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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3 300 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 0.985633307217 Henry Cohn, 2026.
3 477 0.985650812954 Henry Cohn, 2026.
3 478 0.985679876222 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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3 494 0.986186402493 Henry Cohn, 2024.
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3 497 0.986267131233 Henry Cohn, 2024.
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3 499 0.986323180888 Henry Cohn, 2024.
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 0.989693744145 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 0.989969934192 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 0.990079194397 Henry Cohn, 2026.
3 694 0.990105158152 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 0.990226834172 Henry Cohn, 2026.
3 704 0.990247640312 Henry Cohn, 2026.
3 705 0.990264016667 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 0.990399847262 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 0.990511316356 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 0.990638975129 Henry Cohn, 2026.
3 734 0.990653485474 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 0.990801952935 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 0.991247586150 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 0.991338848666 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 0.991531900704 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 0.991689512983 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 0.991752715892 Henry Cohn, 2026.
3 834 0.991760206283 Henry Cohn, 2026.
3 835 0.991774281058 Henry Cohn, 2026.
3 836 0.991777728475 Henry Cohn, 2026.
3 837 0.991787914621 Henry Cohn, 2026.
3 838 0.991801752919 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 0.991814485211 Henry Cohn, 2026.
3 842 0.991823503475 Henry Cohn, 2026.
3 843 0.991831936552 Henry Cohn, 2026.
3 844 0.991855906888 Henry Cohn, 2026.
3 845 0.991858365803 Henry Cohn, 2026.
3 846 0.991862416879 Henry Cohn, 2026.
3 847 0.991870062534 Henry Cohn, 2026.
3 848 0.991877607735 Henry Cohn, 2026.
3 849 0.991885383843 Henry Cohn, 2026.
3 850 0.991891394850 Henry Cohn, 2026.
3 851 0.991898234566 Henry Cohn, 2026.
3 852 0.991904249523 R. H. Hardin, N. J. A. Sloane, and W. D. Smith, Tables of spherical codes with icosahedral symmetry, 1994–2000.
3 853 0.991918219703 Henry Cohn, 2026.
3 854 0.991935712885 Henry Cohn, 2026.
3 855 0.991949565795 Henry Cohn, 2026.
3 856 0.991960761074 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 0.992009765999 Henry Cohn, 2026.
3 862 0.992022903669 Henry Cohn, 2025.
3 863 0.992032218855 Henry Cohn, 2026.
3 864 0.992045910827 Henry Cohn, 2025.
3 865 0.992052833787 Henry Cohn, 2025.
3 866 0.992060313000 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 0.992098345457 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 0.992112147694 Henry Cohn, 2026.
3 874 0.992126269267 Henry Cohn, 2026.
3 875 0.992138836628 Henry Cohn, 2026.
3 876 0.992145742865 Henry Cohn, 2026.
3 877 0.992154329715 Henry Cohn, 2025.
3 878 0.992165376585 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 0.992206322361 Henry Cohn, 2026.
3 884 0.992214559881 Henry Cohn, 2026.
3 885 0.992224887879 Henry Cohn, 2026.
3 886 0.992238913096 Henry Cohn, 2026.
3 887 0.992242382220 Henry Cohn, 2025.
3 888 0.992258876226 Henry Cohn, 2025.
3 889 0.992266590339 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 0.992296614396 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 0.992347170198 Henry Cohn, 2026.
3 900 0.992357664582 Henry Cohn, 2026.
3 901 0.992361149573 Henry Cohn, 2026.
3 902 0.992374954177 Henry Cohn, 2026.
3 903 0.992382061576 Henry Cohn, 2025.
3 904 0.992391535358 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 0.992490047639 Henry Cohn, 2026.
3 917 0.992499945291 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 0.992536144114 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 0.992577590745 Henry Cohn, 2026.
3 928 0.992583930232 Henry Cohn, 2025.
3 929 0.992590355210 Henry Cohn, 2025.
3 930 0.992598510471 Henry Cohn, 2026.
3 931 0.992609528471 Henry Cohn, 2026.
3 932 0.992614241079 Henry Cohn, 2026.
3 933 0.992624602034 Henry Cohn, 2025.
3 934 0.992631107765 Henry Cohn, 2025.
3 935 0.992638889247 Henry Cohn, 2026.
3 936 0.992646759914 Henry Cohn, 2026.
3 937 0.992652545876 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 0.992712884583 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 0.992739976828 Henry Cohn, 2026.
3 950 0.992751947060 Henry Cohn, 2025.
3 951 0.992762286897 Henry Cohn, 2026.
3 952 0.992771438024 Henry Cohn, 2025.
3 953 0.992778114759 Henry Cohn, 2026.
3 954 0.992783154812 Henry Cohn, 2026.
3 955 0.992791162783 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 0.992869292415 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 0.992940838714 Henry Cohn, 2026.
3 977 0.992953433939 Henry Cohn, 2025.
3 978 0.992962810288 Henry Cohn, 2025.
3 979 0.992966796812 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 0.993060823312 Henry Cohn, 2026.
3 993 0.993062803097 Henry Cohn, 2025.
3 994 0.993068407685 Henry Cohn, 2026.
3 995 0.993078560947 Henry Cohn, 2025.
3 996 0.993085360495 Henry Cohn, 2026.
3 997 0.993095368942 Henry Cohn, 2025.
3 998 0.993098230447 Henry Cohn, 2025.
3 999 0.993105196296 Henry Cohn, 2026.
3 1000 0.993111266855 Henry Cohn, 2025.
3 1001 0.993117495259 Henry Cohn, 2026.
3 1002 0.993125622347 Henry Cohn, 2025.
3 1003 0.993132170420 Henry Cohn, 2025.
3 1004 0.993137613573 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 0.993184403638 Henry Cohn, 2026.
3 1012 0.993192195261 Henry Cohn, 2026.
3 1013 0.993196528382 Henry Cohn, 2026.
3 1014 0.993203054681 Henry Cohn, 2026.
3 1015 0.993209201979 Henry Cohn, 2026.
3 1016 0.993215431797 Henry Cohn, 2026.
3 1017 0.993222604878 Henry Cohn, 2026.
3 1018 0.993230067485 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 0.993243150191 Henry Cohn, 2026.
3 1022 0.993250071049 Henry Cohn, 2026.
3 1023 0.993256367188 Henry Cohn, 2026.
3 1024 0.993263382473 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 0.843226230314 Henry Cohn, 2026.
4 145 0.845004703395 Henry Cohn, 2025.
4 146 0.846045189902 Henry Cohn, 2024.
4 147 0.846906008500 Henry Cohn, 2025.
4 148 0.847320837337 Henry Cohn, 2025.
4 149 0.847701351395 Henry Cohn, 2025.
4 150 0.848008139501 Henry Cohn, 2025.
4 151 0.848395999617 Henry Cohn, 2025.
4 152 0.848746833410 Henry Cohn, 2024.
4 153 0.849106783811 Henry Cohn, 2025.
4 154 0.849448181031 Henry Cohn, 2024.
4 155 0.850528693851 Henry Cohn, 2025.
4 156 0.852364181174 Henry Cohn, 2025.
4 157 0.853098036527 Henry Cohn, 2025.
4 158 0.853541001367 Henry Cohn, 2025.
4 159 0.853851387665 Henry Cohn, 2025.
4 160 0.854015402705 Henry Cohn, 2025.
4 161 0.855036011488 Henry Cohn, 2025.
4 162 0.856011990176 Henry Cohn, 2025.
4 163 0.856498246684 Henry Cohn, 2025.
4 164 0.856668082967 Henry Cohn, 2025.
4 165 0.856908324217 Henry Cohn, 2024.
4 166 0.857225219240 Henry Cohn, 2025.
4 167 0.857623781724 Henry Cohn, 2025.
4 168 0.859313343133 Henry Cohn, 2025.
4 169 0.860417510162 Henry Cohn, 2025.
4 170 0.861320274459 Henry Cohn, 2026.
4 171 0.861877205800 Henry Cohn, 2025.
4 172 0.862352634609 Henry Cohn, 2026, needs more optimization.
4 173 0.862725307388 Henry Cohn, 2025.
4 174 0.863170417348 Henry Cohn, 2026.
4 175 0.863367463185 Henry Cohn, 2025.
4 176 0.863624102971 Henry Cohn, 2025.
4 177 0.863764381494 Henry Cohn, 2025.
4 178 0.863928834672 Henry Cohn, 2025.
4 179 0.864723195011 Henry Cohn, 2025.
4 180 0.865782670861 Henry Cohn, 2025.
4 181 0.866598382577 Henry Cohn, 2025.
4 182 0.867174335033 Henry Cohn, 2025.
4 183 0.867335807322 Henry Cohn, 2025.
4 184 0.867763055785 Henry Cohn, 2025.
4 185 0.868218396424 Henry Cohn, 2026, needs more optimization.
4 186 0.868518800651 Henry Cohn, 2025.
4 187 0.868815006379 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 0.872105849258 Henry Cohn, 2026, needs more optimization.
4 196 0.872623436438 Henry Cohn, 2026, needs more optimization.
4 197 0.873487426793 Henry Cohn, 2025.
4 198 0.874156501901 Henry Cohn, 2025.
4 199 0.875068337345 Henry Cohn, 2026, needs more optimization.
4 200 0.875686480655 Henry Cohn, 2025.
4 201 0.876298855506 Henry Cohn, 2026, needs more optimization.
4 202 0.876662092953 Henry Cohn, 2025.
4 203 0.876809352868 Henry Cohn, 2026, needs more optimization.
4 204 0.877207307342 Henry Cohn, 2026, needs more optimization.
4 205 0.877534211883 Henry Cohn, 2025.
4 206 0.877831247728 Henry Cohn, 2025.
4 207 0.877987055194 Henry Cohn, 2026, needs more optimization.
4 208 0.878215104089 Henry Cohn, 2025.
4 209 0.878614887654 Henry Cohn, 2026, needs more optimization.
4 210 0.879213799752 Henry Cohn, 2025.
4 211 0.879586628106 Henry Cohn, 2025.
4 212 0.879653597334 Henry Cohn, 2026, needs more optimization.
4 213 0.879821147641 Henry Cohn, 2026, needs more optimization.
4 214 0.879945724274 Henry Cohn, 2025.
4 215 0.880272662054 Henry Cohn, 2025.
4 216 0.880905022797 Henry Cohn, 2026, needs more optimization.
4 217 0.881535768813 Henry Cohn, 2025.
4 218 0.881822562818 Henry Cohn, 2026, needs more optimization.
4 219 0.881957670465 Henry Cohn, 2025.
4 220 0.882547029792 Henry Cohn, 2025.
4 221 0.883034423256 Henry Cohn, 2026, needs more optimization.
4 222 0.883456069925 Henry Cohn, 2025.
4 223 0.884138189446 Henry Cohn, 2025.
4 224 0.884684734191 Henry Cohn, 2025.
4 225 0.885119582215 Henry Cohn, 2026, needs more optimization.
4 226 0.885325891137 Henry Cohn, 2026, needs more optimization.
4 227 0.885541386047 Henry Cohn, 2025.
4 228 0.885824040293 Henry Cohn, 2025.
4 229 0.886056617225 Henry Cohn, 2026, needs more optimization.
4 230 0.886372063295 Henry Cohn, 2025.
4 231 0.886825702236 Henry Cohn, 2026, needs more optimization.
4 232 0.887100518143 Henry Cohn, 2026, needs more optimization.
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 0.889105388261 Henry Cohn, 2026, needs more optimization.
4 240 0.889491133869 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 0.890724944080 Henry Cohn, 2026, needs more optimization.
4 245 0.890944651348 Henry Cohn, 2026, needs more optimization.
4 246 0.891230987587 Henry Cohn, 2025.
4 247 0.891664204848 Henry Cohn, 2026, needs more optimization.
4 248 0.891999025063 Henry Cohn, 2026, needs more optimization.
4 249 0.892287508911 Henry Cohn, 2026, needs more optimization.
4 250 0.892630860266 Henry Cohn, 2026, needs more optimization.
4 251 0.893058217316 Henry Cohn, 2026, needs more optimization.
4 252 0.893325096153 Henry Cohn, 2026, needs more optimization.
4 253 0.893448762860 Henry Cohn, 2026, needs more optimization.
4 254 0.893921458915 Henry Cohn, 2026, needs more optimization.
4 255 0.893998043792 Henry Cohn, 2026, needs more optimization.
4 256 0.894519020596 Henry Cohn, 2026, needs more optimization.
4 257 0.894704473601 Henry Cohn, 2026, needs more optimization.
4 258 0.894983407581 Henry Cohn, 2026, needs more optimization.
4 259 0.895410131883 Henry Cohn, 2026, needs more optimization.
4 260 0.895633251473 Henry Cohn, 2026, needs more optimization.
4 261 0.895905321979 Henry Cohn, 2026, needs more optimization.
4 262 0.896205812286 Henry Cohn, 2026, needs more optimization.
4 263 0.896400860461 Henry Cohn, 2026, needs more optimization.
4 264 0.896671974785 Henry Cohn, 2026, needs more optimization.
4 265 0.896833144535 Henry Cohn, 2026, needs more optimization.
4 266 0.897010030544 Henry Cohn, 2026, needs more optimization.
4 267 0.897224130634 Henry Cohn, 2026, needs more optimization.
4 268 0.897364050734 Henry Cohn, 2026, needs more optimization.
4 269 0.897620948775 Henry Cohn, 2026, needs more optimization.
4 270 0.897835806401 Henry Cohn, 2026, needs more optimization.
4 271 0.898148244743 Henry Cohn, 2026, needs more optimization.
4 272 0.898261528854 Henry Cohn, 2026, needs more optimization.
4 273 0.898339685590 Henry Cohn, 2026, needs more optimization.
4 274 0.898509552581 Henry Cohn, 2026, needs more optimization.
4 275 0.898703317971 Henry Cohn, 2026, needs more optimization.
4 276 0.898990529678 Henry Cohn, 2026, needs more optimization.
4 277 0.899343175420 Henry Cohn, 2026, needs more optimization.
4 278 0.899463369945 Henry Cohn, 2026, needs more optimization.
4 279 0.899598176525 Henry Cohn, 2026, needs more optimization.
4 280 0.899641408534 Henry Cohn, 2026, needs more optimization.
4 281 0.900128228514 Henry Cohn, 2026, needs more optimization.
4 282 0.900628397128 Henry Cohn, 2026, needs more optimization.
4 283 0.900999989174 Henry Cohn, 2026, needs more optimization.
4 284 0.901370282618 Henry Cohn, 2026, needs more optimization.
4 285 0.901658073834 Henry Cohn, 2026, needs more optimization.
4 286 0.901879669561 Henry Cohn, 2026, needs more optimization.
4 287 0.902030253803 Henry Cohn, 2026, needs more optimization.
4 288 0.902074383291 Henry Cohn, 2026, needs more optimization.
4 289 0.902147462122 Henry Cohn, 2026, needs more optimization.
4 290 0.902706635097 Henry Cohn, 2026, needs more optimization.
4 291 0.903108410871 Henry Cohn, 2026, needs more optimization.
4 292 0.903481411921 Henry Cohn, 2026, needs more optimization.
4 293 0.903823769043 Henry Cohn, 2026, needs more optimization.
4 294 0.904139899260 Henry Cohn, 2026, needs more optimization.
4 295 0.904227980830 Henry Cohn, 2026, needs more optimization.
4 296 0.904772951026 Henry Cohn, 2026, needs more optimization.
4 297 0.904780672379 Henry Cohn, 2026, needs more optimization.
4 298 0.904878186328 Henry Cohn, 2026, needs more optimization.
4 299 0.905146611996 Henry Cohn, 2026, needs more optimization.
4 300 0.905371027335 Henry Cohn, 2026, needs more optimization.
4 301 0.905598673498 Henry Cohn, 2026, needs more optimization.
4 302 0.905816549231 Henry Cohn, 2026, needs more optimization.
4 303 0.906092883396 Henry Cohn, 2026, needs more optimization.
4 304 0.906254637567 Henry Cohn, 2026, needs more optimization.
4 305 0.906325024508 Henry Cohn, 2026, needs more optimization.
4 306 0.906511554443 Henry Cohn, 2026, needs more optimization.
4 307 0.906770232658 Henry Cohn, 2026, needs more optimization.
4 308 0.906983246118 Henry Cohn, 2026, needs more optimization.
4 309 0.907309805636 Henry Cohn, 2026, needs more optimization.
4 310 0.907346734922 Henry Cohn, 2026, needs more optimization.
4 311 0.907523820544 Henry Cohn, 2026, needs more optimization.
4 312 0.907800795429 Henry Cohn, 2026, needs more optimization.
4 313 0.907999397383 Henry Cohn, 2026, needs more optimization.
4 314 0.908175258934 Henry Cohn, 2026, needs more optimization.
4 315 0.908336357881 Henry Cohn, 2026, needs more optimization.
4 316 0.908440611577 Henry Cohn, 2026, needs more optimization.
4 317 0.908714143411 Henry Cohn, 2026, needs more optimization.
4 318 0.908941299492 Henry Cohn, 2026, needs more optimization.
4 319 0.909153407634 Henry Cohn, 2026, needs more optimization.
4 320 0.909320854901 Henry Cohn, 2026, needs more optimization.
4 321 0.909519336811 Henry Cohn, 2026, needs more optimization.
4 322 0.909578314696 Henry Cohn, 2026, needs more optimization.
4 323 0.909664277020 Henry Cohn, 2026, needs more optimization.
4 324 0.909833171539 Henry Cohn, 2026, needs more optimization.
4 325 0.910040662612 Henry Cohn, 2026, needs more optimization.
4 326 0.910202553176 Henry Cohn, 2026, needs more optimization.
4 327 0.910288142665 Henry Cohn, 2026, needs more optimization.
4 328 0.910395023215 Henry Cohn, 2026, needs more optimization.
4 329 0.910669683988 Henry Cohn, 2026, needs more optimization.
4 330 0.910913211066 Henry Cohn, 2026, needs more optimization.
4 331 0.911137086274 Henry Cohn, 2026, needs more optimization.
4 332 0.911290223999 Henry Cohn, 2026, needs more optimization.
4 333 0.911521024539 Henry Cohn, 2026, needs more optimization.
4 334 0.911635352506 Henry Cohn, 2026, needs more optimization.
4 335 0.911929011357 Henry Cohn, 2026, needs more optimization.
4 336 0.912146098220 Henry Cohn, 2026, needs more optimization.
4 337 0.912392350620 Henry Cohn, 2026, needs more optimization.
4 338 0.912622753554 Henry Cohn, 2026, needs more optimization.
4 339 0.912849496476 Henry Cohn, 2026, needs more optimization.
4 340 0.913082210088 Henry Cohn, 2026, needs more optimization.
4 341 0.913351068550 Henry Cohn, 2026, needs more optimization.
4 342 0.913451258646 Henry Cohn, 2026, needs more optimization.
4 343 0.913635300906 Henry Cohn, 2026, needs more optimization.
4 344 0.913824325681 Henry Cohn, 2026, needs more optimization.
4 345 0.914106284881 Henry Cohn, 2026, needs more optimization.
4 346 0.914199615014 Henry Cohn, 2026, needs more optimization.
4 347 0.914370914137 Henry Cohn, 2026, needs more optimization.
4 348 0.914597659316 Henry Cohn, 2026, needs more optimization.
4 349 0.914787148082 Henry Cohn, 2026, needs more optimization.
4 350 0.914833325744 Henry Cohn, 2026, needs more optimization.
4 351 0.915003300656 Henry Cohn, 2026, needs more optimization.
4 352 0.915197444750 Henry Cohn, 2026, needs more optimization.
4 353 0.915241483582 Henry Cohn, 2026, needs more optimization.
4 354 0.915422024189 Henry Cohn, 2026, needs more optimization.
4 355 0.915511105120 Henry Cohn, 2026, needs more optimization.
4 356 0.915646201741 Henry Cohn, 2026, needs more optimization.
4 357 0.915776007982 Henry Cohn, 2026, needs more optimization.
4 358 0.915936268027 Henry Cohn, 2026, needs more optimization.
4 359 0.916064146263 Henry Cohn, 2026, needs more optimization.
4 360 0.916230419145 Henry Cohn, 2026, needs more optimization.
4 361 0.916289234449 Henry Cohn, 2026, needs more optimization.
4 362 0.916289444182 Henry Cohn, 2026, needs more optimization.
4 363 0.916453598948 Henry Cohn, 2026, needs more optimization.
4 364 0.916570323931 Henry Cohn, 2026, needs more optimization.
4 365 0.916741836614 Henry Cohn, 2026, needs more optimization.
4 366 0.916832584131 Henry Cohn, 2026, needs more optimization.
4 367 0.917147081048 Henry Cohn, 2026, needs more optimization.
4 368 0.917196435639 Henry Cohn, 2026, needs more optimization.
4 369 0.917260106907 Henry Cohn, 2026, needs more optimization.
4 370 0.917318322450 Henry Cohn, 2026, needs more optimization.
4 371 0.917453499805 Henry Cohn, 2026, needs more optimization.
4 372 0.917609931691 Henry Cohn, 2026, needs more optimization.
4 373 0.917879177862 Henry Cohn, 2026, needs more optimization.
4 374 0.918151068673 Henry Cohn, 2026, needs more optimization.
4 375 0.918345810096 Henry Cohn, 2026, needs more optimization.
4 376 0.918498383470 Henry Cohn, 2026, needs more optimization.
4 377 0.918633972988 Henry Cohn, 2026, needs more optimization.
4 378 0.918656801886 Henry Cohn, 2026, needs more optimization.
4 379 0.918873328717 Henry Cohn, 2026, needs more optimization.
4 380 0.918970435062 Henry Cohn, 2026, needs more optimization.
4 381 0.919143222020 Henry Cohn, 2026, needs more optimization.
4 382 0.919185562445 Henry Cohn, 2026, needs more optimization.
4 383 0.919278633917 Henry Cohn, 2026, needs more optimization.
4 384 0.919355742145 Henry Cohn, 2026, needs more optimization.
4 385 0.919376895734 Henry Cohn, 2026, needs more optimization.
4 386 0.919479615480 Henry Cohn, 2026, needs more optimization.
4 387 0.919487036349 Henry Cohn, 2026, needs more optimization.
4 388 0.919700062482 Henry Cohn, 2026, needs more optimization.
4 389 0.919731293676 Henry Cohn, 2026, needs more optimization.
4 390 0.919937828950 Henry Cohn, 2026, needs more optimization.
4 391 0.920141917044 Henry Cohn, 2026, needs more optimization.
4 392 0.920323267604 Henry Cohn, 2026, needs more optimization.
4 393 0.920443343348 Henry Cohn, 2026, needs more optimization.
4 394 0.920474714264 Henry Cohn, 2026, needs more optimization.
4 395 0.920572071483 Henry Cohn, 2026, needs more optimization.
4 396 0.920859602083 Henry Cohn, 2026, needs more optimization.
4 397 0.921007411300 Henry Cohn, 2026, needs more optimization.
4 398 0.921115215589 Henry Cohn, 2026, needs more optimization.
4 399 0.921191916037 Henry Cohn, 2026, needs more optimization.
4 400 0.921399526785 Henry Cohn, 2026, needs more optimization.
4 401 0.921450919242 Henry Cohn, 2026, needs more optimization.
4 402 0.921727139193 Henry Cohn, 2026, needs more optimization.
4 403 0.921795714891 Henry Cohn, 2026, needs more optimization.
4 404 0.921828215529 Henry Cohn, 2026, needs more optimization.
4 405 0.921862996202 Henry Cohn, 2026, needs more optimization.
4 406 0.921915016490 Henry Cohn, 2026, needs more optimization.
4 407 0.921975126605 Henry Cohn, 2026, needs more optimization.
4 408 0.921999084698 Henry Cohn, 2026, needs more optimization.
4 409 0.922341320020 Henry Cohn, 2026, needs more optimization.
4 410 0.922651498313 Henry Cohn, 2026, needs more optimization.
4 411 0.922708465060 Henry Cohn, 2026, needs more optimization.
4 412 0.922995069090 Henry Cohn, 2026, needs more optimization.
4 413 0.923217179480 Henry Cohn, 2026, needs more optimization.
4 414 0.923245593488 Henry Cohn, 2026, needs more optimization.
4 415 0.923433944721 Henry Cohn, 2026, needs more optimization.
4 416 0.923454133261 Henry Cohn, 2026, needs more optimization.
4 417 0.923548539339 Henry Cohn, 2026, needs more optimization.
4 418 0.923602720871 Henry Cohn, 2026, needs more optimization.
4 419 0.923727148602 Henry Cohn, 2026, needs more optimization.
4 420 0.923894894182 Henry Cohn, 2026, needs more optimization.
4 421 0.923987261311 Henry Cohn, 2026, needs more optimization.
4 422 0.924137039995 Henry Cohn, 2026, needs more optimization.
4 423 0.924287708878 Henry Cohn, 2026, needs more optimization.
4 424 0.924506205911 Henry Cohn, 2026, needs more optimization.
4 425 0.924702561607 Henry Cohn, 2026, needs more optimization.
4 426 0.924910242153 Henry Cohn, 2026, needs more optimization.
4 427 0.925108898874 Henry Cohn, 2026, needs more optimization.
4 428 0.925226749281 Henry Cohn, 2026, needs more optimization.
4 429 0.925414627869 Henry Cohn, 2026, needs more optimization.
4 430 0.925533857769 Henry Cohn, 2026, needs more optimization.
4 431 0.925694519375 Henry Cohn, 2026, needs more optimization.
4 432 0.925805709439 Henry Cohn, 2026, needs more optimization.
4 433 0.925937777256 Henry Cohn, 2026, needs more optimization.
4 434 0.926001251118 Henry Cohn, 2026, needs more optimization.
4 435 0.926187495542 Henry Cohn, 2026, needs more optimization.
4 436 0.926277974705 Henry Cohn, 2026, needs more optimization.
4 437 0.926443609567 Henry Cohn, 2026, needs more optimization.
4 438 0.926609925397 Henry Cohn, 2026, needs more optimization.
4 439 0.926763388369 Henry Cohn, 2026, needs more optimization.
4 440 0.926893117915 Henry Cohn, 2026, needs more optimization.
4 441 0.927040019831 Henry Cohn, 2026, needs more optimization.
4 442 0.927162772647 Henry Cohn, 2026, needs more optimization.
4 443 0.927213162664 Henry Cohn, 2026, needs more optimization.
4 444 0.927344137770 Henry Cohn, 2026, needs more optimization.
4 445 0.927431896137 Henry Cohn, 2026, needs more optimization.
4 446 0.927516359703 Henry Cohn, 2026, needs more optimization.
4 447 0.927595870599 Henry Cohn, 2026, needs more optimization.
4 448 0.927714300729 Henry Cohn, 2026, needs more optimization.
4 449 0.927856914720 Henry Cohn, 2026, needs more optimization.
4 450 0.928013062825 Henry Cohn, 2026, needs more optimization.
4 451 0.928084680212 Henry Cohn, 2026, needs more optimization.
4 452 0.928146328596 Henry Cohn, 2026, needs more optimization.
4 453 0.928202153204 Henry Cohn, 2026, needs more optimization.
4 454 0.928310210865 Henry Cohn, 2026, needs more optimization.
4 455 0.928329395768 Henry Cohn, 2026, needs more optimization.
4 456 0.928428854805 Henry Cohn, 2026, needs more optimization.
4 457 0.928550526291 Henry Cohn, 2026, needs more optimization.
4 458 0.928594035434 Henry Cohn, 2026, needs more optimization.
4 459 0.928699214030 Henry Cohn, 2026, needs more optimization.
4 460 0.928759422698 Henry Cohn, 2026, needs more optimization.
4 461 0.928917699357 Henry Cohn, 2026, needs more optimization.
4 462 0.929033207491 Henry Cohn, 2026, needs more optimization.
4 463 0.929131784123 Henry Cohn, 2026, needs more optimization.
4 464 0.929227394550 Henry Cohn, 2026, needs more optimization.
4 465 0.929339758818 Henry Cohn, 2026, needs more optimization.
4 466 0.929509157050 Henry Cohn, 2026, needs more optimization.
4 467 0.929655480731 Henry Cohn, 2026, needs more optimization.
4 468 0.929732602301 Henry Cohn, 2026, needs more optimization.
4 469 0.929860957579 Henry Cohn, 2026, needs more optimization.
4 470 0.929985992560 Henry Cohn, 2026, needs more optimization.
4 471 0.930102839856 Henry Cohn, 2026, needs more optimization.
4 472 0.930285292176 Henry Cohn, 2026, needs more optimization.
4 473 0.930412153897 Henry Cohn, 2026, needs more optimization.
4 474 0.930547417497 Henry Cohn, 2026, needs more optimization.
4 475 0.930659638588 Henry Cohn, 2026, needs more optimization.
4 476 0.930698582971 Henry Cohn, 2026, needs more optimization.
4 477 0.930793460242 Henry Cohn, 2026, needs more optimization.
4 478 0.930962346896 Henry Cohn, 2026, needs more optimization.
4 479 0.930995715922 Henry Cohn, 2026, needs more optimization.
4 480 0.931046316594 Henry Cohn, 2026, needs more optimization.
4 481 0.931141184403 Henry Cohn, 2026, needs more optimization.
4 482 0.931249910758 Henry Cohn, 2026, needs more optimization.
4 483 0.931364128548 Henry Cohn, 2026, needs more optimization.
4 484 0.931488765794 Henry Cohn, 2026, needs more optimization.
4 485 0.931578998891 Henry Cohn, 2026, needs more optimization.
4 486 0.931622594206 Henry Cohn, 2026, needs more optimization.
4 487 0.931710609922 Henry Cohn, 2026, needs more optimization.
4 488 0.931815186391 Henry Cohn, 2026, needs more optimization.
4 489 0.931865713051 Henry Cohn, 2026, needs more optimization.
4 490 0.931970996601 Henry Cohn, 2026, needs more optimization.
4 491 0.932018694983 Henry Cohn, 2026, needs more optimization.
4 492 0.932074265391 Henry Cohn, 2026, needs more optimization.
4 493 0.932143640785 Henry Cohn, 2026, needs more optimization.
4 494 0.932206682280 Henry Cohn, 2026, needs more optimization.
4 495 0.932290551765 Henry Cohn, 2026, needs more optimization.
4 496 0.932382834424 Henry Cohn, 2026, needs more optimization.
4 497 0.932493266064 Henry Cohn, 2026, needs more optimization.
4 498 0.932590475767 Henry Cohn, 2026, needs more optimization.
4 499 0.932636652466 Henry Cohn, 2026, needs more optimization.
4 500 0.932712692545 Henry Cohn, 2026, needs more optimization.
4 501 0.932740575924 Henry Cohn, 2026, needs more optimization.
4 502 0.932867088827 Henry Cohn, 2026, needs more optimization.
4 503 0.932925981883 Henry Cohn, 2026, needs more optimization.
4 504 0.933026819656 Henry Cohn, 2026, needs more optimization.
4 505 0.933095169273 Henry Cohn, 2026, needs more optimization.
4 506 0.933166891839 Henry Cohn, 2026, needs more optimization.
4 507 0.933278815619 Henry Cohn, 2026, needs more optimization.
4 508 0.933352549973 Henry Cohn, 2026, needs more optimization.
4 509 0.933458103093 Henry Cohn, 2026, needs more optimization.
4 510 0.933546921530 Henry Cohn, 2026, needs more optimization.
4 511 0.933643436964 Henry Cohn, 2026, needs more optimization.
4 512 0.933740947788 Henry Cohn, 2026, needs more optimization.
4 513 0.933894886890 Henry Cohn, 2026, needs more optimization.
4 514 0.933945377103 Henry Cohn, 2026, needs more optimization.
4 515 0.934030628815 Henry Cohn, 2026, needs more optimization.
4 516 0.934177981021 Henry Cohn, 2026, needs more optimization.
4 517 0.934196552198 Henry Cohn, 2026, needs more optimization.
4 518 0.934307647833 Henry Cohn, 2026, needs more optimization.
4 519 0.934447530152 Henry Cohn, 2026, needs more optimization.
4 520 0.934505445141 Henry Cohn, 2026, needs more optimization.
4 521 0.934590569938 Henry Cohn, 2026, needs more optimization.
4 522 0.934733534668 Henry Cohn, 2026, needs more optimization.
4 523 0.934787854923 Henry Cohn, 2026, needs more optimization.
4 524 0.934877468119 Henry Cohn, 2026, needs more optimization.
4 525 0.934989612353 Henry Cohn, 2026, needs more optimization.
4 526 0.935086521779 Henry Cohn, 2026, needs more optimization.
4 527 0.935179813895 Henry Cohn, 2026, needs more optimization.
4 528 0.935249779907 Henry Cohn, 2026, needs more optimization.
4 529 0.935293902732 Henry Cohn, 2026, needs more optimization.
4 530 0.935328115541 Henry Cohn, 2026, needs more optimization.
4 531 0.935459011007 Henry Cohn, 2026, needs more optimization.
4 532 0.935524050940 Henry Cohn, 2026, needs more optimization.
4 533 0.935593734491 Henry Cohn, 2026, needs more optimization.
4 534 0.935717330983 Henry Cohn, 2026, needs more optimization.
4 535 0.935749119893 Henry Cohn, 2026, needs more optimization.
4 536 0.935866188807 Henry Cohn, 2026, needs more optimization.
4 537 0.935869559922 Henry Cohn, 2026, needs more optimization.
4 538 0.936005796432 Henry Cohn, 2026, needs more optimization.
4 539 0.936072337797 Henry Cohn, 2026, needs more optimization.
4 540 0.936169895207 Henry Cohn, 2026, needs more optimization.
4 541 0.936205557490 Henry Cohn, 2026, needs more optimization.
4 542 0.936274034135 Henry Cohn, 2026, needs more optimization.
4 543 0.936389174192 Henry Cohn, 2026, needs more optimization.
4 544 0.936455569199 Henry Cohn, 2026, needs more optimization.
4 545 0.936535893626 Henry Cohn, 2026, needs more optimization.
4 546 0.936575161858 Henry Cohn, 2026, needs more optimization.
4 547 0.936601832719 Henry Cohn, 2026, needs more optimization.
4 548 0.936672950854 Henry Cohn, 2026, needs more optimization.
4 549 0.936740888737 Henry Cohn, 2026, needs more optimization.
4 550 0.936832286483 Henry Cohn, 2026, needs more optimization.
4 551 0.936862202771 Henry Cohn, 2026, needs more optimization.
4 552 0.936983167821 Henry Cohn, 2026, needs more optimization.
4 553 0.937070117827 Henry Cohn, 2026, needs more optimization.
4 554 0.937187623852 Henry Cohn, 2026, needs more optimization.
4 555 0.937290401585 Henry Cohn, 2026, needs more optimization.
4 556 0.937344222242 Henry Cohn, 2026, needs more optimization.
4 557 0.937413258664 Henry Cohn, 2026, needs more optimization.
4 558 0.937538556882 Henry Cohn, 2026, needs more optimization.
4 559 0.937610759085 Henry Cohn, 2026, needs more optimization.
4 560 0.937706995693 Henry Cohn, 2026, needs more optimization.
4 561 0.937742567854 Henry Cohn, 2026, needs more optimization.
