union of 585 points in 29 dimensions and 2 points in 1 dimension.
30 588 0.200053323442 Henry Cohn, 2026, needs more optimization.
30 590 0.200053764173 Henry Cohn, 2026, needs more optimization.
30 592 0.200062139434 Henry Cohn, 2026, needs more optimization.
30 593 0.226837055978 Orthogonal union of 577 points in 25 dimensions and 16 points in 5 dimensions.
30 594 0.227891986078 Orthogonal union of 578 points in 25 dimensions and 16 points in 5 dimensions.
30 595 0.228517196126 Orthogonal union of 579 points in 25 dimensions and 16 points in 5 dimensions.
30 596 0.229079598080 Orthogonal union of 580 points in 25 dimensions and 16 points in 5 dimensions.
30 597 0.229882834554 Orthogonal union of 581 points in 25 dimensions and 16 points in 5 dimensions.
30 598 0.230043706448 Orthogonal union of 582 points in 25 dimensions and 16 points in 5 dimensions.
30 599 0.231345472037 Orthogonal union of 583 points in 25 dimensions and 16 points in 5 dimensions.
30 600 0.232207827229 Orthogonal union of 584 points in 25 dimensions and 16 points in 5 dimensions.
30 601 0.232479376363 Orthogonal union of 585 points in 25 dimensions and 16 points in 5 dimensions.
30 602 0.233414506364 Orthogonal union of 586 points in 25 dimensions and 16 points in 5 dimensions.
30 603 0.234451135578 Orthogonal union of 587 points in 25 dimensions and 16 points in 5 dimensions.
30 604 0.234601320648 Orthogonal union of 588 points in 25 dimensions and 16 points in 5 dimensions.
30 606 0.234709607414 Henry Cohn, 2026, needs more optimization.
30 610 0.235091300202 Henry Cohn, 2026, needs more optimization.
30 614 0.235465046891 Henry Cohn, 2026, needs more optimization.
30 618 0.235855990042 Henry Cohn, 2026, needs more optimization.
30 622 0.236283134550 Henry Cohn, 2026, needs more optimization.
30 626 0.236692697312 Henry Cohn, 2026, needs more optimization.
30 630 0.237049794754 Henry Cohn, 2026, needs more optimization.
30 634 0.237359466234 Henry Cohn, 2026, needs more optimization.
30 638 0.237634263679 Henry Cohn, 2026, needs more optimization.
30 642 0.237945572967 Henry Cohn, 2026, needs more optimization.
30 646 0.238639110757 Henry Cohn, 2026, needs more optimization.
30 650 0.240140226664 Henry Cohn, 2026, needs more optimization.
30 652 0.241064041064 Orthogonal union of 650 points in 29 dimensions and 2 points in 1 dimension.
30 654 0.241119808214 Henry Cohn, 2026, needs more optimization.
30 658 0.241496221149 Henry Cohn, 2026, needs more optimization.
30 753 0.241876760769 Henry Cohn, 2026, needs more optimization.
30 756 0.241876760773 Henry Cohn, 2026, needs more optimization.
30 760 0.241925625139 Henry Cohn, 2026, needs more optimization.
30 761 0.241950281887 Henry Cohn, 2026, needs more optimization.
30 762 0.242081556052 Henry Cohn, 2026, needs more optimization.
30 763 0.242164991546 Henry Cohn, 2026, needs more optimization.
30 764 0.242384661864 Henry Cohn, 2026, needs more optimization.
30 765 0.242392395246 Henry Cohn, 2026, needs more optimization.
30 766 0.242459554182 Henry Cohn, 2026, needs more optimization.
30 768 0.242467139304 Henry Cohn, 2026, needs more optimization.
30 769 0.242574154413 Henry Cohn, 2026, needs more optimization.
30 770 0.242680905222 Henry Cohn, 2026, needs more optimization.
30 771 0.242680905223 Henry Cohn, 2026, needs more optimization.
30 773 0.242776851311 Henry Cohn, 2026, needs more optimization.
30 774 0.242885672851 Henry Cohn, 2026, needs more optimization.
30 775 0.242943797204 Henry Cohn, 2026, needs more optimization.
30 776 0.242972196720 Henry Cohn, 2026, needs more optimization.
30 784 0.243121114841 Henry Cohn, 2026, needs more optimization.
30 785 0.243324797753 Henry Cohn, 2026, needs more optimization.
30 787 0.243395533989 Henry Cohn, 2026, needs more optimization.
30 788 0.243475443276 Henry Cohn, 2026, needs more optimization.
30 789 0.243552256241 Henry Cohn, 2026, needs more optimization.
30 790 0.243552256242 Henry Cohn, 2026, needs more optimization.
30 791 0.243582852941 Henry Cohn, 2026, needs more optimization.
30 792 0.243746872918 Henry Cohn, 2026, needs more optimization.
30 793 0.243836202980 Henry Cohn, 2026, needs more optimization.
30 794 0.243872893011 Henry Cohn, 2026, needs more optimization.
30 795 0.243941978332 Henry Cohn, 2026, needs more optimization.
30 796 0.243970074892 Henry Cohn, 2026, needs more optimization.
30 797 0.244113578437 Henry Cohn, 2026, needs more optimization.
30 798 0.244300782865 Henry Cohn, 2026, needs more optimization.
30 800 0.244391367413 Henry Cohn, 2026, needs more optimization.
30 801 0.244457331487 Henry Cohn, 2026, needs more optimization.
30 802 0.244485774379 Henry Cohn, 2026, needs more optimization.
30 803 0.244525683668 Henry Cohn, 2026, needs more optimization.
30 804 0.244633413963 Henry Cohn, 2026, needs more optimization.
30 805 0.244866437581 Henry Cohn, 2026, needs more optimization.
30 806 0.244888157091 Henry Cohn, 2026, needs more optimization.
30 807 0.244992647071 Henry Cohn, 2026, needs more optimization.
30 808 0.244999996408 Henry Cohn, 2026, needs more optimization.
30 809 0.245120331088 Henry Cohn, 2026, needs more optimization.
30 810 0.245233411191 Henry Cohn, 2026, needs more optimization.
30 811 0.245293601967 Henry Cohn, 2026, needs more optimization.
30 812 0.245487044643 Henry Cohn, 2026, needs more optimization.
30 813 0.245520822640 Henry Cohn, 2026, needs more optimization.
30 814 0.245565983927 Henry Cohn, 2026, needs more optimization.
30 815 0.245662769910 Henry Cohn, 2026, needs more optimization.
30 816 0.245687927109 Henry Cohn, 2026, needs more optimization.
30 817 0.245743681581 Henry Cohn, 2026, needs more optimization.
30 818 0.245939187523 Henry Cohn, 2026, needs more optimization.
30 819 0.245966283813 Henry Cohn, 2026, needs more optimization.
30 820 0.246059522281 Henry Cohn, 2026, needs more optimization.
30 821 0.246119064012 Henry Cohn, 2026, needs more optimization.
30 822 0.246128185579 Henry Cohn, 2026, needs more optimization.
30 823 0.246192585721 Henry Cohn, 2026, needs more optimization.
30 824 0.246233868303 Henry Cohn, 2026, needs more optimization.
30 825 0.246258670940 Henry Cohn, 2026, needs more optimization.
30 826 0.246387783692 Henry Cohn, 2026, needs more optimization.
30 827 0.246498127902 Henry Cohn, 2026, needs more optimization.
30 828 0.246547878675 Henry Cohn, 2026, needs more optimization.
30 829 0.246625917659 Henry Cohn, 2026, needs more optimization.
30 830 0.246675162575 Henry Cohn, 2026, needs more optimization.
30 831 0.246689552461 Henry Cohn, 2026, needs more optimization.
30 833 0.246847740330 Henry Cohn, 2026, needs more optimization.
30 834 0.246872453417 Henry Cohn, 2026, needs more optimization.
30 835 0.246927042335 Henry Cohn, 2026, needs more optimization.
30 836 0.247009706496 Henry Cohn, 2026, needs more optimization.
30 838 0.247018481400 Henry Cohn, 2026, needs more optimization.
30 839 0.247103302624 Henry Cohn, 2026, needs more optimization.
30 840 0.247125707741 Henry Cohn, 2026, needs more optimization.
30 841 0.247165008319 Henry Cohn, 2026, needs more optimization.
30 842 0.247171606760 Henry Cohn, 2026, needs more optimization.
30 843 0.247236224085 Henry Cohn, 2026, needs more optimization.
30 844 0.247288692617 Henry Cohn, 2026, needs more optimization.
30 845 0.247395526398 Henry Cohn, 2026, needs more optimization.
30 846 0.247477116213 Henry Cohn, 2026, needs more optimization.
30 847 0.247516380024 Henry Cohn, 2026, needs more optimization.
30 848 0.247583820949 Henry Cohn, 2026, needs more optimization.
30 849 0.247729698094 Henry Cohn, 2026, needs more optimization.
30 850 0.247754224721 Henry Cohn, 2026, needs more optimization.
30 851 0.247766978070 Henry Cohn, 2026, needs more optimization.
30 852 0.247799856430 Henry Cohn, 2026, needs more optimization.
30 853 0.247828909642 Henry Cohn, 2026, needs more optimization.
30 854 0.247903388538 Henry Cohn, 2026, needs more optimization.
30 855 0.247921572871 Henry Cohn, 2026, needs more optimization.
30 856 0.247934425625 Henry Cohn, 2026, needs more optimization.
30 857 0.247958263318 Henry Cohn, 2026, needs more optimization.
30 858 0.248075455761 Henry Cohn, 2026, needs more optimization.
30 859 0.248086884826 Henry Cohn, 2026, needs more optimization.
30 862 0.248097138605 Henry Cohn, 2026, needs more optimization.
30 863 0.248142541625 Henry Cohn, 2026, needs more optimization.
30 864 0.248182454805 Henry Cohn, 2026, needs more optimization.
30 865 0.248209344609 Henry Cohn, 2026, needs more optimization.
30 866 0.248269022013 Henry Cohn, 2026, needs more optimization.
30 867 0.248280822237 Henry Cohn, 2026, needs more optimization.
30 868 0.248289358213 Henry Cohn, 2026, needs more optimization.
30 869 0.248353212684 Henry Cohn, 2026, needs more optimization.
30 870 0.248356716671 Henry Cohn, 2026, needs more optimization.
30 871 0.248379918034 Henry Cohn, 2026, needs more optimization.
30 872 0.248385298926 Henry Cohn, 2026, needs more optimization.
30 873 0.248460929795 Henry Cohn, 2026, needs more optimization.
30 874 0.248489005299 Henry Cohn, 2026, needs more optimization.
30 875 0.248489272590 Henry Cohn, 2026, needs more optimization.
30 876 0.248504381633 Henry Cohn, 2026, needs more optimization.
30 877 0.248533928222 Henry Cohn, 2026, needs more optimization.
30 878 0.248580993437 Henry Cohn, 2026, needs more optimization.
30 879 0.248615380709 Henry Cohn, 2026, needs more optimization.
30 880 0.248649934274 Henry Cohn, 2026, needs more optimization.
30 881 0.248749764482 Henry Cohn, 2026, needs more optimization.
30 883 0.248749764485 Henry Cohn, 2026, needs more optimization.
30 884 0.248790005647 Henry Cohn, 2026, needs more optimization.
30 885 0.248802283055 Henry Cohn, 2026, needs more optimization.
30 886 0.248811237023 Henry Cohn, 2026, needs more optimization.
30 887 0.248864858840 Henry Cohn, 2026, needs more optimization.
30 888 0.248885312406 Henry Cohn, 2026, needs more optimization.
30 889 0.248894959637 Henry Cohn, 2026, needs more optimization.
30 891 0.248908590194 Henry Cohn, 2026, needs more optimization.
30 892 0.248913648927 Henry Cohn, 2026, needs more optimization.
30 893 0.248925172348 Henry Cohn, 2026, needs more optimization.
30 894 0.249002930714 Henry Cohn, 2026, needs more optimization.
30 895 0.249036806916 Henry Cohn, 2026, needs more optimization.
30 896 0.249059671536 Henry Cohn, 2026, needs more optimization.
30 897 0.249125892055 Henry Cohn, 2026, needs more optimization.
30 898 0.249133758617 Henry Cohn, 2026, needs more optimization.
30 899 0.249164778135 Henry Cohn, 2026, needs more optimization.
30 900 0.249187059354 Henry Cohn, 2026, needs more optimization.
30 904 0.249233761044 Henry Cohn, 2026, needs more optimization.
30 907 0.249233761048 Henry Cohn, 2026, needs more optimization.
30 908 0.249250870524 Henry Cohn, 2026, needs more optimization.
30 909 0.249270335779 Henry Cohn, 2026, needs more optimization.
30 911 0.249305726755 Henry Cohn, 2026, needs more optimization.
30 912 0.249338298055 Henry Cohn, 2026, needs more optimization.
30 913 0.249339302944 Henry Cohn, 2026, needs more optimization.
30 915 0.249408041356 Henry Cohn, 2026, needs more optimization.
30 917 0.249410522002 Henry Cohn, 2026, needs more optimization.
30 918 0.249416608247 Henry Cohn, 2026, needs more optimization.
30 919 0.249436035038 Henry Cohn, 2026, needs more optimization.
30 920 0.249447540837 Henry Cohn, 2026, needs more optimization.
30 921 0.249462584520 Henry Cohn, 2026, needs more optimization.
30 922 0.249466004892 Henry Cohn, 2026, needs more optimization.
30 924 0.249469081691 Henry Cohn, 2026, needs more optimization.
30 925 0.249478820205 Henry Cohn, 2026, needs more optimization.
30 926 0.249504192830 Henry Cohn, 2026, needs more optimization.
30 928 0.249515725630 Henry Cohn, 2026, needs more optimization.
30 929 0.249534842473 Henry Cohn, 2026, needs more optimization.
30 931 0.249536843571 Henry Cohn, 2026, needs more optimization.
30 932 0.249538124589 Henry Cohn, 2026, needs more optimization.
30 935 0.249561294503 Henry Cohn, 2026, needs more optimization.
30 936 0.249570584059 Henry Cohn, 2026, needs more optimization.
30 937 0.249585952724 Henry Cohn, 2026, needs more optimization.
30 938 0.249616831012 Henry Cohn, 2026, needs more optimization.
30 939 0.249638861965 Henry Cohn, 2026, needs more optimization.
30 940 0.249659154844 Henry Cohn, 2026, needs more optimization.
30 941 0.249668032070 Henry Cohn, 2026, needs more optimization.
30 942 0.249672071706 Henry Cohn, 2026, needs more optimization.
30 943 0.249673204244 Henry Cohn, 2026, needs more optimization.
30 945 0.249719517410 Henry Cohn, 2026, needs more optimization.
30 946 0.249731467091 Henry Cohn, 2026, needs more optimization.
30 951 0.249732280973 Henry Cohn, 2026, needs more optimization.
30 952 0.249739163392 Henry Cohn, 2026, needs more optimization.
30 954 0.249759620365 Henry Cohn, 2026, needs more optimization.
30 957 0.249760762882 Henry Cohn, 2026, needs more optimization.
30 958 0.249770799071 Henry Cohn, 2026, needs more optimization.
30 959 0.249780368517 Henry Cohn, 2026, needs more optimization.
30 960 0.249790234216 Henry Cohn, 2026, needs more optimization.
30 961 0.249808781435 Henry Cohn, 2026, needs more optimization.
30 962 0.249814349217 Henry Cohn, 2026, needs more optimization.
30 964 0.249825055668 Henry Cohn, 2026, needs more optimization.
30 965 0.249849604423 Henry Cohn, 2026, needs more optimization.
30 968 0.249850438346 Henry Cohn, 2026, needs more optimization.
30 969 0.249852450531 Henry Cohn, 2026, needs more optimization.
30 970 0.249853274221 Henry Cohn, 2026, needs more optimization.
30 972 0.249853711812 Henry Cohn, 2026, needs more optimization.
30 979 0.249856509683 Henry Cohn, 2026, needs more optimization.
30 980 0.249858931342 Henry Cohn, 2026, needs more optimization.
30 981 0.249864635857 Henry Cohn, 2026, needs more optimization.
30 982 0.249869446091 Henry Cohn, 2026, needs more optimization.
30 983 0.249878908620 Henry Cohn, 2026, needs more optimization.
30 984 0.249895302796 Henry Cohn, 2026, needs more optimization.
30 993 0.249901342491 Henry Cohn, 2026, needs more optimization.
30 995 0.249902199077 Henry Cohn, 2026, needs more optimization.
30 996 0.249908840006 Henry Cohn, 2026, needs more optimization.
30 997 0.249911333245 Henry Cohn, 2026, needs more optimization.
30 998 0.249915238465 Henry Cohn, 2026, needs more optimization.
30 1002 0.249949597777 Henry Cohn, 2026, needs more optimization.
30 1003 0.249961313037 Henry Cohn, 2026, needs more optimization.
30 1006 0.249968056974 Henry Cohn, 2026, needs more optimization.
30 1007 0.249972752570 Henry Cohn, 2026, needs more optimization.
30 1008 0.249982323678 Henry Cohn, 2026, needs more optimization.
30 1012 0.249985420945 Henry Cohn, 2026, needs more optimization.
30 1013 0.249990552578 Henry Cohn, 2026, needs more optimization.
30 1014 0.249993520765 Henry Cohn, 2026, needs more optimization.
30 1015 0.250007498810 Henry Cohn, 2026, needs more optimization.
30 1018 0.250026442856 Henry Cohn, 2026, needs more optimization.
30 1019 0.250027874901 Henry Cohn, 2026, needs more optimization.
30 1020 0.250036815690 Henry Cohn, 2026, needs more optimization.
30 1021 0.250058249439 Henry Cohn, 2026, needs more optimization.
30 1022 0.250069452780 Henry Cohn, 2026, needs more optimization.
30 1023 0.250087063632 Henry Cohn, 2026, needs more optimization.
30 1024 0.250090425259 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 0.030325216616 Henry Cohn, 2026, needs more optimization.
31 65 0.038587061312 Ilmari Vahteristo, 2026.
31 66 0.040710793741 Henry Cohn, 2026, needs more optimization.
31 67 0.043134050006 Henry Cohn, 2026, needs more optimization.
31 68 0.043324044266 Henry Cohn, 2026, needs more optimization.
31 69 0.043538634462 Henry Cohn, 2026, needs more optimization.
31 70 0.043787493775 Henry Cohn, 2026, needs more optimization.
31 71 0.044034236203 Henry Cohn, 2026, needs more optimization.
31 72 0.044583881522 Henry Cohn, 2026, needs more optimization.
31 73 0.048691227081 Henry Cohn, 2026, needs more optimization.
31 74 0.050068906658 Henry Cohn, 2026, needs more optimization.
31 75 0.051097142864 Henry Cohn, 2026, needs more optimization.
31 76 0.052578474484 Henry Cohn, 2026, needs more optimization.
31 77 0.054468176290 Ilmari Vahteristo, 2026.
31 78 0.055755125850 Henry Cohn, 2026, needs more optimization.
31 79 0.057285189631 Ilmari Vahteristo, 2026.
31 80 0.058638157280 Ilmari Vahteristo, 2026.
31 81 0.060011874851 Ilmari Vahteristo, 2026.
31 82 0.061360497543 Henry Cohn, 2026, needs more optimization.
31 83 0.061682454688 Henry Cohn, 2026, needs more optimization.
31 84 0.062652681104 Henry Cohn, 2026, needs more optimization.
31 85 0.063452446807 Henry Cohn, 2026, needs more optimization.
31 86 0.064512139059 Henry Cohn, 2026, needs more optimization.
31 87 0.065619149752 Henry Cohn, 2026, needs more optimization.
31 88 0.067223307140 Henry Cohn, 2026, needs more optimization.
31 89 0.069596930641 Henry Cohn, 2026, needs more optimization.
31 90 0.071124886555 Henry Cohn, 2026, needs more optimization.
31 91 0.072108555360 Henry Cohn, 2026, needs more optimization.
31 92 0.073158660173 Henry Cohn, 2026, needs more optimization.
31 93 0.074056359519 Henry Cohn, 2026, needs more optimization.
31 94 0.074944641937 Henry Cohn, 2026, needs more optimization.
31 95 0.075956287140 Henry Cohn, 2026, needs more optimization.
31 96 0.076046097199 Henry Cohn, 2026, needs more optimization.
31 97 0.076531817938 Henry Cohn, 2026, needs more optimization.
31 98 0.076842155335 Henry Cohn, 2026, needs more optimization.
31 99 0.076884242302 Henry Cohn, 2026, needs more optimization.
31 100 0.076928946092 Henry Cohn, 2026, needs more optimization.
31 101 0.076991739075 Henry Cohn, 2026, needs more optimization.
31 102 0.077155223458 Henry Cohn, 2026, needs more optimization.
31 103 0.077296138734 Henry Cohn, 2026, needs more optimization.
31 104 0.077401070294 Henry Cohn, 2026, needs more optimization.
31 105 0.077815147677 Henry Cohn, 2026, needs more optimization.
31 106 0.078227955178 Henry Cohn, 2026, needs more optimization.
31 107 0.078762320848 Henry Cohn, 2026, needs more optimization.
31 108 0.079523994794 Henry Cohn, 2026, needs more optimization.
31 109 0.079853122455 Henry Cohn, 2026, needs more optimization.
31 110 0.080553787147 Henry Cohn, 2026, needs more optimization.
31 111 0.080664448264 Henry Cohn, 2026, needs more optimization.
31 112 0.080739352548 Henry Cohn, 2026, needs more optimization.
31 113 0.081339754384 Henry Cohn, 2026, needs more optimization.
31 114 0.081871728079 Henry Cohn, 2026, needs more optimization.
31 115 0.082456612919 Henry Cohn, 2026, needs more optimization.
31 116 0.083371330980 Henry Cohn, 2026, needs more optimization.
31 117 0.084483653947 Henry Cohn, 2026, needs more optimization.
31 118 0.085723717898 Henry Cohn, 2026, needs more optimization.
31 119 0.086897669205 Henry Cohn, 2026, needs more optimization.
31 120 0.087844519837 Henry Cohn, 2026, needs more optimization.
31 121 0.088325096133 Henry Cohn, 2026, needs more optimization.
31 122 0.088727578361 Henry Cohn, 2026, needs more optimization.
31 123 0.088884902741 Henry Cohn, 2026, needs more optimization.
31 124 0.089206300374 Henry Cohn, 2026, needs more optimization.
31 125 0.089609400793 Henry Cohn, 2026, needs more optimization.
31 126 0.089923267752 Henry Cohn, 2026, needs more optimization.
31 127 0.090331299113 Henry Cohn, 2026, needs more optimization.
31 128 0.090621899615 Henry Cohn, 2026, needs more optimization.
31 129 0.090757888841 Henry Cohn, 2026, needs more optimization.
31 130 0.091274922067 Henry Cohn, 2026, needs more optimization.
31 131 0.092328860934 Henry Cohn, 2026, needs more optimization.
31 132 0.093190738521 Henry Cohn, 2026, needs more optimization.
31 133 0.094606477480 Henry Cohn, 2026, needs more optimization.
31 134 0.095448357853 Henry Cohn, 2026, needs more optimization.
31 135 0.096348341677 Henry Cohn, 2026, needs more optimization.
31 136 0.097760271961 Henry Cohn, 2026, needs more optimization.
31 137 0.098801227526 Henry Cohn, 2026, needs more optimization.
31 138 0.099762218841 Henry Cohn, 2026, needs more optimization.
31 139 0.100459784728 Henry Cohn, 2026, needs more optimization.
31 140 0.102422166238 Henry Cohn, 2026, needs more optimization.
31 141 0.102478843476 Henry Cohn, 2026, needs more optimization.
31 142 0.102494593718 Henry Cohn, 2026, needs more optimization.
31 143 0.102507706916 Henry Cohn, 2026, needs more optimization.
31 144 0.102565682949 Henry Cohn, 2026, needs more optimization.
31 145 0.102694774029 Henry Cohn, 2026, needs more optimization.
31 146 0.102851684934 Henry Cohn, 2026, needs more optimization.
31 147 0.103822486786 Henry Cohn, 2026, needs more optimization.
31 148 0.104757380322 Henry Cohn, 2026, needs more optimization.
31 149 0.105241075846 Henry Cohn, 2026, needs more optimization.
31 150 0.106275090447 Henry Cohn, 2026, needs more optimization.
31 151 0.107207111028 Henry Cohn, 2026, needs more optimization.
31 152 0.107984512466 Henry Cohn, 2026, needs more optimization.
31 153 0.108742896634 Henry Cohn, 2026, needs more optimization.
31 154 0.109419893089 Henry Cohn, 2026, needs more optimization.
31 155 0.109986285199 Henry Cohn, 2026, needs more optimization.
31 156 0.110202674835 Henry Cohn, 2026, needs more optimization.
31 157 0.110367715912 Henry Cohn, 2026, needs more optimization.
31 158 0.110466553846 Henry Cohn, 2026, needs more optimization.
31 159 0.110683803280 Henry Cohn, 2026, needs more optimization.
31 160 0.111217540401 Henry Cohn, 2026, needs more optimization.
31 161 0.111539507563 Henry Cohn, 2026, needs more optimization.
31 162 0.112468247005 Henry Cohn, 2026, needs more optimization.
31 163 0.113078481523 Henry Cohn, 2026, needs more optimization.
31 164 0.113823417183 Henry Cohn, 2026, needs more optimization.
31 165 0.115183868344 Henry Cohn, 2026, needs more optimization.
31 166 0.116356734148 Henry Cohn, 2026, needs more optimization.
31 167 0.117502666481 Henry Cohn, 2026, needs more optimization.
31 168 0.118819070702 Henry Cohn, 2026, needs more optimization.
31 169 0.119636177555 Henry Cohn, 2026, needs more optimization.
31 170 0.120660659360 Henry Cohn, 2026, needs more optimization.
31 171 0.121398286319 Henry Cohn, 2026, needs more optimization.
31 172 0.122052749996 Henry Cohn, 2026, needs more optimization.
31 173 0.123043185398 Henry Cohn, 2026, needs more optimization.
31 174 0.123654081023 Henry Cohn, 2026, needs more optimization.
31 175 0.124763897973 Henry Cohn, 2026, needs more optimization.
31 176 0.125771223722 Henry Cohn, 2026, needs more optimization.
31 177 0.126364877112 Henry Cohn, 2026, needs more optimization.
31 178 0.127056451657 Henry Cohn, 2026, needs more optimization.
31 179 0.127668293746 Henry Cohn, 2026, needs more optimization.
31 180 0.128381723655 Henry Cohn, 2026, needs more optimization.