4 562 0.937820476134 Henry Cohn, 2026, needs more optimization.
4 563 0.937891473943 Henry Cohn, 2026, needs more optimization.
4 564 0.937947609218 Henry Cohn, 2026, needs more optimization.
4 565 0.938003035555 Henry Cohn, 2026, needs more optimization.
4 566 0.938115847652 Henry Cohn, 2026, needs more optimization.
4 567 0.938193448268 Henry Cohn, 2026, needs more optimization.
4 568 0.938271633305 Henry Cohn, 2026, needs more optimization.
4 569 0.938348151715 Henry Cohn, 2026, needs more optimization.
4 570 0.938370883080 Henry Cohn, 2026, needs more optimization.
4 571 0.938422632741 Henry Cohn, 2026, needs more optimization.
4 572 0.938488563032 Henry Cohn, 2026, needs more optimization.
4 573 0.938582243366 Henry Cohn, 2026, needs more optimization.
4 574 0.938671786926 Henry Cohn, 2026, needs more optimization.
4 575 0.938791155677 Henry Cohn, 2026, needs more optimization.
4 576 0.938877627759 Henry Cohn, 2026, needs more optimization.
4 577 0.938908010886 Henry Cohn, 2026, needs more optimization.
4 578 0.938954707664 Henry Cohn, 2026, needs more optimization.
4 579 0.939069500151 Henry Cohn, 2026, needs more optimization.
4 580 0.939156937373 Henry Cohn, 2026, needs more optimization.
4 581 0.939205608154 Henry Cohn, 2026, needs more optimization.
4 582 0.939272926028 Henry Cohn, 2026, needs more optimization.
4 583 0.939309753419 Henry Cohn, 2026, needs more optimization.
4 584 0.939336702795 Henry Cohn, 2026, needs more optimization.
4 585 0.939435176969 Henry Cohn, 2026, needs more optimization.
4 586 0.939488882797 Henry Cohn, 2026, needs more optimization.
4 587 0.939552487801 Henry Cohn, 2026, needs more optimization.
4 588 0.939564372045 Henry Cohn, 2026, needs more optimization.
4 589 0.939653904279 Henry Cohn, 2026, needs more optimization.
4 590 0.939669499244 Henry Cohn, 2026, needs more optimization.
4 591 0.939779551948 Henry Cohn, 2026, needs more optimization.
4 593 0.939833915960 Henry Cohn, 2026, needs more optimization.
4 594 0.939850699080 Henry Cohn, 2026, needs more optimization.
4 595 0.939922750403 Henry Cohn, 2026, needs more optimization.
4 596 0.939974798818 Henry Cohn, 2026, needs more optimization.
4 597 0.939993548798 Henry Cohn, 2026, needs more optimization.
4 598 0.940087677811 Henry Cohn, 2026, needs more optimization.
4 599 0.940161442626 Henry Cohn, 2026, needs more optimization.
4 600 0.940194638041 Henry Cohn, 2026, needs more optimization.
4 601 0.940235959643 Henry Cohn, 2026, needs more optimization.
4 602 0.940353352180 Henry Cohn, 2026, needs more optimization.
4 603 0.940409639769 Henry Cohn, 2026, needs more optimization.
4 604 0.940534640970 Henry Cohn, 2026, needs more optimization.
4 605 0.940625131768 Henry Cohn, 2026, needs more optimization.
4 606 0.940631961613 Henry Cohn, 2026, needs more optimization.
4 607 0.940714252634 Henry Cohn, 2026, needs more optimization.
4 608 0.940770862069 Henry Cohn, 2026, needs more optimization.
4 609 0.940851753534 Henry Cohn, 2026, needs more optimization.
4 610 0.940924042276 Henry Cohn, 2026, needs more optimization.
4 611 0.940976408367 Henry Cohn, 2026, needs more optimization.
4 612 0.941046272800 Henry Cohn, 2026, needs more optimization.
4 613 0.941073182884 Henry Cohn, 2026, needs more optimization.
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4 615 0.941259635690 Henry Cohn, 2026, needs more optimization.
4 616 0.941277044557 Henry Cohn, 2026, needs more optimization.
4 617 0.941341426907 Henry Cohn, 2026, needs more optimization.
4 618 0.941404691805 Henry Cohn, 2026, needs more optimization.
4 619 0.941455302527 Henry Cohn, 2026, needs more optimization.
4 620 0.941518479280 Henry Cohn, 2026, needs more optimization.
4 621 0.941560432986 Henry Cohn, 2026, needs more optimization.
4 622 0.941658796976 Henry Cohn, 2026, needs more optimization.
4 623 0.941714409253 Henry Cohn, 2026, needs more optimization.
4 624 0.941776206438 Henry Cohn, 2026, needs more optimization.
4 625 0.941848322154 Henry Cohn, 2026, needs more optimization.
4 626 0.941965603848 Henry Cohn, 2026, needs more optimization.
4 627 0.942008974185 Henry Cohn, 2026, needs more optimization.
4 628 0.942086591337 Henry Cohn, 2026, needs more optimization.
4 629 0.942156101659 Henry Cohn, 2026, needs more optimization.
4 630 0.942228243971 Henry Cohn, 2026, needs more optimization.
4 631 0.942293746278 Henry Cohn, 2026, needs more optimization.
4 632 0.942329374959 Henry Cohn, 2026, needs more optimization.
4 633 0.942418935457 Henry Cohn, 2026, needs more optimization.
4 634 0.942501940232 Henry Cohn, 2026, needs more optimization.
4 635 0.942536750469 Henry Cohn, 2026, needs more optimization.
4 636 0.942598864958 Henry Cohn, 2026, needs more optimization.
4 637 0.942633549020 Henry Cohn, 2026, needs more optimization.
4 638 0.942698156143 Henry Cohn, 2026, needs more optimization.
4 639 0.942766051617 Henry Cohn, 2026, needs more optimization.
4 640 0.942794145973 Henry Cohn, 2026, needs more optimization.
4 641 0.942881751480 Henry Cohn, 2026, needs more optimization.
4 642 0.942978821558 Henry Cohn, 2026, needs more optimization.
4 644 0.943075061826 Henry Cohn, 2026, needs more optimization.
4 645 0.943124543214 Henry Cohn, 2026, needs more optimization.
4 646 0.943177017091 Henry Cohn, 2026, needs more optimization.
4 647 0.943218474673 Henry Cohn, 2026, needs more optimization.
4 648 0.943260244919 Henry Cohn, 2026, needs more optimization.
4 649 0.943283198918 Henry Cohn, 2026, needs more optimization.
4 650 0.943299693201 Henry Cohn, 2026, needs more optimization.
4 651 0.943346611455 Henry Cohn, 2026, needs more optimization.
4 652 0.943380686996 Henry Cohn, 2026, needs more optimization.
4 654 0.943397321222 Henry Cohn, 2026, needs more optimization.
4 655 0.943454479436 Henry Cohn, 2026, needs more optimization.
4 656 0.943491565235 Henry Cohn, 2026, needs more optimization.
4 657 0.943551562583 Henry Cohn, 2026, needs more optimization.
4 658 0.943560838034 Henry Cohn, 2026, needs more optimization.
4 659 0.943580826685 Henry Cohn, 2026, needs more optimization.
4 660 0.943604845812 Henry Cohn, 2026, needs more optimization.
4 661 0.943626945910 Henry Cohn, 2026, needs more optimization.
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4 663 0.943724813900 Henry Cohn, 2026, needs more optimization.
4 664 0.943761897689 Henry Cohn, 2026, needs more optimization.
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4 666 0.943819049994 Henry Cohn, 2026, needs more optimization.
4 667 0.943842869935 Henry Cohn, 2026, needs more optimization.
4 668 0.943870021204 Henry Cohn, 2026, needs more optimization.
4 669 0.943901387612 Henry Cohn, 2026, needs more optimization.
4 670 0.943982534852 Henry Cohn, 2026, needs more optimization.
4 671 0.944010641051 Henry Cohn, 2026, needs more optimization.
4 672 0.944050437968 Henry Cohn, 2026, needs more optimization.
4 673 0.944128162085 Henry Cohn, 2026, needs more optimization.
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4 675 0.944339086672 Henry Cohn, 2026, needs more optimization.
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4 677 0.944404539732 Henry Cohn, 2026, needs more optimization.
4 678 0.944519247018 Henry Cohn, 2026, needs more optimization.
4 679 0.944596477357 Henry Cohn, 2026, needs more optimization.
4 680 0.944691324074 Henry Cohn, 2026, needs more optimization.
4 681 0.944730001485 Henry Cohn, 2026, needs more optimization.
4 682 0.944806191486 Henry Cohn, 2026, needs more optimization.
4 683 0.944851289917 Henry Cohn, 2026, needs more optimization.
4 684 0.944924533752 Henry Cohn, 2026, needs more optimization.
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4 688 0.945245206414 Henry Cohn, 2026, needs more optimization.
4 689 0.945294034069 Henry Cohn, 2026, needs more optimization.
4 690 0.945377342690 Henry Cohn, 2026, needs more optimization.
4 691 0.945468858739 Henry Cohn, 2026, needs more optimization.
4 692 0.945518189629 Henry Cohn, 2026, needs more optimization.
4 693 0.945626347837 Henry Cohn, 2026, needs more optimization.
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4 695 0.945737657107 Henry Cohn, 2026, needs more optimization.
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4 702 0.946218549456 Henry Cohn, 2026, needs more optimization.
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4 710 0.946571027355 Henry Cohn, 2026, needs more optimization.
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4 718 0.946936801830 Henry Cohn, 2026, needs more optimization.
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4 724 0.947199845853 Henry Cohn, 2026, needs more optimization.
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4 727 0.947279885336 Henry Cohn, 2026, needs more optimization.
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4 732 0.947529049779 Henry Cohn, 2026, needs more optimization.
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4 735 0.947589951100 Henry Cohn, 2026, needs more optimization.
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4 739 0.947725726747 Henry Cohn, 2026, needs more optimization.
4 740 0.947759606168 Henry Cohn, 2026, needs more optimization.
4 741 0.947832471299 Henry Cohn, 2026, needs more optimization.
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4 743 0.947886681549 Henry Cohn, 2026, needs more optimization.
4 744 0.947956952826 Henry Cohn, 2026, needs more optimization.
4 745 0.948015055216 Henry Cohn, 2026, needs more optimization.
4 746 0.948074030023 Henry Cohn, 2026, needs more optimization.
4 747 0.948125799574 Henry Cohn, 2026, needs more optimization.
4 748 0.948151421467 Henry Cohn, 2026, needs more optimization.
4 749 0.948195678386 Henry Cohn, 2026, needs more optimization.
4 750 0.948261752992 Henry Cohn, 2026, needs more optimization.
4 751 0.948306164441 Henry Cohn, 2026, needs more optimization.
4 752 0.948342814063 Henry Cohn, 2026, needs more optimization.
4 753 0.948358166944 Henry Cohn, 2026, needs more optimization.
4 754 0.948387183161 Henry Cohn, 2026, needs more optimization.
4 755 0.948409654453 Henry Cohn, 2026, needs more optimization.
4 756 0.948453199247 Henry Cohn, 2026, needs more optimization.
4 757 0.948497408029 Henry Cohn, 2026, needs more optimization.
4 758 0.948590864299 Henry Cohn, 2026, needs more optimization.
4 759 0.948625604047 Henry Cohn, 2026, needs more optimization.
4 760 0.948681948073 Henry Cohn, 2026, needs more optimization.
4 761 0.948717507939 Henry Cohn, 2026, needs more optimization.
4 762 0.948795592422 Henry Cohn, 2026, needs more optimization.
4 763 0.948854012623 Henry Cohn, 2026, needs more optimization.
4 764 0.948861949571 Henry Cohn, 2026, needs more optimization.
4 765 0.948872223053 Henry Cohn, 2026, needs more optimization.
4 766 0.948927823067 Henry Cohn, 2026, needs more optimization.
4 767 0.948959292376 Henry Cohn, 2026, needs more optimization.
4 768 0.948995283520 Henry Cohn, 2026, needs more optimization.
4 769 0.949081351260 Henry Cohn, 2026, needs more optimization.
4 771 0.949106808196 Henry Cohn, 2026, needs more optimization.
4 772 0.949174828773 Henry Cohn, 2026, needs more optimization.
4 773 0.949240522941 Henry Cohn, 2026, needs more optimization.
4 774 0.949314277406 Henry Cohn, 2026, needs more optimization.
4 775 0.949353119003 Henry Cohn, 2026, needs more optimization.
4 776 0.949391473437 Henry Cohn, 2026, needs more optimization.
4 777 0.949422393252 Henry Cohn, 2026, needs more optimization.
4 778 0.949489123677 Henry Cohn, 2026, needs more optimization.
4 779 0.949549603792 Henry Cohn, 2026, needs more optimization.
4 780 0.949578522700 Henry Cohn, 2026, needs more optimization.
4 781 0.949588247234 Henry Cohn, 2026, needs more optimization.
4 782 0.949598681397 Henry Cohn, 2026, needs more optimization.
4 783 0.949673976874 Henry Cohn, 2026, needs more optimization.
4 784 0.949712449587 Henry Cohn, 2026, needs more optimization.
4 785 0.949731281245 Henry Cohn, 2026, needs more optimization.
4 787 0.949803758662 Henry Cohn, 2026, needs more optimization.
4 788 0.949824235299 Henry Cohn, 2026, needs more optimization.
4 789 0.949872602356 Henry Cohn, 2026, needs more optimization.
4 790 0.949914656538 Henry Cohn, 2026, needs more optimization.
4 791 0.949939890917 Henry Cohn, 2026, needs more optimization.
4 792 0.950005244011 Henry Cohn, 2026, needs more optimization.
4 794 0.950033655718 Henry Cohn, 2026, needs more optimization.
4 795 0.950070401014 Henry Cohn, 2026, needs more optimization.
4 796 0.950091977282 Henry Cohn, 2026, needs more optimization.
4 797 0.950112658102 Henry Cohn, 2026, needs more optimization.
4 798 0.950160532292 Henry Cohn, 2026, needs more optimization.
4 799 0.950194610493 Henry Cohn, 2026, needs more optimization.
4 800 0.950234835061 Henry Cohn, 2026, needs more optimization.
4 801 0.950248967361 Henry Cohn, 2026, needs more optimization.
4 802 0.950271901315 Henry Cohn, 2026, needs more optimization.
4 803 0.950289335457 Henry Cohn, 2026, needs more optimization.
4 804 0.950293143741 Henry Cohn, 2026, needs more optimization.
4 805 0.950315972040 Henry Cohn, 2026, needs more optimization.
4 806 0.950357603986 Henry Cohn, 2026, needs more optimization.
4 807 0.950392937483 Henry Cohn, 2026, needs more optimization.
4 808 0.950429552597 Henry Cohn, 2026, needs more optimization.
4 809 0.950435168385 Henry Cohn, 2026, needs more optimization.
4 810 0.950454569788 Henry Cohn, 2026, needs more optimization.
4 811 0.950489424969 Henry Cohn, 2026, needs more optimization.
4 812 0.950498096443 Henry Cohn, 2026, needs more optimization.
4 813 0.950524145021 Henry Cohn, 2026, needs more optimization.
4 814 0.950537274106 Henry Cohn, 2026, needs more optimization.
4 815 0.950566527860 Henry Cohn, 2026, needs more optimization.
4 816 0.950596492538 Henry Cohn, 2026, needs more optimization.
4 817 0.950615899448 Henry Cohn, 2026, needs more optimization.
4 818 0.950633486493 Henry Cohn, 2026, needs more optimization.
4 819 0.950646411670 Henry Cohn, 2026, needs more optimization.
4 820 0.950655675212 Henry Cohn, 2026, needs more optimization.
4 821 0.950682983228 Henry Cohn, 2026, needs more optimization.
4 823 0.950731498900 Henry Cohn, 2026, needs more optimization.
4 840 0.950797547280 Henry Cohn, 2025, needs more optimization.
4 841 0.951027346931 Henry Cohn, 2026, needs more optimization.
4 842 0.951116889776 Henry Cohn, 2026, needs more optimization.
4 843 0.951207280717 Henry Cohn, 2026, needs more optimization.
4 844 0.951291501480 Henry Cohn, 2026, needs more optimization.
4 845 0.951341906845 Henry Cohn, 2026, needs more optimization.
4 846 0.951454048018 Henry Cohn, 2026, needs more optimization.
4 847 0.951501093000 Henry Cohn, 2026, needs more optimization.
4 848 0.951604065135 Henry Cohn, 2026, needs more optimization.
4 849 0.951679562133 Henry Cohn, 2026, needs more optimization.
4 850 0.951739940180 Henry Cohn, 2026, needs more optimization.
4 851 0.951832488688 Henry Cohn, 2026, needs more optimization.
4 852 0.951874779747 Henry Cohn, 2026, needs more optimization.
4 853 0.951947959044 Henry Cohn, 2026, needs more optimization.
4 854 0.952061541405 Henry Cohn, 2026, needs more optimization.
4 855 0.952130713699 Henry Cohn, 2026, needs more optimization.
4 856 0.952185375391 Henry Cohn, 2026, needs more optimization.
4 857 0.952237151621 Henry Cohn, 2026, needs more optimization.
4 858 0.952294889456 Henry Cohn, 2026, needs more optimization.
4 859 0.952356730499 Henry Cohn, 2026, needs more optimization.
4 860 0.952431934014 Henry Cohn, 2026, needs more optimization.
4 861 0.952504398082 Henry Cohn, 2026, needs more optimization.
4 862 0.952569985776 Henry Cohn, 2026, needs more optimization.
4 863 0.952609481698 Henry Cohn, 2026, needs more optimization.
4 864 0.952670458326 Henry Cohn, 2026, needs more optimization.
4 865 0.952726402216 Henry Cohn, 2026, needs more optimization.
4 866 0.952816625396 Henry Cohn, 2026, needs more optimization.
4 869 0.952861283898 Henry Cohn, 2026, needs more optimization.
4 870 0.952869309228 Henry Cohn, 2026, needs more optimization.
4 871 0.952906192098 Henry Cohn, 2026, needs more optimization.
4 872 0.952934377001 Henry Cohn, 2026, needs more optimization.
4 873 0.952967270202 Henry Cohn, 2026, needs more optimization.
4 874 0.952971377067 Henry Cohn, 2026, needs more optimization.
4 875 0.953037872190 Henry Cohn, 2026, needs more optimization.
4 876 0.953059205051 Henry Cohn, 2026, needs more optimization.
4 877 0.953098678995 Henry Cohn, 2026, needs more optimization.
4 878 0.953151735909 Henry Cohn, 2026, needs more optimization.
4 879 0.953184627937 Henry Cohn, 2026, needs more optimization.
4 880 0.953233951981 Henry Cohn, 2026, needs more optimization.
4 881 0.953269037562 Henry Cohn, 2026, needs more optimization.
4 882 0.953317859619 Henry Cohn, 2026, needs more optimization.
4 883 0.953332430950 Henry Cohn, 2026, needs more optimization.
4 884 0.953361057329 Henry Cohn, 2026, needs more optimization.
4 885 0.953386781716 Henry Cohn, 2026, needs more optimization.
4 886 0.953413320322 Henry Cohn, 2026, needs more optimization.
4 887 0.953449184709 Henry Cohn, 2026, needs more optimization.
4 888 0.953479173497 Henry Cohn, 2026, needs more optimization.
4 889 0.953504644060 Henry Cohn, 2026, needs more optimization.
4 890 0.953561541002 Henry Cohn, 2026, needs more optimization.
4 891 0.953630824367 Henry Cohn, 2026, needs more optimization.
4 892 0.953667580142 Henry Cohn, 2026, needs more optimization.
4 893 0.953702156298 Henry Cohn, 2026, needs more optimization.
4 894 0.953736513482 Henry Cohn, 2026, needs more optimization.
4 895 0.953764574453 Henry Cohn, 2026, needs more optimization.
4 896 0.953779852047 Henry Cohn, 2026, needs more optimization.
4 898 0.953814441260 Henry Cohn, 2026, needs more optimization.
4 900 0.953851750600 Henry Cohn, 2026, needs more optimization.
4 901 0.953874864875 Henry Cohn, 2026, needs more optimization.
4 902 0.953899734952 Henry Cohn, 2026, needs more optimization.
4 903 0.953976930699 Henry Cohn, 2026, needs more optimization.
4 904 0.954037235799 Henry Cohn, 2026, needs more optimization.
4 905 0.954066797650 Henry Cohn, 2026, needs more optimization.
4 906 0.954115770617 Henry Cohn, 2026, needs more optimization.
4 909 0.954137635066 Henry Cohn, 2026, needs more optimization.
4 910 0.954151332805 Henry Cohn, 2026, needs more optimization.
4 911 0.954159764980 Henry Cohn, 2026, needs more optimization.
4 912 0.954165365648 Henry Cohn, 2026, needs more optimization.
4 913 0.954172052436 Henry Cohn, 2026, needs more optimization.
4 914 0.954220073373 Henry Cohn, 2026, needs more optimization.
4 915 0.954231844390 Henry Cohn, 2026, needs more optimization.
4 916 0.954261534948 Henry Cohn, 2026, needs more optimization.
4 917 0.954328509523 Henry Cohn, 2026, needs more optimization.
4 918 0.954363553623 Henry Cohn, 2026, needs more optimization.
4 919 0.954437091524 Henry Cohn, 2026, needs more optimization.
4 920 0.954456278351 Henry Cohn, 2026, needs more optimization.
4 921 0.954471348481 Henry Cohn, 2026, needs more optimization.
4 922 0.954502370888 Henry Cohn, 2026, needs more optimization.
4 923 0.954563941408 Henry Cohn, 2026, needs more optimization.
4 924 0.954599493204 Henry Cohn, 2026, needs more optimization.
4 925 0.954668954704 Henry Cohn, 2026, needs more optimization.
4 926 0.954669420970 Henry Cohn, 2026, needs more optimization.
4 927 0.954723638166 Henry Cohn, 2026, needs more optimization.
4 928 0.954755562880 Henry Cohn, 2026, needs more optimization.
4 929 0.954796565195 Henry Cohn, 2026, needs more optimization.
4 930 0.954869871641 Henry Cohn, 2026, needs more optimization.
4 931 0.954896099920 Henry Cohn, 2026, needs more optimization.
4 932 0.954976642883 Henry Cohn, 2026, needs more optimization.
4 934 0.955034040449 Henry Cohn, 2026, needs more optimization.
4 935 0.955046833225 Henry Cohn, 2026, needs more optimization.
4 936 0.955099735087 Henry Cohn, 2026, needs more optimization.
4 937 0.955106628506 Henry Cohn, 2026, needs more optimization.
4 938 0.955138419770 Henry Cohn, 2026, needs more optimization.
4 939 0.955163492545 Henry Cohn, 2026, needs more optimization.
4 940 0.955188396553 Henry Cohn, 2026, needs more optimization.
4 941 0.955234504955 Henry Cohn, 2026, needs more optimization.
4 942 0.955290891294 Henry Cohn, 2026, needs more optimization.
4 943 0.955314237364 Henry Cohn, 2026, needs more optimization.
4 944 0.955347863307 Henry Cohn, 2026, needs more optimization.
4 945 0.955381076074 Henry Cohn, 2026, needs more optimization.
4 946 0.955427724547 Henry Cohn, 2026, needs more optimization.
4 947 0.955430063858 Henry Cohn, 2026, needs more optimization.
4 948 0.955467463909 Henry Cohn, 2026, needs more optimization.
4 949 0.955547987483 Henry Cohn, 2026, needs more optimization.
4 950 0.955590258469 Henry Cohn, 2026, needs more optimization.
4 951 0.955617683018 Henry Cohn, 2026, needs more optimization.
4 952 0.955672153191 Henry Cohn, 2026, needs more optimization.
4 954 0.955686597080 Henry Cohn, 2026, needs more optimization.
4 955 0.955693847501 Henry Cohn, 2026, needs more optimization.
4 956 0.955730989361 Henry Cohn, 2026, needs more optimization.
4 957 0.955770959427 Henry Cohn, 2026, needs more optimization.
4 958 0.955789785580 Henry Cohn, 2026, needs more optimization.
4 959 0.955825037995 Henry Cohn, 2026, needs more optimization.
4 960 0.955881222031 Henry Cohn, 2026, needs more optimization.
4 961 0.955918572458 Henry Cohn, 2026, needs more optimization.
4 962 0.955978023320 Henry Cohn, 2026, needs more optimization.
4 963 0.956041091488 Henry Cohn, 2026, needs more optimization.
4 964 0.956086426012 Henry Cohn, 2026, needs more optimization.
4 966 0.956087490806 Henry Cohn, 2026, needs more optimization.
4 967 0.956101089444 Henry Cohn, 2026, needs more optimization.
4 968 0.956111453601 Henry Cohn, 2026, needs more optimization.
4 969 0.956124379199 Henry Cohn, 2026, needs more optimization.
4 970 0.956140607699 Henry Cohn, 2026, needs more optimization.
4 971 0.956152434980 Henry Cohn, 2026, needs more optimization.
4 972 0.956185851073 Henry Cohn, 2026, needs more optimization.
4 974 0.956203922352 Henry Cohn, 2026, needs more optimization.
4 975 0.956204581297 Henry Cohn, 2026, needs more optimization.
4 976 0.956246925089 Henry Cohn, 2026, needs more optimization.
4 977 0.956318740732 Henry Cohn, 2026, needs more optimization.
4 978 0.956357981234 Henry Cohn, 2026, needs more optimization.
4 979 0.956400558418 Henry Cohn, 2026, needs more optimization.
4 980 0.956461607240 Henry Cohn, 2026, needs more optimization.
4 981 0.956495707210 Henry Cohn, 2026, needs more optimization.
4 982 0.956556526945 Henry Cohn, 2026, needs more optimization.
4 983 0.956626315669 Henry Cohn, 2026, needs more optimization.
4 985 0.956656131273 Henry Cohn, 2026, needs more optimization.
4 986 0.956664929345 Henry Cohn, 2026, needs more optimization.
4 987 0.956692701029 Henry Cohn, 2026, needs more optimization.
4 988 0.956715893225 Henry Cohn, 2026, needs more optimization.
4 989 0.956782613578 Henry Cohn, 2026, needs more optimization.
4 990 0.956820587091 Henry Cohn, 2026, needs more optimization.
4 991 0.956852106770 Henry Cohn, 2026, needs more optimization.
4 992 0.956896482603 Henry Cohn, 2026, needs more optimization.
4 993 0.956958721352 Henry Cohn, 2026, needs more optimization.
4 994 0.957006908202 Henry Cohn, 2026, needs more optimization.
4 995 0.957060592612 Henry Cohn, 2026, needs more optimization.
4 996 0.957130548203 Henry Cohn, 2026, needs more optimization.
4 997 0.957160869659 Henry Cohn, 2026, needs more optimization.
4 998 0.957178103784 Henry Cohn, 2026, needs more optimization.
4 999 0.957215620059 Henry Cohn, 2026, needs more optimization.
4 1000 0.957268139633 Henry Cohn, 2026, needs more optimization.
4 1001 0.957294845096 Henry Cohn, 2026, needs more optimization.
4 1002 0.957330279658 Henry Cohn, 2026, needs more optimization.
4 1003 0.957357605909 Henry Cohn, 2026, needs more optimization.
4 1004 0.957399433083 Henry Cohn, 2026, needs more optimization.
4 1005 0.957417876421 Henry Cohn, 2026, needs more optimization.
4 1006 0.957432663905 Henry Cohn, 2026, needs more optimization.
4 1007 0.957452428989 Henry Cohn, 2026, needs more optimization.
4 1008 0.957461064796 Henry Cohn, 2026, needs more optimization.
4 1009 0.957490800755 Henry Cohn, 2026, needs more optimization.
4 1010 0.957525328761 Henry Cohn, 2026, needs more optimization.
4 1012 0.957604553965 Henry Cohn, 2026, needs more optimization.
4 1014 0.957632447765 Henry Cohn, 2026, needs more optimization.
4 1015 0.957677070010 Henry Cohn, 2026, needs more optimization.
4 1016 0.957697635151 Henry Cohn, 2026, needs more optimization.
4 1017 0.957740324818 Henry Cohn, 2026, needs more optimization.
4 1018 0.957766047035 Henry Cohn, 2026, needs more optimization.
4 1019 0.957769181890 Henry Cohn, 2026, needs more optimization.
4 1020 0.957781838134 Henry Cohn, 2026, needs more optimization.
4 1021 0.957830659911 Henry Cohn, 2026, needs more optimization.
4 1022 0.957857627836 Henry Cohn, 2026, needs more optimization.
4 1023 0.957910185433 Henry Cohn, 2026, needs more optimization.
4 1024 0.957916234082 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 0.724187141008 Henry Cohn, 2026, needs more optimization.
5 133 0.725083698451 Henry Cohn, 2026, needs more optimization.
5 134 0.726667486234 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 0.731003426111 Henry Cohn, 2026, needs more optimization.
5 140 0.731880138963 Henry Cohn, 2025.
5 141 0.732919531703 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 0.739521287108 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 0.743483872288 Henry Cohn, 2026, needs more optimization.
5 159 0.743825044322 Henry Cohn, 2025.
5 160 0.744143092099 Henry Cohn, 2025.
5 161 0.747768123526 Henry Cohn, 2025.
5 162 0.748843925322 Henry Cohn, 2025.
5 163 0.750218552457 Henry Cohn, 2025.
5 164 0.750876806783 Henry Cohn, 2025.
5 165 0.752079878060 Henry Cohn, 2025.
5 166 0.752534073395 Henry Cohn, 2025.
5 167 0.753532673949 Henry Cohn, 2025.
5 168 0.754218675211 Henry Cohn, 2025.
5 169 0.755416175364 Henry Cohn, 2025.
5 170 0.755993792807 Henry Cohn, 2025.
5 171 0.756800051039 Henry Cohn, 2025.
5 172 0.757288355849 Henry Cohn, 2025.
5 173 0.758616069413 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 0.762581521154 Henry Cohn, 2026, needs more optimization.
5 178 0.763315108223 Henry Cohn, 2025.
5 179 0.763498214795 Henry Cohn, 2026, needs more optimization.
5 180 0.763782659007 Henry Cohn, 2026, needs more optimization.
5 181 0.764619435205 Henry Cohn, 2026, needs more optimization.
5 182 0.765130861667 Henry Cohn, 2026, needs more optimization.
5 183 0.765582256268 Henry Cohn, 2026, needs more optimization.
5 184 0.766276753134 Henry Cohn, 2026, needs more optimization.
5 185 0.766837208597 Henry Cohn, 2026, needs more optimization.
5 186 0.767264937530 Henry Cohn, 2026, needs more optimization.
5 187 0.767582661917 Henry Cohn, 2026, needs more optimization.
5 188 0.768346994303 Henry Cohn, 2026, needs more optimization.
5 189 0.769128122465 Henry Cohn, 2026, needs more optimization.
5 190 0.769550253078 Henry Cohn, 2026, needs more optimization.
5 191 0.770477151449 Henry Cohn, 2025.
5 192 0.771106184963 Henry Cohn, 2026, needs more optimization.
5 193 0.771230914259 Henry Cohn, 2026, needs more optimization.
5 194 0.772357310102 Henry Cohn, 2025.
5 195 0.772914025091 Henry Cohn, 2025.
5 196 0.773688919192 Henry Cohn, 2026, needs more optimization.
5 197 0.774086857888 Henry Cohn, 2026, needs more optimization.
5 198 0.774803572050 Henry Cohn, 2026, needs more optimization.
5 199 0.775242540360 Henry Cohn, 2025.
5 200 0.775814258853 Henry Cohn, 2025.
5 201 0.776374141702 Henry Cohn, 2026, needs more optimization.
5 202 0.776940932733 Henry Cohn, 2026, needs more optimization.
5 203 0.777755218102 Henry Cohn, 2026, needs more optimization.
5 204 0.778262339953 Henry Cohn, 2025.
5 205 0.779048071982 Henry Cohn, 2025.
5 206 0.779280532790 Henry Cohn, 2026, needs more optimization.
5 207 0.779746321587 Henry Cohn, 2026, needs more optimization.
5 208 0.780477848172 Henry Cohn, 2026, needs more optimization.
5 209 0.780858538099 Henry Cohn, 2026, needs more optimization.
5 210 0.781759257868 Henry Cohn, 2026, needs more optimization.
5 211 0.782016374826 Henry Cohn, 2026, needs more optimization.
5 212 0.782682152515 Henry Cohn, 2026, needs more optimization.
5 213 0.783136054900 Henry Cohn, 2026, needs more optimization.
5 214 0.783539867009 Henry Cohn, 2026, needs more optimization.
5 215 0.784181120034 Henry Cohn, 2026, needs more optimization.
5 216 0.784528913218 Henry Cohn, 2026, needs more optimization.
5 217 0.785214582623 Henry Cohn, 2026, needs more optimization.
5 218 0.785996484357 Henry Cohn, 2025.
5 219 0.786598220991 Henry Cohn, 2026, needs more optimization.
5 220 0.787019961677 Henry Cohn, 2026, needs more optimization.
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 0.789487512917 Henry Cohn, 2026, needs more optimization.
5 227 0.789764362583 Henry Cohn, 2026, needs more optimization.
5 228 0.790364928477 Henry Cohn, 2026, needs more optimization.
5 229 0.790654443894 Henry Cohn, 2026, needs more optimization.
5 230 0.791399820481 Henry Cohn, 2026, needs more optimization.
5 231 0.791480810352 Henry Cohn, 2026, needs more optimization.
5 232 0.792366546711 Henry Cohn, 2026, needs more optimization.
5 233 0.792635276154 Henry Cohn, 2026, needs more optimization.
5 234 0.792918508426 Henry Cohn, 2026, needs more optimization.
5 235 0.793373115729 Henry Cohn, 2026, needs more optimization.
5 236 0.793999476029 Henry Cohn, 2026, needs more optimization.
5 237 0.794422977065 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 0.796363909950 Henry Cohn, 2026, needs more optimization.
5 243 0.796601631746 Henry Cohn, 2026, needs more optimization.
5 244 0.796967438714 Henry Cohn, 2026, needs more optimization.
5 245 0.797264978382 Henry Cohn, 2026, needs more optimization.
5 246 0.797740685154 Henry Cohn, 2026, needs more optimization.
5 247 0.797961445690 Henry Cohn, 2026, needs more optimization.
5 248 0.798551741465 Henry Cohn, 2026, needs more optimization.
5 249 0.798774889919 Henry Cohn, 2026, needs more optimization.
5 250 0.798943495579 Henry Cohn, 2026, needs more optimization.
5 251 0.799363123529 Henry Cohn, 2026, needs more optimization.
5 252 0.799656170621 Henry Cohn, 2026, needs more optimization.
5 253 0.800146780510 Henry Cohn, 2026, needs more optimization.
5 254 0.800362371338 Henry Cohn, 2026, needs more optimization.
5 255 0.800626488462 Henry Cohn, 2026, needs more optimization.
5 256 0.801146365371 Henry Cohn, 2026, needs more optimization.
5 257 0.801509868780 Henry Cohn, 2026, needs more optimization.
5 258 0.801980632819 Henry Cohn, 2026, needs more optimization.