31 181 0.129251132184 Henry Cohn, 2026, needs more optimization.
31 182 0.129706064675 Henry Cohn, 2026, needs more optimization.
31 183 0.129765434118 Henry Cohn, 2026, needs more optimization.
31 184 0.131354484654 Henry Cohn, 2026, needs more optimization.
31 185 0.131593419227 Henry Cohn, 2026, needs more optimization.
31 186 0.131882891110 Henry Cohn, 2026, needs more optimization.
31 187 0.131904314736 Henry Cohn, 2026, needs more optimization.
31 188 0.132646899997 Henry Cohn, 2026, needs more optimization.
31 189 0.132815880196 Henry Cohn, 2026, needs more optimization.
31 190 0.132862119350 Henry Cohn, 2026, needs more optimization.
31 191 0.133043611167 Henry Cohn, 2026, needs more optimization.
31 192 0.133248152435 Henry Cohn, 2026, needs more optimization.
31 193 0.133336339099 Henry Cohn, 2026, needs more optimization.
31 194 0.133413213997 Henry Cohn, 2026, needs more optimization.
31 195 0.133760570021 Henry Cohn, 2026, needs more optimization.
31 196 0.133954398227 Henry Cohn, 2026, needs more optimization.
31 197 0.134012083391 Henry Cohn, 2026, needs more optimization.
31 198 0.134336715438 Henry Cohn, 2026, needs more optimization.
31 199 0.134613289334 Henry Cohn, 2026, needs more optimization.
31 200 0.134735987852 Henry Cohn, 2026, needs more optimization.
31 201 0.135039657125 Henry Cohn, 2026, needs more optimization.
31 202 0.135900340426 Henry Cohn, 2026, needs more optimization.
31 203 0.136750801304 Henry Cohn, 2026, needs more optimization.
31 204 0.137364167602 Henry Cohn, 2026, needs more optimization.
31 205 0.137534137820 Henry Cohn, 2026, needs more optimization.
31 206 0.138237068996 Henry Cohn, 2026, needs more optimization.
31 207 0.138689633306 Henry Cohn, 2026, needs more optimization.
31 208 0.140077995388 Henry Cohn, 2026, needs more optimization.
31 209 0.140270918191 Henry Cohn, 2026, needs more optimization.
31 210 0.140531077818 Henry Cohn, 2026, needs more optimization.
31 211 0.140544390306 Henry Cohn, 2026, needs more optimization.
31 212 0.140752408754 Henry Cohn, 2026, needs more optimization.
31 213 0.140844230601 Henry Cohn, 2026, needs more optimization.
31 214 0.140917387532 Henry Cohn, 2026, needs more optimization.
31 215 0.141026128177 Henry Cohn, 2026, needs more optimization.
31 216 0.141135316362 Henry Cohn, 2026, needs more optimization.
31 217 0.141225569395 Henry Cohn, 2026, needs more optimization.
31 218 0.141309940323 Henry Cohn, 2026, needs more optimization.
31 219 0.141544152141 Henry Cohn, 2026, needs more optimization.
31 220 0.141918948822 Henry Cohn, 2026, needs more optimization.
31 221 0.141979640792 Henry Cohn, 2026, needs more optimization.
31 222 0.142057840546 Henry Cohn, 2026, needs more optimization.
31 223 0.142108909193 Henry Cohn, 2026, needs more optimization.
31 224 0.142165236540 Henry Cohn, 2026, needs more optimization.
31 225 0.142531456788 Henry Cohn, 2026, needs more optimization.
31 226 0.142820242875 Henry Cohn, 2026, needs more optimization.
31 227 0.142972400103 Henry Cohn, 2026, needs more optimization.
31 228 0.143198539612 Henry Cohn, 2026, needs more optimization.
31 229 0.143790628679 Henry Cohn, 2026, needs more optimization.
31 230 0.144364147702 Henry Cohn, 2026, needs more optimization.
31 231 0.144763465017 Henry Cohn, 2026, needs more optimization.
31 232 0.144900582618 Henry Cohn, 2026, needs more optimization.
31 233 0.145276499009 Henry Cohn, 2026, needs more optimization.
31 234 0.145346773767 Henry Cohn, 2026, needs more optimization.
31 235 0.145415596679 Henry Cohn, 2026, needs more optimization.
31 236 0.145518132015 Henry Cohn, 2026, needs more optimization.
31 237 0.145639989376 Henry Cohn, 2026, needs more optimization.
31 238 0.145808939908 Henry Cohn, 2026, needs more optimization.
31 239 0.145936442140 Henry Cohn, 2026, needs more optimization.
31 240 0.146048093460 Henry Cohn, 2026, needs more optimization.
31 241 0.146088604508 Henry Cohn, 2026, needs more optimization.
31 242 0.146220488420 Henry Cohn, 2026, needs more optimization.
31 243 0.146421833288 Henry Cohn, 2026, needs more optimization.
31 244 0.146544906261 Henry Cohn, 2026, needs more optimization.
31 245 0.146703592115 Henry Cohn, 2026, needs more optimization.
31 246 0.146843836244 Henry Cohn, 2026, needs more optimization.
31 247 0.147020861064 Henry Cohn, 2026, needs more optimization.
31 248 0.147085896315 Henry Cohn, 2026, needs more optimization.
31 249 0.147165085115 Henry Cohn, 2026, needs more optimization.
31 250 0.147603445875 Henry Cohn, 2026, needs more optimization.
31 251 0.147763776793 Henry Cohn, 2026, needs more optimization.
31 252 0.147962455025 Henry Cohn, 2026, needs more optimization.
31 253 0.148039003445 Henry Cohn, 2026, needs more optimization.
31 254 0.148160581923 Henry Cohn, 2026, needs more optimization.
31 255 0.148377961395 Henry Cohn, 2026, needs more optimization.
31 256 0.148389402275 Henry Cohn, 2026, needs more optimization.
31 257 0.148536899884 Henry Cohn, 2026, needs more optimization.
31 258 0.148582492602 Henry Cohn, 2026, needs more optimization.
31 259 0.148601540320 Henry Cohn, 2026, needs more optimization.
31 260 0.148704823187 Henry Cohn, 2026, needs more optimization.
31 261 0.149417993793 Henry Cohn, 2026, needs more optimization.
31 262 0.149833594255 Henry Cohn, 2026, needs more optimization.
31 263 0.149983971476 Henry Cohn, 2026, needs more optimization.
31 264 0.150142842710 Henry Cohn, 2026, needs more optimization.
31 265 0.150360920151 Henry Cohn, 2026, needs more optimization.
31 266 0.151664841130 Henry Cohn, 2026, needs more optimization.
31 267 0.152095130672 Henry Cohn, 2026, needs more optimization.
31 268 0.152772455168 Henry Cohn, 2026, needs more optimization.
31 269 0.154102367893 Henry Cohn, 2026, needs more optimization.
31 270 0.155433139292 Henry Cohn, 2026, needs more optimization.
31 271 0.155757088744 Henry Cohn, 2026, needs more optimization.
31 272 0.156213864894 Henry Cohn, 2026, needs more optimization.
31 273 0.156846541355 Henry Cohn, 2026, needs more optimization.
31 274 0.157128958581 Henry Cohn, 2026, needs more optimization.
31 275 0.157696404174 Henry Cohn, 2026, needs more optimization.
31 276 0.158051977135 Henry Cohn, 2026, needs more optimization.
31 277 0.158492179333 Henry Cohn, 2026, needs more optimization.
31 278 0.159075084204 Henry Cohn, 2026, needs more optimization.
31 279 0.159469018964 Henry Cohn, 2026, needs more optimization.
31 280 0.159829218141 Henry Cohn, 2026, needs more optimization.
31 281 0.160594798884 Henry Cohn, 2026, needs more optimization.
31 282 0.161164654725 Henry Cohn, 2026, needs more optimization.
31 283 0.161302892212 Henry Cohn, 2026, needs more optimization.
31 284 0.161399003364 Henry Cohn, 2026, needs more optimization.
31 285 0.161441145704 Henry Cohn, 2026, needs more optimization.
31 286 0.161539354278 Henry Cohn, 2026, needs more optimization.
31 287 0.161587149190 Henry Cohn, 2026, needs more optimization.
31 288 0.161684561713 Henry Cohn, 2026, needs more optimization.
31 289 0.161711191363 Henry Cohn, 2026, needs more optimization.
31 290 0.161749070240 Henry Cohn, 2026, needs more optimization.
31 291 0.161751791450 Henry Cohn, 2026, needs more optimization.
31 292 0.161811927475 Henry Cohn, 2026, needs more optimization.
31 293 0.161822347347 Henry Cohn, 2026, needs more optimization.
31 294 0.161826874113 Henry Cohn, 2026, needs more optimization.
31 295 0.161849986921 Henry Cohn, 2026, needs more optimization.
31 296 0.161871242089 Henry Cohn, 2026, needs more optimization.
31 297 0.161916349429 Henry Cohn, 2026, needs more optimization.
31 298 0.161953161836 Henry Cohn, 2026, needs more optimization.
31 299 0.162110892923 Henry Cohn, 2026, needs more optimization.
31 300 0.162400010123 Henry Cohn, 2026, needs more optimization.
31 301 0.162955496535 Henry Cohn, 2026, needs more optimization.
31 302 0.164605063582 Orthogonal union of 300 points in 30 dimensions and 2 points in 1 dimension.
31 303 0.164747688579 Orthogonal union of 301 points in 30 dimensions and 2 points in 1 dimension.
31 304 0.165552292076 Henry Cohn, 2026, needs more optimization.
31 305 0.165585981557 Henry Cohn, 2026, needs more optimization.
31 306 0.165591461572 Henry Cohn, 2026, needs more optimization.
31 307 0.166666666662 Henry Cohn, 2025, needs more optimization.
31 309 0.166686188122 Orthogonal union of 299 points in 27 dimensions and 10 points in 4 dimensions.
31 310 0.166696298850 Orthogonal union of 300 points in 27 dimensions and 10 points in 4 dimensions.
31 311 0.166799257665 Orthogonal union of 301 points in 27 dimensions and 10 points in 4 dimensions.
31 312 0.170818468627 Orthogonal union of 300 points in 26 dimensions and 12 points in 5 dimensions.
31 313 0.171964316023 Orthogonal union of 301 points in 26 dimensions and 12 points in 5 dimensions.
31 314 0.175623792013 Henry Cohn, 2026, needs more optimization.
31 315 0.175683376665 Henry Cohn, 2025, needs more optimization.
31 316 0.175728673343 Henry Cohn, 2026, needs more optimization.
31 317 0.175792168087 Henry Cohn, 2026, needs more optimization.
31 318 0.175798079510 Henry Cohn, 2026, needs more optimization.
31 320 0.175814222432 Henry Cohn, 2026, needs more optimization.
31 321 0.175847644698 Henry Cohn, 2025, needs more optimization.
31 322 0.175880645854 Henry Cohn, 2026, needs more optimization.
31 323 0.176086193436 Henry Cohn, 2026, needs more optimization.
31 326 0.176566681371 Henry Cohn, 2026, needs more optimization.
31 330 0.177890436803 Henry Cohn, 2026, needs more optimization.
31 332 0.179417147936 Henry Cohn, 2026, needs more optimization.
31 334 0.179418673018 Henry Cohn, 2026, needs more optimization.
31 337 0.179816597375 Henry Cohn, 2026, needs more optimization.
31 338 0.179816597507 Henry Cohn, 2026, needs more optimization.
31 342 0.180525865504 Henry Cohn, 2026, needs more optimization.
31 346 0.181115523530 Henry Cohn, 2026, needs more optimization.
31 350 0.181592931627 Henry Cohn, 2026, needs more optimization.
31 354 0.182123822051 Henry Cohn, 2026, needs more optimization.
31 358 0.182842228516 Henry Cohn, 2026, needs more optimization.
31 362 0.183440152657 Henry Cohn, 2026, needs more optimization.
31 366 0.184190020056 Henry Cohn, 2026, needs more optimization.
31 370 0.185172547775 Henry Cohn, 2026, needs more optimization.
31 374 0.186154097322 Henry Cohn, 2026, needs more optimization.
31 378 0.187220631079 Henry Cohn, 2026, needs more optimization.
31 382 0.188097382404 Henry Cohn, 2026, needs more optimization.
31 386 0.189294030038 Henry Cohn, 2026, needs more optimization.
31 406 0.190088389105 Henry Cohn, 2026, needs more optimization.
31 413 0.190088389108 Henry Cohn, 2026, needs more optimization.
31 415 0.190137665515 Henry Cohn, 2026, needs more optimization.
31 416 0.190239389346 Henry Cohn, 2026, needs more optimization.
31 417 0.190548867742 Henry Cohn, 2026, needs more optimization.
31 418 0.190590966326 Henry Cohn, 2026, needs more optimization.
31 419 0.190762371723 Henry Cohn, 2026, needs more optimization.
31 420 0.190796326527 Henry Cohn, 2026, needs more optimization.
31 421 0.190978624066 Henry Cohn, 2026, needs more optimization.
31 422 0.191237190251 Henry Cohn, 2026, needs more optimization.
31 423 0.191463620641 Henry Cohn, 2026, needs more optimization.
31 424 0.191823470729 Henry Cohn, 2026, needs more optimization.
31 425 0.191950417615 Henry Cohn, 2026, needs more optimization.
31 426 0.192146192749 Henry Cohn, 2026, needs more optimization.
31 427 0.192246659204 Henry Cohn, 2026, needs more optimization.
31 428 0.192465389818 Henry Cohn, 2026, needs more optimization.
31 429 0.192848674739 Henry Cohn, 2026, needs more optimization.
31 430 0.192923812320 Henry Cohn, 2026, needs more optimization.
31 431 0.193033384812 Henry Cohn, 2026, needs more optimization.
31 432 0.193409245985 Henry Cohn, 2026, needs more optimization.
31 433 0.193615974091 Henry Cohn, 2026, needs more optimization.
31 434 0.193692353415 Henry Cohn, 2026, needs more optimization.
31 435 0.193837871483 Henry Cohn, 2026, needs more optimization.
31 436 0.193993206080 Henry Cohn, 2026, needs more optimization.
31 437 0.194367879103 Henry Cohn, 2026, needs more optimization.
31 438 0.194518318841 Henry Cohn, 2026, needs more optimization.
31 441 0.194666333137 Henry Cohn, 2026, needs more optimization.
31 442 0.194691630362 Henry Cohn, 2026, needs more optimization.
31 443 0.194989605313 Henry Cohn, 2026, needs more optimization.
31 444 0.195397553547 Henry Cohn, 2026, needs more optimization.
31 445 0.195619446163 Henry Cohn, 2026, needs more optimization.
31 446 0.195619446165 Henry Cohn, 2026, needs more optimization.
31 448 0.195698705329 Henry Cohn, 2026, needs more optimization.
31 449 0.195918980712 Henry Cohn, 2026, needs more optimization.
31 450 0.195958690089 Henry Cohn, 2026, needs more optimization.
31 451 0.196053810671 Henry Cohn, 2026, needs more optimization.
31 452 0.196182238863 Henry Cohn, 2026, needs more optimization.
31 453 0.196213959293 Henry Cohn, 2026, needs more optimization.
31 454 0.196366724206 Henry Cohn, 2026, needs more optimization.
31 455 0.196373800179 Henry Cohn, 2026, needs more optimization.
31 456 0.196483090607 Henry Cohn, 2026, needs more optimization.
31 457 0.196552178439 Henry Cohn, 2026, needs more optimization.
31 458 0.196601503270 Henry Cohn, 2026, needs more optimization.
31 459 0.196894792556 Henry Cohn, 2026, needs more optimization.
31 460 0.196924654989 Henry Cohn, 2026, needs more optimization.
31 461 0.197104006483 Henry Cohn, 2026, needs more optimization.
31 462 0.197104006487 Henry Cohn, 2026, needs more optimization.
31 463 0.197239654485 Henry Cohn, 2026, needs more optimization.
31 465 0.197290158030 Henry Cohn, 2026, needs more optimization.
31 467 0.197301921675 Henry Cohn, 2026, needs more optimization.
31 468 0.197521203859 Henry Cohn, 2026, needs more optimization.
31 469 0.197602453251 Henry Cohn, 2026, needs more optimization.
31 470 0.197634047944 Henry Cohn, 2026, needs more optimization.
31 471 0.197679168489 Henry Cohn, 2026, needs more optimization.
31 472 0.197721974396 Henry Cohn, 2026, needs more optimization.
31 473 0.197804333053 Henry Cohn, 2026, needs more optimization.
31 474 0.197944907046 Henry Cohn, 2026, needs more optimization.
31 476 0.198142425172 Henry Cohn, 2026, needs more optimization.
31 477 0.198221918443 Henry Cohn, 2026, needs more optimization.
31 478 0.198287011697 Henry Cohn, 2026, needs more optimization.
31 481 0.198341784062 Henry Cohn, 2026, needs more optimization.
31 482 0.198424996262 Henry Cohn, 2026, needs more optimization.
31 483 0.198467579419 Henry Cohn, 2026, needs more optimization.
31 484 0.198508849436 Henry Cohn, 2026, needs more optimization.
31 486 0.198701356102 Henry Cohn, 2026, needs more optimization.
31 487 0.198826536718 Henry Cohn, 2026, needs more optimization.
31 489 0.198935502157 Henry Cohn, 2026, needs more optimization.
31 491 0.198999241190 Henry Cohn, 2026, needs more optimization.
31 493 0.199097278079 Henry Cohn, 2026, needs more optimization.
31 494 0.199116711686 Henry Cohn, 2026, needs more optimization.
31 495 0.199136889524 Henry Cohn, 2026, needs more optimization.
31 499 0.199242435109 Henry Cohn, 2026, needs more optimization.
31 501 0.199242435110 Henry Cohn, 2026, needs more optimization.
31 503 0.199300356163 Henry Cohn, 2026, needs more optimization.
31 504 0.199317702722 Henry Cohn, 2026, needs more optimization.
31 507 0.199345071773 Henry Cohn, 2026, needs more optimization.
31 510 0.199359562043 Henry Cohn, 2026, needs more optimization.
31 511 0.199360583105 Henry Cohn, 2026, needs more optimization.
31 512 0.199447963387 Henry Cohn, 2026, needs more optimization.
31 516 0.199489505412 Henry Cohn, 2026, needs more optimization.
31 519 0.199504707629 Henry Cohn, 2026, needs more optimization.
31 521 0.199523911650 Henry Cohn, 2026, needs more optimization.
31 522 0.199536115505 Henry Cohn, 2026, needs more optimization.
31 523 0.199552857089 Henry Cohn, 2026, needs more optimization.
31 524 0.199582564547 Henry Cohn, 2026, needs more optimization.
31 525 0.199595001817 Henry Cohn, 2026, needs more optimization.
31 526 0.199603611128 Henry Cohn, 2026, needs more optimization.
31 527 0.199618081585 Henry Cohn, 2026, needs more optimization.
31 528 0.199629100691 Henry Cohn, 2026, needs more optimization.
31 529 0.199641956467 Henry Cohn, 2026, needs more optimization.
31 531 0.199706488207 Henry Cohn, 2026, needs more optimization.
31 533 0.199711392289 Henry Cohn, 2026, needs more optimization.
31 535 0.199719571993 Henry Cohn, 2026, needs more optimization.
31 536 0.199740018073 Henry Cohn, 2026, needs more optimization.
31 537 0.199755300142 Henry Cohn, 2026, needs more optimization.
31 538 0.199763516779 Henry Cohn, 2026, needs more optimization.
31 539 0.199766914739 Henry Cohn, 2026, needs more optimization.
31 540 0.199782574674 Henry Cohn, 2026, needs more optimization.
31 544 0.199800732790 Henry Cohn, 2026, needs more optimization.
31 545 0.199820342619 Henry Cohn, 2026, needs more optimization.
31 549 0.199828886063 Henry Cohn, 2026, needs more optimization.
31 550 0.199830630962 Henry Cohn, 2026, needs more optimization.
31 551 0.199831430650 Henry Cohn, 2026, needs more optimization.
31 552 0.199840181666 Henry Cohn, 2026, needs more optimization.
31 553 0.199861735904 Henry Cohn, 2026, needs more optimization.
31 554 0.199866009668 Henry Cohn, 2026, needs more optimization.
31 555 0.199867722388 Henry Cohn, 2026, needs more optimization.
31 556 0.199882905533 Henry Cohn, 2026, needs more optimization.
31 557 0.199890652777 Henry Cohn, 2026, needs more optimization.
31 558 0.199895946521 Henry Cohn, 2026, needs more optimization.
31 559 0.199896187870 Henry Cohn, 2026, needs more optimization.
31 560 0.199905676537 Henry Cohn, 2026, needs more optimization.
31 561 0.199908781076 Henry Cohn, 2026, needs more optimization.
31 562 0.199910272630 Henry Cohn, 2026, needs more optimization.
31 563 0.199911388864 Henry Cohn, 2026, needs more optimization.
31 564 0.199921607890 Henry Cohn, 2026, needs more optimization.
31 567 0.199923772548 Henry Cohn, 2026, needs more optimization.
31 568 0.199947414272 Henry Cohn, 2026, needs more optimization.
31 570 0.199953138179 Henry Cohn, 2026, needs more optimization.
31 571 0.199954229379 Henry Cohn, 2026, needs more optimization.
31 572 0.199969921292 Henry Cohn, 2026, needs more optimization.
31 573 0.199972871853 Henry Cohn, 2026, needs more optimization.
31 574 0.199973710758 Henry Cohn, 2026, needs more optimization.
31 575 0.199975208992 Henry Cohn, 2026, needs more optimization.
31 577 0.199983342787 Henry Cohn, 2026, needs more optimization.
31 578 0.199984574285 Henry Cohn, 2026, needs more optimization.
31 579 0.199985964552 Henry Cohn, 2026, needs more optimization.
31 583 0.199993074281 Henry Cohn, 2026, needs more optimization.
31 585 0.199997819436 Henry Cohn, 2026, needs more optimization.
31 586 0.200000125390 Henry Cohn, 2026, needs more optimization.
31 589 0.200002611498 Henry Cohn, 2026, needs more optimization.
31 590 0.200002741993 Henry Cohn, 2026, needs more optimization.
31 591 0.200005009269 Henry Cohn, 2026, needs more optimization.
31 595 0.200005009489 Henry Cohn, 2026, needs more optimization.
31 597 0.200006232923 Henry Cohn, 2026, needs more optimization.
31 598 0.200007821657 Henry Cohn, 2026, needs more optimization.
31 600 0.200009348794 Henry Cohn, 2026, needs more optimization.
31 602 0.200011116643 Henry Cohn, 2026, needs more optimization.
31 604 0.200015098892 Henry Cohn, 2026, needs more optimization.
31 605 0.200019950239 Henry Cohn, 2026, needs more optimization.
31 608 0.200020194637 Henry Cohn, 2026, needs more optimization.
31 610 0.200022024831 Henry Cohn, 2026, needs more optimization.
31 611 0.200028137929 Henry Cohn, 2026, needs more optimization.
31 614 0.200033671216 Henry Cohn, 2026, needs more optimization.
31 616 0.200034078018 Henry Cohn, 2026, needs more optimization.
31 617 0.200072525989 Henry Cohn, 2026, needs more optimization.
31 619 0.200081099162 Henry Cohn, 2026, needs more optimization.
31 624 0.200099669636 Henry Cohn, 2026, needs more optimization.
31 625 0.200112129418 Henry Cohn, 2026, needs more optimization.
31 626 0.200119677605 Henry Cohn, 2026, needs more optimization.
31 627 0.200167956713 Henry Cohn, 2026, needs more optimization.
31 628 0.200200337433 Henry Cohn, 2026, needs more optimization.
31 629 0.200206812402 Henry Cohn, 2026, needs more optimization.
31 631 0.200249564394 Henry Cohn, 2026, needs more optimization.
31 632 0.200378652771 Henry Cohn, 2026, needs more optimization.
31 633 0.200435107306 Henry Cohn, 2026, needs more optimization.
31 634 0.200563703812 Henry Cohn, 2026, needs more optimization.
31 635 0.200669409158 Henry Cohn, 2026, needs more optimization.
31 636 0.200676062233 Henry Cohn, 2026, needs more optimization.
31 637 0.200770070603 Henry Cohn, 2026, needs more optimization.
31 638 0.200842676840 Henry Cohn, 2026, needs more optimization.
31 639 0.200976808993 Henry Cohn, 2026, needs more optimization.
31 640 0.201132979514 Henry Cohn, 2026, needs more optimization.
31 641 0.201304258037 Henry Cohn, 2026, needs more optimization.
31 642 0.201481515623 Henry Cohn, 2026, needs more optimization.
31 643 0.201570778422 Henry Cohn, 2026, needs more optimization.
31 644 0.201896089994 Henry Cohn, 2026, needs more optimization.
31 645 0.202134010566 Henry Cohn, 2026, needs more optimization.
31 646 0.202430420126 Henry Cohn, 2026, needs more optimization.
31 647 0.202687481539 Henry Cohn, 2026, needs more optimization.
31 648 0.202955122101 Henry Cohn, 2026, needs more optimization.
31 649 0.203255555988 Henry Cohn, 2026, needs more optimization.
31 650 0.203583719387 Henry Cohn, 2026, needs more optimization.
31 651 0.203987884162 Henry Cohn, 2026, needs more optimization.
31 652 0.204280102105 Henry Cohn, 2026, needs more optimization.
31 653 0.204714937820 Henry Cohn, 2026, needs more optimization.
31 654 0.205019034315 Henry Cohn, 2026, needs more optimization.
31 655 0.205301442180 Henry Cohn, 2026, needs more optimization.
31 656 0.205585634137 Henry Cohn, 2026, needs more optimization.
31 657 0.205909461943 Henry Cohn, 2026, needs more optimization.
31 658 0.206192455320 Henry Cohn, 2026, needs more optimization.
31 659 0.206619280660 Henry Cohn, 2026, needs more optimization.
31 660 0.207089901911 Henry Cohn, 2026, needs more optimization.
31 661 0.207377713620 Henry Cohn, 2026, needs more optimization.
31 662 0.207769846495 Henry Cohn, 2026, needs more optimization.
31 663 0.208119932924 Henry Cohn, 2026, needs more optimization.
31 664 0.208492013768 Henry Cohn, 2026, needs more optimization.
31 665 0.208866001745 Henry Cohn, 2026, needs more optimization.
31 666 0.209130166751 Henry Cohn, 2026, needs more optimization.
31 667 0.209455370892 Henry Cohn, 2026, needs more optimization.