5 259 0.802392535562 Henry Cohn, 2026, needs more optimization.
5 260 0.802829967962 Henry Cohn, 2026, needs more optimization.
5 261 0.803199820448 Henry Cohn, 2026, needs more optimization.
5 262 0.803528360555 Henry Cohn, 2026, needs more optimization.
5 263 0.803880218189 Henry Cohn, 2026, needs more optimization.
5 264 0.804084303973 Henry Cohn, 2026, needs more optimization.
5 265 0.804462834670 Henry Cohn, 2026, needs more optimization.
5 266 0.804570298424 Henry Cohn, 2026, needs more optimization.
5 267 0.804874157653 Henry Cohn, 2026, needs more optimization.
5 268 0.805063737635 Henry Cohn, 2026, needs more optimization.
5 269 0.805324439847 Henry Cohn, 2026, needs more optimization.
5 270 0.805499872660 Henry Cohn, 2026, needs more optimization.
5 271 0.805743891315 Henry Cohn, 2026, needs more optimization.
5 272 0.806012197376 Henry Cohn, 2026, needs more optimization.
5 273 0.806036065648 Henry Cohn, 2026, needs more optimization.
5 274 0.806118425454 Henry Cohn, 2026, needs more optimization.
5 275 0.806249054272 Henry Cohn, 2026, needs more optimization.
5 276 0.806327594127 Henry Cohn, 2026, needs more optimization.
5 277 0.806497635179 Henry Cohn, 2026, needs more optimization.
5 278 0.806701548341 Henry Cohn, 2026, needs more optimization.
5 279 0.806784388823 Henry Cohn, 2026, needs more optimization.
5 280 0.807057746991 Henry Cohn, 2026, needs more optimization.
5 281 0.807116888907 Henry Cohn, 2026, needs more optimization.
5 282 0.807162642350 Henry Cohn, 2026, needs more optimization.
5 283 0.807742881408 Henry Cohn, 2026, needs more optimization.
5 284 0.808229872091 Henry Cohn, 2026, needs more optimization.
5 285 0.808654465991 Henry Cohn, 2026, needs more optimization.
5 286 0.809185175248 Henry Cohn, 2026, needs more optimization.
5 287 0.809590224842 Henry Cohn, 2026, needs more optimization.
5 288 0.810243548578 Henry Cohn, 2026, needs more optimization.
5 289 0.810467950037 Henry Cohn, 2026, needs more optimization.
5 290 0.811082699196 Henry Cohn, 2026, needs more optimization.
5 291 0.811567081168 Henry Cohn, 2026, needs more optimization.
5 292 0.812264766317 Henry Cohn, 2026, needs more optimization.
5 293 0.812702082856 Henry Cohn, 2026, needs more optimization.
5 294 0.813141356892 Henry Cohn, 2026, needs more optimization.
5 295 0.813706219251 Henry Cohn, 2026, needs more optimization.
5 296 0.813997556738 Henry Cohn, 2026, needs more optimization.
5 297 0.814426606964 Henry Cohn, 2026, needs more optimization.
5 298 0.815068522820 Henry Cohn, 2026, needs more optimization.
5 299 0.815433700290 Henry Cohn, 2026, needs more optimization.
5 300 0.815847945049 Henry Cohn, 2026, needs more optimization.
5 301 0.816439864336 Henry Cohn, 2026, needs more optimization.
5 302 0.817000628229 Henry Cohn, 2026, needs more optimization.
5 303 0.817467399235 Henry Cohn, 2026, needs more optimization.
5 304 0.817789676700 Henry Cohn, 2026, needs more optimization.
5 305 0.818194019506 Henry Cohn, 2026, needs more optimization.
5 306 0.818530939462 Henry Cohn, 2026, needs more optimization.
5 307 0.818934851712 Henry Cohn, 2026, needs more optimization.
5 308 0.819271321405 Henry Cohn, 2026, needs more optimization.
5 309 0.819566375721 Henry Cohn, 2026, needs more optimization.
5 310 0.819767650541 Henry Cohn, 2026, needs more optimization.
5 311 0.819769769663 Henry Cohn, 2026, needs more optimization.
5 312 0.819825844493 Henry Cohn, 2026, needs more optimization.
5 313 0.819884378378 Henry Cohn, 2026, needs more optimization.
5 314 0.819894759266 Henry Cohn, 2026, needs more optimization.
5 315 0.819899440325 Henry Cohn, 2026, needs more optimization.
5 316 0.819976090320 Henry Cohn, 2026, needs more optimization.
5 317 0.820646158632 Henry Cohn, 2026, needs more optimization.
5 318 0.820664764640 Henry Cohn, 2026, needs more optimization.
5 319 0.820667173021 Henry Cohn, 2026, needs more optimization.
5 320 0.821596486069 Henry Cohn, 2026, needs more optimization.
5 321 0.822702002696 Henry Cohn, 2026, needs more optimization.
5 322 0.822902681624 Henry Cohn, 2026, needs more optimization.
5 323 0.822918193956 Henry Cohn, 2026, needs more optimization.
5 324 0.822943675018 Henry Cohn, 2026, needs more optimization.
5 325 0.822974915068 Henry Cohn, 2026, needs more optimization.
5 326 0.823027595539 Henry Cohn, 2026, needs more optimization.
5 327 0.823305698030 Henry Cohn, 2026, needs more optimization.
5 328 0.823394562055 Henry Cohn, 2026, needs more optimization.
5 329 0.823615076562 Henry Cohn, 2026, needs more optimization.
5 330 0.823791763428 Henry Cohn, 2026, needs more optimization.
5 331 0.824021212075 Henry Cohn, 2026, needs more optimization.
5 332 0.824347308729 Henry Cohn, 2026, needs more optimization.
5 333 0.824467791708 Henry Cohn, 2026, needs more optimization.
5 334 0.825002020012 Henry Cohn, 2026, needs more optimization.
5 335 0.825225407097 Henry Cohn, 2026, needs more optimization.
5 336 0.825281832636 Henry Cohn, 2026, needs more optimization.
5 337 0.825624432415 Henry Cohn, 2026, needs more optimization.
5 338 0.826152232993 Henry Cohn, 2026, needs more optimization.
5 339 0.826203255682 Henry Cohn, 2026, needs more optimization.
5 340 0.826640793262 Henry Cohn, 2026, needs more optimization.
5 341 0.827022551476 Henry Cohn, 2026, needs more optimization.
5 342 0.827291050475 Henry Cohn, 2026, needs more optimization.
5 343 0.827696675110 Henry Cohn, 2026, needs more optimization.
5 344 0.828104246400 Henry Cohn, 2026, needs more optimization.
5 345 0.828322254422 Henry Cohn, 2026, needs more optimization.
5 346 0.828818672140 Henry Cohn, 2026, needs more optimization.
5 347 0.828872701980 Henry Cohn, 2026, needs more optimization.
5 348 0.829154162433 Henry Cohn, 2026, needs more optimization.
5 349 0.829302401173 Henry Cohn, 2026, needs more optimization.
5 350 0.829486500247 Henry Cohn, 2026, needs more optimization.
5 351 0.830147878331 Henry Cohn, 2026, needs more optimization.
5 352 0.830241854033 Henry Cohn, 2026, needs more optimization.
5 353 0.830245006848 Henry Cohn, 2026, needs more optimization.
5 354 0.830492647248 Henry Cohn, 2026, needs more optimization.
5 355 0.830858259443 Henry Cohn, 2026, needs more optimization.
5 356 0.831107682893 Henry Cohn, 2026, needs more optimization.
5 357 0.831486296389 Henry Cohn, 2026, needs more optimization.
5 358 0.831860304769 Henry Cohn, 2026, needs more optimization.
5 359 0.832232724929 Henry Cohn, 2026, needs more optimization.
5 360 0.832259257793 Henry Cohn, 2026, needs more optimization.
5 361 0.834145696742 Henry Cohn, 2026, needs more optimization.
5 362 0.834231166057 Henry Cohn, 2026, needs more optimization.
5 363 0.834584871786 Henry Cohn, 2026, needs more optimization.
5 364 0.834691996310 Henry Cohn, 2026, needs more optimization.
5 365 0.834929375987 Henry Cohn, 2026, needs more optimization.
5 366 0.835125698056 Henry Cohn, 2026, needs more optimization.
5 367 0.835373441658 Henry Cohn, 2026, needs more optimization.
5 368 0.835708496640 Henry Cohn, 2026, needs more optimization.
5 369 0.835720320942 Henry Cohn, 2026, needs more optimization.
5 370 0.836064198777 Henry Cohn, 2026, needs more optimization.
5 371 0.836309885090 Henry Cohn, 2026, needs more optimization.
5 372 0.836619294519 Henry Cohn, 2026, needs more optimization.
5 373 0.836633475601 Henry Cohn, 2026, needs more optimization.
5 374 0.836791458446 Henry Cohn, 2026, needs more optimization.
5 375 0.837046724114 Henry Cohn, 2026, needs more optimization.
5 376 0.837283314064 Henry Cohn, 2026, needs more optimization.
5 377 0.837548034154 Henry Cohn, 2026, needs more optimization.
5 378 0.837908280709 Henry Cohn, 2026, needs more optimization.
5 379 0.837988731266 Henry Cohn, 2026, needs more optimization.
5 380 0.838229781969 Henry Cohn, 2026, needs more optimization.
5 381 0.838348986038 Henry Cohn, 2026, needs more optimization.
5 382 0.838647523023 Henry Cohn, 2026, needs more optimization.
5 383 0.838823928909 Henry Cohn, 2026, needs more optimization.
5 384 0.839228926725 Henry Cohn, 2026, needs more optimization.
5 385 0.839335931529 Henry Cohn, 2026, needs more optimization.
5 386 0.839578317903 Henry Cohn, 2026, needs more optimization.
5 387 0.839747262758 Henry Cohn, 2026, needs more optimization.
5 388 0.839886880624 Henry Cohn, 2026, needs more optimization.
5 389 0.840121261227 Henry Cohn, 2026, needs more optimization.
5 390 0.840451066772 Henry Cohn, 2026, needs more optimization.
5 391 0.840660261466 Henry Cohn, 2026, needs more optimization.
5 392 0.840783453684 Henry Cohn, 2026, needs more optimization.
5 393 0.841204409458 Henry Cohn, 2026, needs more optimization.
5 394 0.841353030167 Henry Cohn, 2026, needs more optimization.
5 395 0.841442234317 Henry Cohn, 2026, needs more optimization.
5 396 0.841694252346 Henry Cohn, 2026, needs more optimization.
5 397 0.841836013314 Henry Cohn, 2026, needs more optimization.
5 398 0.841992584619 Henry Cohn, 2026, needs more optimization.
5 399 0.842175193930 Henry Cohn, 2026, needs more optimization.
5 400 0.842497833839 Henry Cohn, 2026, needs more optimization.
5 401 0.842725463037 Henry Cohn, 2026, needs more optimization.
5 402 0.843026926648 Henry Cohn, 2026, needs more optimization.
5 403 0.843089449826 Henry Cohn, 2026, needs more optimization.
5 404 0.843116106749 Henry Cohn, 2026, needs more optimization.
5 405 0.843325259457 Henry Cohn, 2026, needs more optimization.
5 406 0.843607409913 Henry Cohn, 2026, needs more optimization.
5 407 0.843763804093 Henry Cohn, 2026, needs more optimization.
5 408 0.843899226243 Henry Cohn, 2026, needs more optimization.
5 409 0.843947101580 Henry Cohn, 2026, needs more optimization.
5 410 0.844110012405 Henry Cohn, 2026, needs more optimization.
5 411 0.844386697653 Henry Cohn, 2026, needs more optimization.
5 412 0.844531696294 Henry Cohn, 2026, needs more optimization.
5 413 0.844818431986 Henry Cohn, 2026, needs more optimization.
5 414 0.844822723360 Henry Cohn, 2026, needs more optimization.
5 415 0.845185343702 Henry Cohn, 2026, needs more optimization.
5 416 0.845416525960 Henry Cohn, 2026, needs more optimization.
5 417 0.845506241444 Henry Cohn, 2026, needs more optimization.
5 418 0.845720587004 Henry Cohn, 2026, needs more optimization.
5 419 0.845792397945 Henry Cohn, 2026, needs more optimization.
5 420 0.845957913619 Henry Cohn, 2026, needs more optimization.
5 421 0.846099736420 Henry Cohn, 2026, needs more optimization.
5 422 0.846421802129 Henry Cohn, 2026, needs more optimization.
5 423 0.846470642433 Henry Cohn, 2026, needs more optimization.
5 424 0.846758865234 Henry Cohn, 2026, needs more optimization.
5 425 0.846980719040 Henry Cohn, 2026, needs more optimization.
5 426 0.847135383546 Henry Cohn, 2026, needs more optimization.
5 427 0.847335413996 Henry Cohn, 2026, needs more optimization.
5 428 0.847531344689 Henry Cohn, 2026, needs more optimization.
5 429 0.847674282560 Henry Cohn, 2026, needs more optimization.
5 430 0.847930486792 Henry Cohn, 2026, needs more optimization.
5 431 0.848160874453 Henry Cohn, 2026, needs more optimization.
5 432 0.848274196015 Henry Cohn, 2026, needs more optimization.
5 433 0.848469233379 Henry Cohn, 2026, needs more optimization.
5 434 0.848708703539 Henry Cohn, 2026, needs more optimization.
5 435 0.848871445098 Henry Cohn, 2026, needs more optimization.
5 436 0.848995482741 Henry Cohn, 2026, needs more optimization.
5 437 0.849135958715 Henry Cohn, 2026, needs more optimization.
5 438 0.849418408285 Henry Cohn, 2026, needs more optimization.
5 439 0.849638718782 Henry Cohn, 2026, needs more optimization.
5 440 0.849705568529 Henry Cohn, 2026, needs more optimization.
5 441 0.849895857395 Henry Cohn, 2026, needs more optimization.
5 442 0.849989534759 Henry Cohn, 2026, needs more optimization.
5 443 0.850145256248 Henry Cohn, 2026, needs more optimization.
5 444 0.850500678821 Henry Cohn, 2026, needs more optimization.
5 445 0.850636634893 Henry Cohn, 2026, needs more optimization.
5 446 0.850845692589 Henry Cohn, 2026, needs more optimization.
5 447 0.850999142662 Henry Cohn, 2026, needs more optimization.
5 448 0.851074640550 Henry Cohn, 2026, needs more optimization.
5 449 0.851138518533 Henry Cohn, 2026, needs more optimization.
5 450 0.851516335385 Henry Cohn, 2026, needs more optimization.
5 451 0.851713059115 Henry Cohn, 2026, needs more optimization.
5 452 0.851801424273 Henry Cohn, 2026, needs more optimization.
5 453 0.851811961819 Henry Cohn, 2026, needs more optimization.
5 454 0.852032650073 Henry Cohn, 2026, needs more optimization.
5 455 0.852312901529 Henry Cohn, 2026, needs more optimization.
5 456 0.852377896402 Henry Cohn, 2026, needs more optimization.
5 457 0.852583908060 Henry Cohn, 2026, needs more optimization.
5 458 0.852749928331 Henry Cohn, 2026, needs more optimization.
5 459 0.852815579110 Henry Cohn, 2026, needs more optimization.
5 460 0.853047498302 Henry Cohn, 2026, needs more optimization.
5 461 0.853252822338 Henry Cohn, 2026, needs more optimization.
5 462 0.853456937225 Henry Cohn, 2026, needs more optimization.
5 463 0.853568686030 Henry Cohn, 2026, needs more optimization.
5 464 0.853635078614 Henry Cohn, 2026, needs more optimization.
5 465 0.853859042268 Henry Cohn, 2026, needs more optimization.
5 466 0.854014314387 Henry Cohn, 2026, needs more optimization.
5 467 0.854078698951 Henry Cohn, 2026, needs more optimization.
5 468 0.854361049834 Henry Cohn, 2026, needs more optimization.
5 469 0.854477290420 Henry Cohn, 2026, needs more optimization.
5 470 0.854641358572 Henry Cohn, 2026, needs more optimization.
5 471 0.854696122603 Henry Cohn, 2026, needs more optimization.
5 472 0.854822723310 Henry Cohn, 2026, needs more optimization.
5 473 0.854972334428 Henry Cohn, 2026, needs more optimization.
5 474 0.855270725081 Henry Cohn, 2026, needs more optimization.
5 475 0.855295106824 Henry Cohn, 2026, needs more optimization.
5 476 0.855453961387 Henry Cohn, 2026, needs more optimization.
5 477 0.855638948496 Henry Cohn, 2026, needs more optimization.
5 478 0.855801132925 Henry Cohn, 2026, needs more optimization.
5 479 0.855927827393 Henry Cohn, 2026, needs more optimization.
5 480 0.856092908441 Henry Cohn, 2026, needs more optimization.
5 481 0.856279242016 Henry Cohn, 2026, needs more optimization.
5 482 0.856448655594 Henry Cohn, 2026, needs more optimization.
5 483 0.856666032323 Henry Cohn, 2026, needs more optimization.
5 484 0.856718276147 Henry Cohn, 2026, needs more optimization.
5 485 0.856724818161 Henry Cohn, 2026, needs more optimization.
5 486 0.856885710089 Henry Cohn, 2026, needs more optimization.
5 487 0.857090871159 Henry Cohn, 2026, needs more optimization.
5 488 0.857251233779 Henry Cohn, 2026, needs more optimization.
5 489 0.857364619330 Henry Cohn, 2026, needs more optimization.
5 490 0.857429285939 Henry Cohn, 2026, needs more optimization.
5 491 0.857605594894 Henry Cohn, 2026, needs more optimization.
5 492 0.857834737224 Henry Cohn, 2026, needs more optimization.
5 493 0.857883901848 Henry Cohn, 2026, needs more optimization.
5 494 0.857963133010 Henry Cohn, 2026, needs more optimization.
5 495 0.858160413845 Henry Cohn, 2026, needs more optimization.
5 496 0.858498526404 Henry Cohn, 2026, needs more optimization.
5 497 0.858641826453 Henry Cohn, 2026, needs more optimization.
5 498 0.858744156564 Henry Cohn, 2026, needs more optimization.
5 499 0.858856164813 Henry Cohn, 2026, needs more optimization.
5 500 0.859119039039 Henry Cohn, 2026, needs more optimization.
5 501 0.859273724202 Henry Cohn, 2026, needs more optimization.
5 502 0.859510623621 Henry Cohn, 2026, needs more optimization.
5 503 0.859514438749 Henry Cohn, 2026, needs more optimization.
5 504 0.859623860412 Henry Cohn, 2026, needs more optimization.
5 505 0.859744204804 Henry Cohn, 2026, needs more optimization.
5 506 0.859869282671 Henry Cohn, 2026, needs more optimization.
5 507 0.860051529622 Henry Cohn, 2026, needs more optimization.
5 508 0.860211091585 Henry Cohn, 2026, needs more optimization.
5 509 0.860292921288 Henry Cohn, 2026, needs more optimization.
5 510 0.860470291070 Henry Cohn, 2026, needs more optimization.
5 511 0.860639581030 Henry Cohn, 2026, needs more optimization.
5 512 0.860675237591 Henry Cohn, 2026, needs more optimization.
5 513 0.860739037358 Henry Cohn, 2026, needs more optimization.
5 514 0.860858029640 Henry Cohn, 2026, needs more optimization.
5 515 0.861001525740 Henry Cohn, 2026, needs more optimization.
5 516 0.861225259937 Henry Cohn, 2026, needs more optimization.
5 517 0.861329066828 Henry Cohn, 2026, needs more optimization.
5 518 0.861498365161 Henry Cohn, 2026, needs more optimization.
5 519 0.861612515514 Henry Cohn, 2026, needs more optimization.
5 520 0.861726044945 Henry Cohn, 2026, needs more optimization.
5 521 0.861742187795 Henry Cohn, 2026, needs more optimization.
5 522 0.861957752900 Henry Cohn, 2026, needs more optimization.
5 523 0.862196440381 Henry Cohn, 2026, needs more optimization.
5 524 0.862353312128 Henry Cohn, 2026, needs more optimization.
5 525 0.862466257153 Henry Cohn, 2026, needs more optimization.
5 526 0.862651255057 Henry Cohn, 2026, needs more optimization.
5 527 0.862662182984 Henry Cohn, 2026, needs more optimization.
5 528 0.862819191893 Henry Cohn, 2026, needs more optimization.
5 529 0.862971444099 Henry Cohn, 2026, needs more optimization.
5 530 0.863034513662 Henry Cohn, 2026, needs more optimization.
5 531 0.863198494522 Henry Cohn, 2026, needs more optimization.
5 532 0.863297815499 Henry Cohn, 2026, needs more optimization.
5 533 0.863513722590 Henry Cohn, 2026, needs more optimization.
5 534 0.863655847299 Henry Cohn, 2026, needs more optimization.
5 535 0.863754587293 Henry Cohn, 2026, needs more optimization.
5 536 0.863917054713 Henry Cohn, 2026, needs more optimization.
5 537 0.863997905122 Henry Cohn, 2026, needs more optimization.
5 538 0.864136908338 Henry Cohn, 2026, needs more optimization.
5 539 0.864270299803 Henry Cohn, 2026, needs more optimization.
5 540 0.864344399090 Henry Cohn, 2026, needs more optimization.
5 541 0.864609158034 Henry Cohn, 2026, needs more optimization.
5 542 0.864725986216 Henry Cohn, 2026, needs more optimization.
5 543 0.864793386698 Henry Cohn, 2026, needs more optimization.
5 544 0.864939169497 Henry Cohn, 2026, needs more optimization.
5 545 0.865015341661 Henry Cohn, 2026, needs more optimization.
5 546 0.865112385884 Henry Cohn, 2026, needs more optimization.
5 547 0.865277758218 Henry Cohn, 2026, needs more optimization.
5 548 0.865415903857 Henry Cohn, 2026, needs more optimization.
5 549 0.865494824741 Henry Cohn, 2026, needs more optimization.
5 550 0.865545667520 Henry Cohn, 2026, needs more optimization.
5 551 0.865760030616 Henry Cohn, 2026, needs more optimization.
5 552 0.865806323430 Henry Cohn, 2026, needs more optimization.
5 553 0.865976677990 Henry Cohn, 2026, needs more optimization.
5 554 0.866167744458 Henry Cohn, 2026, needs more optimization.
5 555 0.866201713850 Henry Cohn, 2026, needs more optimization.
5 556 0.866234467366 Henry Cohn, 2026, needs more optimization.
5 557 0.866443558884 Henry Cohn, 2026, needs more optimization.
5 558 0.866542977190 Henry Cohn, 2026, needs more optimization.
5 559 0.866798399394 Henry Cohn, 2026, needs more optimization.
5 560 0.867042356926 Henry Cohn, 2026, needs more optimization.
5 561 0.867130887161 Henry Cohn, 2026, needs more optimization.
5 562 0.867326894061 Henry Cohn, 2026, needs more optimization.
5 563 0.867392728617 Henry Cohn, 2026, needs more optimization.
5 564 0.867447737084 Henry Cohn, 2026, needs more optimization.
5 565 0.867448056489 Henry Cohn, 2026, needs more optimization.
5 566 0.867577067911 Henry Cohn, 2026, needs more optimization.
5 567 0.867774996468 Henry Cohn, 2026, needs more optimization.
5 568 0.867878789300 Henry Cohn, 2026, needs more optimization.
5 569 0.867970883632 Henry Cohn, 2026, needs more optimization.
5 570 0.868180683945 Henry Cohn, 2026, needs more optimization.
5 571 0.868345300687 Henry Cohn, 2026, needs more optimization.
5 572 0.868388796956 Henry Cohn, 2026, needs more optimization.
5 573 0.868458834573 Henry Cohn, 2026, needs more optimization.
5 574 0.868669966136 Henry Cohn, 2026, needs more optimization.
5 575 0.868673105434 Henry Cohn, 2026, needs more optimization.
5 576 0.868815834752 Henry Cohn, 2026, needs more optimization.
5 577 0.868904304181 Henry Cohn, 2026, needs more optimization.
5 578 0.868972329452 Henry Cohn, 2026, needs more optimization.
5 579 0.869113182138 Henry Cohn, 2026, needs more optimization.
5 580 0.869327357226 Henry Cohn, 2026, needs more optimization.
5 581 0.869456018293 Henry Cohn, 2026, needs more optimization.
5 582 0.869545807728 Henry Cohn, 2026, needs more optimization.
5 583 0.869629256610 Henry Cohn, 2026, needs more optimization.
5 584 0.869718585108 Henry Cohn, 2026, needs more optimization.
5 585 0.869901993936 Henry Cohn, 2026, needs more optimization.
5 586 0.870017299168 Henry Cohn, 2026, needs more optimization.
5 588 0.870107100251 Henry Cohn, 2026, needs more optimization.
5 589 0.870178634342 Henry Cohn, 2026, needs more optimization.
5 590 0.870359510918 Henry Cohn, 2026, needs more optimization.
5 591 0.870388620091 Henry Cohn, 2026, needs more optimization.
5 592 0.870455223420 Henry Cohn, 2026, needs more optimization.
5 593 0.870582144528 Henry Cohn, 2026, needs more optimization.
5 594 0.870750705425 Henry Cohn, 2026, needs more optimization.
5 595 0.870835988970 Henry Cohn, 2026, needs more optimization.
5 596 0.870945672104 Henry Cohn, 2026, needs more optimization.
5 597 0.871048137014 Henry Cohn, 2026, needs more optimization.
5 598 0.871208987054 Henry Cohn, 2026, needs more optimization.
5 599 0.871298168445 Henry Cohn, 2026, needs more optimization.
5 600 0.871360365810 Henry Cohn, 2026, needs more optimization.
5 601 0.871578814176 Henry Cohn, 2026, needs more optimization.
5 602 0.871605572400 Henry Cohn, 2026, needs more optimization.
5 603 0.871662201911 Henry Cohn, 2026, needs more optimization.
5 604 0.871771195881 Henry Cohn, 2026, needs more optimization.
5 605 0.871774883251 Henry Cohn, 2026, needs more optimization.
5 606 0.871844457890 Henry Cohn, 2026, needs more optimization.
5 607 0.871979295410 Henry Cohn, 2026, needs more optimization.
5 608 0.872079590279 Henry Cohn, 2026, needs more optimization.
5 609 0.872283935062 Henry Cohn, 2026, needs more optimization.
5 610 0.872406869261 Henry Cohn, 2026, needs more optimization.
5 611 0.872431832189 Henry Cohn, 2026, needs more optimization.
5 612 0.872598230666 Henry Cohn, 2026, needs more optimization.
5 613 0.872704272016 Henry Cohn, 2026, needs more optimization.
5 614 0.872796758477 Henry Cohn, 2026, needs more optimization.
5 615 0.872904066799 Henry Cohn, 2026, needs more optimization.
5 616 0.873073647321 Henry Cohn, 2026, needs more optimization.
5 617 0.873159585517 Henry Cohn, 2026, needs more optimization.
5 618 0.873315472505 Henry Cohn, 2026, needs more optimization.
5 619 0.873435293668 Henry Cohn, 2026, needs more optimization.
5 620 0.873499001512 Henry Cohn, 2026, needs more optimization.
5 621 0.873606368396 Henry Cohn, 2026, needs more optimization.
5 622 0.873699945019 Henry Cohn, 2026, needs more optimization.
5 623 0.873822361902 Henry Cohn, 2026, needs more optimization.
5 624 0.873944726924 Henry Cohn, 2026, needs more optimization.
5 625 0.874078312429 Henry Cohn, 2026, needs more optimization.
5 626 0.874134425174 Henry Cohn, 2026, needs more optimization.
5 627 0.874158646858 Henry Cohn, 2026, needs more optimization.
5 628 0.874315803180 Henry Cohn, 2026, needs more optimization.
5 629 0.874426916157 Henry Cohn, 2026, needs more optimization.
5 630 0.874594180208 Henry Cohn, 2026, needs more optimization.
5 631 0.874687730051 Henry Cohn, 2026, needs more optimization.
5 632 0.874760778782 Henry Cohn, 2026, needs more optimization.
5 633 0.874924394407 Henry Cohn, 2026, needs more optimization.
5 634 0.874983889718 Henry Cohn, 2026, needs more optimization.
5 635 0.875117704221 Henry Cohn, 2026, needs more optimization.
5 636 0.875252377277 Henry Cohn, 2026, needs more optimization.
5 637 0.875303685077 Henry Cohn, 2026, needs more optimization.
5 638 0.875330782401 Henry Cohn, 2026, needs more optimization.
5 639 0.875442406564 Henry Cohn, 2026, needs more optimization.
5 641 0.875599921812 Henry Cohn, 2026, needs more optimization.
5 642 0.875652188300 Henry Cohn, 2026, needs more optimization.
5 643 0.875787893834 Henry Cohn, 2026, needs more optimization.
5 644 0.875957815213 Henry Cohn, 2026, needs more optimization.
5 645 0.876026162051 Henry Cohn, 2026, needs more optimization.
5 646 0.876165824585 Henry Cohn, 2026, needs more optimization.
5 647 0.876314435824 Henry Cohn, 2026, needs more optimization.
5 648 0.876316911961 Henry Cohn, 2026, needs more optimization.
5 649 0.876446100452 Henry Cohn, 2026, needs more optimization.
5 650 0.876533376542 Henry Cohn, 2026, needs more optimization.
5 651 0.876617244523 Henry Cohn, 2026, needs more optimization.
5 652 0.876644082375 Henry Cohn, 2026, needs more optimization.
5 653 0.876699100515 Henry Cohn, 2026, needs more optimization.
5 654 0.876791917773 Henry Cohn, 2026, needs more optimization.
5 655 0.876925181754 Henry Cohn, 2026, needs more optimization.
5 656 0.877022821188 Henry Cohn, 2026, needs more optimization.
5 657 0.877225866644 Henry Cohn, 2026, needs more optimization.
5 658 0.877301292749 Henry Cohn, 2026, needs more optimization.
5 659 0.877365365673 Henry Cohn, 2026, needs more optimization.
5 661 0.877460092492 Henry Cohn, 2026, needs more optimization.
5 662 0.877553136026 Henry Cohn, 2026, needs more optimization.
5 663 0.877659625216 Henry Cohn, 2026, needs more optimization.
5 664 0.877785607630 Henry Cohn, 2026, needs more optimization.
5 665 0.877794103890 Henry Cohn, 2026, needs more optimization.
5 666 0.877866044291 Henry Cohn, 2026, needs more optimization.
5 667 0.877976792981 Henry Cohn, 2026, needs more optimization.
5 668 0.878030764698 Henry Cohn, 2026, needs more optimization.
5 669 0.878195560322 Henry Cohn, 2026, needs more optimization.
5 670 0.878215744126 Henry Cohn, 2026, needs more optimization.
5 671 0.878392720049 Henry Cohn, 2026, needs more optimization.
5 672 0.878491727293 Henry Cohn, 2026, needs more optimization.
5 673 0.878564056571 Henry Cohn, 2026, needs more optimization.
5 674 0.878675826146 Henry Cohn, 2026, needs more optimization.
5 675 0.878686755194 Henry Cohn, 2026, needs more optimization.
5 676 0.878812302903 Henry Cohn, 2026, needs more optimization.
5 677 0.878924138549 Henry Cohn, 2026, needs more optimization.
5 678 0.879053174335 Henry Cohn, 2026, needs more optimization.
5 679 0.879134079611 Henry Cohn, 2026, needs more optimization.
5 680 0.879182488060 Henry Cohn, 2026, needs more optimization.
5 681 0.879262663206 Henry Cohn, 2026, needs more optimization.
5 682 0.879373407234 Henry Cohn, 2026, needs more optimization.
5 683 0.879417308991 Henry Cohn, 2026, needs more optimization.
5 684 0.879565971310 Henry Cohn, 2026, needs more optimization.
5 685 0.879583771535 Henry Cohn, 2026, needs more optimization.
5 686 0.879611506362 Henry Cohn, 2026, needs more optimization.
5 687 0.879846039935 Henry Cohn, 2026, needs more optimization.
5 688 0.879938133446 Henry Cohn, 2026, needs more optimization.
5 689 0.880045029912 Henry Cohn, 2026, needs more optimization.
5 690 0.880054744766 Henry Cohn, 2026, needs more optimization.
5 691 0.880168821131 Henry Cohn, 2026, needs more optimization.
5 692 0.880295851358 Henry Cohn, 2026, needs more optimization.
5 693 0.880338305801 Henry Cohn, 2026, needs more optimization.
5 694 0.880434990743 Henry Cohn, 2026, needs more optimization.
5 695 0.880518456972 Henry Cohn, 2026, needs more optimization.
5 696 0.880562496984 Henry Cohn, 2026, needs more optimization.
5 697 0.880654050443 Henry Cohn, 2026, needs more optimization.
5 698 0.880748341053 Henry Cohn, 2026, needs more optimization.
5 699 0.880827452986 Henry Cohn, 2026, needs more optimization.
5 700 0.880837284768 Henry Cohn, 2026, needs more optimization.
5 701 0.881054770169 Henry Cohn, 2026, needs more optimization.
5 703 0.881075378288 Henry Cohn, 2026, needs more optimization.
5 704 0.881231209574 Henry Cohn, 2026, needs more optimization.
5 705 0.881260922792 Henry Cohn, 2026, needs more optimization.
5 706 0.881384442487 Henry Cohn, 2026, needs more optimization.
5 707 0.881490907047 Henry Cohn, 2026, needs more optimization.
5 708 0.881611839007 Henry Cohn, 2026, needs more optimization.
5 709 0.881734206339 Henry Cohn, 2026, needs more optimization.
5 710 0.881742719173 Henry Cohn, 2026, needs more optimization.
5 711 0.881809560307 Henry Cohn, 2026, needs more optimization.
5 712 0.881890086840 Henry Cohn, 2026, needs more optimization.
5 713 0.882000527911 Henry Cohn, 2026, needs more optimization.
5 714 0.882079983807 Henry Cohn, 2026, needs more optimization.
5 715 0.882171950407 Henry Cohn, 2026, needs more optimization.
5 716 0.882286247748 Henry Cohn, 2026, needs more optimization.
5 717 0.882319844692 Henry Cohn, 2026, needs more optimization.
5 718 0.882448099525 Henry Cohn, 2026, needs more optimization.
5 719 0.882448416712 Henry Cohn, 2026, needs more optimization.
5 720 0.882579799033 Henry Cohn, 2026, needs more optimization.
5 721 0.882668520698 Henry Cohn, 2026, needs more optimization.
5 722 0.882768843292 Henry Cohn, 2026, needs more optimization.
5 723 0.882833570463 Henry Cohn, 2026, needs more optimization.
5 724 0.882946013211 Henry Cohn, 2026, needs more optimization.
5 725 0.882973572173 Henry Cohn, 2026, needs more optimization.
5 726 0.883102838350 Henry Cohn, 2026, needs more optimization.
5 727 0.883130558983 Henry Cohn, 2026, needs more optimization.
5 728 0.883267074066 Henry Cohn, 2026, needs more optimization.
5 729 0.883320153712 Henry Cohn, 2026, needs more optimization.
5 730 0.883353723029 Henry Cohn, 2026, needs more optimization.
5 731 0.883446589769 Henry Cohn, 2026, needs more optimization.