31 668 0.209778411027 Henry Cohn, 2026, needs more optimization.
31 669 0.210056523414 Henry Cohn, 2026, needs more optimization.
31 670 0.210440041205 Henry Cohn, 2026, needs more optimization.
31 671 0.210812036012 Henry Cohn, 2026, needs more optimization.
31 672 0.211188480781 Henry Cohn, 2026, needs more optimization.
31 673 0.211367905422 Henry Cohn, 2026, needs more optimization.
31 674 0.211661012228 Henry Cohn, 2026, needs more optimization.
31 675 0.212063428409 Henry Cohn, 2026, needs more optimization.
31 676 0.212300530230 Henry Cohn, 2026, needs more optimization.
31 677 0.212682778021 Henry Cohn, 2026, needs more optimization.
31 678 0.212933111355 Henry Cohn, 2026, needs more optimization.
31 679 0.213189122402 Henry Cohn, 2026, needs more optimization.
31 680 0.213475506947 Henry Cohn, 2026, needs more optimization.
31 681 0.213783738528 Henry Cohn, 2026, needs more optimization.
31 682 0.214051845127 Henry Cohn, 2026, needs more optimization.
31 683 0.214352854350 Henry Cohn, 2026, needs more optimization.
31 684 0.214565038818 Henry Cohn, 2026, needs more optimization.
31 685 0.214920058267 Henry Cohn, 2026, needs more optimization.
31 686 0.215235811283 Henry Cohn, 2026, needs more optimization.
31 687 0.215618681248 Henry Cohn, 2026, needs more optimization.
31 688 0.215908688137 Henry Cohn, 2026, needs more optimization.
31 689 0.216183069112 Henry Cohn, 2026, needs more optimization.
31 690 0.216471294888 Henry Cohn, 2026, needs more optimization.
31 691 0.216706143433 Henry Cohn, 2026, needs more optimization.
31 692 0.217127415604 Henry Cohn, 2026, needs more optimization.
31 693 0.217497856557 Henry Cohn, 2026, needs more optimization.
31 694 0.217777081465 Henry Cohn, 2026, needs more optimization.
31 695 0.218015500532 Henry Cohn, 2026, needs more optimization.
31 696 0.218236569908 Henry Cohn, 2026, needs more optimization.
31 697 0.218466502395 Henry Cohn, 2026, needs more optimization.
31 698 0.218664436227 Henry Cohn, 2026, needs more optimization.
31 699 0.218898525312 Henry Cohn, 2026, needs more optimization.
31 700 0.219142456219 Henry Cohn, 2026, needs more optimization.
31 701 0.219424913708 Henry Cohn, 2026, needs more optimization.
31 702 0.219751285296 Henry Cohn, 2026, needs more optimization.
31 703 0.220067555699 Henry Cohn, 2026, needs more optimization.
31 704 0.220350371561 Henry Cohn, 2026, needs more optimization.
31 705 0.220624542595 Henry Cohn, 2026, needs more optimization.
31 706 0.220767636183 Henry Cohn, 2026, needs more optimization.
31 707 0.221088008819 Henry Cohn, 2026, needs more optimization.
31 708 0.221324778667 Henry Cohn, 2026, needs more optimization.
31 709 0.221570513266 Henry Cohn, 2026, needs more optimization.
31 710 0.221866410832 Henry Cohn, 2026, needs more optimization.
31 711 0.222115861165 Henry Cohn, 2026, needs more optimization.
31 712 0.222365613888 Henry Cohn, 2026, needs more optimization.
31 713 0.222664927368 Henry Cohn, 2026, needs more optimization.
31 714 0.222873930818 Henry Cohn, 2026, needs more optimization.
31 715 0.223169556834 Henry Cohn, 2026, needs more optimization.
31 716 0.223389225629 Henry Cohn, 2026, needs more optimization.
31 717 0.223694818906 Henry Cohn, 2026, needs more optimization.
31 718 0.224022851989 Henry Cohn, 2026, needs more optimization.
31 719 0.224264036359 Henry Cohn, 2026, needs more optimization.
31 720 0.224500396769 Henry Cohn, 2026, needs more optimization.
31 721 0.224726978536 Henry Cohn, 2026, needs more optimization.
31 722 0.224980209137 Henry Cohn, 2026, needs more optimization.
31 723 0.225218611590 Henry Cohn, 2026, needs more optimization.
31 724 0.225522928399 Henry Cohn, 2026, needs more optimization.
31 725 0.225670919815 Henry Cohn, 2026, needs more optimization.
31 726 0.225933716128 Henry Cohn, 2026, needs more optimization.
31 727 0.226174687868 Henry Cohn, 2026, needs more optimization.
31 728 0.226356440721 Henry Cohn, 2026, needs more optimization.
31 729 0.226651605896 Henry Cohn, 2026, needs more optimization.
31 730 0.226850782418 Henry Cohn, 2026, needs more optimization.
31 731 0.227079826406 Henry Cohn, 2026, needs more optimization.
31 732 0.227296974530 Henry Cohn, 2026, needs more optimization.
31 733 0.227466599802 Henry Cohn, 2026, needs more optimization.
31 734 0.227762673004 Henry Cohn, 2026, needs more optimization.
31 735 0.227949825736 Henry Cohn, 2026, needs more optimization.
31 736 0.228189836647 Henry Cohn, 2026, needs more optimization.
31 737 0.228488573119 Henry Cohn, 2026, needs more optimization.
31 738 0.228749408277 Henry Cohn, 2026, needs more optimization.
31 739 0.228951174333 Henry Cohn, 2026, needs more optimization.
31 740 0.229168882499 Henry Cohn, 2026, needs more optimization.
31 741 0.229320628309 Henry Cohn, 2026, needs more optimization.
31 742 0.229543854879 Henry Cohn, 2026, needs more optimization.
31 743 0.229858588602 Henry Cohn, 2026, needs more optimization.
31 744 0.230105586810 Henry Cohn, 2026, needs more optimization.
31 745 0.230353070821 Henry Cohn, 2026, needs more optimization.
31 746 0.230529780440 Henry Cohn, 2026, needs more optimization.
31 747 0.230772845024 Henry Cohn, 2026, needs more optimization.
31 748 0.231024949049 Henry Cohn, 2026, needs more optimization.
31 749 0.231179123858 Henry Cohn, 2026, needs more optimization.
31 750 0.231428977748 Henry Cohn, 2026, needs more optimization.
31 751 0.231608019906 Henry Cohn, 2026, needs more optimization.
31 752 0.231839206269 Henry Cohn, 2026, needs more optimization.
31 753 0.232075541400 Henry Cohn, 2026, needs more optimization.
31 754 0.232234059585 Henry Cohn, 2026, needs more optimization.
31 755 0.232408264768 Henry Cohn, 2026, needs more optimization.
31 756 0.232600665846 Henry Cohn, 2026, needs more optimization.
31 757 0.232714394959 Henry Cohn, 2026, needs more optimization.
31 758 0.232934967232 Henry Cohn, 2026, needs more optimization.
31 759 0.233169737470 Henry Cohn, 2026, needs more optimization.
31 760 0.233394264910 Henry Cohn, 2026, needs more optimization.
31 761 0.233579113200 Henry Cohn, 2026, needs more optimization.
31 762 0.233772392752 Henry Cohn, 2026, needs more optimization.
31 763 0.233981347636 Henry Cohn, 2026, needs more optimization.
31 764 0.234117893305 Henry Cohn, 2026, needs more optimization.
31 765 0.234314729037 Henry Cohn, 2026, needs more optimization.
31 766 0.234479879758 Henry Cohn, 2026, needs more optimization.
31 767 0.234696622570 Henry Cohn, 2026, needs more optimization.
31 768 0.234862377891 Henry Cohn, 2026, needs more optimization.
31 769 0.235035888744 Henry Cohn, 2026, needs more optimization.
31 770 0.235188104400 Henry Cohn, 2026, needs more optimization.
31 771 0.235312029814 Henry Cohn, 2026, needs more optimization.
31 772 0.235567322293 Henry Cohn, 2026, needs more optimization.
31 773 0.235750151660 Henry Cohn, 2026, needs more optimization.
31 774 0.235912667321 Henry Cohn, 2026, needs more optimization.
31 775 0.236130980460 Henry Cohn, 2026, needs more optimization.
31 776 0.236335169775 Henry Cohn, 2026, needs more optimization.
31 777 0.236491673167 Henry Cohn, 2026, needs more optimization.
31 778 0.236702200745 Henry Cohn, 2026, needs more optimization.
31 779 0.236859482496 Henry Cohn, 2026, needs more optimization.
31 780 0.237088484291 Henry Cohn, 2026, needs more optimization.
31 781 0.237246496269 Henry Cohn, 2026, needs more optimization.
31 782 0.237459812696 Henry Cohn, 2026, needs more optimization.
31 783 0.237651946507 Henry Cohn, 2026, needs more optimization.
31 784 0.237893973228 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 0.029441166533 Henry Cohn, 2026, needs more optimization.
32 67 0.037489253696 Ilmari Vahteristo, 2026.
32 68 0.039710724854 Henry Cohn, 2026, needs more optimization.
32 69 0.042615993445 Henry Cohn, 2026, needs more optimization.
32 70 0.042762186512 Henry Cohn, 2026, needs more optimization.
32 71 0.043042345599 Henry Cohn, 2026, needs more optimization.
32 72 0.043340506643 Henry Cohn, 2026, needs more optimization.
32 73 0.043649527764 Henry Cohn, 2026, needs more optimization.
32 74 0.044346811774 Ilmari Vahteristo, 2026.
32 75 0.046983087364 Ilmari Vahteristo, 2026.
32 76 0.049042197562 Henry Cohn, 2026, needs more optimization.
32 77 0.049882260370 Henry Cohn, 2026, needs more optimization.
32 78 0.051414444819 Henry Cohn, 2026, needs more optimization.
32 79 0.053166694900 Ilmari Vahteristo, 2026.
32 80 0.054903707556 Henry Cohn, 2026, needs more optimization.
32 81 0.055652201104 Ilmari Vahteristo, 2026.
32 82 0.057015816311 Ilmari Vahteristo, 2026.
32 83 0.058225444681 Ilmari Vahteristo, 2026.
32 84 0.059657784537 Henry Cohn, 2026, needs more optimization.
32 85 0.060925480899 Henry Cohn, 2026, needs more optimization.
32 86 0.062006479142 Henry Cohn, 2026, needs more optimization.
32 87 0.063187077029 Henry Cohn, 2026, needs more optimization.
32 88 0.064359806873 Henry Cohn, 2026, needs more optimization.
32 89 0.065582105027 Henry Cohn, 2026, needs more optimization.
32 90 0.066424862472 Henry Cohn, 2026, needs more optimization.
32 91 0.067775431586 Henry Cohn, 2026, needs more optimization.
32 92 0.068708894977 Henry Cohn, 2026, needs more optimization.
32 93 0.069830640093 Henry Cohn, 2026, needs more optimization.
32 94 0.070659157354 Henry Cohn, 2026, needs more optimization.
32 95 0.071717020134 Henry Cohn, 2026, needs more optimization.
32 96 0.072866087236 Henry Cohn, 2026, needs more optimization.
32 97 0.073898376462 Henry Cohn, 2026, needs more optimization.
32 98 0.074757551325 Henry Cohn, 2026, needs more optimization.
32 99 0.075634390348 Henry Cohn, 2026, needs more optimization.
32 100 0.075727405672 Henry Cohn, 2026, needs more optimization.
32 101 0.075940928453 Henry Cohn, 2026, needs more optimization.
32 102 0.076409096042 Henry Cohn, 2026, needs more optimization.
32 103 0.076810158552 Henry Cohn, 2026, needs more optimization.
32 104 0.076963644534 Henry Cohn, 2026, needs more optimization.
32 105 0.077085292560 Henry Cohn, 2026, needs more optimization.
32 106 0.077298513993 Henry Cohn, 2026, needs more optimization.
32 107 0.077429840087 Henry Cohn, 2026, needs more optimization.
32 108 0.077645639590 Henry Cohn, 2026, needs more optimization.
32 109 0.077922450683 Henry Cohn, 2026, needs more optimization.
32 110 0.078056579735 Henry Cohn, 2026, needs more optimization.
32 111 0.078890320737 Henry Cohn, 2026, needs more optimization.
32 112 0.079498099894 Henry Cohn, 2026, needs more optimization.
32 113 0.079894749360 Henry Cohn, 2026, needs more optimization.
32 114 0.080591120913 Henry Cohn, 2026, needs more optimization.
32 115 0.080644771190 Henry Cohn, 2026, needs more optimization.
32 116 0.080914992274 Henry Cohn, 2026, needs more optimization.
32 117 0.080994875503 Henry Cohn, 2026, needs more optimization.
32 118 0.081659658803 Henry Cohn, 2026, needs more optimization.
32 119 0.082502674862 Henry Cohn, 2026, needs more optimization.
32 120 0.083465320166 Henry Cohn, 2026, needs more optimization.
32 121 0.084554139069 Henry Cohn, 2026, needs more optimization.
32 122 0.085353236124 Henry Cohn, 2026, needs more optimization.
32 123 0.086495747576 Henry Cohn, 2026, needs more optimization.
32 124 0.087059283629 Henry Cohn, 2026, needs more optimization.
32 125 0.088023910803 Henry Cohn, 2026, needs more optimization.
32 126 0.088202670412 Henry Cohn, 2026, needs more optimization.
32 127 0.088536804223 Henry Cohn, 2026, needs more optimization.
32 128 0.088920199455 Henry Cohn, 2026, needs more optimization.
32 129 0.089262579074 Henry Cohn, 2026, needs more optimization.
32 130 0.089599650797 Henry Cohn, 2026, needs more optimization.
32 131 0.089746268932 Henry Cohn, 2026, needs more optimization.
32 132 0.089804391570 Henry Cohn, 2026, needs more optimization.
32 133 0.090010896999 Henry Cohn, 2026, needs more optimization.
32 134 0.090174333237 Henry Cohn, 2026, needs more optimization.
32 135 0.090204306750 Henry Cohn, 2026, needs more optimization.
32 136 0.090915150448 Henry Cohn, 2026, needs more optimization.
32 137 0.092209887551 Henry Cohn, 2026, needs more optimization.
32 138 0.093228943770 Henry Cohn, 2026, needs more optimization.
32 139 0.094988279044 Henry Cohn, 2026, needs more optimization.
32 140 0.096198716787 Henry Cohn, 2026, needs more optimization.
32 141 0.097510534137 Henry Cohn, 2026, needs more optimization.
32 142 0.098149204483 Henry Cohn, 2026, needs more optimization.
32 143 0.099285692889 Henry Cohn, 2026, needs more optimization.
32 144 0.100023536397 Henry Cohn, 2026, needs more optimization.
32 145 0.100740921567 Henry Cohn, 2026, needs more optimization.
32 146 0.102242334315 Henry Cohn, 2026, needs more optimization.
32 147 0.102323309208 Henry Cohn, 2026, needs more optimization.
32 149 0.102456816881 Henry Cohn, 2026, needs more optimization.
32 151 0.102501522332 Henry Cohn, 2026, needs more optimization.
32 152 0.102972485441 Henry Cohn, 2026, needs more optimization.
32 153 0.103685586180 Henry Cohn, 2026, needs more optimization.
32 154 0.104140427624 Henry Cohn, 2026, needs more optimization.
32 155 0.105320845206 Henry Cohn, 2026, needs more optimization.
32 156 0.105926665934 Henry Cohn, 2026, needs more optimization.
32 157 0.106533005256 Henry Cohn, 2026, needs more optimization.
32 158 0.107102606713 Henry Cohn, 2026, needs more optimization.
32 159 0.107330372182 Henry Cohn, 2026, needs more optimization.
32 160 0.108096610129 Henry Cohn, 2026, needs more optimization.
32 161 0.108291145375 Henry Cohn, 2026, needs more optimization.
32 162 0.108676291751 Henry Cohn, 2026, needs more optimization.
32 163 0.109377596864 Henry Cohn, 2026, needs more optimization.
32 164 0.109560375463 Henry Cohn, 2026, needs more optimization.
32 165 0.110273717526 Henry Cohn, 2026, needs more optimization.
32 166 0.110631224944 Henry Cohn, 2026, needs more optimization.
32 167 0.112584932175 Henry Cohn, 2026, needs more optimization.
32 168 0.113712165297 Henry Cohn, 2026, needs more optimization.
32 169 0.113857641809 Henry Cohn, 2026, needs more optimization.
32 170 0.114657446013 Henry Cohn, 2026, needs more optimization.
32 171 0.115022966255 Henry Cohn, 2026, needs more optimization.
32 172 0.115840284723 Henry Cohn, 2026, needs more optimization.
32 173 0.116658212413 Henry Cohn, 2026, needs more optimization.
32 174 0.117549582251 Henry Cohn, 2026, needs more optimization.
32 175 0.118177394545 Henry Cohn, 2026, needs more optimization.
32 176 0.119025618264 Henry Cohn, 2026, needs more optimization.
32 177 0.119592725483 Henry Cohn, 2026, needs more optimization.
32 178 0.120418872558 Henry Cohn, 2026, needs more optimization.
32 179 0.121444615752 Henry Cohn, 2026, needs more optimization.
32 180 0.121966363193 Henry Cohn, 2026, needs more optimization.
32 181 0.122754483684 Henry Cohn, 2026, needs more optimization.
32 182 0.123469211838 Henry Cohn, 2026, needs more optimization.
32 183 0.124137146130 Henry Cohn, 2026, needs more optimization.
32 184 0.125019992129 Henry Cohn, 2026, needs more optimization.
32 185 0.125751758175 Henry Cohn, 2026, needs more optimization.
32 186 0.126202970913 Henry Cohn, 2026, needs more optimization.
32 187 0.126981387373 Henry Cohn, 2026, needs more optimization.
32 188 0.127638593889 Henry Cohn, 2026, needs more optimization.
32 189 0.128536524720 Henry Cohn, 2026, needs more optimization.
32 190 0.129003582809 Henry Cohn, 2026, needs more optimization.
32 191 0.130808671839 Henry Cohn, 2026, needs more optimization.
32 192 0.130940593111 Henry Cohn, 2026, needs more optimization.
32 193 0.131067861733 Henry Cohn, 2026, needs more optimization.
32 194 0.131238712363 Henry Cohn, 2026, needs more optimization.
32 195 0.131433575453 Henry Cohn, 2026, needs more optimization.
32 196 0.131886143110 Henry Cohn, 2026, needs more optimization.
32 197 0.132083460386 Henry Cohn, 2026, needs more optimization.
32 198 0.132189041340 Henry Cohn, 2026, needs more optimization.
32 199 0.132511637884 Henry Cohn, 2026, needs more optimization.
32 200 0.132668968705 Henry Cohn, 2026, needs more optimization.
32 201 0.132748232523 Henry Cohn, 2026, needs more optimization.
32 202 0.132937852212 Henry Cohn, 2026, needs more optimization.
32 203 0.133265582354 Henry Cohn, 2026, needs more optimization.
32 204 0.133571812837 Henry Cohn, 2026, needs more optimization.
32 205 0.133762121678 Henry Cohn, 2026, needs more optimization.
32 206 0.133925436568 Henry Cohn, 2026, needs more optimization.
32 207 0.134235174063 Henry Cohn, 2026, needs more optimization.
32 208 0.134420452538 Henry Cohn, 2026, needs more optimization.
32 209 0.134560054284 Henry Cohn, 2026, needs more optimization.
32 210 0.134993085250 Henry Cohn, 2026, needs more optimization.
32 211 0.135574181637 Henry Cohn, 2026, needs more optimization.
32 212 0.135902304508 Henry Cohn, 2026, needs more optimization.
32 213 0.136448417878 Henry Cohn, 2026, needs more optimization.
32 214 0.137189914830 Henry Cohn, 2026, needs more optimization.
32 215 0.137422336858 Henry Cohn, 2026, needs more optimization.
32 216 0.137930063428 Henry Cohn, 2026, needs more optimization.
32 217 0.139856402186 Henry Cohn, 2026, needs more optimization.
32 218 0.139905578807 Henry Cohn, 2026, needs more optimization.
32 219 0.139994528000 Henry Cohn, 2026, needs more optimization.
32 220 0.140166375585 Henry Cohn, 2026, needs more optimization.
32 221 0.140299808538 Henry Cohn, 2026, needs more optimization.
32 222 0.140460062395 Henry Cohn, 2026, needs more optimization.
32 223 0.140540830386 Henry Cohn, 2026, needs more optimization.
32 224 0.140753342102 Henry Cohn, 2026, needs more optimization.
32 225 0.140757070802 Henry Cohn, 2026, needs more optimization.
32 226 0.140896421767 Henry Cohn, 2026, needs more optimization.
32 227 0.141179809351 Henry Cohn, 2026, needs more optimization.
32 228 0.141248087781 Henry Cohn, 2026, needs more optimization.
32 229 0.141420945200 Henry Cohn, 2026, needs more optimization.
32 230 0.141503637771 Henry Cohn, 2026, needs more optimization.
32 231 0.141750663186 Henry Cohn, 2026, needs more optimization.
32 232 0.141909409444 Henry Cohn, 2026, needs more optimization.
32 233 0.142036375599 Henry Cohn, 2026, needs more optimization.
32 234 0.142131439956 Henry Cohn, 2026, needs more optimization.
32 235 0.142623138146 Henry Cohn, 2026, needs more optimization.
32 236 0.142699838121 Henry Cohn, 2026, needs more optimization.
32 237 0.142777469645 Henry Cohn, 2026, needs more optimization.
32 238 0.142903038425 Henry Cohn, 2026, needs more optimization.
32 239 0.143079482008 Henry Cohn, 2026, needs more optimization.
32 240 0.143627436475 Henry Cohn, 2026, needs more optimization.
32 241 0.143698079394 Henry Cohn, 2026, needs more optimization.
32 242 0.144207569991 Henry Cohn, 2026, needs more optimization.
32 243 0.144306680495 Henry Cohn, 2026, needs more optimization.
32 244 0.144649090833 Henry Cohn, 2026, needs more optimization.
32 245 0.144878853186 Henry Cohn, 2026, needs more optimization.
32 246 0.144958595424 Henry Cohn, 2026, needs more optimization.
32 247 0.145263511528 Henry Cohn, 2026, needs more optimization.
32 248 0.145394724957 Henry Cohn, 2026, needs more optimization.
32 249 0.145762301364 Henry Cohn, 2026, needs more optimization.
32 250 0.145794270462 Henry Cohn, 2026, needs more optimization.
32 251 0.146021734551 Henry Cohn, 2026, needs more optimization.
32 252 0.146061601586 Henry Cohn, 2026, needs more optimization.
32 253 0.146263884779 Henry Cohn, 2026, needs more optimization.
32 254 0.146396196521 Henry Cohn, 2026, needs more optimization.
32 255 0.146486267223 Henry Cohn, 2026, needs more optimization.
32 256 0.147025382600 Henry Cohn, 2026, needs more optimization.
32 257 0.147306451115 Henry Cohn, 2026, needs more optimization.
32 258 0.147511240480 Henry Cohn, 2026, needs more optimization.
32 259 0.147551342796 Henry Cohn, 2026, needs more optimization.
32 260 0.147575898787 Henry Cohn, 2026, needs more optimization.
32 261 0.147808636304 Henry Cohn, 2026, needs more optimization.
32 262 0.147924717817 Henry Cohn, 2026, needs more optimization.
32 263 0.147943904509 Henry Cohn, 2026, needs more optimization.
32 264 0.148179330890 Henry Cohn, 2026, needs more optimization.
32 265 0.148249290524 Henry Cohn, 2026, needs more optimization.
32 266 0.148771841964 Henry Cohn, 2026, needs more optimization.
32 267 0.149182118908 Henry Cohn, 2026, needs more optimization.
32 268 0.149388010861 Henry Cohn, 2026, needs more optimization.
32 269 0.150621737791 Henry Cohn, 2026, needs more optimization.
32 270 0.150829820224 Henry Cohn, 2026, needs more optimization.
32 271 0.151212516005 Henry Cohn, 2026, needs more optimization.
32 272 0.151656179259 Henry Cohn, 2026, needs more optimization.
32 273 0.152110395228 Henry Cohn, 2026, needs more optimization.
32 274 0.152303192385 Henry Cohn, 2026, needs more optimization.
32 275 0.152874555700 Henry Cohn, 2026, needs more optimization.
32 276 0.153252452302 Henry Cohn, 2026, needs more optimization.
32 277 0.154137000656 Henry Cohn, 2026, needs more optimization.
32 278 0.154442151955 Henry Cohn, 2026, needs more optimization.
32 279 0.154674206685 Henry Cohn, 2026, needs more optimization.
32 280 0.154996796763 Henry Cohn, 2026, needs more optimization.
32 281 0.155448775026 Henry Cohn, 2026, needs more optimization.
32 282 0.155665716613 Henry Cohn, 2026, needs more optimization.
32 283 0.156100369445 Henry Cohn, 2026, needs more optimization.
32 284 0.156301723992 Henry Cohn, 2026, needs more optimization.
32 285 0.156969800825 Henry Cohn, 2026, needs more optimization.
32 286 0.157347568063 Henry Cohn, 2026, needs more optimization.
32 287 0.157681489421 Henry Cohn, 2026, needs more optimization.
32 288 0.158074768766 Henry Cohn, 2026, needs more optimization.
32 289 0.158269246282 Henry Cohn, 2026, needs more optimization.
32 290 0.158535714295 Henry Cohn, 2026, needs more optimization.
32 291 0.158827380537 Henry Cohn, 2026, needs more optimization.
32 292 0.159296764852 Henry Cohn, 2026, needs more optimization.
32 293 0.159618856127 Henry Cohn, 2026, needs more optimization.
32 294 0.160137539579 Henry Cohn, 2026, needs more optimization.
32 295 0.160697481756 Henry Cohn, 2026, needs more optimization.
32 296 0.160848214937 Henry Cohn, 2026, needs more optimization.
32 297 0.160990488831 Henry Cohn, 2026, needs more optimization.
32 298 0.161000144594 Henry Cohn, 2026, needs more optimization.
32 300 0.161249710811 Henry Cohn, 2026, needs more optimization.
32 301 0.162110892923 Orthogonal union of 299 points in 31 dimensions and 2 points in 1 dimension.
32 302 0.162400010123 Orthogonal union of 300 points in 31 dimensions and 2 points in 1 dimension.
32 303 0.162955496535 Orthogonal union of 301 points in 31 dimensions and 2 points in 1 dimension.
32 304 0.164101020235 Henry Cohn, 2026, needs more optimization.
32 306 0.164186663433 Henry Cohn, 2026, needs more optimization.