5 732 0.883521282902 Henry Cohn, 2026, needs more optimization.
5 733 0.883611045566 Henry Cohn, 2026, needs more optimization.
5 734 0.883710902643 Henry Cohn, 2026, needs more optimization.
5 735 0.883761069898 Henry Cohn, 2026, needs more optimization.
5 736 0.883818603024 Henry Cohn, 2026, needs more optimization.
5 737 0.883896428072 Henry Cohn, 2026, needs more optimization.
5 738 0.883981982966 Henry Cohn, 2026, needs more optimization.
5 739 0.884123641992 Henry Cohn, 2026, needs more optimization.
5 740 0.884182141495 Henry Cohn, 2026, needs more optimization.
5 741 0.884315138410 Henry Cohn, 2026, needs more optimization.
5 742 0.884397811607 Henry Cohn, 2026, needs more optimization.
5 743 0.884522960630 Henry Cohn, 2026, needs more optimization.
5 744 0.884621362500 Henry Cohn, 2026, needs more optimization.
5 745 0.884677829620 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 0.885001228066 Henry Cohn, 2026, needs more optimization.
5 749 0.885005529528 Henry Cohn, 2026, needs more optimization.
5 750 0.885050909781 Henry Cohn, 2026, needs more optimization.
5 751 0.885132825074 Henry Cohn, 2026, needs more optimization.
5 752 0.885197308532 Henry Cohn, 2026, needs more optimization.
5 753 0.885242594284 Henry Cohn, 2026, needs more optimization.
5 754 0.885352064928 Henry Cohn, 2026, needs more optimization.
5 755 0.885381905064 Henry Cohn, 2026, needs more optimization.
5 756 0.885424459802 Henry Cohn, 2026, needs more optimization.
5 757 0.885559418307 Henry Cohn, 2026, needs more optimization.
5 758 0.885605364874 Henry Cohn, 2026, needs more optimization.
5 759 0.885659175343 Henry Cohn, 2026, needs more optimization.
5 760 0.885730906451 Henry Cohn, 2026, needs more optimization.
5 761 0.885826563222 Henry Cohn, 2026, needs more optimization.
5 762 0.885895655651 Henry Cohn, 2026, needs more optimization.
5 763 0.885997167451 Henry Cohn, 2026, needs more optimization.
5 764 0.886068745964 Henry Cohn, 2026, needs more optimization.
5 765 0.886160157497 Henry Cohn, 2026, needs more optimization.
5 766 0.886236102432 Henry Cohn, 2026, needs more optimization.
5 767 0.886268718692 Henry Cohn, 2026, needs more optimization.
5 768 0.886292453892 Henry Cohn, 2026, needs more optimization.
5 769 0.886332511139 Henry Cohn, 2026, needs more optimization.
5 770 0.886435857111 Henry Cohn, 2026, needs more optimization.
5 771 0.886544429624 Henry Cohn, 2026, needs more optimization.
5 772 0.886580171023 Henry Cohn, 2026, needs more optimization.
5 773 0.886689261639 Henry Cohn, 2026, needs more optimization.
5 774 0.886760394981 Henry Cohn, 2026, needs more optimization.
5 775 0.886853249770 Henry Cohn, 2026, needs more optimization.
5 776 0.886949266594 Henry Cohn, 2026, needs more optimization.
5 777 0.886985397660 Henry Cohn, 2026, needs more optimization.
5 778 0.887075231884 Henry Cohn, 2026, needs more optimization.
5 779 0.887168255911 Henry Cohn, 2026, needs more optimization.
5 780 0.887282002983 Henry Cohn, 2026, needs more optimization.
5 781 0.887289284737 Henry Cohn, 2026, needs more optimization.
5 782 0.887305652108 Henry Cohn, 2026, needs more optimization.
5 783 0.887367171922 Henry Cohn, 2026, needs more optimization.
5 784 0.887453511073 Henry Cohn, 2026, needs more optimization.
5 785 0.887484414840 Henry Cohn, 2026, needs more optimization.
5 786 0.887534494654 Henry Cohn, 2026, needs more optimization.
5 787 0.887654054410 Henry Cohn, 2026, needs more optimization.
5 788 0.887728284656 Henry Cohn, 2026, needs more optimization.
5 789 0.887818721738 Henry Cohn, 2026, needs more optimization.
5 790 0.887923995003 Henry Cohn, 2026, needs more optimization.
5 791 0.887932982297 Henry Cohn, 2026, needs more optimization.
5 792 0.888004025348 Henry Cohn, 2026, needs more optimization.
5 793 0.888089084640 Henry Cohn, 2026, needs more optimization.
5 794 0.888131290601 Henry Cohn, 2026, needs more optimization.
5 795 0.888209389121 Henry Cohn, 2026, needs more optimization.
5 796 0.888235352654 Henry Cohn, 2026, needs more optimization.
5 797 0.888319012919 Henry Cohn, 2026, needs more optimization.
5 798 0.888463660847 Henry Cohn, 2026, needs more optimization.
5 799 0.888482165277 Henry Cohn, 2026, needs more optimization.
5 800 0.888523943461 Henry Cohn, 2026, needs more optimization.
5 801 0.888576453533 Henry Cohn, 2026, needs more optimization.
5 802 0.888651755539 Henry Cohn, 2026, needs more optimization.
5 803 0.888846384602 Henry Cohn, 2026, needs more optimization.
5 804 0.888899981016 Henry Cohn, 2026, needs more optimization.
5 805 0.888922030986 Henry Cohn, 2026, needs more optimization.
5 806 0.888959915917 Henry Cohn, 2026, needs more optimization.
5 807 0.889023343566 Henry Cohn, 2026, needs more optimization.
5 808 0.889141674123 Henry Cohn, 2026, needs more optimization.
5 809 0.889276573860 Henry Cohn, 2026, needs more optimization.
5 810 0.889364932063 Henry Cohn, 2026, needs more optimization.
5 811 0.889445249692 Henry Cohn, 2026, needs more optimization.
5 812 0.889465251480 Henry Cohn, 2026, needs more optimization.
5 813 0.889580506739 Henry Cohn, 2026, needs more optimization.
5 814 0.889700407705 Henry Cohn, 2026, needs more optimization.
5 815 0.889705105688 Henry Cohn, 2026, needs more optimization.
5 816 0.889726089314 Henry Cohn, 2026, needs more optimization.
5 817 0.889750457854 Henry Cohn, 2026, needs more optimization.
5 818 0.889858426673 Henry Cohn, 2026, needs more optimization.
5 819 0.889881910352 Henry Cohn, 2026, needs more optimization.
5 820 0.889895314663 Henry Cohn, 2026, needs more optimization.
5 821 0.890020424110 Henry Cohn, 2026, needs more optimization.
5 822 0.890074125701 Henry Cohn, 2026, needs more optimization.
5 823 0.890179677018 Henry Cohn, 2026, needs more optimization.
5 824 0.890283437509 Henry Cohn, 2026, needs more optimization.
5 825 0.890400230819 Henry Cohn, 2026, needs more optimization.
5 826 0.890418593260 Henry Cohn, 2026, needs more optimization.
5 827 0.890438354077 Henry Cohn, 2026, needs more optimization.
5 829 0.890563772753 Henry Cohn, 2026, needs more optimization.
5 830 0.890668604624 Henry Cohn, 2026, needs more optimization.
5 831 0.890725853439 Henry Cohn, 2026, needs more optimization.
5 832 0.890731009104 Henry Cohn, 2026, needs more optimization.
5 833 0.890756391620 Henry Cohn, 2026, needs more optimization.
5 834 0.890796625063 Henry Cohn, 2026, needs more optimization.
5 835 0.890946025531 Henry Cohn, 2026, needs more optimization.
5 836 0.891033531559 Henry Cohn, 2026, needs more optimization.
5 837 0.891119903867 Henry Cohn, 2026, needs more optimization.
5 838 0.891211613257 Henry Cohn, 2026, needs more optimization.
5 839 0.891247427273 Henry Cohn, 2026, needs more optimization.
5 840 0.891307991324 Henry Cohn, 2026, needs more optimization.
5 841 0.891410698094 Henry Cohn, 2026, needs more optimization.
5 842 0.891451579999 Henry Cohn, 2026, needs more optimization.
5 843 0.891531245316 Henry Cohn, 2026, needs more optimization.
5 844 0.891561002982 Henry Cohn, 2026, needs more optimization.
5 845 0.891613253026 Henry Cohn, 2026, needs more optimization.
5 846 0.891712764423 Henry Cohn, 2026, needs more optimization.
5 847 0.891744285824 Henry Cohn, 2026, needs more optimization.
5 848 0.891846811688 Henry Cohn, 2026, needs more optimization.
5 849 0.891890847202 Henry Cohn, 2026, needs more optimization.
5 850 0.891955829260 Henry Cohn, 2026, needs more optimization.
5 851 0.891967568836 Henry Cohn, 2026, needs more optimization.
5 852 0.892104327698 Henry Cohn, 2026, needs more optimization.
5 853 0.892112174024 Henry Cohn, 2026, needs more optimization.
5 854 0.892203056941 Henry Cohn, 2026, needs more optimization.
5 855 0.892246425310 Henry Cohn, 2026, needs more optimization.
5 856 0.892364658170 Henry Cohn, 2026, needs more optimization.
5 857 0.892370870304 Henry Cohn, 2026, needs more optimization.
5 858 0.892427569330 Henry Cohn, 2026, needs more optimization.
5 859 0.892566542098 Henry Cohn, 2026, needs more optimization.
5 861 0.892615233834 Henry Cohn, 2026, needs more optimization.
5 862 0.892633545289 Henry Cohn, 2026, needs more optimization.
5 863 0.892733677157 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 0.892904743891 Henry Cohn, 2026, needs more optimization.
5 867 0.893042661460 Henry Cohn, 2026, needs more optimization.
5 869 0.893085570046 Henry Cohn, 2026, needs more optimization.
5 870 0.893175007337 Henry Cohn, 2026, needs more optimization.
5 871 0.893283270078 Henry Cohn, 2026, needs more optimization.
5 872 0.893319410813 Henry Cohn, 2026, needs more optimization.
5 873 0.893361771830 Henry Cohn, 2026, needs more optimization.
5 874 0.893400866570 Henry Cohn, 2026, needs more optimization.
5 875 0.893521583314 Henry Cohn, 2026, needs more optimization.
5 876 0.893548182156 Henry Cohn, 2026, needs more optimization.
5 877 0.893649994099 Henry Cohn, 2026, needs more optimization.
5 878 0.893670715463 Henry Cohn, 2026, needs more optimization.
5 879 0.893775434319 Henry Cohn, 2026, needs more optimization.
5 880 0.893825623814 Henry Cohn, 2026, needs more optimization.
5 881 0.893831772503 Henry Cohn, 2026, needs more optimization.
5 882 0.893837092931 Henry Cohn, 2026, needs more optimization.
5 883 0.893949213091 Henry Cohn, 2026, needs more optimization.
5 884 0.894029295666 Henry Cohn, 2026, needs more optimization.
5 885 0.894100859177 Henry Cohn, 2026, needs more optimization.
5 886 0.894153827970 Henry Cohn, 2026, needs more optimization.
5 887 0.894245219453 Henry Cohn, 2026, needs more optimization.
5 888 0.894317269404 Henry Cohn, 2026, needs more optimization.
5 889 0.894360818200 Henry Cohn, 2026, needs more optimization.
5 890 0.894452360937 Henry Cohn, 2026, needs more optimization.
5 891 0.894501848264 Henry Cohn, 2026, needs more optimization.
5 892 0.894550981163 Henry Cohn, 2026, needs more optimization.
5 893 0.894619899254 Henry Cohn, 2026, needs more optimization.
5 895 0.894657307623 Henry Cohn, 2026, needs more optimization.
5 896 0.894746968957 Henry Cohn, 2026, needs more optimization.
5 897 0.894812632756 Henry Cohn, 2026, needs more optimization.
5 898 0.894835076705 Henry Cohn, 2026, needs more optimization.
5 900 0.894959145179 Henry Cohn, 2026, needs more optimization.
5 901 0.895014268967 Henry Cohn, 2026, needs more optimization.
5 902 0.895052744446 Henry Cohn, 2026, needs more optimization.
5 903 0.895175178705 Henry Cohn, 2026, needs more optimization.
5 904 0.895272378488 Henry Cohn, 2026, needs more optimization.
5 905 0.895302104449 Henry Cohn, 2026, needs more optimization.
5 907 0.895394111196 Henry Cohn, 2026, needs more optimization.
5 908 0.895481889695 Henry Cohn, 2026, needs more optimization.
5 909 0.895518918561 Henry Cohn, 2026, needs more optimization.
5 910 0.895634444360 Henry Cohn, 2026, needs more optimization.
5 911 0.895718433231 Henry Cohn, 2026, needs more optimization.
5 912 0.895719049230 Henry Cohn, 2026, needs more optimization.
5 913 0.895793631650 Henry Cohn, 2026, needs more optimization.
5 915 0.895849956395 Henry Cohn, 2026, needs more optimization.
5 916 0.895960203106 Henry Cohn, 2026, needs more optimization.
5 917 0.896006215630 Henry Cohn, 2026, needs more optimization.
5 918 0.896124408708 Henry Cohn, 2026, needs more optimization.
5 919 0.896149094448 Henry Cohn, 2026, needs more optimization.
5 920 0.896189355248 Henry Cohn, 2026, needs more optimization.
5 921 0.896283184988 Henry Cohn, 2026, needs more optimization.
5 922 0.896299367702 Henry Cohn, 2026, needs more optimization.
5 923 0.896355300641 Henry Cohn, 2026, needs more optimization.
5 924 0.896388444779 Henry Cohn, 2026, needs more optimization.
5 925 0.896425417295 Henry Cohn, 2026, needs more optimization.
5 926 0.896481306862 Henry Cohn, 2026, needs more optimization.
5 927 0.896487306270 Henry Cohn, 2026, needs more optimization.
5 928 0.896569485813 Henry Cohn, 2026, needs more optimization.
5 929 0.896654620476 Henry Cohn, 2026, needs more optimization.
5 930 0.896763136734 Henry Cohn, 2026, needs more optimization.
5 931 0.896781234362 Henry Cohn, 2026, needs more optimization.
5 932 0.896865164192 Henry Cohn, 2026, needs more optimization.
5 933 0.896900572555 Henry Cohn, 2026, needs more optimization.
5 934 0.896953703222 Henry Cohn, 2026, needs more optimization.
5 935 0.897003500640 Henry Cohn, 2026, needs more optimization.
5 936 0.897027558127 Henry Cohn, 2026, needs more optimization.
5 937 0.897104199547 Henry Cohn, 2026, needs more optimization.
5 938 0.897155130344 Henry Cohn, 2026, needs more optimization.
5 939 0.897233261578 Henry Cohn, 2026, needs more optimization.
5 940 0.897277977031 Henry Cohn, 2026, needs more optimization.
5 941 0.897321498263 Henry Cohn, 2026, needs more optimization.
5 942 0.897410929171 Henry Cohn, 2026, needs more optimization.
5 943 0.897431270412 Henry Cohn, 2026, needs more optimization.
5 944 0.897512109439 Henry Cohn, 2026, needs more optimization.
5 945 0.897588156006 Henry Cohn, 2026, needs more optimization.
5 946 0.897634109990 Henry Cohn, 2026, needs more optimization.
5 947 0.897695475793 Henry Cohn, 2026, needs more optimization.
5 948 0.897766689493 Henry Cohn, 2026, needs more optimization.
5 949 0.897825944993 Henry Cohn, 2026, needs more optimization.
5 950 0.897857869517 Henry Cohn, 2026, needs more optimization.
5 951 0.897925170440 Henry Cohn, 2026, needs more optimization.
5 952 0.897962714349 Henry Cohn, 2026, needs more optimization.
5 953 0.898021771998 Henry Cohn, 2026, needs more optimization.
5 956 0.898025457371 Henry Cohn, 2026, needs more optimization.
5 957 0.898115471790 Henry Cohn, 2026, needs more optimization.
5 958 0.898219956768 Henry Cohn, 2026, needs more optimization.
5 959 0.898260181092 Henry Cohn, 2026, needs more optimization.
5 960 0.898289902430 Henry Cohn, 2026, needs more optimization.
5 961 0.898385779763 Henry Cohn, 2026, needs more optimization.
5 962 0.898403117484 Henry Cohn, 2026, needs more optimization.
5 963 0.898410557948 Henry Cohn, 2026, needs more optimization.
5 964 0.898493859423 Henry Cohn, 2026, needs more optimization.
5 965 0.898529483577 Henry Cohn, 2026, needs more optimization.
5 966 0.898630809542 Henry Cohn, 2026, needs more optimization.
5 967 0.898679585919 Henry Cohn, 2026, needs more optimization.
5 968 0.898748012783 Henry Cohn, 2026, needs more optimization.
5 969 0.898833400484 Henry Cohn, 2026, needs more optimization.
5 970 0.898835264474 Henry Cohn, 2026, needs more optimization.
5 971 0.898912637608 Henry Cohn, 2026, needs more optimization.
5 972 0.898934492153 Henry Cohn, 2026, needs more optimization.
5 973 0.898985722995 Henry Cohn, 2026, needs more optimization.
5 974 0.899077700729 Henry Cohn, 2026, needs more optimization.
5 975 0.899118102467 Henry Cohn, 2026, needs more optimization.
5 976 0.899128987927 Henry Cohn, 2026, needs more optimization.
5 977 0.899171518062 Henry Cohn, 2026, needs more optimization.
5 978 0.899286216641 Henry Cohn, 2026, needs more optimization.
5 979 0.899330762464 Henry Cohn, 2026, needs more optimization.
5 980 0.899369063445 Henry Cohn, 2026, needs more optimization.
5 981 0.899408940551 Henry Cohn, 2026, needs more optimization.
5 982 0.899488269956 Henry Cohn, 2026, needs more optimization.
5 983 0.899574316921 Henry Cohn, 2026, needs more optimization.
5 984 0.899580482465 Henry Cohn, 2026, needs more optimization.
5 985 0.899626984712 Henry Cohn, 2026, needs more optimization.
5 986 0.899704087949 Henry Cohn, 2026, needs more optimization.
5 987 0.899727877587 Henry Cohn, 2026, needs more optimization.
5 988 0.899779379449 Henry Cohn, 2026, needs more optimization.
5 990 0.899888763914 Henry Cohn, 2026, needs more optimization.
5 991 0.899900653833 Henry Cohn, 2026, needs more optimization.
5 992 0.899964135048 Henry Cohn, 2026, needs more optimization.
5 993 0.900001109379 Henry Cohn, 2026, needs more optimization.
5 994 0.900067149074 Henry Cohn, 2026, needs more optimization.
5 995 0.900138297185 Henry Cohn, 2026, needs more optimization.
5 996 0.900252513777 Henry Cohn, 2026, needs more optimization.
5 997 0.900271690689 Henry Cohn, 2026, needs more optimization.
5 998 0.900327748537 Henry Cohn, 2026, needs more optimization.
5 999 0.900427130226 Henry Cohn, 2026, needs more optimization.
5 1000 0.900429284337 Henry Cohn, 2026, needs more optimization.
5 1001 0.900483967010 Henry Cohn, 2026, needs more optimization.
5 1002 0.900539707220 Henry Cohn, 2026, needs more optimization.
5 1003 0.900552414524 Henry Cohn, 2026, needs more optimization.
5 1004 0.900582617483 Henry Cohn, 2026, needs more optimization.
5 1005 0.900670288827 Henry Cohn, 2026, needs more optimization.
5 1006 0.900731655304 Henry Cohn, 2026, needs more optimization.
5 1007 0.900802529908 Henry Cohn, 2026, needs more optimization.
5 1008 0.900860734316 Henry Cohn, 2026, needs more optimization.
5 1009 0.900881883581 Henry Cohn, 2026, needs more optimization.
5 1010 0.900934645293 Henry Cohn, 2026, needs more optimization.
5 1011 0.900984737345 Henry Cohn, 2026, needs more optimization.
5 1012 0.900997774335 Henry Cohn, 2026, needs more optimization.
5 1013 0.901038648767 Henry Cohn, 2026, needs more optimization.
5 1014 0.901116729774 Henry Cohn, 2026, needs more optimization.
5 1015 0.901119958893 Henry Cohn, 2026, needs more optimization.
5 1016 0.901125860435 Henry Cohn, 2026, needs more optimization.
5 1017 0.901177582334 Henry Cohn, 2026, needs more optimization.
5 1018 0.901218938693 Henry Cohn, 2026, needs more optimization.
5 1020 0.901325150248 Henry Cohn, 2026, needs more optimization.
5 1021 0.901426659429 Henry Cohn, 2026, needs more optimization.
5 1022 0.901503741400 Henry Cohn, 2026, needs more optimization.
5 1023 0.901550007526 Henry Cohn, 2026, needs more optimization.
5 1024 0.901599156838 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 0.524373608780 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 0.539382071135 Henry Cohn, 2026.
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 0.557588802583 Henry Cohn, 2026.
6 92 0.560971622256 Henry Cohn, 2025.
6 93 0.563013323310 Henry Cohn, 2023.
6 94 0.565350375903 Henry Cohn, 2024.
6 95 0.565789396150 Henry Cohn, 2023.
6 96 0.565950871118 Henry Cohn, 2023.
6 97 0.568133461901 Henry Cohn, 2025.
6 98 0.571052839653 Henry Cohn, 2026, needs more optimization.
6 99 0.573881665753 Henry Cohn, 2023.
6 100 0.574916276575 Henry Cohn, 2024.
6 101 0.578322911677 Henry Cohn, 2026.
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 0.584228700283 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 0.599076646174 Henry Cohn, 2026.
6 121 0.603706262945 Henry Cohn, 2026, needs more optimization.
6 122 0.606015494381 Henry Cohn, 2026.
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 0.610385711272 Henry Cohn, 2026.
6 127 0.616513281003 Henry Cohn, 2026.
6 128 0.619107420038 Henry Cohn, 2025.
6 129 0.620224367829 Henry Cohn, 2025.
6 130 0.623555026016 Henry Cohn, 2026, needs more optimization.
6 132 0.624698587770 Henry Cohn, 2026, needs more optimization.
6 133 0.626200566070 Henry Cohn, 2026, needs more optimization.
6 134 0.628625329659 Henry Cohn, 2026, needs more optimization.
6 135 0.630530656158 Henry Cohn, 2026, needs more optimization.
6 136 0.631774376880 Henry Cohn, 2026, needs more optimization.
6 137 0.633402294823 Henry Cohn, 2025.
6 138 0.634581555668 Henry Cohn, 2026, needs more optimization.
6 139 0.636159190170 Henry Cohn, 2026, needs more optimization.
6 140 0.637374263264 Henry Cohn, 2026, needs more optimization.
6 141 0.639556760326 Henry Cohn, 2026, needs more optimization.
6 142 0.639907748183 Henry Cohn, 2026, needs more optimization.
6 143 0.641418520213 Henry Cohn, 2026, needs more optimization.
6 144 0.642197636629 Henry Cohn, 2026, needs more optimization.
6 145 0.643736949113 Henry Cohn, 2026, needs more optimization.
6 146 0.644837265936 Henry Cohn, 2026, needs more optimization.
6 147 0.645786741328 Henry Cohn, 2026, needs more optimization.
6 148 0.646695007680 Henry Cohn, 2026, needs more optimization.
6 149 0.648305403697 Henry Cohn, 2026, needs more optimization.
6 150 0.649234363496 Henry Cohn, 2026, needs more optimization.
6 151 0.649894104895 Henry Cohn, 2026, needs more optimization.
6 152 0.651373135987 Henry Cohn, 2026, needs more optimization.
6 153 0.651424838401 Henry Cohn, 2026, needs more optimization.
6 154 0.651931377269 Henry Cohn, 2026, needs more optimization.
6 155 0.652677694649 Henry Cohn, 2026, needs more optimization.
6 156 0.653218985086 Henry Cohn, 2026, needs more optimization.
6 157 0.653907784761 Henry Cohn, 2026, needs more optimization.
6 158 0.654174169895 Henry Cohn, 2026, needs more optimization.
6 159 0.654917506618 Henry Cohn, 2026, needs more optimization.
6 160 0.655640276044 Henry Cohn, 2026, needs more optimization.
6 161 0.656176883937 Henry Cohn, 2026, needs more optimization.
6 162 0.656801528989 Henry Cohn, 2026, needs more optimization.
6 163 0.657623485879 Henry Cohn, 2026, needs more optimization.
6 164 0.658348653642 Henry Cohn, 2026, needs more optimization.
6 165 0.659084509520 Henry Cohn, 2026, needs more optimization.
6 166 0.659965352661 Henry Cohn, 2026, needs more optimization.
6 167 0.660355875176 Henry Cohn, 2026, needs more optimization.
6 168 0.660627594087 Henry Cohn, 2026, needs more optimization.
6 169 0.661755034915 Henry Cohn, 2026, needs more optimization.
6 170 0.662663966597 Henry Cohn, 2026, needs more optimization.
6 171 0.663635354345 Henry Cohn, 2026, needs more optimization.
6 172 0.664135030350 Henry Cohn, 2026, needs more optimization.
6 173 0.664451438570 Henry Cohn, 2026, needs more optimization.
6 174 0.664871170855 Henry Cohn, 2026, needs more optimization.
6 175 0.665443411314 Henry Cohn, 2026, needs more optimization.
6 176 0.666108525418 Henry Cohn, 2026, needs more optimization.
6 177 0.667548831820 Henry Cohn, 2026, needs more optimization.
6 178 0.668632913251 Henry Cohn, 2026, needs more optimization.
6 179 0.670345232736 Henry Cohn, 2026, needs more optimization.
6 180 0.671450816649 Henry Cohn, 2026, needs more optimization.
6 181 0.671964509250 Henry Cohn, 2026, needs more optimization.
6 182 0.672777040837 Henry Cohn, 2026, needs more optimization.
6 183 0.673125015652 Henry Cohn, 2026, needs more optimization.
6 184 0.673943978182 Henry Cohn, 2026, needs more optimization.
6 185 0.674404408042 Henry Cohn, 2026, needs more optimization.
6 186 0.674794448749 Henry Cohn, 2026, needs more optimization.
6 187 0.675998306019 Henry Cohn, 2026, needs more optimization.
6 188 0.676600132239 Henry Cohn, 2026, needs more optimization.
6 189 0.677344946215 Henry Cohn, 2026, needs more optimization.
6 190 0.677401365461 Henry Cohn, 2026, needs more optimization.
6 191 0.678569045193 Henry Cohn, 2026, needs more optimization.
6 192 0.679447003997 Henry Cohn, 2026, needs more optimization.
6 193 0.679736288064 Henry Cohn, 2026, needs more optimization.
6 194 0.680563908208 Henry Cohn, 2026, needs more optimization.
6 195 0.681332654790 Henry Cohn, 2026, needs more optimization.
6 196 0.681796491932 Henry Cohn, 2026, needs more optimization.
6 197 0.682623517458 Henry Cohn, 2026, needs more optimization.
6 198 0.682973028241 Henry Cohn, 2026, needs more optimization.
6 199 0.683513013447 Henry Cohn, 2026, needs more optimization.
6 200 0.684371957443 Henry Cohn, 2026, needs more optimization.
6 201 0.684423960591 Henry Cohn, 2026, needs more optimization.
6 202 0.684695807095 Henry Cohn, 2026, needs more optimization.
6 203 0.685464316067 Henry Cohn, 2026, needs more optimization.
6 204 0.686169073940 Henry Cohn, 2026, needs more optimization.
6 205 0.686256448955 Henry Cohn, 2026, needs more optimization.
6 206 0.687047370550 Henry Cohn, 2026, needs more optimization.
6 207 0.687792664686 Henry Cohn, 2026, needs more optimization.
6 208 0.688117863620 Henry Cohn, 2026, needs more optimization.
6 209 0.689071781042 Henry Cohn, 2026, needs more optimization.
6 210 0.689980568095 Henry Cohn, 2026, needs more optimization.
6 211 0.690718009394 Henry Cohn, 2026, needs more optimization.
6 212 0.691219417789 Henry Cohn, 2026, needs more optimization.
6 213 0.691670583504 Henry Cohn, 2026, needs more optimization.
6 214 0.692291109957 Henry Cohn, 2026, needs more optimization.
6 215 0.692811106835 Henry Cohn, 2026, needs more optimization.
6 216 0.693329460551 Henry Cohn, 2026, needs more optimization.
6 217 0.694031973733 Henry Cohn, 2026, needs more optimization.
6 218 0.694428135519 Henry Cohn, 2026, needs more optimization.
6 219 0.695082508504 Henry Cohn, 2026, needs more optimization.
6 220 0.695147508927 Henry Cohn, 2026, needs more optimization.
6 221 0.695418366142 Henry Cohn, 2026, needs more optimization.
6 222 0.695867575619 Henry Cohn, 2026, needs more optimization.
6 223 0.696382860650 Henry Cohn, 2026, needs more optimization.
6 224 0.697123573666 Henry Cohn, 2026, needs more optimization.
6 225 0.697415855437 Henry Cohn, 2026, needs more optimization.
6 226 0.698152817700 Henry Cohn, 2026, needs more optimization.
6 227 0.698332098024 Henry Cohn, 2026, needs more optimization.
6 228 0.698900642486 Henry Cohn, 2026, needs more optimization.
6 229 0.699495105657 Henry Cohn, 2026, needs more optimization.
6 243 0.7 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
10⁢x−7
6 244 0.704214331982 Henry Cohn, 2026, needs more optimization.
6 245 0.704217044364 Henry Cohn, 2026, needs more optimization.
6 246 0.704219251248 Henry Cohn, 2026, needs more optimization.
6 247 0.704231949681 Henry Cohn, 2026, needs more optimization.
6 248 0.704240574867 Henry Cohn, 2026, needs more optimization.
6 249 0.704292059089 Henry Cohn, 2026, needs more optimization.
6 250 0.704518261682 Henry Cohn, 2026, needs more optimization.
6 251 0.704633493524 Henry Cohn, 2026, needs more optimization.
6 252 0.704733044721 Henry Cohn, 2026, needs more optimization.
6 253 0.704943057429 Henry Cohn, 2026, needs more optimization.
6 254 0.705091774338 Henry Cohn, 2026, needs more optimization.
6 255 0.705179409302 Henry Cohn, 2026, needs more optimization.
6 256 0.705185020829 Henry Cohn, 2026, needs more optimization.
6 257 0.705534061682 Henry Cohn, 2026, needs more optimization.
6 258 0.706001286265 Henry Cohn, 2026, needs more optimization.
6 259 0.706716718620 Henry Cohn, 2026, needs more optimization.
6 260 0.707187161626 Henry Cohn, 2026, needs more optimization.
6 261 0.707854912557 Henry Cohn, 2026, needs more optimization.
6 262 0.708781132136 Henry Cohn, 2026, needs more optimization.
6 263 0.710063792606 Henry Cohn, 2026, needs more optimization.
6 264 0.710650942206 Henry Cohn, 2026, needs more optimization.
6 265 0.711650054738 Henry Cohn, 2026, needs more optimization.
6 266 0.712056168670 Henry Cohn, 2026, needs more optimization.
6 267 0.712797549744 Henry Cohn, 2026, needs more optimization.
6 268 0.713562920042 Henry Cohn, 2026, needs more optimization.
6 269 0.714387721064 Henry Cohn, 2026, needs more optimization.
6 270 0.715103885640 Henry Cohn, 2026, needs more optimization.
6 271 0.715205998837 Henry Cohn, 2026, needs more optimization.
6 272 0.716089085569 Henry Cohn, 2026, needs more optimization.
6 273 0.716893104407 Henry Cohn, 2026, needs more optimization.
6 274 0.717514910119 Henry Cohn, 2026, needs more optimization.
6 275 0.718335585946 Henry Cohn, 2026, needs more optimization.
6 276 0.718940111656 Henry Cohn, 2026, needs more optimization.
6 277 0.719526311651 Henry Cohn, 2026, needs more optimization.
6 278 0.720059929303 Henry Cohn, 2026, needs more optimization.
6 279 0.720808142580 Henry Cohn, 2026, needs more optimization.
6 280 0.721717943618 Henry Cohn, 2026, needs more optimization.
6 281 0.722086825600 Henry Cohn, 2026, needs more optimization.
6 282 0.722619927857 Henry Cohn, 2026, needs more optimization.
6 283 0.723455769982 Henry Cohn, 2026, needs more optimization.
6 284 0.723878054469 Henry Cohn, 2026, needs more optimization.
6 285 0.724560497992 Henry Cohn, 2026, needs more optimization.
6 286 0.725092148394 Henry Cohn, 2026, needs more optimization.
6 287 0.725213375558 Henry Cohn, 2026, needs more optimization.
6 288 0.725968021465 Henry Cohn, 2026, needs more optimization.
6 289 0.726303037526 Henry Cohn, 2026, needs more optimization.
6 290 0.726303490256 Henry Cohn, 2026, needs more optimization.
6 291 0.726997243048 Henry Cohn, 2026, needs more optimization.
6 292 0.727966382883 Henry Cohn, 2026, needs more optimization.
6 293 0.728393704046 Henry Cohn, 2026, needs more optimization.
6 294 0.728865960567 Henry Cohn, 2026, needs more optimization.
6 295 0.729392049748 Henry Cohn, 2026, needs more optimization.
6 296 0.729924070292 Henry Cohn, 2026, needs more optimization.
6 297 0.730480993091 Henry Cohn, 2026, needs more optimization.
6 298 0.730862704559 Henry Cohn, 2026, needs more optimization.
6 299 0.731065269230 Henry Cohn, 2026, needs more optimization.
6 300 0.731541023755 Henry Cohn, 2026, needs more optimization.
6 301 0.732020939485 Henry Cohn, 2026, needs more optimization.
6 302 0.732595312598 Henry Cohn, 2026, needs more optimization.
6 303 0.732976794742 Henry Cohn, 2026, needs more optimization.
6 304 0.733051544429 Henry Cohn, 2026, needs more optimization.
6 305 0.733453239030 Henry Cohn, 2026, needs more optimization.
6 306 0.733858919586 Henry Cohn, 2026, needs more optimization.
6 307 0.734340126145 Henry Cohn, 2026, needs more optimization.
6 308 0.734493516578 Henry Cohn, 2026, needs more optimization.
6 309 0.734839795040 Henry Cohn, 2026, needs more optimization.
6 310 0.734988030498 Henry Cohn, 2026, needs more optimization.
6 311 0.735649734843 Henry Cohn, 2026, needs more optimization.
6 312 0.736468296564 Henry Cohn, 2026, needs more optimization.
6 313 0.736730526827 Henry Cohn, 2026, needs more optimization.
6 314 0.737283817280 Henry Cohn, 2026, needs more optimization.
6 315 0.737795174178 Henry Cohn, 2026, needs more optimization.
6 316 0.738122550699 Henry Cohn, 2026, needs more optimization.
6 317 0.738591889613 Henry Cohn, 2026, needs more optimization.
6 318 0.738920082353 Henry Cohn, 2026, needs more optimization.
6 319 0.739356384050 Henry Cohn, 2026, needs more optimization.
6 320 0.739819633211 Henry Cohn, 2026, needs more optimization.
6 321 0.740393944078 Henry Cohn, 2026, needs more optimization.
6 322 0.740718623472 Henry Cohn, 2026, needs more optimization.
6 323 0.741210649064 Henry Cohn, 2026, needs more optimization.
6 324 0.741485325885 Henry Cohn, 2026, needs more optimization.
6 325 0.742104555349 Henry Cohn, 2026, needs more optimization.
6 326 0.742386151341 Henry Cohn, 2026, needs more optimization.
6 327 0.742830477483 Henry Cohn, 2026, needs more optimization.
6 328 0.742903969411 Henry Cohn, 2026, needs more optimization.
6 329 0.743338600552 Henry Cohn, 2026, needs more optimization.
6 330 0.743703583645 Henry Cohn, 2026, needs more optimization.
6 331 0.744121710687 Henry Cohn, 2026, needs more optimization.
6 332 0.744378718199 Henry Cohn, 2026, needs more optimization.
6 333 0.744405980710 Henry Cohn, 2026, needs more optimization.
6 334 0.744694202748 Henry Cohn, 2026, needs more optimization.
6 335 0.745158051995 Henry Cohn, 2026, needs more optimization.
6 336 0.745795172280 Henry Cohn, 2026, needs more optimization.
6 337 0.746050970072 Henry Cohn, 2026, needs more optimization.
6 338 0.746536971803 Henry Cohn, 2026, needs more optimization.
6 339 0.746541603081 Henry Cohn, 2026, needs more optimization.
6 340 0.746547986694 Henry Cohn, 2026, needs more optimization.
6 341 0.746549883292 Henry Cohn, 2026, needs more optimization.
6 342 0.746555037918 Henry Cohn, 2026, needs more optimization.
6 343 0.748202167728 Henry Cohn, 2026, needs more optimization.
6 344 0.748891333107 Henry Cohn, 2026, needs more optimization.
6 345 0.749168886017 Henry Cohn, 2026, needs more optimization.
6 346 0.749361533116 Henry Cohn, 2026, needs more optimization.
6 347 0.749672574610 Henry Cohn, 2026, needs more optimization.
6 348 0.750060948395 Henry Cohn, 2026, needs more optimization.
6 349 0.750323250801 Henry Cohn, 2026, needs more optimization.
6 350 0.750535324476 Henry Cohn, 2026, needs more optimization.
6 351 0.750816019938 Henry Cohn, 2026, needs more optimization.
6 352 0.751193914021 Henry Cohn, 2026, needs more optimization.
6 353 0.751504887645 Henry Cohn, 2026, needs more optimization.
6 354 0.751708606277 Henry Cohn, 2026, needs more optimization.
6 355 0.751897960907 Henry Cohn, 2026, needs more optimization.
6 356 0.752155817206 Henry Cohn, 2026, needs more optimization.
6 357 0.752448097554 Henry Cohn, 2026, needs more optimization.
6 358 0.752900568948 Henry Cohn, 2026, needs more optimization.
6 359 0.753214276804 Henry Cohn, 2026, needs more optimization.
6 360 0.753274216061 Henry Cohn, 2026, needs more optimization.
6 361 0.753654823539 Henry Cohn, 2026, needs more optimization.
6 362 0.754036385989 Henry Cohn, 2026, needs more optimization.
6 363 0.754171666559 Henry Cohn, 2026, needs more optimization.
6 364 0.754584362196 Henry Cohn, 2026, needs more optimization.
6 365 0.754730094611 Henry Cohn, 2026, needs more optimization.
6 366 0.755033159139 Henry Cohn, 2026, needs more optimization.
6 367 0.755304775937 Henry Cohn, 2026, needs more optimization.
6 368 0.755545835701 Henry Cohn, 2026, needs more optimization.
6 369 0.755896016357 Henry Cohn, 2026, needs more optimization.
6 370 0.756120322210 Henry Cohn, 2026, needs more optimization.
6 371 0.756596597102 Henry Cohn, 2026, needs more optimization.
6 372 0.756708751555 Henry Cohn, 2026, needs more optimization.
6 373 0.757069107626 Henry Cohn, 2026, needs more optimization.
6 374 0.757276680262 Henry Cohn, 2026, needs more optimization.
6 375 0.757515425326 Henry Cohn, 2026, needs more optimization.
6 376 0.757932486918 Henry Cohn, 2026, needs more optimization.
6 377 0.758238448337 Henry Cohn, 2026, needs more optimization.
6 378 0.758516647450 Henry Cohn, 2026, needs more optimization.
6 379 0.758930303618 Henry Cohn, 2026, needs more optimization.
6 380 0.759285270974 Henry Cohn, 2026, needs more optimization.
6 381 0.759315681996 Henry Cohn, 2026, needs more optimization.
6 382 0.759565261061 Henry Cohn, 2026, needs more optimization.
6 383 0.759719251767 Henry Cohn, 2026, needs more optimization.
6 384 0.759900544934 Henry Cohn, 2026, needs more optimization.
6 385 0.760343385918 Henry Cohn, 2026, needs more optimization.
6 386 0.760402937703 Henry Cohn, 2026, needs more optimization.
6 387 0.760719444247 Henry Cohn, 2026, needs more optimization.
6 388 0.761103588001 Henry Cohn, 2026, needs more optimization.
6 389 0.761321938609 Henry Cohn, 2026, needs more optimization.
6 390 0.761732629859 Henry Cohn, 2026, needs more optimization.
6 391 0.761760837067 Henry Cohn, 2026, needs more optimization.
6 392 0.762107141674 Henry Cohn, 2026, needs more optimization.
6 393 0.762148874386 Henry Cohn, 2026, needs more optimization.
6 394 0.762400453393 Henry Cohn, 2026, needs more optimization.
6 395 0.762812968804 Henry Cohn, 2026, needs more optimization.
6 396 0.763176294718 Henry Cohn, 2026, needs more optimization.
6 397 0.763240840724 Henry Cohn, 2026, needs more optimization.
6 398 0.763525214275 Henry Cohn, 2026, needs more optimization.
6 399 0.763765083321 Henry Cohn, 2026, needs more optimization.
6 400 0.763942548172 Henry Cohn, 2026, needs more optimization.
6 401 0.764137764512 Henry Cohn, 2026, needs more optimization.
6 402 0.764356411199 Henry Cohn, 2026, needs more optimization.
6 403 0.764560638481 Henry Cohn, 2026, needs more optimization.
6 404 0.764922317775 Henry Cohn, 2026, needs more optimization.
6 405 0.765054741062 Henry Cohn, 2026, needs more optimization.
6 406 0.765290033697 Henry Cohn, 2026, needs more optimization.
6 407 0.765558142569 Henry Cohn, 2026, needs more optimization.
6 408 0.765779557930 Henry Cohn, 2026, needs more optimization.
6 409 0.765831148886 Henry Cohn, 2026, needs more optimization.
6 410 0.766022340131 Henry Cohn, 2026, needs more optimization.
6 411 0.766327670037 Henry Cohn, 2026, needs more optimization.
6 412 0.766595711269 Henry Cohn, 2026, needs more optimization.
6 413 0.766740123867 Henry Cohn, 2026, needs more optimization.
6 414 0.767058246746 Henry Cohn, 2026, needs more optimization.
6 415 0.767456892465 Henry Cohn, 2026, needs more optimization.
6 416 0.767678150088 Henry Cohn, 2026, needs more optimization.
6 417 0.768023740286 Henry Cohn, 2026, needs more optimization.
6 418 0.768203515980 Henry Cohn, 2026, needs more optimization.
6 419 0.768533640357 Henry Cohn, 2026, needs more optimization.
6 420 0.768690404929 Henry Cohn, 2026, needs more optimization.
6 421 0.768860046907 Henry Cohn, 2026, needs more optimization.
6 422 0.769117292066 Henry Cohn, 2026, needs more optimization.
6 423 0.769300297291 Henry Cohn, 2026, needs more optimization.
6 424 0.769580904269 Henry Cohn, 2026, needs more optimization.
6 425 0.769840281198 Henry Cohn, 2026, needs more optimization.
6 426 0.770191265789 Henry Cohn, 2026, needs more optimization.
6 427 0.770336513195 Henry Cohn, 2026, needs more optimization.
6 428 0.770411128880 Henry Cohn, 2026, needs more optimization.
6 429 0.770591789302 Henry Cohn, 2026, needs more optimization.
6 430 0.770829912016 Henry Cohn, 2026, needs more optimization.
6 431 0.770925030532 Henry Cohn, 2026, needs more optimization.
6 432 0.771069561286 Henry Cohn, 2026, needs more optimization.
6 433 0.771344619295 Henry Cohn, 2026, needs more optimization.
6 434 0.771486064621 Henry Cohn, 2026, needs more optimization.
6 435 0.771805456311 Henry Cohn, 2026, needs more optimization.
6 436 0.771863083636 Henry Cohn, 2026, needs more optimization.
6 437 0.771972294216 Henry Cohn, 2026, needs more optimization.
6 438 0.772163508726 Henry Cohn, 2026, needs more optimization.
6 439 0.772518977507 Henry Cohn, 2026, needs more optimization.
6 440 0.772640335775 Henry Cohn, 2026, needs more optimization.
6 441 0.772902618770 Henry Cohn, 2026, needs more optimization.
6 442 0.773090756072 Henry Cohn, 2026, needs more optimization.
6 443 0.773270775521 Henry Cohn, 2026, needs more optimization.
6 444 0.773412983481 Henry Cohn, 2026, needs more optimization.
6 445 0.773776834974 Henry Cohn, 2026, needs more optimization.
6 446 0.774049840558 Henry Cohn, 2026, needs more optimization.
6 447 0.774219579340 Henry Cohn, 2026, needs more optimization.
6 448 0.774389360074 Henry Cohn, 2026, needs more optimization.
6 449 0.774715564894 Henry Cohn, 2026, needs more optimization.
6 450 0.774868963242 Henry Cohn, 2026, needs more optimization.
6 451 0.775059592595 Henry Cohn, 2026, needs more optimization.
6 452 0.775210611819 Henry Cohn, 2026, needs more optimization.
6 453 0.775427933814 Henry Cohn, 2026, needs more optimization.
6 454 0.775484338150 Henry Cohn, 2026, needs more optimization.
6 455 0.775851904355 Henry Cohn, 2026, needs more optimization.
6 456 0.776065837256 Henry Cohn, 2026, needs more optimization.
6 457 0.776317727491 Henry Cohn, 2026, needs more optimization.
6 458 0.776423525888 Henry Cohn, 2026, needs more optimization.
6 459 0.776691088803 Henry Cohn, 2026, needs more optimization.
6 460 0.776749991557 Henry Cohn, 2026, needs more optimization.
6 461 0.776781921430 Henry Cohn, 2026, needs more optimization.
6 462 0.777138816529 Henry Cohn, 2026, needs more optimization.
6 463 0.777397157650 Henry Cohn, 2026, needs more optimization.
6 464 0.777457802657 Henry Cohn, 2026, needs more optimization.
6 465 0.777667537334 Henry Cohn, 2026, needs more optimization.
6 466 0.777933925273 Henry Cohn, 2026, needs more optimization.
6 467 0.778021401390 Henry Cohn, 2026, needs more optimization.
6 468 0.778283817393 Henry Cohn, 2026, needs more optimization.
6 469 0.778332728225 Henry Cohn, 2026, needs more optimization.
6 470 0.778723094738 Henry Cohn, 2026, needs more optimization.
6 471 0.778907830407 Henry Cohn, 2026, needs more optimization.
6 472 0.779177696568 Henry Cohn, 2026, needs more optimization.
6 473 0.779471824607 Henry Cohn, 2026, needs more optimization.
6 474 0.779643692088 Henry Cohn, 2026, needs more optimization.
6 475 0.779709336640 Henry Cohn, 2026, needs more optimization.
6 476 0.779729342486 Henry Cohn, 2026, needs more optimization.
6 477 0.779845800520 Henry Cohn, 2026, needs more optimization.
6 478 0.780134864785 Henry Cohn, 2026, needs more optimization.
6 479 0.780345118019 Henry Cohn, 2026, needs more optimization.
6 480 0.780549519265 Henry Cohn, 2026, needs more optimization.
6 481 0.780689764050 Henry Cohn, 2026, needs more optimization.
6 482 0.780898078138 Henry Cohn, 2026, needs more optimization.
6 483 0.781072904845 Henry Cohn, 2026, needs more optimization.
6 484 0.781412531914 Henry Cohn, 2026, needs more optimization.
6 485 0.781546914264 Henry Cohn, 2026, needs more optimization.
6 486 0.781660145405 Henry Cohn, 2026, needs more optimization.
6 487 0.781958212081 Henry Cohn, 2026, needs more optimization.
6 488 0.782128785215 Henry Cohn, 2026, needs more optimization.
6 489 0.782405330104 Henry Cohn, 2026, needs more optimization.
6 490 0.782444004213 Henry Cohn, 2026, needs more optimization.
6 491 0.782698713410 Henry Cohn, 2026, needs more optimization.
6 492 0.782825714368 Henry Cohn, 2026, needs more optimization.
6 493 0.783013910240 Henry Cohn, 2026, needs more optimization.
6 495 0.783279162777 Henry Cohn, 2026, needs more optimization.
6 496 0.783456559421 Henry Cohn, 2026, needs more optimization.
6 497 0.783693772948 Henry Cohn, 2026, needs more optimization.
6 499 0.783843599248 Henry Cohn, 2026, needs more optimization.
6 500 0.784065928674 Henry Cohn, 2026, needs more optimization.
6 501 0.784441336347 Henry Cohn, 2026, needs more optimization.
6 502 0.784673620070 Henry Cohn, 2026, needs more optimization.
6 503 0.784867452507 Henry Cohn, 2026, needs more optimization.
6 504 0.785009921235 Henry Cohn, 2026, needs more optimization.
6 505 0.785170689776 Henry Cohn, 2026, needs more optimization.
6 506 0.785349358685 Henry Cohn, 2026, needs more optimization.
6 507 0.785475467984 Henry Cohn, 2026, needs more optimization.
6 508 0.785639224837 Henry Cohn, 2026, needs more optimization.
6 509 0.785865272084 Henry Cohn, 2026, needs more optimization.
6 510 0.786023105682 Henry Cohn, 2026, needs more optimization.
6 511 0.786283158151 Henry Cohn, 2026, needs more optimization.
6 512 0.786370672214 Henry Cohn, 2026, needs more optimization.
6 513 0.786404959025 Henry Cohn, 2026, needs more optimization.
6 514 0.786567482215 Henry Cohn, 2026, needs more optimization.
6 515 0.786634588347 Henry Cohn, 2026, needs more optimization.
6 516 0.786777466776 Henry Cohn, 2026, needs more optimization.
6 517 0.786997718513 Henry Cohn, 2026, needs more optimization.
6 518 0.787268568654 Henry Cohn, 2026, needs more optimization.
6 519 0.787284028215 Henry Cohn, 2026, needs more optimization.
6 520 0.787432851822 Henry Cohn, 2026, needs more optimization.
6 521 0.787666344614 Henry Cohn, 2026, needs more optimization.
6 522 0.787798487373 Henry Cohn, 2026, needs more optimization.
6 523 0.788009236049 Henry Cohn, 2026, needs more optimization.
6 524 0.788345421055 Henry Cohn, 2026, needs more optimization.
6 525 0.788433426265 Henry Cohn, 2026, needs more optimization.
6 526 0.788566356778 Henry Cohn, 2026, needs more optimization.
6 527 0.788870111750 Henry Cohn, 2026, needs more optimization.
6 528 0.788921691585 Henry Cohn, 2026, needs more optimization.
6 529 0.789115910940 Henry Cohn, 2026, needs more optimization.
6 530 0.789226199764 Henry Cohn, 2026, needs more optimization.
6 531 0.789408828693 Henry Cohn, 2026, needs more optimization.
6 532 0.789543915680 Henry Cohn, 2026, needs more optimization.
6 533 0.789727244810 Henry Cohn, 2026, needs more optimization.
6 534 0.789760065728 Henry Cohn, 2026, needs more optimization.
6 535 0.790018767685 Henry Cohn, 2026, needs more optimization.
6 536 0.790059516593 Henry Cohn, 2026, needs more optimization.
6 537 0.790291350179 Henry Cohn, 2026, needs more optimization.
6 538 0.790478365732 Henry Cohn, 2026, needs more optimization.
6 539 0.790494554180 Henry Cohn, 2026, needs more optimization.
6 540 0.790697985779 Henry Cohn, 2026, needs more optimization.
6 541 0.790880305526 Henry Cohn, 2026, needs more optimization.
6 542 0.790908761312 Henry Cohn, 2026, needs more optimization.
6 543 0.791100931043 Henry Cohn, 2026, needs more optimization.
6 544 0.791288437202 Henry Cohn, 2026, needs more optimization.
6 545 0.791483622978 Henry Cohn, 2026, needs more optimization.
6 546 0.791755916150 Henry Cohn, 2026, needs more optimization.
6 547 0.791800379344 Henry Cohn, 2026, needs more optimization.
6 548 0.791973549224 Henry Cohn, 2026, needs more optimization.
6 549 0.792113364494 Henry Cohn, 2026, needs more optimization.
6 550 0.792222891274 Henry Cohn, 2026, needs more optimization.
6 551 0.792465381851 Henry Cohn, 2026, needs more optimization.
6 552 0.792564280954 Henry Cohn, 2026, needs more optimization.
6 553 0.792707873718 Henry Cohn, 2026, needs more optimization.
6 554 0.792868756983 Henry Cohn, 2026, needs more optimization.
6 555 0.793006936497 Henry Cohn, 2026, needs more optimization.
6 556 0.793262982798 Henry Cohn, 2026, needs more optimization.
6 557 0.793316328175 Henry Cohn, 2026, needs more optimization.
6 558 0.793372948421 Henry Cohn, 2026, needs more optimization.
6 559 0.793488773786 Henry Cohn, 2026, needs more optimization.
6 560 0.793755760563 Henry Cohn, 2026, needs more optimization.
6 561 0.793994329167 Henry Cohn, 2026, needs more optimization.
6 562 0.793996299293 Henry Cohn, 2026, needs more optimization.
6 563 0.794250829418 Henry Cohn, 2026, needs more optimization.
6 564 0.794253967026 Henry Cohn, 2026, needs more optimization.
6 565 0.794506217320 Henry Cohn, 2026, needs more optimization.
6 566 0.794658714503 Henry Cohn, 2026, needs more optimization.
6 567 0.794788183260 Henry Cohn, 2026, needs more optimization.
6 568 0.795018452115 Henry Cohn, 2026, needs more optimization.
6 569 0.795032747820 Henry Cohn, 2026, needs more optimization.
6 570 0.795196714325 Henry Cohn, 2026, needs more optimization.
6 571 0.795277566833 Henry Cohn, 2026, needs more optimization.
6 572 0.795409762512 Henry Cohn, 2026, needs more optimization.
6 573 0.795580874697 Henry Cohn, 2026, needs more optimization.
6 574 0.795729467936 Henry Cohn, 2026, needs more optimization.
6 575 0.795893621428 Henry Cohn, 2026, needs more optimization.
6 576 0.796081573936 Henry Cohn, 2026, needs more optimization.
6 577 0.796219001417 Henry Cohn, 2026, needs more optimization.
6 578 0.796342097236 Henry Cohn, 2026, needs more optimization.
6 579 0.796573114363 Henry Cohn, 2026, needs more optimization.
6 580 0.796707973055 Henry Cohn, 2026, needs more optimization.
6 581 0.796758294788 Henry Cohn, 2026, needs more optimization.
6 582 0.796972315420 Henry Cohn, 2026, needs more optimization.
6 583 0.797076663191 Henry Cohn, 2026, needs more optimization.
6 584 0.797352118779 Henry Cohn, 2026, needs more optimization.
6 585 0.797378790386 Henry Cohn, 2026, needs more optimization.
6 586 0.797381686757 Henry Cohn, 2026, needs more optimization.
6 587 0.797553916120 Henry Cohn, 2026, needs more optimization.
6 588 0.797691367524 Henry Cohn, 2026, needs more optimization.
6 589 0.797825547456 Henry Cohn, 2026, needs more optimization.
6 590 0.797972009416 Henry Cohn, 2026, needs more optimization.
6 591 0.798144116961 Henry Cohn, 2026, needs more optimization.
6 592 0.798371979798 Henry Cohn, 2026, needs more optimization.
6 593 0.798463632130 Henry Cohn, 2026, needs more optimization.
6 594 0.798658889526 Henry Cohn, 2026, needs more optimization.
6 595 0.798789508357 Henry Cohn, 2026, needs more optimization.
6 596 0.798984708536 Henry Cohn, 2026, needs more optimization.
6 597 0.799202808178 Henry Cohn, 2026, needs more optimization.
6 598 0.799236702514 Henry Cohn, 2026, needs more optimization.
6 599 0.799378007431 Henry Cohn, 2026, needs more optimization.
6 600 0.799536968093 Henry Cohn, 2026, needs more optimization.
6 601 0.799682623268 Henry Cohn, 2026, needs more optimization.
6 602 0.799796194517 Henry Cohn, 2026, needs more optimization.
6 603 0.799922347986 Henry Cohn, 2026, needs more optimization.
6 604 0.800063809248 Henry Cohn, 2026, needs more optimization.
6 605 0.800222366937 Henry Cohn, 2026, needs more optimization.
6 606 0.800235605266 Henry Cohn, 2026, needs more optimization.
6 607 0.800476625333 Henry Cohn, 2026, needs more optimization.
6 608 0.800491226466 Henry Cohn, 2026, needs more optimization.
6 609 0.800680842930 Henry Cohn, 2026, needs more optimization.
6 610 0.800892056646 Henry Cohn, 2026, needs more optimization.
6 611 0.801006752766 Henry Cohn, 2026, needs more optimization.
6 612 0.801128959303 Henry Cohn, 2026, needs more optimization.
6 613 0.801183620717 Henry Cohn, 2026, needs more optimization.
6 614 0.801476745920 Henry Cohn, 2026, needs more optimization.
6 615 0.801483572042 Henry Cohn, 2026, needs more optimization.
6 616 0.801657461132 Henry Cohn, 2026, needs more optimization.
6 617 0.801680370737 Henry Cohn, 2026, needs more optimization.
6 618 0.801847403272 Henry Cohn, 2026, needs more optimization.
6 619 0.801909073688 Henry Cohn, 2026, needs more optimization.
6 620 0.802010011247 Henry Cohn, 2026, needs more optimization.
6 621 0.802201298720 Henry Cohn, 2026, needs more optimization.
6 622 0.802440844954 Henry Cohn, 2026, needs more optimization.
6 623 0.802563301201 Henry Cohn, 2026, needs more optimization.
6 624 0.802580355221 Henry Cohn, 2026, needs more optimization.
6 625 0.802735885908 Henry Cohn, 2026, needs more optimization.
6 626 0.802896073078 Henry Cohn, 2026, needs more optimization.
6 627 0.802915880751 Henry Cohn, 2026, needs more optimization.
6 628 0.803035176128 Henry Cohn, 2026, needs more optimization.
6 629 0.803242445295 Henry Cohn, 2026, needs more optimization.
6 630 0.803297541420 Henry Cohn, 2026, needs more optimization.
6 631 0.803416106333 Henry Cohn, 2026, needs more optimization.
6 632 0.803605772994 Henry Cohn, 2026, needs more optimization.
6 633 0.803781426368 Henry Cohn, 2026, needs more optimization.
6 634 0.803997640754 Henry Cohn, 2026, needs more optimization.
6 635 0.804014706476 Henry Cohn, 2026, needs more optimization.
6 636 0.804103547677 Henry Cohn, 2026, needs more optimization.
6 637 0.804234655507 Henry Cohn, 2026, needs more optimization.
6 638 0.804381146885 Henry Cohn, 2026, needs more optimization.
6 639 0.804382436077 Henry Cohn, 2026, needs more optimization.
6 640 0.804612931464 Henry Cohn, 2026, needs more optimization.
6 641 0.804633644335 Henry Cohn, 2026, needs more optimization.
6 642 0.804668410382 Henry Cohn, 2026, needs more optimization.
6 643 0.804820274064 Henry Cohn, 2026, needs more optimization.
6 644 0.804976278735 Henry Cohn, 2026, needs more optimization.
6 645 0.805198978527 Henry Cohn, 2026, needs more optimization.
6 646 0.805334972374 Henry Cohn, 2026, needs more optimization.
6 647 0.805429196816 Henry Cohn, 2026, needs more optimization.
6 648 0.805452601325 Henry Cohn, 2026, needs more optimization.
6 649 0.805559948735 Henry Cohn, 2026, needs more optimization.
6 650 0.805657404477 Henry Cohn, 2026, needs more optimization.
6 651 0.805873415099 Henry Cohn, 2026, needs more optimization.
6 652 0.805952437252 Henry Cohn, 2026, needs more optimization.
6 653 0.806111298892 Henry Cohn, 2026, needs more optimization.
6 654 0.806232665153 Henry Cohn, 2026, needs more optimization.
6 655 0.806370421493 Henry Cohn, 2026, needs more optimization.
6 656 0.806399266131 Henry Cohn, 2026, needs more optimization.
6 657 0.806540546620 Henry Cohn, 2026, needs more optimization.
6 658 0.806629067522 Henry Cohn, 2026, needs more optimization.
6 659 0.806726859609 Henry Cohn, 2026, needs more optimization.
6 660 0.806752400653 Henry Cohn, 2026, needs more optimization.
6 661 0.806950403948 Henry Cohn, 2026, needs more optimization.
6 662 0.807140568422 Henry Cohn, 2026, needs more optimization.
6 663 0.807312985979 Henry Cohn, 2026, needs more optimization.
6 664 0.807324859750 Henry Cohn, 2026, needs more optimization.
6 665 0.807592714408 Henry Cohn, 2026, needs more optimization.
6 666 0.807597532223 Henry Cohn, 2026, needs more optimization.
6 667 0.807786480659 Henry Cohn, 2026, needs more optimization.
6 668 0.807789473820 Henry Cohn, 2026, needs more optimization.
6 669 0.807829937695 Henry Cohn, 2026, needs more optimization.
6 670 0.807893715855 Henry Cohn, 2026, needs more optimization.
6 671 0.808072362315 Henry Cohn, 2026, needs more optimization.
6 672 0.808174355720 Henry Cohn, 2026, needs more optimization.
6 673 0.808351996361 Henry Cohn, 2026, needs more optimization.
6 674 0.808460508945 Henry Cohn, 2026, needs more optimization.
6 675 0.808652003372 Henry Cohn, 2026, needs more optimization.
6 676 0.808765975285 Henry Cohn, 2026, needs more optimization.
6 677 0.808942999676 Henry Cohn, 2026, needs more optimization.
6 678 0.809016962041 Henry Cohn, 2026, needs more optimization.
6 679 0.809101282866 Henry Cohn, 2026, needs more optimization.
6 680 0.809238337309 Henry Cohn, 2026, needs more optimization.
6 681 0.809411445123 Henry Cohn, 2026, needs more optimization.
6 682 0.809552071038 Henry Cohn, 2026, needs more optimization.
6 683 0.809593237491 Henry Cohn, 2026, needs more optimization.
6 684 0.809734912034 Henry Cohn, 2026, needs more optimization.
6 685 0.809811239231 Henry Cohn, 2026, needs more optimization.
6 686 0.809956063307 Henry Cohn, 2026, needs more optimization.
6 687 0.809983124543 Henry Cohn, 2026, needs more optimization.
6 688 0.810155401529 Henry Cohn, 2026, needs more optimization.
6 689 0.810281633568 Henry Cohn, 2026, needs more optimization.
6 690 0.810400020892 Henry Cohn, 2026, needs more optimization.
6 691 0.810496638005 Henry Cohn, 2026, needs more optimization.
6 692 0.810679355316 Henry Cohn, 2026, needs more optimization.
6 693 0.810688012896 Henry Cohn, 2026, needs more optimization.
6 694 0.810878989953 Henry Cohn, 2026, needs more optimization.
6 695 0.810916172827 Henry Cohn, 2026, needs more optimization.
6 696 0.811111043520 Henry Cohn, 2026, needs more optimization.
6 697 0.811174065944 Henry Cohn, 2026, needs more optimization.
6 698 0.811432936187 Henry Cohn, 2026, needs more optimization.
6 699 0.811552260784 Henry Cohn, 2026, 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 0.811763594652 Henry Cohn, 2026, needs more optimization.
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6 704 0.811928557726 Henry Cohn, 2026, needs more optimization.
6 705 0.812054764924 Henry Cohn, 2026, needs more optimization.
6 706 0.812163218256 Henry Cohn, 2026, needs more optimization.
6 707 0.812335571108 Henry Cohn, 2026, needs more optimization.
6 708 0.812496661838 Henry Cohn, 2026, needs more optimization.
6 709 0.812618775138 Henry Cohn, 2026, needs more optimization.
6 710 0.812669789043 Henry Cohn, 2026, needs more optimization.
6 711 0.812812207167 Henry Cohn, 2026, needs more optimization.
6 712 0.812906358989 Henry Cohn, 2026, needs more optimization.
6 713 0.813050278956 Henry Cohn, 2026, needs more optimization.
6 714 0.813172908945 Henry Cohn, 2026, needs more optimization.
6 715 0.813303124903 Henry Cohn, 2026, needs more optimization.
6 716 0.813309596186 Henry Cohn, 2026, needs more optimization.
6 717 0.813337972575 Henry Cohn, 2026, needs more optimization.
6 718 0.813482714570 Henry Cohn, 2026, needs more optimization.
6 719 0.813643087512 Henry Cohn, 2026, needs more optimization.
6 720 0.813664827355 Henry Cohn, 2026, needs more optimization.
6 721 0.813835008971 Henry Cohn, 2026, needs more optimization.
6 723 0.814000679931 Henry Cohn, 2026, needs more optimization.
6 724 0.814062971517 Henry Cohn, 2026, needs more optimization.
6 725 0.814201397096 Henry Cohn, 2026, needs more optimization.
6 726 0.814321956308 Henry Cohn, 2026, needs more optimization.
6 727 0.814498584486 Henry Cohn, 2026, needs more optimization.
6 728 0.814498657111 Henry Cohn, 2026, needs more optimization.
6 729 0.814559969022 Henry Cohn, 2026, needs more optimization.
6 730 0.814687639846 Henry Cohn, 2026, needs more optimization.
6 732 0.814855972662 Henry Cohn, 2026, needs more optimization.
6 733 0.814957838351 Henry Cohn, 2026, needs more optimization.
6 734 0.815069220671 Henry Cohn, 2026, needs more optimization.
6 735 0.815093388369 Henry Cohn, 2026, needs more optimization.
6 736 0.815218780938 Henry Cohn, 2026, needs more optimization.
6 737 0.815385011196 Henry Cohn, 2026, needs more optimization.
6 738 0.815600653184 Henry Cohn, 2026, needs more optimization.
6 739 0.815700530201 Henry Cohn, 2026, needs more optimization.
6 740 0.815845601653 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 0.816041656153 Henry Cohn, 2026, needs more optimization.
6 744 0.816072924951 Henry Cohn, 2026, needs more optimization.
6 745 0.816245691524 Henry Cohn, 2026, needs more optimization.
6 746 0.816301031660 Henry Cohn, 2026, needs more optimization.
6 747 0.816544516540 Henry Cohn, 2026, needs more optimization.
6 748 0.816625591172 Henry Cohn, 2026, needs more optimization.
6 749 0.816632471131 Henry Cohn, 2026, needs more optimization.
6 750 0.816829324442 Henry Cohn, 2026, needs more optimization.
6 751 0.816984297270 Henry Cohn, 2026, needs more optimization.
6 752 0.817000737748 Henry Cohn, 2026, needs more optimization.
6 753 0.817178994707 Henry Cohn, 2026, needs more optimization.
6 754 0.817256284445 Henry Cohn, 2026, needs more optimization.
6 755 0.817288147287 Henry Cohn, 2026, needs more optimization.
6 756 0.817397575349 Henry Cohn, 2026, needs more optimization.
6 757 0.817474379864 Henry Cohn, 2026, needs more optimization.
6 758 0.817489785979 Henry Cohn, 2026, needs more optimization.
6 759 0.817676074159 Henry Cohn, 2026, needs more optimization.
6 760 0.817708225532 Henry Cohn, 2026, needs more optimization.
6 761 0.817737248258 Henry Cohn, 2026, needs more optimization.
6 762 0.817949462966 Henry Cohn, 2026, needs more optimization.
6 763 0.818096737360 Henry Cohn, 2026, needs more optimization.
6 764 0.818247581166 Henry Cohn, 2026, needs more optimization.
6 765 0.818327552097 Henry Cohn, 2026, needs more optimization.
6 767 0.818383937257 Henry Cohn, 2026, needs more optimization.
6 768 0.818581361961 Henry Cohn, 2026, needs more optimization.
6 769 0.818678374637 Henry Cohn, 2026, needs more optimization.
6 770 0.818801033727 Henry Cohn, 2026, needs more optimization.
6 771 0.818867523779 Henry Cohn, 2026, needs more optimization.
6 772 0.818932450167 Henry Cohn, 2026, needs more optimization.
6 773 0.818945991491 Henry Cohn, 2026, needs more optimization.
6 775 0.819103862352 Henry Cohn, 2026, needs more optimization.
6 776 0.819247769169 Henry Cohn, 2026, needs more optimization.
6 777 0.819321049883 Henry Cohn, 2026, needs more optimization.
6 778 0.819511933132 Henry Cohn, 2026, needs more optimization.
6 779 0.819546500545 Henry Cohn, 2026, needs more optimization.
6 780 0.819676897937 Henry Cohn, 2026, needs more optimization.
6 781 0.819705871458 Henry Cohn, 2026, needs more optimization.
6 782 0.819728268763 Henry Cohn, 2026, needs more optimization.
6 783 0.819852423609 Henry Cohn, 2026, needs more optimization.
6 784 0.819949114002 Henry Cohn, 2026, needs more optimization.
6 785 0.820045095152 Henry Cohn, 2026, needs more optimization.
6 786 0.820162296273 Henry Cohn, 2026, needs more optimization.
6 787 0.820188023823 Henry Cohn, 2026, needs more optimization.
6 788 0.820384503528 Henry Cohn, 2026, needs more optimization.
6 789 0.820415475366 Henry Cohn, 2026, needs more optimization.
6 790 0.820536619466 Henry Cohn, 2026, needs more optimization.
6 791 0.820635783448 Henry Cohn, 2026, needs more optimization.
6 792 0.820797563343 Henry Cohn, 2026, needs more optimization.
6 793 0.820802127452 Henry Cohn, 2026, needs more optimization.
6 794 0.820988632271 Henry Cohn, 2026, needs more optimization.
6 795 0.820994556846 Henry Cohn, 2026, needs more optimization.
6 796 0.821013871992 Henry Cohn, 2026, needs more optimization.
6 797 0.821084043137 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 0.821481974975 Henry Cohn, 2026, needs more optimization.
6 801 0.821607337766 Henry Cohn, 2026, needs more optimization.
6 802 0.821670709678 Henry Cohn, 2026, needs more optimization.
6 803 0.821748880532 Henry Cohn, 2026, needs more optimization.