32 307 0.164251856881 Henry Cohn, 2025, needs more optimization.
32 308 0.164285835602 Henry Cohn, 2026, needs more optimization.
32 310 0.164491317113 Henry Cohn, 2026, needs more optimization.
32 311 0.164665715925 Henry Cohn, 2025, needs more optimization.
32 312 0.164736038826 Henry Cohn, 2026, needs more optimization.
32 314 0.164772653135 Henry Cohn, 2026, needs more optimization.
32 315 0.164812333655 Henry Cohn, 2025, needs more optimization.
32 318 0.166518175275 Henry Cohn, 2026, needs more optimization.
32 322 0.166647303673 Henry Cohn, 2026, needs more optimization.
32 326 0.166819551212 Henry Cohn, 2026, needs more optimization.
32 330 0.167072121095 Henry Cohn, 2026, needs more optimization.
32 334 0.167517673556 Henry Cohn, 2026, needs more optimization.
32 338 0.168185185174 Henry Cohn, 2026, needs more optimization.
32 342 0.168938212196 Henry Cohn, 2026, needs more optimization.
32 346 0.169539778085 Henry Cohn, 2026, needs more optimization.
32 350 0.170552775644 Henry Cohn, 2026, needs more optimization.
32 354 0.171758076999 Henry Cohn, 2026, needs more optimization.
32 356 0.173388183642 Henry Cohn, 2026, needs more optimization.
32 357 0.177208538829 Henry Cohn, 2026, needs more optimization.
32 358 0.177211909064 Henry Cohn, 2026, needs more optimization.
32 360 0.177294100324 Henry Cohn, 2026, needs more optimization.
32 362 0.177336700360 Henry Cohn, 2025, needs more optimization.
32 363 0.177355864571 Henry Cohn, 2025, needs more optimization.
32 364 0.177398869824 Henry Cohn, 2026, needs more optimization.
32 365 0.177403896667 Henry Cohn, 2025, needs more optimization.
32 366 0.177445954405 Henry Cohn, 2026, needs more optimization.
32 367 0.177668635338 Henry Cohn, 2026, needs more optimization.
32 368 0.177952192805 Henry Cohn, 2026, needs more optimization.
32 369 0.177979746530 Henry Cohn, 2025, needs more optimization.
32 370 0.178013006291 Henry Cohn, 2026, needs more optimization.
32 372 0.178066563597 Henry Cohn, 2026, needs more optimization.
32 373 0.178265672389 Henry Cohn, 2025, needs more optimization.
32 374 0.178265717273 Henry Cohn, 2026, needs more optimization.
32 375 0.178311620647 Henry Cohn, 2025, needs more optimization.
32 376 0.178315324403 Henry Cohn, 2026, needs more optimization.
32 378 0.178354796160 Henry Cohn, 2026, needs more optimization.
32 379 0.178383961332 Henry Cohn, 2025, needs more optimization.
32 380 0.179031117557 Henry Cohn, 2026, needs more optimization.
32 381 0.179045766806 Henry Cohn, 2025, needs more optimization.
32 382 0.179081630972 Henry Cohn, 2026, needs more optimization.
32 383 0.179152446284 Henry Cohn, 2025, needs more optimization.
32 384 0.179335801156 Henry Cohn, 2026, needs more optimization.
32 385 0.179356786400 Henry Cohn, 2025, needs more optimization.
32 386 0.179705506434 Henry Cohn, 2026, needs more optimization.
32 387 0.179718957095 Henry Cohn, 2025, needs more optimization.
32 388 0.179719254092 Henry Cohn, 2026, needs more optimization.
32 389 0.179852843579 Henry Cohn, 2025, needs more optimization.
32 390 0.179979027204 Henry Cohn, 2026, needs more optimization.
32 392 0.180688469816 Henry Cohn, 2026, needs more optimization.
32 393 0.180975856164 Henry Cohn, 2025, needs more optimization.
32 394 0.181060583568 Henry Cohn, 2026, needs more optimization.
32 395 0.181155096192 Henry Cohn, 2025, needs more optimization.
32 396 0.181231835319 Henry Cohn, 2026, needs more optimization.
32 397 0.181317830477 Henry Cohn, 2025, needs more optimization.
32 398 0.181518114397 Henry Cohn, 2026, needs more optimization.
32 399 0.181848571961 Henry Cohn, 2025, needs more optimization.
32 400 0.181945095808 Henry Cohn, 2026, needs more optimization.
32 401 0.181978777586 Henry Cohn, 2025, needs more optimization.
32 402 0.182206621640 Henry Cohn, 2026, needs more optimization.
32 403 0.182570899265 Henry Cohn, 2025, needs more optimization.
32 404 0.182661426610 Henry Cohn, 2026, needs more optimization.
32 405 0.182835710464 Henry Cohn, 2025, needs more optimization.
32 406 0.182845520577 Henry Cohn, 2026, needs more optimization.
32 407 0.182885908892 Henry Cohn, 2025, needs more optimization.
32 408 0.182925577504 Henry Cohn, 2026, needs more optimization.
32 409 0.183280877984 Henry Cohn, 2025, needs more optimization.
32 410 0.185012603326 Henry Cohn, 2026, needs more optimization.
32 412 0.185037443171 Henry Cohn, 2026, needs more optimization.
32 413 0.185059418161 Henry Cohn, 2025, needs more optimization.
32 414 0.185227745447 Henry Cohn, 2026, needs more optimization.
32 415 0.185270695609 Henry Cohn, 2025, needs more optimization.
32 416 0.185691300174 Henry Cohn, 2026, needs more optimization.
32 417 0.185767568064 Henry Cohn, 2025, needs more optimization.
32 418 0.185782735587 Henry Cohn, 2026, needs more optimization.
32 419 0.185849386954 Henry Cohn, 2025, needs more optimization.
32 420 0.186556419984 Henry Cohn, 2026, needs more optimization.
32 421 0.187264751378 Henry Cohn, 2025, needs more optimization.
32 422 0.187353822861 Henry Cohn, 2026, needs more optimization.
32 423 0.187500608309 Henry Cohn, 2025, needs more optimization.
32 424 0.187677162520 Henry Cohn, 2026, needs more optimization.
32 425 0.187748169214 Henry Cohn, 2025, needs more optimization.
32 426 0.187860154898 Henry Cohn, 2026, needs more optimization.
32 427 0.189248292876 Henry Cohn, 2025, needs more optimization.
32 428 0.189407459282 Henry Cohn, 2026, needs more optimization.
32 429 0.189496872293 Henry Cohn, 2025, needs more optimization.
32 430 0.189512475721 Henry Cohn, 2026, needs more optimization.
32 431 0.189613919573 Henry Cohn, 2025, needs more optimization.
32 432 0.190096051699 Henry Cohn, 2026, needs more optimization.
32 433 0.190140646596 Henry Cohn, 2025, needs more optimization.
32 434 0.190246898229 Henry Cohn, 2026, needs more optimization.
32 435 0.190275021051 Henry Cohn, 2025, needs more optimization.
32 436 0.190279279138 Henry Cohn, 2026, needs more optimization.
32 437 0.190412575829 Henry Cohn, 2025, needs more optimization.
32 438 0.190492707402 Henry Cohn, 2026, needs more optimization.
32 439 0.190594556573 Henry Cohn, 2025, needs more optimization.
32 440 0.190598729392 Henry Cohn, 2026, needs more optimization.
32 442 0.190669844112 Henry Cohn, 2026, needs more optimization.
32 443 0.190970654280 Henry Cohn, 2025, needs more optimization.
32 444 0.191765080937 Henry Cohn, 2026, needs more optimization.
32 445 0.192031953805 Henry Cohn, 2025, needs more optimization.
32 446 0.192153657670 Henry Cohn, 2026, needs more optimization.
32 447 0.192198301060 Henry Cohn, 2025, needs more optimization.
32 448 0.192575448488 Henry Cohn, 2026, needs more optimization.
32 449 0.192604978591 Henry Cohn, 2025, needs more optimization.
32 450 0.193699061574 Henry Cohn, 2026, needs more optimization.
32 451 0.193708611047 Henry Cohn, 2025, needs more optimization.
32 452 0.193764059023 Henry Cohn, 2026, needs more optimization.
32 453 0.193774937757 Henry Cohn, 2025, needs more optimization.
32 454 0.193776698256 Henry Cohn, 2026, needs more optimization.
32 455 0.193793357389 Henry Cohn, 2025, needs more optimization.
32 456 0.193820455278 Henry Cohn, 2026, needs more optimization.
32 457 0.193850961075 Henry Cohn, 2025, needs more optimization.
32 458 0.193862662558 Henry Cohn, 2026, needs more optimization.
32 459 0.193983485564 Henry Cohn, 2025, needs more optimization.
32 460 0.194028782886 Henry Cohn, 2026, needs more optimization.
32 461 0.194081363290 Henry Cohn, 2025, needs more optimization.
32 462 0.194272218707 Henry Cohn, 2026, needs more optimization.
32 463 0.194514027621 Henry Cohn, 2025, needs more optimization.
32 475 0.194585894404 Henry Cohn, 2026, needs more optimization.
32 476 0.194625910466 Henry Cohn, 2026, needs more optimization.
32 477 0.194819665278 Henry Cohn, 2026, needs more optimization.
32 478 0.194876954764 Henry Cohn, 2026, needs more optimization.
32 480 0.195306404357 Henry Cohn, 2026, needs more optimization.
32 481 0.195444795747 Henry Cohn, 2026, needs more optimization.
32 482 0.195600206158 Henry Cohn, 2026, needs more optimization.
32 483 0.195797503294 Henry Cohn, 2026, needs more optimization.
32 484 0.195800697360 Henry Cohn, 2026, needs more optimization.
32 485 0.195829686028 Henry Cohn, 2026, needs more optimization.
32 486 0.195882477937 Henry Cohn, 2026, needs more optimization.
32 488 0.195905421024 Henry Cohn, 2026, needs more optimization.
32 489 0.195926887597 Henry Cohn, 2026, needs more optimization.
32 490 0.196064033032 Henry Cohn, 2026, needs more optimization.
32 491 0.196093541766 Henry Cohn, 2026, needs more optimization.
32 492 0.196278750658 Henry Cohn, 2026, needs more optimization.
32 493 0.196599988199 Henry Cohn, 2026, needs more optimization.
32 494 0.196622343896 Henry Cohn, 2026, needs more optimization.
32 495 0.196675430752 Henry Cohn, 2026, needs more optimization.
32 497 0.196732739383 Henry Cohn, 2026, needs more optimization.
32 498 0.196880448757 Henry Cohn, 2026, needs more optimization.
32 500 0.196940543351 Henry Cohn, 2026, needs more optimization.
32 501 0.197216214415 Henry Cohn, 2026, needs more optimization.
32 502 0.197259583702 Henry Cohn, 2026, needs more optimization.
32 504 0.197317034586 Henry Cohn, 2026, needs more optimization.
32 505 0.197338423710 Henry Cohn, 2026, needs more optimization.
32 506 0.197388562721 Henry Cohn, 2026, needs more optimization.
32 508 0.197916761142 Henry Cohn, 2026, needs more optimization.
32 509 0.197960517141 Henry Cohn, 2026, needs more optimization.
32 510 0.198029407264 Henry Cohn, 2026, needs more optimization.
32 511 0.198123401175 Henry Cohn, 2026, needs more optimization.
32 512 0.199359562043 Orthogonal union of 510 points in 31 dimensions and 2 points in 1 dimension.
32 513 0.199360583105 Orthogonal union of 511 points in 31 dimensions and 2 points in 1 dimension.
32 514 0.199405108985 Henry Cohn, 2026, needs more optimization.
32 515 0.199410670327 Henry Cohn, 2026, needs more optimization.
32 516 0.199426209172 Henry Cohn, 2026, needs more optimization.
32 517 0.199432734449 Henry Cohn, 2026, needs more optimization.
32 518 0.199443035209 Henry Cohn, 2026, needs more optimization.
32 521 0.199504707629 Orthogonal union of 519 points in 31 dimensions and 2 points in 1 dimension.
32 523 0.199523911650 Orthogonal union of 521 points in 31 dimensions and 2 points in 1 dimension.
32 524 0.199536115505 Henry Cohn, 2026, needs more optimization.
32 525 0.199552857089 Henry Cohn, 2026, needs more optimization.
32 526 0.199557584950 Henry Cohn, 2026, needs more optimization.
32 528 0.199558754784 Henry Cohn, 2026, needs more optimization.
32 529 0.199572873539 Henry Cohn, 2025, needs more optimization.
32 530 0.199587006903 Henry Cohn, 2026, needs more optimization.
32 532 0.199587261641 Henry Cohn, 2026, needs more optimization.
32 534 0.199607741290 Henry Cohn, 2026, needs more optimization.
32 538 0.199675123058 Henry Cohn, 2026, needs more optimization.
32 540 0.199684128978 Henry Cohn, 2026, needs more optimization.
32 542 0.199707556181 Henry Cohn, 2026, needs more optimization.
32 543 0.199715301377 Henry Cohn, 2026, needs more optimization.
32 546 0.199730149648 Henry Cohn, 2026, needs more optimization.
32 548 0.199734949274 Henry Cohn, 2026, needs more optimization.
32 550 0.199740995765 Henry Cohn, 2026, needs more optimization.
32 552 0.199745278477 Henry Cohn, 2026, needs more optimization.