6 804 0.821750245087 Henry Cohn, 2026, needs more optimization.
6 805 0.821871979322 Henry Cohn, 2026, needs more optimization.
6 806 0.821921623509 Henry Cohn, 2026, needs more optimization.
6 807 0.821977942102 Henry Cohn, 2026, needs more optimization.
6 808 0.822048831744 Henry Cohn, 2026, needs more optimization.
6 809 0.822190048511 Henry Cohn, 2026, needs more optimization.
6 810 0.822294687962 Henry Cohn, 2026, needs more optimization.
6 811 0.822367686459 Henry Cohn, 2026, needs more optimization.
6 812 0.822489404520 Henry Cohn, 2026, needs more optimization.
6 813 0.822677958208 Henry Cohn, 2026, needs more optimization.
6 814 0.822717523257 Henry Cohn, 2026, needs more optimization.
6 815 0.822797156665 Henry Cohn, 2026, needs more optimization.
6 816 0.822858370429 Henry Cohn, 2026, needs more optimization.
6 817 0.822998901940 Henry Cohn, 2026, needs more optimization.
6 818 0.823070950896 Henry Cohn, 2026, needs more optimization.
6 820 0.823197653188 Henry Cohn, 2026, needs more optimization.
6 821 0.823343216906 Henry Cohn, 2026, needs more optimization.
6 822 0.823470854434 Henry Cohn, 2026, needs more optimization.
6 823 0.823657744802 Henry Cohn, 2026, needs more optimization.
6 824 0.823657744809 Henry Cohn, 2026, needs more optimization.
6 825 0.823713391194 Henry Cohn, 2026, needs more optimization.
6 826 0.823935255997 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 0.824082528948 Henry Cohn, 2026, needs more optimization.
6 830 0.824179992361 Henry Cohn, 2026, needs more optimization.
6 831 0.824248440844 Henry Cohn, 2026, needs more optimization.
6 832 0.824352666243 Henry Cohn, 2026, needs more optimization.
6 833 0.824410474997 Henry Cohn, 2026, needs more optimization.
6 834 0.824524105411 Henry Cohn, 2026, needs more optimization.
6 836 0.824548809050 Henry Cohn, 2026, needs more optimization.
6 837 0.824666021690 Henry Cohn, 2026, needs more optimization.
6 838 0.824748156093 Henry Cohn, 2026, needs more optimization.
6 839 0.824882413738 Henry Cohn, 2026, needs more optimization.
6 840 0.824916981005 Henry Cohn, 2026, needs more optimization.
6 841 0.824997445981 Henry Cohn, 2026, needs more optimization.
6 842 0.825133256924 Henry Cohn, 2026, needs more optimization.
6 843 0.825316420528 Henry Cohn, 2026, needs more optimization.
6 844 0.825321761379 Henry Cohn, 2026, needs more optimization.
6 845 0.825414144971 Henry Cohn, 2026, 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 0.825581597195 Henry Cohn, 2026, needs more optimization.
6 849 0.825823138881 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 0.826300906057 Henry Cohn, 2026, needs more optimization.
6 855 0.826396832791 Henry Cohn, 2026, needs more optimization.
6 856 0.826415296291 Henry Cohn, 2026, needs more optimization.
6 857 0.826561308892 Henry Cohn, 2026, needs more optimization.
6 858 0.826654545559 Henry Cohn, 2026, needs more optimization.
6 859 0.826683416254 Henry Cohn, 2026, needs more optimization.
6 860 0.826836651775 Henry Cohn, 2026, needs more optimization.
6 861 0.826928892488 Henry Cohn, 2026, needs more optimization.
6 862 0.826931289699 Henry Cohn, 2026, needs more optimization.
6 863 0.827054251320 Henry Cohn, 2026, needs more optimization.
6 864 0.827100003459 Henry Cohn, 2026, needs more optimization.
6 865 0.827291287241 Henry Cohn, 2026, needs more optimization.
6 866 0.827291384274 Henry Cohn, 2026, needs more optimization.
6 867 0.827298829250 Henry Cohn, 2026, needs more optimization.
6 869 0.827384782147 Henry Cohn, 2026, needs more optimization.
6 870 0.827586603988 Henry Cohn, 2026, needs more optimization.
6 871 0.827593079427 Henry Cohn, 2026, needs more optimization.
6 873 0.827680468290 Henry Cohn, 2026, needs more optimization.
6 874 0.827688558727 Henry Cohn, 2026, needs more optimization.
6 875 0.827689991808 Henry Cohn, 2026, needs more optimization.
6 876 0.827695459728 Henry Cohn, 2026, needs more optimization.
6 877 0.827861809404 Henry Cohn, 2026, needs more optimization.
6 878 0.827883412572 Henry Cohn, 2026, needs more optimization.
6 879 0.827925476245 Henry Cohn, 2026, needs more optimization.
6 881 0.827994208687 Henry Cohn, 2026, needs more optimization.
6 882 0.828018817004 Henry Cohn, 2026, needs more optimization.
6 883 0.828094035035 Henry Cohn, 2026, needs more optimization.
6 884 0.828165027113 Henry Cohn, 2026, needs more optimization.
6 885 0.828334230117 Henry Cohn, 2026, needs more optimization.
6 886 0.828363089792 Henry Cohn, 2026, needs more optimization.
6 888 0.828484256719 Henry Cohn, 2026, needs more optimization.
6 889 0.828562591897 Henry Cohn, 2026, needs more optimization.
6 890 0.828638428519 Henry Cohn, 2026, needs more optimization.
6 891 0.828640223526 Henry Cohn, 2026, needs more optimization.
6 892 0.828776243863 Henry Cohn, 2026, needs more optimization.
6 893 0.828837897976 Henry Cohn, 2026, needs more optimization.
6 894 0.828877503154 Henry Cohn, 2026, needs more optimization.
6 895 0.828881568622 Henry Cohn, 2026, needs more optimization.
6 896 0.828937943030 Henry Cohn, 2026, needs more optimization.
6 897 0.829037305882 Henry Cohn, 2026, needs more optimization.
6 899 0.829108967396 Henry Cohn, 2026, needs more optimization.
6 900 0.829133134280 Henry Cohn, 2026, needs more optimization.
6 902 0.829386655054 Henry Cohn, 2026, needs more optimization.
6 903 0.829467147285 Henry Cohn, 2026, needs more optimization.
6 904 0.829579885466 Henry Cohn, 2026, needs more optimization.
6 905 0.829683541482 Henry Cohn, 2026, needs more optimization.
6 906 0.829750699183 Henry Cohn, 2026, needs more optimization.
6 908 0.829806080974 Henry Cohn, 2026, needs more optimization.
6 909 0.829949608073 Henry Cohn, 2026, needs more optimization.
6 911 0.830013556041 Henry Cohn, 2026, needs more optimization.
6 912 0.830080303052 Henry Cohn, 2026, needs more optimization.
6 913 0.830126216968 Henry Cohn, 2026, needs more optimization.
6 914 0.830198336491 Henry Cohn, 2026, needs more optimization.
6 918 0.830493087953 Henry Cohn, 2026, needs more optimization.
6 919 0.830522869358 Henry Cohn, 2026, needs more optimization.
6 921 0.830658539037 Henry Cohn, 2026, needs more optimization.
6 922 0.830777306182 Henry Cohn, 2026, needs more optimization.
6 925 0.830819407653 Henry Cohn, 2026, needs more optimization.
6 926 0.830900321599 Henry Cohn, 2026, needs more optimization.
6 928 0.831178826454 Henry Cohn, 2026, needs more optimization.
6 930 0.831255497897 Henry Cohn, 2026, needs more optimization.
6 934 0.831389231484 Henry Cohn, 2026, needs more optimization.
6 935 0.831391080818 Henry Cohn, 2026, needs more optimization.
6 937 0.831482603132 Henry Cohn, 2026, needs more optimization.
6 938 0.831503324537 Henry Cohn, 2026, needs more optimization.
6 940 0.831753119562 Henry Cohn, 2026, needs more optimization.
6 941 0.831754718627 Henry Cohn, 2026, needs more optimization.
6 942 0.831781326809 Henry Cohn, 2026, needs more optimization.
6 943 0.831800997009 Henry Cohn, 2026, needs more optimization.
6 946 0.831937779679 Henry Cohn, 2026, needs more optimization.
6 947 0.831994779470 Henry Cohn, 2026, needs more optimization.
6 948 0.832076066582 Henry Cohn, 2026, needs more optimization.
6 949 0.832096944785 Henry Cohn, 2026, needs more optimization.
6 950 0.832111023559 Henry Cohn, 2026, needs more optimization.
6 952 0.832249368456 Henry Cohn, 2026, needs more optimization.
6 954 0.832256069617 Henry Cohn, 2026, needs more optimization.
6 957 0.832366725503 Henry Cohn, 2026, needs more optimization.
6 958 0.832370407715 Henry Cohn, 2026, needs more optimization.
6 959 0.832466852558 Henry Cohn, 2026, needs more optimization.
6 960 0.832495451185 Henry Cohn, 2026, needs more optimization.
6 961 0.832513737160 Henry Cohn, 2026, needs more optimization.
6 962 0.832568796324 Henry Cohn, 2026, needs more optimization.
6 963 0.832627122620 Henry Cohn, 2026, needs more optimization.
6 964 0.832684164558 Henry Cohn, 2026, needs more optimization.
6 965 0.832775002865 Henry Cohn, 2026, needs more optimization.
6 966 0.832781242728 Henry Cohn, 2026, needs more optimization.
6 967 0.832807732849 Henry Cohn, 2026, needs more optimization.
6 968 0.832876194812 Henry Cohn, 2026, needs more optimization.
6 969 0.832876974108 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
6 995 0.835147328984 Henry Cohn, 2026, needs more optimization.
6 997 0.835155366401 Henry Cohn, 2026, needs more optimization.
6 999 0.836316510208 Henry Cohn, 2026, needs more optimization.
6 1000 0.836317460813 Henry Cohn, 2026, needs more optimization.
6 1002 0.836834217372 Henry Cohn, 2026, needs more optimization.
6 1004 0.837111421018 Henry Cohn, 2026, needs more optimization.
6 1005 0.837186633187 Henry Cohn, 2026, needs more optimization.
6 1006 0.837296187052 Henry Cohn, 2026, needs more optimization.
6 1007 0.837383046645 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 0.837631503487 Henry Cohn, 2026, needs more optimization.
6 1012 0.837670486599 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 0.837936295891 Henry Cohn, 2026, needs more optimization.
6 1016 0.837942972524 Henry Cohn, 2026, 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 0.838336726890 Henry Cohn, 2026, needs more optimization.
6 1021 0.838338012976 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 0.838621068075 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 0.458141126431 Henry Cohn, 2026.
7 82 0.461219223470 Henry Cohn, 2025.
7 83 0.461669205843 Henry Cohn, 2024.
7 84 0.464981341724 Henry Cohn, 2026, needs more optimization.
7 86 0.466580867327 Henry Cohn, 2025, needs more optimization.
7 87 0.469578821552 Henry Cohn, 2024.
7 88 0.473067267884 Henry Cohn, 2024.
7 89 0.474976955660 Henry Cohn, 2026.
7 90 0.475294477919 Henry Cohn, 2024.
7 91 0.478229178177 Henry Cohn, 2026, needs more optimization.
7 92 0.480306853225 Henry Cohn, 2025.
7 93 0.481986229589 Henry Cohn, 2026, needs more optimization.
7 95 0.482130625709 Henry Cohn, 2026, needs more optimization.
7 96 0.482651330945 Henry Cohn, 2026.
7 97 0.487296284314 Henry Cohn, 2025.
7 98 0.489141129031 Henry Cohn, 2026.
7 99 0.493979786805 Henry Cohn, 2026, needs more optimization.
7 100 0.495549749737 Henry Cohn, 2026, needs more optimization.
7 101 0.496146444076 Henry Cohn, 2026, needs more optimization.
7 102 0.496644029542 Henry Cohn, 2026, needs more optimization.
7 103 0.497386916299 Henry Cohn, 2026, needs more optimization.
7 104 0.497599262312 Henry Cohn, 2026.
7 105 0.498692559408 Henry Cohn, 2026, needs more optimization.
7 106 0.498777078408 Henry Cohn, 2026, needs more optimization.
7 107 0.499130290381 Henry Cohn, 2026, needs more optimization.
7 108 0.499809013797 Henry Cohn, 2026, needs more optimization.
7 109 0.499954923872 Henry Cohn, 2026, needs more optimization.
7 110 0.499981213336 Henry Cohn, 2026, needs more optimization.
7 111 0.499999997329 Henry Cohn, 2026, needs more optimization.
7 112 0.499999997661 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 0.513834831907 Henry Cohn, 2026.
7 129 0.518758185597 Henry Cohn, 2026, needs more optimization.
7 130 0.518784543554 Henry Cohn, 2026, needs more optimization.
7 131 0.519151866069 Henry Cohn, 2026, needs more optimization.
7 132 0.519151866689 Henry Cohn, 2026, needs more optimization.
7 133 0.519151870204 Henry Cohn, 2026, needs more optimization.
7 134 0.519151870614 Henry Cohn, 2026, needs more optimization.
7 135 0.519151872163 Henry Cohn, 2026, needs more optimization.
7 136 0.519153914324 Henry Cohn, 2026, needs more optimization.
7 137 0.519751518195 Henry Cohn, 2024.
7 138 0.527218738805 Henry Cohn, 2025.
7 139 0.531596049568 Henry Cohn, 2026, needs more optimization.
7 140 0.531596084438 Henry Cohn, 2026, needs more optimization.
7 141 0.531596175137 Henry Cohn, 2026, needs more optimization.
7 142 0.531596747571 Henry Cohn, 2026, needs more optimization.
7 144 0.531669019056 Henry Cohn, 2026, needs more optimization.
7 145 0.532675341295 Henry Cohn, 2026, needs more optimization.
7 146 0.532827634323 Henry Cohn, 2026, needs more optimization.
7 147 0.533479772596 Henry Cohn, 2024.
7 148 0.533995828316 Henry Cohn, 2026.
7 149 0.546227668567 Henry Cohn, 2026, needs more optimization.
7 150 0.546227855075 Henry Cohn, 2026, needs more optimization.
7 151 0.546228013705 Henry Cohn, 2026, needs more optimization.
7 152 0.546228847327 Henry Cohn, 2026, needs more optimization.
7 153 0.546267402383 Henry Cohn, 2026, needs more optimization.
7 154 0.546280951687 Henry Cohn, 2026, needs more optimization.
7 155 0.546473223133 Henry Cohn, 2026, needs more optimization.
7 156 0.552238346566 Henry Cohn, 2026, needs more optimization.
7 157 0.557009334225 Henry Cohn, 2026, needs more optimization.
7 158 0.559633797379 Henry Cohn, 2026, needs more optimization.
7 159 0.559644236453 Henry Cohn, 2026, needs more optimization.
7 160 0.560412786814 Henry Cohn, 2026, needs more optimization.
7 161 0.560413041208 Henry Cohn, 2026, needs more optimization.
7 163 0.561660700029 Henry Cohn, 2026, needs more optimization.
7 168 0.561688600449 Henry Cohn, 2026, needs more optimization.
7 169 0.563583205369 Henry Cohn, 2026, needs more optimization.
7 170 0.563591848887 Henry Cohn, 2026, needs more optimization.
7 171 0.568981022111 Henry Cohn, 2026, needs more optimization.
7 172 0.569971783887 Henry Cohn, 2026, needs more optimization.
7 173 0.569971784570 Henry Cohn, 2026, needs more optimization.
7 174 0.569971788887 Henry Cohn, 2026, needs more optimization.
7 175 0.569971801054 Henry Cohn, 2026, needs more optimization.
7 176 0.570443884151 Henry Cohn, 2026, needs more optimization.
7 177 0.570453557788 Henry Cohn, 2026, needs more optimization.
7 178 0.570455793860 Henry Cohn, 2026, needs more optimization.
7 179 0.570549047327 Henry Cohn, 2026, needs more optimization.
7 180 0.570549101152 Henry Cohn, 2026, needs more optimization.
7 181 0.573146559703 Henry Cohn, 2026, needs more optimization.
7 182 0.577350269190 J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment. Math. 5 (1996), 139–159, https://projecteuclid.org/euclid.em/1047565645; B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly, and A. Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math. 18 (2009), 257–283, https://projecteuclid.org/euclid.em/1259158465.
3⁢x2−1
7 183 0.587486165228 Henry Cohn, 2026, needs more optimization.
7 184 0.589765669975 Henry Cohn, 2026, needs more optimization.
7 198 0.590112298788 Henry Cohn, 2026.
19⁢x3−9⁢x2−3⁢x+1
7 199 0.592916760089 Henry Cohn, 2026, needs more optimization.
7 200 0.595559146646 Henry Cohn, 2026, needs more optimization.
7 201 0.596861653357 Henry Cohn, 2026, needs more optimization.
7 202 0.599151632148 Henry Cohn, 2026, needs more optimization.
7 203 0.600871941776 Henry Cohn, 2026, needs more optimization.
7 204 0.601299950225 Henry Cohn, 2026, needs more optimization.
7 205 0.602648660108 Henry Cohn, 2026, needs more optimization.
7 206 0.603494862283 Henry Cohn, 2026, needs more optimization.
7 207 0.603919702628 Henry Cohn, 2026, needs more optimization.
7 208 0.606763550975 Henry Cohn, 2026, needs more optimization.
7 209 0.608565642267 Henry Cohn, 2026, needs more optimization.
7 210 0.611003056101 Henry Cohn, 2026, needs more optimization.
7 211 0.612977838758 Henry Cohn, 2026, needs more optimization.
7 212 0.614998295922 Henry Cohn, 2026, needs more optimization.
7 213 0.616279897529 Henry Cohn, 2026, needs more optimization.
7 214 0.617517285799 Henry Cohn, 2026, needs more optimization.
7 215 0.618366659977 Henry Cohn, 2026, needs more optimization.
7 216 0.619532430993 Henry Cohn, 2026, needs more optimization.
7 217 0.620462145149 Henry Cohn, 2026, needs more optimization.
7 218 0.621368072363 Henry Cohn, 2024, needs more optimization.
7 219 0.621875887342 Henry Cohn, 2026, needs more optimization.
7 220 0.622558843629 Henry Cohn, 2026, needs more optimization.
7 221 0.623342871721 Henry Cohn, 2026, needs more optimization.
7 222 0.624330387165 Henry Cohn, 2026, needs more optimization.
7 223 0.624821718091 Henry Cohn, 2026, needs more optimization.
7 224 0.625180925072 Henry Cohn, 2026, needs more optimization.
7 225 0.625872966956 Henry Cohn, 2024, needs more optimization.
7 226 0.627125280327 Henry Cohn, 2026, needs more optimization.
7 227 0.627339043264 Henry Cohn, 2026, needs more optimization.
7 228 0.628052208750 Henry Cohn, 2026, needs more optimization.
7 229 0.629153057879 Henry Cohn, 2026, needs more optimization.
7 230 0.629647636488 Henry Cohn, 2026, needs more optimization.
7 231 0.630481427611 Henry Cohn, 2026, needs more optimization.
7 232 0.631246727706 Henry Cohn, 2026, needs more optimization.
7 233 0.631901836958 Henry Cohn, 2024, needs more optimization.
7 234 0.632516489950 Henry Cohn, 2026, needs more optimization.
7 235 0.633010303713 Henry Cohn, 2026, needs more optimization.
7 236 0.633843322950 Henry Cohn, 2026, needs more optimization.
7 237 0.634225597288 Henry Cohn, 2026, needs more optimization.
7 238 0.634654813102 Henry Cohn, 2026, needs more optimization.
7 239 0.635356766795 Henry Cohn, 2024, needs more optimization.
7 240 0.635658800258 Henry Cohn, 2026, needs more optimization.
7 241 0.636574622746 Henry Cohn, 2026, needs more optimization.
7 242 0.636910879847 Henry Cohn, 2026, needs more optimization.
7 243 0.637505092172 Henry Cohn, 2026, needs more optimization.
7 244 0.638074544159 Henry Cohn, 2026, needs more optimization.
7 245 0.638570510921 Henry Cohn, 2026, needs more optimization.
7 246 0.638764807854 Henry Cohn, 2026, needs more optimization.
7 247 0.639330225406 Henry Cohn, 2026, needs more optimization.
7 248 0.640032640832 Henry Cohn, 2026, needs more optimization.
7 249 0.640342667067 Henry Cohn, 2026, needs more optimization.
7 250 0.640818440770 Henry Cohn, 2026, needs more optimization.
7 251 0.641150733822 Henry Cohn, 2026, needs more optimization.
7 252 0.641612435026 Henry Cohn, 2026, needs more optimization.
7 253 0.641863048850 Henry Cohn, 2026, needs more optimization.
7 254 0.642223860685 Henry Cohn, 2026, needs more optimization.
7 255 0.642915011423 Henry Cohn, 2026, needs more optimization.
7 256 0.643605637033 Henry Cohn, 2026, needs more optimization.
7 257 0.644259631314 Henry Cohn, 2026, needs more optimization.
7 258 0.644645132278 Henry Cohn, 2026, needs more optimization.
7 259 0.645125507060 Henry Cohn, 2026, needs more optimization.
7 260 0.645626516686 Henry Cohn, 2026, needs more optimization.
7 261 0.645658195687 Henry Cohn, 2026, needs more optimization.
7 262 0.646033877885 Henry Cohn, 2026, needs more optimization.
7 263 0.646756819710 Henry Cohn, 2026, needs more optimization.
7 264 0.647297735912 Henry Cohn, 2026, needs more optimization.
7 265 0.648068259133 Henry Cohn, 2026, needs more optimization.
7 266 0.648347731329 Henry Cohn, 2026, needs more optimization.
7 267 0.648840865244 Henry Cohn, 2026, needs more optimization.
7 268 0.649117344986 Henry Cohn, 2026, needs more optimization.
7 269 0.649436293310 Henry Cohn, 2026, needs more optimization.
7 270 0.649744577381 Henry Cohn, 2026, needs more optimization.
7 271 0.650140293437 Henry Cohn, 2026, needs more optimization.
7 272 0.650471890777 Henry Cohn, 2026, needs more optimization.
7 273 0.650888925789 Henry Cohn, 2026, needs more optimization.
7 274 0.651364224153 Henry Cohn, 2026, needs more optimization.
7 275 0.651639755753 Henry Cohn, 2026, needs more optimization.
7 276 0.651930717104 Henry Cohn, 2026, needs more optimization.
7 277 0.652290236435 Henry Cohn, 2026, needs more optimization.
7 278 0.653059895809 Henry Cohn, 2026, needs more optimization.
7 279 0.653531633329 Henry Cohn, 2026, needs more optimization.
7 280 0.653848191136 Henry Cohn, 2026, needs more optimization.
7 281 0.654246811179 Henry Cohn, 2026, needs more optimization.
7 282 0.654854717540 Henry Cohn, 2026, needs more optimization.
7 283 0.655302409427 Henry Cohn, 2026, needs more optimization.
7 284 0.655832213649 Henry Cohn, 2026, needs more optimization.
7 285 0.656367014280 Henry Cohn, 2026, needs more optimization.
7 286 0.656835658238 Henry Cohn, 2026, needs more optimization.
7 287 0.657327561040 Henry Cohn, 2026, needs more optimization.
7 288 0.657534747696 Henry Cohn, 2026, needs more optimization.
7 289 0.657971668693 Henry Cohn, 2026, needs more optimization.
7 290 0.658434278219 Henry Cohn, 2026, needs more optimization.
7 291 0.658827631103 Henry Cohn, 2026, needs more optimization.
7 292 0.659216676839 Henry Cohn, 2026, needs more optimization.
7 293 0.659660916650 Henry Cohn, 2026, needs more optimization.
7 294 0.660002582538 Henry Cohn, 2026, needs more optimization.
7 295 0.660440880927 Henry Cohn, 2026, needs more optimization.
7 296 0.660903714935 Henry Cohn, 2026, needs more optimization.
7 297 0.661204583733 Henry Cohn, 2026, needs more optimization.
7 298 0.661736502396 Henry Cohn, 2026, needs more optimization.
7 299 0.662353441729 Henry Cohn, 2026, needs more optimization.
7 300 0.662622691641 Henry Cohn, 2026, needs more optimization.
7 301 0.662928432550 Henry Cohn, 2026, needs more optimization.
7 302 0.663251996083 Henry Cohn, 2026, needs more optimization.
7 303 0.663934324988 Henry Cohn, 2026, needs more optimization.
7 304 0.664327094267 Henry Cohn, 2026, needs more optimization.
7 305 0.664329559543 Henry Cohn, 2026, needs more optimization.
7 306 0.664476113843 Henry Cohn, 2026, needs more optimization.
7 307 0.665082951854 Henry Cohn, 2026, needs more optimization.
7 308 0.665456388324 Henry Cohn, 2026, needs more optimization.
7 309 0.665887093467 Henry Cohn, 2026, needs more optimization.
7 310 0.666322360080 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 0.668524326903 Henry Cohn, 2026, needs more optimization.
7 360 0.669371544227 Henry Cohn, 2026, needs more optimization.
7 361 0.669636472182 Henry Cohn, 2026, needs more optimization.
7 362 0.670193201027 Henry Cohn, 2026, needs more optimization.
7 363 0.670774549510 Henry Cohn, 2026, needs more optimization.
7 364 0.671309711657 Henry Cohn, 2026, needs more optimization.
7 365 0.671898860242 Henry Cohn, 2026, needs more optimization.
7 366 0.672441370985 Henry Cohn, 2026, needs more optimization.
7 367 0.673025160868 Henry Cohn, 2026, needs more optimization.
7 368 0.673293028716 Henry Cohn, 2026, needs more optimization.
7 369 0.674262046214 Henry Cohn, 2026, needs more optimization.
7 370 0.674279573114 Henry Cohn, 2026, needs more optimization.
7 371 0.675097119581 Henry Cohn, 2026, needs more optimization.
7 372 0.675574455753 Henry Cohn, 2026, needs more optimization.
7 373 0.676091601167 Henry Cohn, 2026, needs more optimization.
7 374 0.676562159807 Henry Cohn, 2026, needs more optimization.
7 375 0.676946028480 Henry Cohn, 2026, needs more optimization.
7 376 0.676956636015 Henry Cohn, 2026, needs more optimization.
7 377 0.676964611036 Henry Cohn, 2026, needs more optimization.
7 378 0.676972169154 Henry Cohn, 2026, needs more optimization.
7 379 0.676984669655 Henry Cohn, 2026, needs more optimization.
7 380 0.677009245425 Henry Cohn, 2026, needs more optimization.
7 381 0.677325855910 Henry Cohn, 2026, needs more optimization.
7 382 0.677327153003 Henry Cohn, 2026, needs more optimization.
7 383 0.677805208640 Henry Cohn, 2026, needs more optimization.
7 384 0.678296163997 Henry Cohn, 2026, needs more optimization.
7 385 0.679000760966 Henry Cohn, 2026, needs more optimization.
7 386 0.679627918508 Henry Cohn, 2026, needs more optimization.
7 387 0.679973911580 Henry Cohn, 2026, needs more optimization.
7 388 0.680191012487 Henry Cohn, 2026, needs more optimization.
7 389 0.680618273140 Henry Cohn, 2026, needs more optimization.
7 393 0.680685472089 Henry Cohn, 2026, needs more optimization.
7 394 0.680972941551 Henry Cohn, 2026, needs more optimization.
7 395 0.681054844841 Henry Cohn, 2026, needs more optimization.
7 396 0.681299208828 Henry Cohn, 2026, needs more optimization.
7 397 0.681757776376 Henry Cohn, 2026, needs more optimization.
7 398 0.682503532488 Henry Cohn, 2026, needs more optimization.
7 399 0.682871396738 Henry Cohn, 2026, needs more optimization.
7 402 0.682963701083 Henry Cohn, 2026, needs more optimization.
7 403 0.683033414387 Henry Cohn, 2026, needs more optimization.
7 404 0.683045793851 Henry Cohn, 2026, needs more optimization.
7 405 0.683049466644 Henry Cohn, 2026, needs more optimization.
7 406 0.683142970997 Henry Cohn, 2026, needs more optimization.
7 407 0.683151694244 Henry Cohn, 2026, needs more optimization.
7 408 0.683338125883 Henry Cohn, 2026, needs more optimization.
7 410 0.683626788902 Henry Cohn, 2026, needs more optimization.
7 411 0.683864550035 Henry Cohn, 2026, needs more optimization.
7 412 0.684041729939 Henry Cohn, 2026, needs more optimization.
7 413 0.684621661110 Henry Cohn, 2026, needs more optimization.
7 414 0.685110235717 Henry Cohn, 2026, needs more optimization.
7 415 0.685610272737 Henry Cohn, 2026, needs more optimization.
7 416 0.685962470077 Henry Cohn, 2026, needs more optimization.
7 417 0.686079037172 Henry Cohn, 2026, needs more optimization.
7 418 0.686615495882 Henry Cohn, 2026, needs more optimization.
7 419 0.687010848138 Henry Cohn, 2026, needs more optimization.
7 420 0.687216088036 Henry Cohn, 2026, needs more optimization.
7 421 0.687727242494 Henry Cohn, 2026, needs more optimization.
7 422 0.688498360281 Henry Cohn, 2026, needs more optimization.
7 423 0.688722212010 Henry Cohn, 2026, needs more optimization.
7 424 0.689142035266 Henry Cohn, 2026, needs more optimization.
7 425 0.689434926683 Henry Cohn, 2026, needs more optimization.
7 426 0.689787441876 Henry Cohn, 2026, needs more optimization.
7 427 0.690377312762 Henry Cohn, 2026, needs more optimization.
7 428 0.690620452442 Henry Cohn, 2026, needs more optimization.
7 429 0.691167981515 Henry Cohn, 2026, needs more optimization.
7 430 0.691276906999 Henry Cohn, 2026, needs more optimization.
7 431 0.691665056853 Henry Cohn, 2026, needs more optimization.
7 432 0.692339574197 Henry Cohn, 2026, needs more optimization.
7 433 0.692803977036 Henry Cohn, 2026, needs more optimization.
7 434 0.693529526336 Henry Cohn, 2026, needs more optimization.
7 435 0.693963298123 Henry Cohn, 2026, needs more optimization.
7 436 0.694496320157 Henry Cohn, 2026, needs more optimization.
7 437 0.694862963810 Henry Cohn, 2026, needs more optimization.
7 438 0.695169473139 Henry Cohn, 2026, needs more optimization.
7 439 0.695583918429 Henry Cohn, 2026, needs more optimization.
7 440 0.696109982328 Henry Cohn, 2026, needs more optimization.
7 441 0.696693092836 Henry Cohn, 2026, needs more optimization.
7 442 0.697059025696 Henry Cohn, 2026, needs more optimization.
7 443 0.697326083912 Henry Cohn, 2026, needs more optimization.
7 444 0.697515366373 Henry Cohn, 2026, needs more optimization.
7 445 0.697607669487 Henry Cohn, 2026, needs more optimization.
7 446 0.697897481913 Henry Cohn, 2026, needs more optimization.
7 447 0.698444859257 Henry Cohn, 2026, needs more optimization.
7 448 0.698787005056 Henry Cohn, 2026, needs more optimization.
7 449 0.699265478664 Henry Cohn, 2026, needs more optimization.
7 450 0.699818775823 Henry Cohn, 2026, needs more optimization.
7 451 0.700101957381 Henry Cohn, 2026, needs more optimization.
7 452 0.700504694101 Henry Cohn, 2026, needs more optimization.
7 453 0.700745471899 Henry Cohn, 2026, needs more optimization.
7 454 0.701078126055 Henry Cohn, 2026, needs more optimization.
7 455 0.701430327278 Henry Cohn, 2026, needs more optimization.
7 456 0.701669477266 Henry Cohn, 2026, needs more optimization.
7 457 0.702151008412 Henry Cohn, 2026, needs more optimization.
7 458 0.702511173180 Henry Cohn, 2026, needs more optimization.
7 459 0.702807591075 Henry Cohn, 2026, needs more optimization.
7 460 0.703016199131 Henry Cohn, 2026, needs more optimization.
7 461 0.703580519744 Henry Cohn, 2026, needs more optimization.
7 462 0.703962097455 Henry Cohn, 2026, needs more optimization.
7 463 0.704354793318 Henry Cohn, 2026, needs more optimization.
7 464 0.704638759869 Henry Cohn, 2026, needs more optimization.
7 465 0.704793600650 Henry Cohn, 2026, needs more optimization.
7 466 0.705200742761 Henry Cohn, 2026, needs more optimization.
7 467 0.705392724540 Henry Cohn, 2026, needs more optimization.
7 468 0.705734458748 Henry Cohn, 2026, needs more optimization.
7 469 0.705802289054 Henry Cohn, 2026, needs more optimization.
7 470 0.705942970928 Henry Cohn, 2026, needs more optimization.
7 471 0.706016187145 Henry Cohn, 2026, needs more optimization.
7 472 0.706133859945 Henry Cohn, 2026, needs more optimization.
7 473 0.706253004530 Henry Cohn, 2026, needs more optimization.
7 474 0.706529578586 Henry Cohn, 2026, needs more optimization.
7 475 0.706860210792 Henry Cohn, 2026, needs more optimization.
7 476 0.706911471883 Henry Cohn, 2026, needs more optimization.
7 477 0.707070536562 Henry Cohn, 2026, needs more optimization.
7 478 0.707489830656 Henry Cohn, 2026, needs more optimization.
7 479 0.707548759321 Henry Cohn, 2026, needs more optimization.
7 480 0.707557525023 Henry Cohn, 2026, needs more optimization.
7 481 0.707587125804 Henry Cohn, 2026, needs more optimization.
7 484 0.707652541548 Henry Cohn, 2026, needs more optimization.
7 485 0.707677614345 Henry Cohn, 2026, needs more optimization.
7 486 0.707840307776 Henry Cohn, 2026, needs more optimization.
7 487 0.707874779200 Henry Cohn, 2026, needs more optimization.
7 488 0.707939201966 Henry Cohn, 2026, needs more optimization.
7 489 0.708005886935 Henry Cohn, 2026, needs more optimization.
7 490 0.708062246886 Henry Cohn, 2026, needs more optimization.
7 492 0.708200751300 Henry Cohn, 2026, needs more optimization.
7 493 0.708446331581 Henry Cohn, 2026, needs more optimization.
7 494 0.708885870539 Henry Cohn, 2026, needs more optimization.
7 496 0.709128346343 Henry Cohn, 2026, needs more optimization.
7 497 0.709174259472 Henry Cohn, 2026, needs more optimization.
7 498 0.709284852269 Henry Cohn, 2026, needs more optimization.
7 499 0.709984927894 Henry Cohn, 2026, needs more optimization.
7 500 0.710383025800 Henry Cohn, 2026, needs more optimization.
7 501 0.710428233900 Henry Cohn, 2026, needs more optimization.
7 502 0.710439333278 Henry Cohn, 2026, needs more optimization.
7 503 0.710515544842 Henry Cohn, 2026, needs more optimization.
7 505 0.710943514527 Henry Cohn, 2026, needs more optimization.
7 506 0.710993121463 Henry Cohn, 2026, needs more optimization.
7 507 0.711089194173 Henry Cohn, 2026, needs more optimization.
7 508 0.711117236502 Henry Cohn, 2026, needs more optimization.
7 509 0.711211641738 Henry Cohn, 2026, needs more optimization.
7 510 0.711309849926 Henry Cohn, 2026, needs more optimization.
7 511 0.711382059546 Henry Cohn, 2026, needs more optimization.
7 512 0.711476617059 Henry Cohn, 2026, needs more optimization.
7 515 0.712190732802 Henry Cohn, 2026, needs more optimization.
7 516 0.712197121184 Henry Cohn, 2026, needs more optimization.
7 517 0.712230011698 Henry Cohn, 2026, needs more optimization.
7 518 0.712361475042 Henry Cohn, 2026, needs more optimization.
7 519 0.712394334636 Henry Cohn, 2026, needs more optimization.
7 520 0.712566989012 Henry Cohn, 2026, needs more optimization.
7 527 0.713166347666 Henry Cohn, 2026, needs more optimization.
7 529 0.713180315763 Henry Cohn, 2026, needs more optimization.
7 530 0.713348795711 Henry Cohn, 2026, needs more optimization.
7 531 0.713420834604 Henry Cohn, 2026, needs more optimization.
7 532 0.713429114484 Henry Cohn, 2026, needs more optimization.
7 534 0.713473854395 Henry Cohn, 2026, needs more optimization.
7 536 0.713520778316 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 0.718317265354 Henry Cohn, 2026, needs more optimization.
7 634 0.720028789887 Henry Cohn, 2026, needs more optimization.
7 635 0.721192316541 Henry Cohn, 2026, needs more optimization.
7 636 0.722272203714 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 0.725515318614 Henry Cohn, 2026, needs more optimization.
7 642 0.726062360200 Henry Cohn, 2026, needs more optimization.
7 643 0.726419686186 Henry Cohn, 2026, needs more optimization.
7 644 0.726767117196 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 0.727899087191 Henry Cohn, 2026, needs more optimization.
7 648 0.728313923635 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 0.731381460630 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 0.734592193720 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 0.735521894406 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 0.738033404082 Henry Cohn, 2026, needs more optimization.
7 689 0.738048439406 Henry Cohn, 2026, needs more optimization.
7 691 0.738425625823 Henry Cohn, 2026, needs more optimization.
7 696 0.738426648094 Henry Cohn, 2026, needs more optimization.
7 697 0.738428868419 Henry Cohn, 2026, needs more optimization.
7 699 0.738740293225 Henry Cohn, 2026, needs more optimization.
7 700 0.738811796808 Henry Cohn, 2026, needs more optimization.
7 701 0.739159962564 Henry Cohn, 2026, needs more optimization.
7 702 0.739345043151 Henry Cohn, 2026, needs more optimization.
7 703 0.740305530555 Henry Cohn, 2026, needs more optimization.
7 705 0.740350019833 Henry Cohn, 2026, needs more optimization.
7 708 0.740516964642 Henry Cohn, 2026, needs more optimization.
7 709 0.740586501092 Henry Cohn, 2026, needs more optimization.
7 714 0.740937358221 Henry Cohn, 2026, needs more optimization.
7 719 0.744965652452 Henry Cohn, 2026, needs more optimization.
7 720 0.744968722629 Henry Cohn, 2026, needs more optimization.
7 725 0.745022316508 Henry Cohn, 2026, needs more optimization.
7 730 0.745023961776 Henry Cohn, 2026, needs more optimization.
7 733 0.745195535562 Henry Cohn, 2026, needs more optimization.
7 734 0.749228386848 Henry Cohn, 2026, needs more optimization.
7 735 0.749344630087 Henry Cohn, 2026, needs more optimization.
7 736 0.749544035840 Henry Cohn, 2026, needs more optimization.
7 737 0.749730507760 Henry Cohn, 2026, needs more optimization.
7 738 0.749887073685 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 0.756664645873 Henry Cohn, 2026, needs more optimization.
7 884 0.766415181652 Henry Cohn, 2026, needs more optimization.
7 886 0.766523286556 Henry Cohn, 2026, 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 0.767013917614 Henry Cohn, 2026, needs more optimization.
7 891 0.767082538566 Henry Cohn, 2026, needs more optimization.
7 892 0.767227993104 Henry Cohn, 2026, needs more optimization.
7 893 0.767247696882 Henry Cohn, 2026, needs more optimization.
7 894 0.767252272567 Henry Cohn, 2026, needs more optimization.
7 895 0.767387374914 Henry Cohn, 2026, needs more optimization.
7 896 0.767398491459 Henry Cohn, 2026, needs more optimization.
7 897 0.767677656297 Henry Cohn, 2026, needs more optimization.
7 898 0.767731229371 Henry Cohn, 2026, needs more optimization.
7 899 0.767733011695 Henry Cohn, 2026, needs more optimization.
7 900 0.767809065227 Henry Cohn, 2026, needs more optimization.
7 901 0.768008794983 Henry Cohn, 2026, needs more optimization.
7 902 0.768008833185 Henry Cohn, 2026, needs more optimization.
7 903 0.768134002938 Henry Cohn, 2026, needs more optimization.
7 904 0.768134077399 Henry Cohn, 2026, needs more optimization.
7 905 0.768345236940 Henry Cohn, 2026, needs more optimization.
7 906 0.768384689590 Henry Cohn, 2026, needs more optimization.
7 907 0.768514203211 Henry Cohn, 2026, needs more optimization.
7 908 0.768576497220 Henry Cohn, 2026, needs more optimization.
7 909 0.768709531783 Henry Cohn, 2026, needs more optimization.
7 910 0.768735288169 Henry Cohn, 2026, needs more optimization.
7 911 0.768767032740 Henry Cohn, 2026, needs more optimization.
7 913 0.768953215880 Henry Cohn, 2026, needs more optimization.
7 914 0.768955393906 Henry Cohn, 2026, needs more optimization.
7 915 0.769187741688 Henry Cohn, 2026, needs more optimization.
7 916 0.769191238789 Henry Cohn, 2026, needs more optimization.
7 917 0.769200393090 Henry Cohn, 2026, needs more optimization.
7 918 0.769528626245 Henry Cohn, 2026, needs more optimization.
7 919 0.769532051549 Henry Cohn, 2026, needs more optimization.
7 920 0.769696745050 Henry Cohn, 2026, needs more optimization.
7 921 0.769706695485 Henry Cohn, 2026, needs more optimization.
7 922 0.769875603159 Henry Cohn, 2026, needs more optimization.
7 923 0.769903571307 Henry Cohn, 2026, needs more optimization.
7 924 0.769919758491 Henry Cohn, 2026, needs more optimization.
7 925 0.769960195618 Henry Cohn, 2026, needs more optimization.
7 926 0.769994747633 Henry Cohn, 2026, needs more optimization.
7 927 0.770118986682 Henry Cohn, 2026, needs more optimization.
7 928 0.770251943130 Henry Cohn, 2026, needs more optimization.
7 929 0.770255364563 Henry Cohn, 2026, needs more optimization.
7 930 0.770298030729 Henry Cohn, 2026, needs more optimization.
7 931 0.770575401025 Henry Cohn, 2026, needs more optimization.
7 932 0.770575402692 Henry Cohn, 2026, needs more optimization.
7 933 0.770591440036 Henry Cohn, 2026, needs more optimization.
7 934 0.770626503767 Henry Cohn, 2026, needs more optimization.
7 935 0.770770123599 Henry Cohn, 2026, needs more optimization.
7 936 0.770895281273 Henry Cohn, 2026, needs more optimization.
7 937 0.770895331526 Henry Cohn, 2026, needs more optimization.
7 938 0.771162055906 Henry Cohn, 2026, needs more optimization.
7 939 0.771165078352 Henry Cohn, 2026, 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 0.771354748169 Henry Cohn, 2026, needs more optimization.
7 944 0.771499371592 Henry Cohn, 2026, needs more optimization.
7 945 0.771518466502 Henry Cohn, 2026, needs more optimization.
7 946 0.771739019676 Henry Cohn, 2026, needs more optimization.
7 948 0.771745218075 Henry Cohn, 2026, 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 0.772119402709 Henry Cohn, 2026, 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 0.772591939932 Henry Cohn, 2026, needs more optimization.
7 957 0.772597302979 Henry Cohn, 2026, needs more optimization.
7 958 0.772735313726 Henry Cohn, 2026, needs more optimization.
7 959 0.772735506889 Henry Cohn, 2026, 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 0.773157562321 Henry Cohn, 2026, needs more optimization.
7 964 0.773196782886 Henry Cohn, 2026, needs more optimization.
7 965 0.773197086427 Henry Cohn, 2026, needs more optimization.
7 966 0.773217318052 Henry Cohn, 2026, needs more optimization.
7 967 0.773310420734 Henry Cohn, 2026, needs more optimization.
7 968 0.773530825192 Henry Cohn, 2026, 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 0.773818412149 Henry Cohn, 2026, needs more optimization.
7 972 0.773823609936 Henry Cohn, 2026, needs more optimization.
7 973 0.773830638619 Henry Cohn, 2026, 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 0.774175392552 Henry Cohn, 2026, needs more optimization.
7 977 0.774221215285 Henry Cohn, 2026, needs more optimization.
7 978 0.774227302076 Henry Cohn, 2026, 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 0.774485841129 Henry Cohn, 2026, needs more optimization.
7 982 0.774495818164 Henry Cohn, 2026, needs more optimization.
7 983 0.774644331561 Henry Cohn, 2026, needs more optimization.
7 984 0.774751767921 Henry Cohn, 2026, needs more optimization.
7 985 0.774751938692 Henry Cohn, 2026, needs more optimization.
7 986 0.774770181472 Henry Cohn, 2026, needs more optimization.
7 987 0.774871634708 Henry Cohn, 2026, needs more optimization.
7 988 0.775037192668 Henry Cohn, 2026, needs more optimization.
7 989 0.775060031414 Henry Cohn, 2026, needs more optimization.
7 990 0.775264694900 Henry Cohn, 2026, needs more optimization.
7 991 0.775271333912 Henry Cohn, 2026, needs more optimization.
7 992 0.775420098701 Henry Cohn, 2026, needs more optimization.
7 993 0.775426420725 Henry Cohn, 2026, needs more optimization.
7 994 0.775447201412 Henry Cohn, 2026, needs more optimization.
7 995 0.775628224505 Henry Cohn, 2026, needs more optimization.
7 996 0.775669217867 Henry Cohn, 2026, needs more optimization.
7 997 0.775700632283 Henry Cohn, 2026, needs more optimization.
7 998 0.775766305076 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 0.776020705846 Henry Cohn, 2026, needs more optimization.
7 1002 0.776032594402 Henry Cohn, 2026, needs more optimization.
7 1003 0.776172348939 Henry Cohn, 2026, needs more optimization.
7 1004 0.776180768294 Henry Cohn, 2026, needs more optimization.
7 1005 0.776322338583 Henry Cohn, 2026, needs more optimization.
7 1006 0.776376075236 Henry Cohn, 2026, needs more optimization.
7 1007 0.776421473630 Henry Cohn, 2026, needs more optimization.
7 1008 0.776749718759 Henry Cohn, 2026, needs more optimization.
7 1009 0.776754250145 Henry Cohn, 2026, needs more optimization.
7 1010 0.776791148616 Henry Cohn, 2026, needs more optimization.
7 1012 0.776974728344 Henry Cohn, 2026, needs more optimization.
7 1013 0.777156565391 Henry Cohn, 2026, needs more optimization.
7 1014 0.777175819587 Henry Cohn, 2026, 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 0.777357532292 Henry Cohn, 2026, needs more optimization.
7 1018 0.777404326867 Henry Cohn, 2026, needs more optimization.
7 1019 0.777478741294 Henry Cohn, 2026, needs more optimization.
7 1020 0.777807760317 Henry Cohn, 2026, needs more optimization.
7 1021 0.777823328724 Henry Cohn, 2026, needs more optimization.
7 1022 0.777986944126 Henry Cohn, 2026, needs more optimization.
7 1023 0.777989432909 Henry Cohn, 2026, needs more optimization.
7 1024 0.778003501240 Henry Cohn, 2026, needs more optimization.
8 17 0.087733463324 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
288⁢x3−64⁢x2−8⁢x+1
8 18 0.099469572709 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
8 19 0.111409975027 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 20 0.119496866688 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
224⁢x3+60⁢x2−2⁢x−1
8 21 0.130601937482 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
28⁢x2+4⁢x−1
8 22 0.130601937482 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
28⁢x2+4⁢x−1
8 23 0.157169941990 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
Minimal polynomial listed in plain text data
8 24 0.157692144940 J. Wang, Finding and investigating exact spherical codes, Experiment. Math. 18 (2009), 249–256, https://projecteuclid.org/euclid.em/1259158434.
4⁢x4−4⁢x3−27⁢x2−2⁢x+1
8 25 0.164334174126 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 26 0.172652095036 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 27 0.179856457059 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
Minimal polynomial listed in plain text data
8 28 0.181158420022 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
36⁢x4+24⁢x3−36⁢x2+1
8 29 0.187922490077 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 30 0.203916279404 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 31 0.219706528517 H. Cohn, Small spherical and projective codes, data set, updated 2024, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
8 32 0.227325452024 H. Cohn, Small spherical and projective codes, data set, updated 2023, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
95⁢x2−4⁢x−4
8 33 0.227325452024 Henry Cohn, 2023.
95⁢x2−4⁢x−4
8 34 0.233864616950 Henry Cohn, 2023.
26887680⁢x6+11003904⁢x5−444096⁢x4−594432⁢x3−55800⁢x2−480⁢x−1
8 35 0.236461100794 Henry Cohn, 2023.
4⁢x4+8⁢x3−20⁢x2+1
8 38 0.239920745566 Henry Cohn, 2023.
1088⁢x4−80⁢x2+1
8 39 0.243600150512 Henry Cohn, 2023.
1183744⁢x8+122880⁢x7−575488⁢x6−138240⁢x5+53632⁢x4+14976⁢x3−1568⁢x2−720⁢x+81
8 40 0.265121155593 Henry Cohn, 2025.
8 41 0.269588854450 Henry Cohn, 2025.
8 42 0.276791074187 Henry Cohn, 2023.
8 43 0.285155668748 Henry Cohn, 2025.
8 44 0.288883351523 Henry Cohn, 2026.
8 45 0.293504048474 Henry Cohn, 2025.
8 46 0.298271343353 Henry Cohn, 2025.
8 47 0.301070997037 Henry Cohn, 2025.
8 48 0.306796780995 Henry Cohn, 2025.
8 49 0.310558546149 Henry Cohn, 2025.
8 50 0.315283655377 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 0.403992525071 Henry Cohn, 2026.
8 84 0.405589808949 Henry Cohn, 2026.
8 85 0.413778833762 Henry Cohn, 2025.
8 86 0.416817234155 Henry Cohn, 2026.
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 0.423342112264 Henry Cohn, 2026.
8 93 0.425292127537 Henry Cohn, 2026.
8 94 0.425568012577 Henry Cohn, 2026.
8 95 0.426690121416 Henry Cohn, 2026, needs more optimization.
8 96 0.427338933990 Henry Cohn, 2026.
8 97 0.428526010827 Henry Cohn, 2025.
8 99 0.428564490087 Henry Cohn, 2025.
8 100 0.428571238429 Henry Cohn, 2026, needs more optimization.
8 101 0.428571426315 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 0.447581842171 Henry Cohn, 2026, needs more optimization.
8 116 0.448006674268 Henry Cohn, 2026.
8 117 0.451867492073 Henry Cohn, 2026.
8 118 0.455245746618 Henry Cohn, 2026, needs more optimization.
8 119 0.461332409553 Henry Cohn, 2026, needs more optimization.
8 120 0.461619716207 Henry Cohn, 2026, needs more optimization.
8 121 0.461664940377 Henry Cohn, 2026, needs more optimization.
8 122 0.461887938841 Henry Cohn, 2026, needs more optimization.
8 123 0.462147328730 Henry Cohn, 2026, needs more optimization.
8 124 0.462508226704 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 0.467418206723 Henry Cohn, 2026, needs more optimization.
8 139 0.468665486317 Henry Cohn, 2026, needs more optimization.
8 140 0.470795847712 Henry Cohn, 2026, needs more optimization.
8 141 0.472529422117 Henry Cohn, 2026, needs more optimization.
8 142 0.476422471285 Henry Cohn, 2026, needs more optimization.
8 143 0.476461758967 Henry Cohn, 2026, needs more optimization.
8 144 0.482739621918 Henry Cohn, 2026, needs more optimization.
8 145 0.485585244145 Henry Cohn, 2026, needs more optimization.
8 146 0.488030775373 Henry Cohn, 2026, needs more optimization.
8 147 0.488158592354 Henry Cohn, 2026, needs more optimization.
8 148 0.488571578120 Henry Cohn, 2026, needs more optimization.
8 149 0.489646670945 Henry Cohn, 2026, needs more optimization.
8 150 0.489673088491 Henry Cohn, 2026, needs more optimization.
8 151 0.490671101615 Henry Cohn, 2026, needs more optimization.
8 152 0.491497070093 Henry Cohn, 2026, needs more optimization.
8 153 0.492433618650 Henry Cohn, 2026, needs more optimization.
8 154 0.492641314470 Henry Cohn, 2026, needs more optimization.
8 155 0.493022791992 Henry Cohn, 2026, needs more optimization.
8 156 0.493419402413 Henry Cohn, 2026, needs more optimization.
8 157 0.493611135228 Henry Cohn, 2026, needs more optimization.
8 158 0.494294111648 Henry Cohn, 2026, needs more optimization.
8 159 0.494360989217 Henry Cohn, 2026, needs more optimization.
8 160 0.495474828388 Henry Cohn, 2026, needs more optimization.
8 161 0.496380292879 Henry Cohn, 2026, needs more optimization.
8 162 0.496386422266 Henry Cohn, 2026, needs more optimization.
8 163 0.496832357620 Henry Cohn, 2026, needs more optimization.
8 164 0.497029800553 Henry Cohn, 2026, needs more optimization.
8 166 0.497178479235 Henry Cohn, 2026, needs more optimization.
8 167 0.498016740267 Henry Cohn, 2026, needs more optimization.
8 168 0.498102604948 Henry Cohn, 2026, needs more optimization.
8 169 0.498250039205 Henry Cohn, 2026, needs more optimization.
8 170 0.498787131848 Henry Cohn, 2026, needs more optimization.
8 171 0.499117966144 Henry Cohn, 2026, needs more optimization.
8 172 0.499269248628 Henry Cohn, 2026, needs more optimization.
8 173 0.499489153293 Henry Cohn, 2026, needs more optimization.
8 174 0.499730655327 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 0.544152550356 Henry Cohn, 2026, needs more optimization.
8 243 0.547321909761 Henry Cohn, 2026, needs more optimization.
8 244 0.549404554136 Henry Cohn, 2026, needs more optimization.
8 245 0.551506937718 Henry Cohn, 2026, needs more optimization.
8 246 0.553445397988 Henry Cohn, 2026, needs more optimization.
8 247 0.555292467783 Henry Cohn, 2026, needs more optimization.
8 248 0.557108913844 Henry Cohn, 2026, needs more optimization.
8 249 0.559174293235 Henry Cohn, 2026, needs more optimization.
8 250 0.560485913855 Henry Cohn, 2026, needs more optimization.
8 251 0.561372013377 Henry Cohn, 2026, needs more optimization.
8 252 0.562684715696 Henry Cohn, 2026, needs more optimization.
8 253 0.564114583851 Henry Cohn, 2026, needs more optimization.
8 254 0.564224257552 Henry Cohn, 2026, needs more optimization.
8 255 0.564249155025 Henry Cohn, 2026, needs more optimization.
8 256 0.564581895510 Henry Cohn, 2026, needs more optimization.
8 257 0.564975330689 Henry Cohn, 2026, needs more optimization.
8 258 0.566633040300 Henry Cohn, 2026, needs more optimization.
8 259 0.568555385504 Henry Cohn, 2026, needs more optimization.
8 260 0.568616286071 Henry Cohn, 2026, needs more optimization.
8 261 0.569474413871 Henry Cohn, 2026, needs more optimization.
8 262 0.570036283730 Henry Cohn, 2026, needs more optimization.
8 263 0.571107453287 Henry Cohn, 2026, needs more optimization.
8 264 0.571411225426 Henry Cohn, 2026, needs more optimization.
8 265 0.572182355107 Henry Cohn, 2026, needs more optimization.
8 266 0.572627799395 Henry Cohn, 2026, needs more optimization.
8 267 0.573379129891 Henry Cohn, 2026, needs more optimization.
8 268 0.573583849050 Henry Cohn, 2026, needs more optimization.
8 269 0.574359307921 Henry Cohn, 2026, needs more optimization.
8 270 0.574627466701 Henry Cohn, 2026, needs more optimization.
8 271 0.575530809086 Henry Cohn, 2026, needs more optimization.
8 272 0.576390319284 Henry Cohn, 2026, needs more optimization.
8 273 0.577175122048 Henry Cohn, 2026, needs more optimization.
8 274 0.577466758817 Henry Cohn, 2026, needs more optimization.
8 275 0.577889756854 Henry Cohn, 2026, needs more optimization.
8 276 0.578735523009 Henry Cohn, 2026, needs more optimization.
8 277 0.579506061097 Henry Cohn, 2026, needs more optimization.
8 278 0.579959045145 Henry Cohn, 2026, needs more optimization.
8 279 0.580718689661 Henry Cohn, 2026, needs more optimization.
8 280 0.581396640480 Henry Cohn, 2026, needs more optimization.
8 281 0.581540805812 Henry Cohn, 2026, needs more optimization.
8 282 0.582275550124 Henry Cohn, 2026, needs more optimization.
8 283 0.582807345567 Henry Cohn, 2026, needs more optimization.
8 284 0.582836629087 Henry Cohn, 2026, needs more optimization.
8 285 0.584370594451 Henry Cohn, 2026, needs more optimization.
8 286 0.584417597583 Henry Cohn, 2026, needs more optimization.
8 288 0.584450149969 Henry Cohn, 2026, needs more optimization.
8 289 0.585028579817 Henry Cohn, 2026, needs more optimization.
8 290 0.585254785488 Henry Cohn, 2026, needs more optimization.
8 291 0.586204684358 Henry Cohn, 2026, needs more optimization.
8 292 0.586643761783 Henry Cohn, 2026, needs more optimization.
8 293 0.586654592344 Henry Cohn, 2026, needs more optimization.
8 294 0.586748194284 Henry Cohn, 2026, needs more optimization.
8 295 0.588118517620 Henry Cohn, 2026, needs more optimization.
8 296 0.588207316444 Henry Cohn, 2026, needs more optimization.
8 297 0.589646507074 Henry Cohn, 2026, needs more optimization.
8 300 0.590534306049 Henry Cohn, 2026, needs more optimization.
8 301 0.590554976569 Henry Cohn, 2026, needs more optimization.
8 302 0.590576187048 Henry Cohn, 2026, needs more optimization.
8 303 0.590584677564 Henry Cohn, 2026, needs more optimization.
8 304 0.590598229191 Henry Cohn, 2026, needs more optimization.
8 305 0.590647740454 Henry Cohn, 2026, needs more optimization.
8 306 0.590700045081 Henry Cohn, 2026, needs more optimization.
8 307 0.590776394487 Henry Cohn, 2026, needs more optimization.
8 309 0.590985501490 Henry Cohn, 2026, needs more optimization.
8 310 0.591759663902 Henry Cohn, 2026, needs more optimization.
8 311 0.592711220717 Henry Cohn, 2026, needs more optimization.
8 312 0.593724137257 Henry Cohn, 2026, needs more optimization.
8 313 0.594311633868 Henry Cohn, 2026, needs more optimization.
8 314 0.594431326633 Henry Cohn, 2026, needs more optimization.
8 315 0.594753834671 Henry Cohn, 2026, needs more optimization.
8 316 0.594786810232 Henry Cohn, 2026, needs more optimization.
8 317 0.595146151755 Henry Cohn, 2026, needs more optimization.
8 318 0.595172668407 Henry Cohn, 2026, needs more optimization.
8 319 0.595281168119 Henry Cohn, 2026, needs more optimization.
8 320 0.595813655331 Henry Cohn, 2026, needs more optimization.
8 321 0.596368338815 Henry Cohn, 2026, needs more optimization.
8 322 0.597020095021 Henry Cohn, 2026, needs more optimization.
8 323 0.597607185620 Henry Cohn, 2026, needs more optimization.
8 324 0.598054212093 Henry Cohn, 2026, needs more optimization.
8 325 0.598659645582 Henry Cohn, 2026, needs more optimization.
8 326 0.599045565723 Henry Cohn, 2026, needs more optimization.
8 327 0.599977020827 Henry Cohn, 2026, needs more optimization.
8 328 0.600380325861 Henry Cohn, 2026, needs more optimization.
8 329 0.600659747876 Henry Cohn, 2026, needs more optimization.
8 330 0.600685076211 Henry Cohn, 2026, needs more optimization.
8 331 0.600919067057 Henry Cohn, 2026, needs more optimization.
8 332 0.600930747177 Henry Cohn, 2026, needs more optimization.
8 333 0.601667876662 Henry Cohn, 2026, needs more optimization.
8 334 0.601900348346 Henry Cohn, 2026, needs more optimization.
8 335 0.602175565310 Henry Cohn, 2026, needs more optimization.
8 336 0.602794059673 Henry Cohn, 2026, needs more optimization.
8 337 0.603078372567 Henry Cohn, 2026, needs more optimization.
8 338 0.603396801450 Henry Cohn, 2026, needs more optimization.
8 339 0.603490507949 Henry Cohn, 2026, needs more optimization.
8 340 0.603705674327 Henry Cohn, 2026, needs more optimization.
8 342 0.603921244037 Henry Cohn, 2026, needs more optimization.
8 343 0.604265904514 Henry Cohn, 2026, needs more optimization.
8 344 0.604348072668 Henry Cohn, 2026, needs more optimization.
8 345 0.604487286969 Henry Cohn, 2026, needs more optimization.
8 348 0.604503281212 Henry Cohn, 2026, needs more optimization.
8 349 0.604515562481 Henry Cohn, 2026, needs more optimization.
8 350 0.604526733534 Henry Cohn, 2026, needs more optimization.
8 351 0.604533145639 Henry Cohn, 2026, needs more optimization.
8 352 0.604549808144 Henry Cohn, 2026, needs more optimization.
8 353 0.604549814650 Henry Cohn, 2026, needs more optimization.
8 354 0.604555192274 Henry Cohn, 2026, needs more optimization.
8 355 0.604711733224 Henry Cohn, 2026, needs more optimization.
8 356 0.606397933292 Henry Cohn, 2026, needs more optimization.
8 357 0.606595125920 Henry Cohn, 2026, needs more optimization.
8 358 0.606836254590 Henry Cohn, 2026, needs more optimization.
8 360 0.607069220095 Henry Cohn, 2026, needs more optimization.
8 361 0.615035574813 Henry Cohn, 2026, needs more optimization.
8 362 0.615297974258 Henry Cohn, 2026, needs more optimization.
8 363 0.615368922880 Henry Cohn, 2026, needs more optimization.
8 364 0.615569691823 Henry Cohn, 2026, needs more optimization.
8 365 0.616309481819 Henry Cohn, 2026, needs more optimization.
8 366 0.616702299721 Henry Cohn, 2026, needs more optimization.
8 367 0.617137486830 Henry Cohn, 2026, needs more optimization.
8 368 0.617168829188 Henry Cohn, 2026, needs more optimization.
8 369 0.617226244290 Henry Cohn, 2026, needs more optimization.
8 370 0.617803404265 Henry Cohn, 2026, needs more optimization.
8 371 0.618663111825 Henry Cohn, 2026, needs more optimization.
8 372 0.619028742695 Henry Cohn, 2026, needs more optimization.
8 373 0.619515381463 Henry Cohn, 2026, needs more optimization.
8 374 0.619970258925 Henry Cohn, 2026, needs more optimization.
8 375 0.620709018259 Henry Cohn, 2026, needs more optimization.
8 376 0.621569128611 Henry Cohn, 2026, needs more optimization.
8 377 0.622362370149 Henry Cohn, 2026, needs more optimization.
8 378 0.622633182274 Henry Cohn, 2026, needs more optimization.
8 379 0.623195924184 Henry Cohn, 2026, needs more optimization.
8 380 0.623543786768 Henry Cohn, 2026, needs more optimization.
8 381 0.624184425673 Henry Cohn, 2026, needs more optimization.
8 382 0.624737111534 Henry Cohn, 2026, needs more optimization.
8 383 0.624909908722 Henry Cohn, 2026, needs more optimization.
8 384 0.625063228904 Henry Cohn, 2026, needs more optimization.
8 385 0.625477053593 Henry Cohn, 2026, needs more optimization.
8 386 0.625783128652 Henry Cohn, 2026, needs more optimization.
8 387 0.625950602614 Henry Cohn, 2026, needs more optimization.
8 388 0.626428079277 Henry Cohn, 2026, needs more optimization.
8 389 0.626855368622 Henry Cohn, 2026, needs more optimization.
8 390 0.627194547267 Henry Cohn, 2026, needs more optimization.
8 391 0.627661566129 Henry Cohn, 2026, needs more optimization.
8 392 0.628064392948 Henry Cohn, 2026, needs more optimization.
8 393 0.628189558289 Henry Cohn, 2026, needs more optimization.
8 394 0.628343938249 Henry Cohn, 2026, needs more optimization.
8 395 0.628643205771 Henry Cohn, 2026, needs more optimization.
8 396 0.629057357686 Henry Cohn, 2026, needs more optimization.
8 397 0.629136628571 Henry Cohn, 2026, needs more optimization.
8 398 0.629548570122 Henry Cohn, 2026, needs more optimization.
8 399 0.629878786938 Henry Cohn, 2026, needs more optimization.
8 400 0.630165680647 Henry Cohn, 2026, needs more optimization.
8 401 0.630353679398 Henry Cohn, 2026, needs more optimization.
8 402 0.630589864164 Henry Cohn, 2026, needs more optimization.
8 403 0.630819482066 Henry Cohn, 2026, needs more optimization.
8 404 0.631505497594 Henry Cohn, 2026, needs more optimization.
8 405 0.632009728717 Henry Cohn, 2026, needs more optimization.
8 406 0.632091563101 Henry Cohn, 2026, needs more optimization.
8 407 0.632339327345 Henry Cohn, 2026, needs more optimization.
8 408 0.632622628991 Henry Cohn, 2026, needs more optimization.
8 409 0.632765350887 Henry Cohn, 2026, needs more optimization.
8 410 0.633090363141 Henry Cohn, 2026, needs more optimization.
8 411 0.633356891351 Henry Cohn, 2026, needs more optimization.
8 412 0.633655800688 Henry Cohn, 2026, needs more optimization.
8 413 0.633923853844 Henry Cohn, 2026, needs more optimization.
8 414 0.634138260711 Henry Cohn, 2026, needs more optimization.
8 415 0.634372856018 Henry Cohn, 2026, needs more optimization.
8 416 0.634702204352 Henry Cohn, 2026, needs more optimization.
8 417 0.634800408551 Henry Cohn, 2026, needs more optimization.
8 418 0.634867901262 Henry Cohn, 2026, needs more optimization.
8 419 0.635002426058 Henry Cohn, 2026, needs more optimization.
8 420 0.635098354434 Henry Cohn, 2026, needs more optimization.
8 421 0.635251759240 Henry Cohn, 2026, needs more optimization.
8 422 0.635731150550 Henry Cohn, 2026, needs more optimization.
8 423 0.635767523529 Henry Cohn, 2026, needs more optimization.
8 424 0.636036835583 Henry Cohn, 2026, needs more optimization.
8 425 0.636112310897 Henry Cohn, 2026, needs more optimization.
8 426 0.636209175201 Henry Cohn, 2026, needs more optimization.
8 427 0.636445849671 Henry Cohn, 2026, needs more optimization.
8 428 0.636543012822 Henry Cohn, 2026, needs more optimization.
8 430 0.636925922965 Henry Cohn, 2026, needs more optimization.
8 431 0.637229334005 Henry Cohn, 2026, needs more optimization.
8 432 0.637319394986 Henry Cohn, 2026, needs more optimization.
8 433 0.637692974085 Henry Cohn, 2026, needs more optimization.
8 434 0.637972124956 Henry Cohn, 2026, needs more optimization.
8 435 0.638239708321 Henry Cohn, 2026, needs more optimization.
8 436 0.638480361058 Henry Cohn, 2026, needs more optimization.
8 437 0.638826708749 Henry Cohn, 2026, needs more optimization.
8 438 0.639281435385 Henry Cohn, 2026, needs more optimization.
8 439 0.639530689631 Henry Cohn, 2026, needs more optimization.
8 440 0.639645095552 Henry Cohn, 2026, needs more optimization.
8 441 0.639743079969 Henry Cohn, 2026, needs more optimization.
8 442 0.639965433917 Henry Cohn, 2026, needs more optimization.
8 444 0.640186095480 Henry Cohn, 2026, needs more optimization.
8 445 0.640380513718 Henry Cohn, 2026, needs more optimization.
8 446 0.640638935784 Henry Cohn, 2026, needs more optimization.
8 447 0.640935027849 Henry Cohn, 2026, needs more optimization.
8 448 0.641219342332 Henry Cohn, 2026, needs more optimization.
8 449 0.641516701335 Henry Cohn, 2026, needs more optimization.
8 450 0.641546314516 Henry Cohn, 2026, needs more optimization.
8 451 0.641563980936 Henry Cohn, 2026, needs more optimization.
8 452 0.641581346731 Henry Cohn, 2026, needs more optimization.
8 453 0.641661063170 Henry Cohn, 2026, needs more optimization.
8 454 0.641709280019 Henry Cohn, 2026, needs more optimization.
8 455 0.641755984715 Henry Cohn, 2026, needs more optimization.
8 456 0.641919983005 Henry Cohn, 2026, needs more optimization.
8 457 0.641981935646 Henry Cohn, 2026, needs more optimization.
8 458 0.642006411545 Henry Cohn, 2026, needs more optimization.
8 459 0.642007741900 Henry Cohn, 2026, needs more optimization.
8 460 0.642094607298 Henry Cohn, 2026, needs more optimization.
8 461 0.642139874022 Henry Cohn, 2026, needs more optimization.
8 462 0.642193881551 Henry Cohn, 2026, needs more optimization.
8 463 0.642274166237 Henry Cohn, 2026, needs more optimization.
8 464 0.642317110032 Henry Cohn, 2026, needs more optimization.
8 465 0.642408854730 Henry Cohn, 2026, needs more optimization.
8 466 0.642562063962 Henry Cohn, 2026, needs more optimization.
8 467 0.642700709972 Henry Cohn, 2026, needs more optimization.
8 468 0.642939648729 Henry Cohn, 2026, needs more optimization.
8 469 0.643137322527 Henry Cohn, 2026, needs more optimization.
8 470 0.643315063401 Henry Cohn, 2026, needs more optimization.
8 471 0.643492957876 Henry Cohn, 2026, needs more optimization.
8 472 0.643662698834 Henry Cohn, 2026, needs more optimization.
8 473 0.643829759763 Henry Cohn, 2026, needs more optimization.