32 554 0.199752120142 Henry Cohn, 2026, needs more optimization.
32 556 0.199774357232 Henry Cohn, 2026, needs more optimization.
32 558 0.199778386782 Henry Cohn, 2026, needs more optimization.
32 560 0.199782046435 Henry Cohn, 2026, needs more optimization.
32 564 0.199796886903 Henry Cohn, 2026, needs more optimization.
32 566 0.199809185930 Henry Cohn, 2026, needs more optimization.
32 568 0.199826147563 Henry Cohn, 2026, needs more optimization.
32 570 0.199834625979 Henry Cohn, 2026, needs more optimization.
32 572 0.199838559293 Henry Cohn, 2026, needs more optimization.
32 573 0.199857441710 Henry Cohn, 2025, needs more optimization.
32 576 0.199874346564 Henry Cohn, 2026, needs more optimization.
32 578 0.199896084441 Henry Cohn, 2026, needs more optimization.
32 580 0.199897063468 Henry Cohn, 2026, needs more optimization.
32 582 0.199898288197 Henry Cohn, 2026, needs more optimization.
32 584 0.199916090948 Henry Cohn, 2026, needs more optimization.
32 586 0.199923126352 Henry Cohn, 2026, needs more optimization.
32 588 0.199924608878 Henry Cohn, 2026, needs more optimization.
32 590 0.199938096038 Henry Cohn, 2026, needs more optimization.
32 592 0.199939470789 Henry Cohn, 2026, needs more optimization.
32 594 0.199945993829 Henry Cohn, 2026, needs more optimization.
32 595 0.199968056167 Henry Cohn, 2025, needs more optimization.
32 596 0.199971184268 Henry Cohn, 2026, needs more optimization.
32 598 0.199984217302 Henry Cohn, 2026, needs more optimization.
32 599 0.199999980426 Henry Cohn, 2025, needs more optimization.
32 600 0.200007821657 Orthogonal union of 598 points in 31 dimensions and 2 points in 1 dimension.
32 602 0.200009348794 Orthogonal union of 600 points in 31 dimensions and 2 points in 1 dimension.
32 604 0.200011116643 Orthogonal union of 602 points in 31 dimensions and 2 points in 1 dimension.
32 606 0.200015098892 Orthogonal union of 604 points in 31 dimensions and 2 points in 1 dimension.
32 607 0.200019950239 Orthogonal union of 605 points in 31 dimensions and 2 points in 1 dimension.
32 610 0.200020194637 Orthogonal union of 608 points in 31 dimensions and 2 points in 1 dimension.
32 612 0.200022024831 Orthogonal union of 610 points in 31 dimensions and 2 points in 1 dimension.
32 613 0.200028137929 Orthogonal union of 611 points in 31 dimensions and 2 points in 1 dimension.
32 616 0.200033671216 Orthogonal union of 614 points in 31 dimensions and 2 points in 1 dimension.
32 618 0.200034078018 Orthogonal union of 616 points in 31 dimensions and 2 points in 1 dimension.
32 619 0.200036731298 Henry Cohn, 2026, needs more optimization.
32 630 0.200036910070 Henry Cohn, 2026, needs more optimization.
32 632 0.200043743483 Henry Cohn, 2026, needs more optimization.
32 634 0.200044960441 Henry Cohn, 2026, needs more optimization.
32 641 0.200053936574 Henry Cohn, 2026, needs more optimization.
32 643 0.200068455501 Henry Cohn, 2026, needs more optimization.
32 645 0.200070167949 Henry Cohn, 2026, needs more optimization.
32 646 0.200086821091 Henry Cohn, 2026, needs more optimization.
32 647 0.200096037792 Henry Cohn, 2026, needs more optimization.
32 648 0.200102072777 Henry Cohn, 2026, needs more optimization.
32 649 0.200142840857 Henry Cohn, 2026, needs more optimization.
32 650 0.200152586201 Henry Cohn, 2026, needs more optimization.
32 651 0.200209156615 Henry Cohn, 2026, needs more optimization.
32 652 0.200235447826 Henry Cohn, 2026, needs more optimization.
32 653 0.200284936733 Henry Cohn, 2026, needs more optimization.
32 654 0.200298741452 Henry Cohn, 2026, needs more optimization.
32 655 0.200363245949 Henry Cohn, 2026, needs more optimization.
32 656 0.200427789859 Henry Cohn, 2026, needs more optimization.
32 657 0.200465282747 Henry Cohn, 2026, needs more optimization.
32 658 0.200741842672 Henry Cohn, 2026, needs more optimization.
32 659 0.200946365433 Henry Cohn, 2026, needs more optimization.
32 660 0.200998749317 Henry Cohn, 2026, needs more optimization.
32 662 0.201466527639 Henry Cohn, 2026, needs more optimization.
32 663 0.201698384674 Henry Cohn, 2026, needs more optimization.
32 664 0.202046998658 Henry Cohn, 2026, needs more optimization.
32 665 0.202619875722 Henry Cohn, 2026, needs more optimization.
32 666 0.202666474104 Henry Cohn, 2026, needs more optimization.
32 667 0.202906294631 Henry Cohn, 2026, needs more optimization.
32 668 0.203042620254 Henry Cohn, 2026, needs more optimization.
32 672 0.203662150903 Henry Cohn, 2026, needs more optimization.
32 673 0.203958474647 Henry Cohn, 2026, needs more optimization.
32 674 0.204155966878 Henry Cohn, 2026, needs more optimization.
32 675 0.204771126185 Henry Cohn, 2026, needs more optimization.
32 676 0.204867464048 Henry Cohn, 2026, needs more optimization.
32 677 0.204955999918 Henry Cohn, 2026, needs more optimization.
32 678 0.205945459320 Henry Cohn, 2026, needs more optimization.
32 679 0.205991344149 Henry Cohn, 2026, needs more optimization.
32 680 0.206363846627 Henry Cohn, 2026, needs more optimization.
32 681 0.206759935380 Henry Cohn, 2026, needs more optimization.
32 682 0.206870889905 Henry Cohn, 2026, needs more optimization.
32 683 0.207109265800 Henry Cohn, 2026, needs more optimization.
32 684 0.207282171495 Henry Cohn, 2026, needs more optimization.
32 685 0.207890651763 Henry Cohn, 2026, needs more optimization.
32 686 0.207943422918 Henry Cohn, 2026, needs more optimization.
32 687 0.208033073448 Henry Cohn, 2026, needs more optimization.
32 688 0.208267431880 Henry Cohn, 2026, needs more optimization.
32 689 0.208698322503 Henry Cohn, 2026, needs more optimization.
32 690 0.208869801407 Henry Cohn, 2026, needs more optimization.
32 691 0.208915821612 Henry Cohn, 2026, needs more optimization.
32 692 0.208938032833 Henry Cohn, 2026, needs more optimization.
32 693 0.208998464628 Henry Cohn, 2026, needs more optimization.
32 694 0.209475842482 Henry Cohn, 2026, needs more optimization.
32 695 0.209808696074 Henry Cohn, 2026, needs more optimization.
32 697 0.210772537185 Henry Cohn, 2026, needs more optimization.
32 698 0.211195307635 Henry Cohn, 2026, needs more optimization.
32 699 0.211359398163 Henry Cohn, 2026, needs more optimization.
32 700 0.211587576771 Henry Cohn, 2026, needs more optimization.
32 701 0.211727214669 Henry Cohn, 2026, needs more optimization.
32 703 0.212026705747 Henry Cohn, 2026, needs more optimization.
32 704 0.212244411370 Henry Cohn, 2026, needs more optimization.
32 705 0.212749946805 Henry Cohn, 2026, needs more optimization.
32 706 0.212877581747 Henry Cohn, 2026, needs more optimization.
32 707 0.212916574261 Henry Cohn, 2026, needs more optimization.
32 708 0.213275492584 Henry Cohn, 2026, needs more optimization.
32 709 0.213310702721 Henry Cohn, 2026, needs more optimization.
32 710 0.214515450893 Henry Cohn, 2026, needs more optimization.
32 711 0.214707356311 Henry Cohn, 2026, needs more optimization.
32 712 0.214768385354 Henry Cohn, 2026, needs more optimization.
32 713 0.214904492381 Henry Cohn, 2026, needs more optimization.
32 714 0.215014387075 Henry Cohn, 2026, needs more optimization.
32 715 0.215043454831 Henry Cohn, 2026, needs more optimization.
32 716 0.215289596522 Henry Cohn, 2026, needs more optimization.
32 717 0.215387224848 Henry Cohn, 2026, needs more optimization.
32 718 0.216584548031 Henry Cohn, 2026, needs more optimization.
32 719 0.216654337642 Henry Cohn, 2026, needs more optimization.
32 720 0.216826994211 Henry Cohn, 2026, needs more optimization.
32 721 0.216877295642 Henry Cohn, 2026, needs more optimization.
32 722 0.217235649262 Henry Cohn, 2026, needs more optimization.
32 723 0.217312033602 Henry Cohn, 2026, needs more optimization.
32 725 0.217881718842 Henry Cohn, 2026, needs more optimization.
32 726 0.218186562449 Henry Cohn, 2026, needs more optimization.
32 727 0.218229142672 Henry Cohn, 2026, needs more optimization.
32 728 0.218266486027 Henry Cohn, 2026, needs more optimization.
32 729 0.218315743398 Henry Cohn, 2026, needs more optimization.
32 730 0.218388367965 Henry Cohn, 2026, needs more optimization.
32 731 0.219259560652 Henry Cohn, 2026, needs more optimization.
32 732 0.219482125276 Henry Cohn, 2026, needs more optimization.
32 733 0.219520443228 Henry Cohn, 2026, needs more optimization.
32 734 0.219803652351 Henry Cohn, 2026, needs more optimization.
32 735 0.219815180062 Henry Cohn, 2026, needs more optimization.
32 736 0.220239339671 Henry Cohn, 2026, needs more optimization.
32 737 0.220308170085 Henry Cohn, 2026, needs more optimization.
32 738 0.220599424320 Henry Cohn, 2026, needs more optimization.
32 739 0.220713399800 Henry Cohn, 2026, needs more optimization.
32 740 0.220739691141 Henry Cohn, 2026, needs more optimization.
32 741 0.221655754641 Henry Cohn, 2026, needs more optimization.
32 742 0.221677098014 Henry Cohn, 2026, needs more optimization.
32 743 0.221811940990 Henry Cohn, 2026, needs more optimization.
32 744 0.221847957762 Henry Cohn, 2026, needs more optimization.
32 745 0.221997186128 Henry Cohn, 2026, needs more optimization.
32 746 0.222053228501 Henry Cohn, 2026, needs more optimization.
32 747 0.222282102130 Henry Cohn, 2026, needs more optimization.
32 748 0.222299886308 Henry Cohn, 2026, needs more optimization.
32 749 0.222314888533 Henry Cohn, 2026, needs more optimization.
32 750 0.223481780469 Henry Cohn, 2026, needs more optimization.
32 751 0.223522863679 Henry Cohn, 2026, needs more optimization.
32 752 0.223639529089 Henry Cohn, 2026, needs more optimization.
32 753 0.223773565754 Henry Cohn, 2026, needs more optimization.
32 754 0.223809447104 Henry Cohn, 2026, needs more optimization.
32 755 0.224020914822 Henry Cohn, 2026, needs more optimization.
32 756 0.224040642953 Henry Cohn, 2026, needs more optimization.
32 757 0.224203944566 Henry Cohn, 2026, needs more optimization.
32 758 0.224495623066 Henry Cohn, 2026, needs more optimization.
32 759 0.225251441859 Henry Cohn, 2026, needs more optimization.
32 760 0.225331084086 Henry Cohn, 2026, needs more optimization.
32 762 0.225486850904 Henry Cohn, 2026, needs more optimization.
32 763 0.225694073373 Henry Cohn, 2026, needs more optimization.
32 764 0.225722044703 Henry Cohn, 2026, needs more optimization.
32 765 0.225750769062 Henry Cohn, 2026, needs more optimization.
32 766 0.226393162302 Henry Cohn, 2026, needs more optimization.
32 767 0.226529410839 Henry Cohn, 2026, needs more optimization.
32 768 0.226567723326 Henry Cohn, 2026, needs more optimization.
32 769 0.226776835653 Henry Cohn, 2026, needs more optimization.
32 770 0.226802950074 Henry Cohn, 2026, needs more optimization.
32 771 0.227805332298 Henry Cohn, 2026, needs more optimization.
32 772 0.227829716239 Henry Cohn, 2026, needs more optimization.
32 773 0.227953465731 Henry Cohn, 2026, needs more optimization.
32 774 0.228000010988 Henry Cohn, 2026, needs more optimization.
32 775 0.228008919019 Henry Cohn, 2026, needs more optimization.
32 776 0.228197529717 Henry Cohn, 2026, needs more optimization.
32 778 0.228429030179 Henry Cohn, 2026, needs more optimization.
32 779 0.228700382966 Henry Cohn, 2026, needs more optimization.
32 780 0.228833234660 Henry Cohn, 2026, needs more optimization.
32 781 0.228909314066 Henry Cohn, 2026, needs more optimization.
32 782 0.228980992051 Henry Cohn, 2026, needs more optimization.
32 783 0.229014978217 Henry Cohn, 2026, needs more optimization.
32 784 0.229110875812 Henry Cohn, 2026, needs more optimization.
32 785 0.229275828634 Henry Cohn, 2026, needs more optimization.
32 786 0.237603426352 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