8 474 0.643843983724 Henry Cohn, 2026, needs more optimization.
8 475 0.644065034728 Henry Cohn, 2026, needs more optimization.
8 476 0.644208074293 Henry Cohn, 2026, needs more optimization.
8 477 0.644358569102 Henry Cohn, 2026, needs more optimization.
8 478 0.644665574083 Henry Cohn, 2026, needs more optimization.
8 479 0.644788308564 Henry Cohn, 2026, needs more optimization.
8 480 0.645252901831 Henry Cohn, 2026, needs more optimization.
8 481 0.645399147712 Henry Cohn, 2026, needs more optimization.
8 482 0.645563752791 Henry Cohn, 2026, needs more optimization.
8 483 0.645638474515 Henry Cohn, 2026, needs more optimization.
8 484 0.646179409330 Henry Cohn, 2026, needs more optimization.
8 485 0.646399627706 Henry Cohn, 2026, needs more optimization.
8 486 0.646824436258 Henry Cohn, 2026, needs more optimization.
8 487 0.647274675730 Henry Cohn, 2026, needs more optimization.
8 488 0.647391773657 Henry Cohn, 2026, needs more optimization.
8 489 0.647422664843 Henry Cohn, 2026, needs more optimization.
8 490 0.647746061764 Henry Cohn, 2026, needs more optimization.
8 491 0.648014292054 Henry Cohn, 2026, needs more optimization.
8 492 0.648482104428 Henry Cohn, 2026, needs more optimization.
8 493 0.648785847970 Henry Cohn, 2026, needs more optimization.
8 494 0.649081277669 Henry Cohn, 2026, needs more optimization.
8 496 0.649083687090 Henry Cohn, 2026, needs more optimization.
8 497 0.649160130207 Henry Cohn, 2026, needs more optimization.
8 498 0.649187484716 Henry Cohn, 2026, needs more optimization.
8 499 0.649395524055 Henry Cohn, 2026, needs more optimization.
8 500 0.649646311245 Henry Cohn, 2026, needs more optimization.
8 501 0.650034863231 Henry Cohn, 2026, needs more optimization.
8 503 0.650244449751 Henry Cohn, 2026, needs more optimization.
8 504 0.650352824140 Henry Cohn, 2026, needs more optimization.
8 505 0.650424615206 Henry Cohn, 2026, needs more optimization.
8 506 0.651023277842 Henry Cohn, 2026, needs more optimization.
8 507 0.651488772124 Henry Cohn, 2026, needs more optimization.
8 508 0.651605620119 Henry Cohn, 2026, needs more optimization.
8 509 0.651810395122 Henry Cohn, 2026, needs more optimization.
8 510 0.652116983273 Henry Cohn, 2026, needs more optimization.
8 511 0.652194582674 Henry Cohn, 2026, needs more optimization.
8 512 0.652240549745 Henry Cohn, 2026, needs more optimization.
8 513 0.652403112156 Henry Cohn, 2026, needs more optimization.
8 515 0.652442214055 Henry Cohn, 2026, needs more optimization.
8 516 0.652723229139 Henry Cohn, 2026, needs more optimization.
8 517 0.652830311711 Henry Cohn, 2026, needs more optimization.
8 518 0.653060912756 Henry Cohn, 2026, needs more optimization.
8 519 0.653310870234 Henry Cohn, 2026, needs more optimization.
8 520 0.653669709613 Henry Cohn, 2026, needs more optimization.
8 521 0.653803057214 Henry Cohn, 2026, needs more optimization.
8 522 0.654356486869 Henry Cohn, 2026, needs more optimization.
8 523 0.654791605250 Henry Cohn, 2026, needs more optimization.
8 524 0.654906001171 Henry Cohn, 2026, needs more optimization.
8 525 0.655231581346 Henry Cohn, 2026, needs more optimization.
8 526 0.655416149425 Henry Cohn, 2026, needs more optimization.
8 527 0.655579159343 Henry Cohn, 2026, needs more optimization.
8 528 0.655804067455 Henry Cohn, 2026, needs more optimization.
8 529 0.655996700068 Henry Cohn, 2026, needs more optimization.
8 530 0.656291158030 Henry Cohn, 2026, needs more optimization.
8 532 0.656461467059 Henry Cohn, 2026, needs more optimization.
8 533 0.656499125593 Henry Cohn, 2026, needs more optimization.
8 534 0.656528605291 Henry Cohn, 2026, needs more optimization.
8 535 0.656805830150 Henry Cohn, 2026, needs more optimization.
8 536 0.657120480960 Henry Cohn, 2026, needs more optimization.
8 537 0.657171852003 Henry Cohn, 2026, needs more optimization.
8 538 0.657363950911 Henry Cohn, 2026, needs more optimization.
8 539 0.657528444504 Henry Cohn, 2026, needs more optimization.
8 540 0.657863222764 Henry Cohn, 2026, needs more optimization.
8 542 0.658040326792 Henry Cohn, 2026, needs more optimization.
8 543 0.658333774611 Henry Cohn, 2026, needs more optimization.
8 544 0.658659158307 Henry Cohn, 2026, needs more optimization.
8 545 0.658881317538 Henry Cohn, 2026, needs more optimization.
8 546 0.659022239856 Henry Cohn, 2026, needs more optimization.
8 547 0.659357199056 Henry Cohn, 2026, needs more optimization.
8 548 0.659555883532 Henry Cohn, 2026, needs more optimization.
8 550 0.659645257345 Henry Cohn, 2026, needs more optimization.
8 551 0.659978855199 Henry Cohn, 2026, needs more optimization.
8 552 0.660513853614 Henry Cohn, 2026, needs more optimization.
8 553 0.660643203480 Henry Cohn, 2026, needs more optimization.
8 554 0.660786727055 Henry Cohn, 2026, needs more optimization.
8 555 0.660881511420 Henry Cohn, 2026, needs more optimization.
8 556 0.661124515927 Henry Cohn, 2026, needs more optimization.
8 557 0.661277063533 Henry Cohn, 2026, needs more optimization.
8 558 0.661421001938 Henry Cohn, 2026, needs more optimization.
8 559 0.661764388162 Henry Cohn, 2026, needs more optimization.
8 560 0.661972949073 Henry Cohn, 2026, needs more optimization.
8 561 0.662111220159 Henry Cohn, 2026, needs more optimization.
8 562 0.662375014752 Henry Cohn, 2026, needs more optimization.
8 563 0.662552610526 Henry Cohn, 2026, needs more optimization.
8 564 0.662663479583 Henry Cohn, 2026, needs more optimization.
8 566 0.662790222330 Henry Cohn, 2026, needs more optimization.
8 567 0.662856586155 Henry Cohn, 2026, needs more optimization.
8 568 0.662952426372 Henry Cohn, 2026, needs more optimization.
8 569 0.663192669691 Henry Cohn, 2026, needs more optimization.
8 570 0.663207717048 Henry Cohn, 2026, needs more optimization.
8 571 0.663352730899 Henry Cohn, 2026, needs more optimization.
8 572 0.663595874938 Henry Cohn, 2026, needs more optimization.
8 573 0.663610961919 Henry Cohn, 2026, needs more optimization.
8 574 0.663842480877 Henry Cohn, 2026, needs more optimization.
8 575 0.663973266149 Henry Cohn, 2026, needs more optimization.
8 576 0.664110642118 Henry Cohn, 2026, needs more optimization.
8 577 0.664176143562 Henry Cohn, 2026, needs more optimization.
8 578 0.664215836085 Henry Cohn, 2026, needs more optimization.
8 580 0.664450851107 Henry Cohn, 2026, needs more optimization.
8 581 0.664591890274 Henry Cohn, 2026, needs more optimization.
8 582 0.664646487178 Henry Cohn, 2026, needs more optimization.
8 583 0.664833345957 Henry Cohn, 2026, needs more optimization.
8 584 0.664848372227 Henry Cohn, 2026, needs more optimization.
8 585 0.664909918139 Henry Cohn, 2026, needs more optimization.
8 586 0.664933686756 Henry Cohn, 2026, needs more optimization.
8 587 0.665046347881 Henry Cohn, 2026, needs more optimization.
8 588 0.665123466805 Henry Cohn, 2026, needs more optimization.
8 589 0.665250543714 Henry Cohn, 2026, needs more optimization.
8 591 0.665456715870 Henry Cohn, 2026, needs more optimization.
8 592 0.665492590715 Henry Cohn, 2026, needs more optimization.
8 593 0.665509950957 Henry Cohn, 2026, needs more optimization.
8 596 0.665519552795 Henry Cohn, 2026, needs more optimization.
8 598 0.665533200319 Henry Cohn, 2026, needs more optimization.
8 599 0.665545111538 Henry Cohn, 2026, needs more optimization.
8 601 0.665565994531 Henry Cohn, 2026, needs more optimization.
8 602 0.665588568045 Henry Cohn, 2026, needs more optimization.
8 603 0.665616527972 Henry Cohn, 2026, needs more optimization.
8 604 0.665653020096 Henry Cohn, 2026, needs more optimization.
8 605 0.665660030935 Henry Cohn, 2026, needs more optimization.
8 606 0.665714219958 Henry Cohn, 2026, needs more optimization.
8 607 0.665748754309 Henry Cohn, 2026, needs more optimization.
8 611 0.665786918779 Henry Cohn, 2026, needs more optimization.
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8 619 0.665941854073 Henry Cohn, 2026, needs more optimization.
8 620 0.665977674436 Henry Cohn, 2026, needs more optimization.
8 621 0.666024250258 Henry Cohn, 2026, needs more optimization.
8 622 0.666034329958 Henry Cohn, 2026, needs more optimization.
8 623 0.666046791580 Henry Cohn, 2026, needs more optimization.
8 624 0.666094106771 Henry Cohn, 2026, needs more optimization.
8 625 0.666180769432 Henry Cohn, 2026, needs more optimization.
8 626 0.666227631614 Henry Cohn, 2026, needs more optimization.
8 627 0.666254677493 Henry Cohn, 2026, needs more optimization.
8 628 0.666319546889 Henry Cohn, 2026, needs more optimization.
8 629 0.666375987569 Henry Cohn, 2026, needs more optimization.
8 630 0.666433008260 Henry Cohn, 2026, needs more optimization.
8 631 0.666474742709 Henry Cohn, 2026, needs more optimization.
8 632 0.666569997051 Henry Cohn, 2026, needs more optimization.
8 633 0.666645243475 Henry Cohn, 2026, needs more optimization.
8 634 0.666772482764 Henry Cohn, 2026, needs more optimization.
8 635 0.667084160808 Henry Cohn, 2026, needs more optimization.
8 636 0.667230386345 Henry Cohn, 2026, needs more optimization.
8 637 0.667291262223 Henry Cohn, 2026, needs more optimization.
8 638 0.667420863166 Henry Cohn, 2026, needs more optimization.
8 639 0.667464599104 Henry Cohn, 2026, needs more optimization.
8 640 0.667525188207 Henry Cohn, 2026, needs more optimization.
8 641 0.667530803583 Henry Cohn, 2026, needs more optimization.
8 642 0.667875247052 Henry Cohn, 2026, needs more optimization.
8 643 0.668075009958 Henry Cohn, 2026, needs more optimization.
8 644 0.668424038733 Henry Cohn, 2026, needs more optimization.
8 646 0.668630973177 Henry Cohn, 2026, needs more optimization.
8 650 0.668832333855 Henry Cohn, 2026, needs more optimization.
8 651 0.668896523811 Henry Cohn, 2026, needs more optimization.
8 654 0.668914596800 Henry Cohn, 2026, needs more optimization.
8 655 0.668999435820 Henry Cohn, 2026, needs more optimization.
8 657 0.669270831580 Henry Cohn, 2026, needs more optimization.
8 660 0.669328404960 Henry Cohn, 2026, needs more optimization.
8 663 0.669408989414 Henry Cohn, 2026, needs more optimization.
8 664 0.669572509045 Henry Cohn, 2026, needs more optimization.
8 665 0.669686886327 Henry Cohn, 2026, needs more optimization.
8 666 0.670024530133 Henry Cohn, 2026, needs more optimization.
8 667 0.670097775813 Henry Cohn, 2026, needs more optimization.
8 668 0.670351105852 Henry Cohn, 2026, needs more optimization.
8 669 0.670582375453 Henry Cohn, 2026, needs more optimization.
8 670 0.670709194764 Henry Cohn, 2026, needs more optimization.
8 671 0.670938691379 Henry Cohn, 2026, needs more optimization.
8 672 0.671046544446 Henry Cohn, 2026, needs more optimization.
8 673 0.671320718711 Henry Cohn, 2026, needs more optimization.
8 674 0.671729498798 Henry Cohn, 2026, needs more optimization.
8 675 0.672116527926 Henry Cohn, 2026, needs more optimization.
8 676 0.672172744832 Henry Cohn, 2026, needs more optimization.
8 677 0.672650633670 Henry Cohn, 2026, needs more optimization.
8 678 0.672995735763 Henry Cohn, 2026, needs more optimization.
8 679 0.673282000632 Henry Cohn, 2026, needs more optimization.
8 680 0.673552071197 Henry Cohn, 2026, needs more optimization.
8 681 0.673572852720 Henry Cohn, 2026, needs more optimization.
8 683 0.673578228527 Henry Cohn, 2026, needs more optimization.
8 684 0.673625591665 Henry Cohn, 2026, needs more optimization.
8 685 0.674208367684 Henry Cohn, 2026, needs more optimization.
8 686 0.674319570317 Henry Cohn, 2026, needs more optimization.
8 687 0.674699333291 Henry Cohn, 2026, needs more optimization.
8 688 0.675053608975 Henry Cohn, 2026, needs more optimization.
8 689 0.675382939446 Henry Cohn, 2026, needs more optimization.
8 690 0.675648872238 Henry Cohn, 2026, needs more optimization.
8 691 0.676272399369 Henry Cohn, 2026, needs more optimization.
8 692 0.676532144055 Henry Cohn, 2026, needs more optimization.
8 693 0.677095689478 Henry Cohn, 2026, needs more optimization.
8 694 0.677720847558 Henry Cohn, 2026, needs more optimization.
8 695 0.677721573610 Henry Cohn, 2026, needs more optimization.
8 696 0.677807974217 Henry Cohn, 2026, needs more optimization.
8 697 0.678009376252 Henry Cohn, 2026, needs more optimization.
8 698 0.678400188852 Henry Cohn, 2026, needs more optimization.
8 699 0.678723450176 Henry Cohn, 2026, needs more optimization.
8 700 0.679032486427 Henry Cohn, 2026, needs more optimization.
8 701 0.679287881901 Henry Cohn, 2026, needs more optimization.
8 702 0.679519789807 Henry Cohn, 2026, needs more optimization.
8 703 0.679972253463 Henry Cohn, 2026, needs more optimization.
8 704 0.680291923658 Henry Cohn, 2026, needs more optimization.
8 705 0.680573879222 Henry Cohn, 2026, needs more optimization.
8 706 0.680696881527 Henry Cohn, 2026, needs more optimization.
8 707 0.680728957791 Henry Cohn, 2026, needs more optimization.
8 708 0.680821837391 Henry Cohn, 2026, needs more optimization.
8 709 0.681157668822 Henry Cohn, 2026, needs more optimization.
8 710 0.681627514502 Henry Cohn, 2026, needs more optimization.
8 711 0.681965264985 Henry Cohn, 2026, needs more optimization.
8 712 0.682034698838 Henry Cohn, 2026, needs more optimization.
8 713 0.682171551071 Henry Cohn, 2026, needs more optimization.
8 714 0.682639584877 Henry Cohn, 2026, needs more optimization.
8 715 0.682650584460 Henry Cohn, 2026, needs more optimization.
8 716 0.683176823760 Henry Cohn, 2026, needs more optimization.
8 717 0.683341759275 Henry Cohn, 2026, needs more optimization.
8 719 0.683763923922 Henry Cohn, 2026, needs more optimization.
8 720 0.684072121390 Henry Cohn, 2026, needs more optimization.
8 721 0.684202840763 Henry Cohn, 2026, needs more optimization.
8 722 0.684389984931 Henry Cohn, 2026, needs more optimization.
8 723 0.684494164407 Henry Cohn, 2026, needs more optimization.
8 724 0.684733088462 Henry Cohn, 2026, needs more optimization.
8 725 0.685116665502 Henry Cohn, 2026, needs more optimization.
8 726 0.685343041708 Henry Cohn, 2026, needs more optimization.
8 727 0.685548781612 Henry Cohn, 2026, needs more optimization.
8 728 0.685674149258 Henry Cohn, 2026, needs more optimization.
8 729 0.685993548386 Henry Cohn, 2026, needs more optimization.
8 730 0.686290644700 Henry Cohn, 2026, needs more optimization.
8 731 0.686458947986 Henry Cohn, 2026, needs more optimization.
8 732 0.686648668405 Henry Cohn, 2026, needs more optimization.
8 733 0.686865794529 Henry Cohn, 2026, needs more optimization.
8 734 0.687107886144 Henry Cohn, 2026, needs more optimization.
8 735 0.687415846788 Henry Cohn, 2026, needs more optimization.
8 736 0.687589593585 Henry Cohn, 2026, needs more optimization.
8 737 0.687716710497 Henry Cohn, 2026, needs more optimization.
8 738 0.687832329126 Henry Cohn, 2026, needs more optimization.
8 739 0.687919729846 Henry Cohn, 2026, needs more optimization.
8 740 0.688060226452 Henry Cohn, 2026, needs more optimization.
8 741 0.688234895699 Henry Cohn, 2026, needs more optimization.
8 742 0.688358479286 Henry Cohn, 2026, needs more optimization.
8 743 0.688608515104 Henry Cohn, 2026, needs more optimization.
8 744 0.688609621632 Henry Cohn, 2026, needs more optimization.
8 745 0.688860650970 Henry Cohn, 2026, needs more optimization.
8 746 0.689020481632 Henry Cohn, 2026, needs more optimization.
8 747 0.689093799993 Henry Cohn, 2026, needs more optimization.
8 748 0.689302183612 Henry Cohn, 2026, needs more optimization.
8 749 0.689456204164 Henry Cohn, 2026, needs more optimization.
8 750 0.689519084764 Henry Cohn, 2026, needs more optimization.
8 751 0.689643639916 Henry Cohn, 2026, needs more optimization.
8 752 0.690036170780 Henry Cohn, 2026, needs more optimization.
8 753 0.690155771987 Henry Cohn, 2026, needs more optimization.
8 754 0.690244211107 Henry Cohn, 2026, needs more optimization.
8 755 0.690248948270 Henry Cohn, 2026, needs more optimization.
8 756 0.690249084645 Henry Cohn, 2026, needs more optimization.
8 757 0.690255799119 Henry Cohn, 2026, needs more optimization.
8 758 0.690262523985 Henry Cohn, 2026, needs more optimization.
8 759 0.690269070376 Henry Cohn, 2026, needs more optimization.
8 760 0.690269106308 Henry Cohn, 2026, needs more optimization.
8 763 0.690327084912 Henry Cohn, 2026, needs more optimization.
8 764 0.691030307594 Henry Cohn, 2026, needs more optimization.
8 765 0.691068492094 Henry Cohn, 2026, needs more optimization.
8 766 0.691078581489 Henry Cohn, 2026, needs more optimization.
8 767 0.691228867482 Henry Cohn, 2026, needs more optimization.
8 768 0.691414954836 Henry Cohn, 2026, needs more optimization.
8 769 0.691494688377 Henry Cohn, 2026, needs more optimization.
8 770 0.691688680229 Henry Cohn, 2026, needs more optimization.
8 772 0.691752608419 Henry Cohn, 2026, needs more optimization.
8 773 0.691766097902 Henry Cohn, 2026, needs more optimization.
8 774 0.691842552989 Henry Cohn, 2026, needs more optimization.
8 775 0.691910904406 Henry Cohn, 2026, needs more optimization.
8 776 0.692385686476 Henry Cohn, 2026, needs more optimization.
8 777 0.692435015184 Henry Cohn, 2026, needs more optimization.
8 778 0.692576340752 Henry Cohn, 2026, needs more optimization.
8 780 0.692648940286 Henry Cohn, 2026, needs more optimization.
8 781 0.692657873215 Henry Cohn, 2026, needs more optimization.
8 782 0.692681697429 Henry Cohn, 2026, needs more optimization.
8 783 0.692772776135 Henry Cohn, 2026, needs more optimization.
8 784 0.692813504199 Henry Cohn, 2026, needs more optimization.
8 785 0.693346607812 Henry Cohn, 2026, needs more optimization.
8 786 0.693681206435 Henry Cohn, 2026, needs more optimization.
8 787 0.693801972779 Henry Cohn, 2026, needs more optimization.
8 788 0.693812228250 Henry Cohn, 2026, needs more optimization.
8 789 0.694266147106 Henry Cohn, 2026, needs more optimization.
8 790 0.694290331953 Henry Cohn, 2026, needs more optimization.
8 791 0.694296770093 Henry Cohn, 2026, needs more optimization.
8 792 0.694312351532 Henry Cohn, 2026, needs more optimization.
8 794 0.694656585845 Henry Cohn, 2026, needs more optimization.
8 795 0.694697311708 Henry Cohn, 2026, needs more optimization.
8 797 0.694708272228 Henry Cohn, 2026, needs more optimization.
8 799 0.694905811217 Henry Cohn, 2026, needs more optimization.
8 800 0.695325995160 Henry Cohn, 2026, needs more optimization.
8 801 0.695377084442 Henry Cohn, 2026, needs more optimization.
8 802 0.695647683856 Henry Cohn, 2026, needs more optimization.
8 803 0.695697198733 Henry Cohn, 2026, needs more optimization.
8 804 0.696071301614 Henry Cohn, 2026, needs more optimization.
8 805 0.696401640756 Henry Cohn, 2026, needs more optimization.
8 806 0.696414561462 Henry Cohn, 2026, needs more optimization.
8 807 0.696422076848 Henry Cohn, 2026, needs more optimization.
8 808 0.696444764266 Henry Cohn, 2026, needs more optimization.
8 809 0.696487691862 Henry Cohn, 2026, needs more optimization.
8 810 0.696521885117 Henry Cohn, 2026, needs more optimization.
8 812 0.696768197284 Henry Cohn, 2026, needs more optimization.
8 813 0.696919738079 Henry Cohn, 2026, needs more optimization.
8 814 0.697605672382 Henry Cohn, 2026, needs more optimization.
8 815 0.697605728528 Henry Cohn, 2026, needs more optimization.
8 817 0.697619071368 Henry Cohn, 2026, needs more optimization.
8 818 0.697629344751 Henry Cohn, 2026, needs more optimization.
8 819 0.697650340279 Henry Cohn, 2026, needs more optimization.
8 820 0.697729151666 Henry Cohn, 2026, 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 0.698103569066 Henry Cohn, 2026, needs more optimization.
8 824 0.698151216442 Henry Cohn, 2026, needs more optimization.
8 825 0.698163591895 Henry Cohn, 2026, needs more optimization.
8 826 0.698261511031 Henry Cohn, 2026, needs more optimization.
8 827 0.698675149318 Henry Cohn, 2026, needs more optimization.
8 828 0.698675407166 Henry Cohn, 2026, needs more optimization.
8 829 0.698693214335 Henry Cohn, 2026, needs more optimization.
8 830 0.699221891715 Henry Cohn, 2026, needs more optimization.
8 831 0.699222026413 Henry Cohn, 2026, needs more optimization.
8 832 0.699222146455 Henry Cohn, 2026, needs more optimization.
8 833 0.699222407491 Henry Cohn, 2026, needs more optimization.
8 834 0.699230804215 Henry Cohn, 2026, needs more optimization.
8 835 0.699533746117 Henry Cohn, 2026, needs more optimization.
8 836 0.699971143101 Henry Cohn, 2026, needs more optimization.
8 837 0.699971169402 Henry Cohn, 2026, needs more optimization.
8 838 0.699971241042 Henry Cohn, 2026, needs more optimization.
8 839 0.699982877422 Henry Cohn, 2026, needs more optimization.
8 840 0.700046926137 Henry Cohn, 2026, needs more optimization.
8 842 0.700535494509 Henry Cohn, 2026, needs more optimization.
8 844 0.700573175497 Henry Cohn, 2026, needs more optimization.
8 845 0.700575988068 Henry Cohn, 2026, needs more optimization.
8 846 0.700576092469 Henry Cohn, 2026, needs more optimization.
8 847 0.700578751344 Henry Cohn, 2026, needs more optimization.
8 848 0.700783071915 Henry Cohn, 2026, needs more optimization.
8 850 0.701188603218 Henry Cohn, 2026, needs more optimization.
8 851 0.701197714656 Henry Cohn, 2026, needs more optimization.
8 852 0.701295181675 Henry Cohn, 2026, needs more optimization.
8 853 0.701619124692 Henry Cohn, 2026, needs more optimization.
8 854 0.701640706236 Henry Cohn, 2026, needs more optimization.
8 855 0.702133356533 Henry Cohn, 2026, needs more optimization.
8 856 0.702133450285 Henry Cohn, 2026, needs more optimization.
8 857 0.702134073912 Henry Cohn, 2026, needs more optimization.
8 858 0.702158024689 Henry Cohn, 2026, needs more optimization.
8 859 0.702361464710 Henry Cohn, 2026, needs more optimization.
8 861 0.702632917745 Henry Cohn, 2026, needs more optimization.
8 863 0.703041731278 Henry Cohn, 2026, needs more optimization.
8 864 0.703070506309 Henry Cohn, 2026, needs more optimization.
8 865 0.703081287529 Henry Cohn, 2026, needs more optimization.
8 866 0.703084011650 Henry Cohn, 2026, needs more optimization.
8 868 0.703394688169 Henry Cohn, 2026, 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 0.703884829355 Henry Cohn, 2026, needs more optimization.
8 874 0.703923027163 Henry Cohn, 2026, needs more optimization.
8 875 0.703930769476 Henry Cohn, 2026, needs more optimization.
8 876 0.703946148476 Henry Cohn, 2026, needs more optimization.
8 877 0.704402839348 Henry Cohn, 2026, needs more optimization.
8 878 0.704406666060 Henry Cohn, 2026, needs more optimization.
8 879 0.704407074553 Henry Cohn, 2026, needs more optimization.
8 880 0.704438321454 Henry Cohn, 2026, needs more optimization.
8 881 0.704446445261 Henry Cohn, 2026, needs more optimization.
8 882 0.704494807984 Henry Cohn, 2026, needs more optimization.
8 883 0.704806164006 Henry Cohn, 2026, needs more optimization.
8 884 0.704817142562 Henry Cohn, 2026, needs more optimization.
8 885 0.705056029024 Henry Cohn, 2026, needs more optimization.
8 886 0.705056304362 Henry Cohn, 2026, needs more optimization.
8 887 0.705056595322 Henry Cohn, 2026, needs more optimization.
8 888 0.705062961260 Henry Cohn, 2026, needs more optimization.
8 889 0.705073623871 Henry Cohn, 2026, needs more optimization.
8 890 0.705107470272 Henry Cohn, 2026, needs more optimization.
8 891 0.705705815165 Henry Cohn, 2026, needs more optimization.
8 892 0.705714522941 Henry Cohn, 2026, needs more optimization.
8 893 0.705724204976 Henry Cohn, 2026, needs more optimization.
8 894 0.705729240534 Henry Cohn, 2026, needs more optimization.
8 895 0.705739218309 Henry Cohn, 2026, needs more optimization.
8 896 0.705754703578 Henry Cohn, 2026, needs more optimization.
8 897 0.705757934230 Henry Cohn, 2026, needs more optimization.
8 898 0.705814273927 Henry Cohn, 2026, needs more optimization.
8 899 0.705814353010 Henry Cohn, 2026, needs more optimization.
8 900 0.705822638591 Henry Cohn, 2026, needs more optimization.
8 901 0.705822864614 Henry Cohn, 2026, needs more optimization.
8 902 0.705822968314 Henry Cohn, 2026, needs more optimization.
8 903 0.705828323949 Henry Cohn, 2026, needs more optimization.
8 904 0.706096536242 Henry Cohn, 2026, needs more optimization.
8 905 0.706100060182 Henry Cohn, 2026, needs more optimization.
8 908 0.706535910974 Henry Cohn, 2026, needs more optimization.
8 909 0.706541204349 Henry Cohn, 2026, needs more optimization.
8 910 0.706543713192 Henry Cohn, 2026, needs more optimization.
8 911 0.706554799541 Henry Cohn, 2026, needs more optimization.
8 913 0.706564486045 Henry Cohn, 2026, needs more optimization.
8 914 0.706564846167 Henry Cohn, 2026, needs more optimization.
8 915 0.707003548339 Henry Cohn, 2026, needs more optimization.
8 916 0.707006582328 Henry Cohn, 2026, needs more optimization.
8 917 0.707008581107 Henry Cohn, 2026, needs more optimization.
8 918 0.707184678890 Henry Cohn, 2026, needs more optimization.
8 919 0.707184708329 Henry Cohn, 2026, needs more optimization.
8 920 0.707187277687 Henry Cohn, 2026, needs more optimization.
8 921 0.707663817855 Henry Cohn, 2026, needs more optimization.
8 922 0.707669772925 Henry Cohn, 2026, needs more optimization.
8 923 0.707670282203 Henry Cohn, 2026, needs more optimization.
8 925 0.707686426426 Henry Cohn, 2026, needs more optimization.
8 926 0.707699948180 Henry Cohn, 2026, needs more optimization.
8 927 0.707984686201 Henry Cohn, 2026, needs more optimization.
8 928 0.707984848160 Henry Cohn, 2026, needs more optimization.
8 930 0.707990289413 Henry Cohn, 2026, needs more optimization.
8 931 0.708050920570 Henry Cohn, 2026, needs more optimization.
8 933 0.708147123053 Henry Cohn, 2026, 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 0.708941287767 Henry Cohn, 2026, needs more optimization.
8 939 0.708945306682 Henry Cohn, 2026, needs more optimization.
8 940 0.708958327591 Henry Cohn, 2026, needs more optimization.
8 941 0.708958393738 Henry Cohn, 2026, needs more optimization.
8 942 0.708961768989 Henry Cohn, 2026, needs more optimization.
8 943 0.708997193124 Henry Cohn, 2026, needs more optimization.
8 944 0.709058252343 Henry Cohn, 2026, needs more optimization.
8 946 0.709187914552 Henry Cohn, 2026, needs more optimization.
8 947 0.709246845504 Henry Cohn, 2026, needs more optimization.
8 948 0.709555237646 Henry Cohn, 2026, needs more optimization.
8 949 0.709555692936 Henry Cohn, 2026, needs more optimization.
8 950 0.709562005888 Henry Cohn, 2026, needs more optimization.
8 952 0.709574031713 Henry Cohn, 2026, needs more optimization.
8 953 0.709585671070 Henry Cohn, 2026, needs more optimization.
8 954 0.709618223393 Henry Cohn, 2026, needs more optimization.
8 955 0.710007758484 Henry Cohn, 2026, needs more optimization.
8 956 0.710019788429 Henry Cohn, 2026, needs more optimization.
8 957 0.710035534953 Henry Cohn, 2026, needs more optimization.
8 958 0.710039029469 Henry Cohn, 2026, needs more optimization.
8 959 0.710342486063 Henry Cohn, 2026, needs more optimization.
8 960 0.710344293237 Henry Cohn, 2026, needs more optimization.
8 961 0.710352045700 Henry Cohn, 2026, needs more optimization.
8 962 0.710752798997 Henry Cohn, 2026, needs more optimization.
8 963 0.710761521867 Henry Cohn, 2026, needs more optimization.
8 964 0.710779230438 Henry Cohn, 2026, needs more optimization.
8 966 0.710787270290 Henry Cohn, 2026, needs more optimization.
8 967 0.710787436558 Henry Cohn, 2026, needs more optimization.
8 968 0.710793893710 Henry Cohn, 2026, needs more optimization.
8 969 0.710840074467 Henry Cohn, 2026, needs more optimization.
8 970 0.710941485244 Henry Cohn, 2026, 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 0.711503373598 Henry Cohn, 2026, needs more optimization.
8 974 0.711564016737 Henry Cohn, 2026, needs more optimization.
8 975 0.711577160620 Henry Cohn, 2026, needs more optimization.
8 976 0.711582265565 Henry Cohn, 2026, needs more optimization.
8 977 0.711605390690 Henry Cohn, 2026, needs more optimization.
8 978 0.711671964312 Henry Cohn, 2026, needs more optimization.
8 979 0.711954112753 Henry Cohn, 2026, needs more optimization.
8 980 0.711961299107 Henry Cohn, 2026, needs more optimization.
8 981 0.712055090895 Henry Cohn, 2026, needs more optimization.
8 983 0.712072951923 Henry Cohn, 2026, needs more optimization.
8 984 0.712085005560 Henry Cohn, 2026, needs more optimization.
8 985 0.712387418444 Henry Cohn, 2026, needs more optimization.
8 986 0.712388288191 Henry Cohn, 2026, needs more optimization.
8 987 0.712402071213 Henry Cohn, 2026, needs more optimization.
8 988 0.712468855396 Henry Cohn, 2026, needs more optimization.
8 989 0.712703811059 Henry Cohn, 2026, needs more optimization.
8 990 0.713085263864 Henry Cohn, 2026, needs more optimization.
8 992 0.713085341264 Henry Cohn, 2026, 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 0.266033138128 Henry Cohn, 2026.
9 52 0.267191024627 Henry Cohn, 2023.
71⁢x2−4⁢x−4
9 53 0.269834758170 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
9 54 0.271671378177 Henry Cohn, 2025.
9 56 0.272133267170 Henry Cohn, 2025.
9 57 0.282916244589 Henry Cohn, 2026.
9 58 0.288070633971 Henry Cohn, 2026.
9 59 0.293943006572 Henry Cohn, 2025.
9 60 0.294882506582 Henry Cohn, 2026.
9 61 0.297699088072 Henry Cohn, 2026, needs more optimization.
9 62 0.299407593895 Henry Cohn, 2026.
9 63 0.302685227391 Henry Cohn, 2025.
9 64 0.306653313780 Henry Cohn, 2023.
9 65 0.310476184868 Henry Cohn, 2026, needs more optimization.
9 66 0.313645759189 Henry Cohn, 2026.
9 67 0.319263707113 Henry Cohn, 2026, needs more optimization.
9 68 0.322050465427 Henry Cohn, 2025.
9 69 0.324666182383 Henry Cohn, 2025.
9 70 0.327715466150 Henry Cohn, 2026, needs more optimization.
9 71 0.328994846980 Henry Cohn, 2026, needs more optimization.
9 72 0.330036093460 Henry Cohn, 2025, needs more optimization.
9 73 0.330041808451 Henry Cohn, 2025, needs more optimization.
9 74 0.330099440293 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 0.378522674620 Henry Cohn, 2026, needs more optimization.
9 103 0.378849371703 Henry Cohn, 2026, needs more optimization.
9 104 0.379137241782 Henry Cohn, 2025, needs more optimization.
9 105 0.391200802386 Henry Cohn, 2026, needs more optimization.
9 106 0.395154146181 Henry Cohn, 2026, needs more optimization.
9 107 0.398135763343 Henry Cohn, 2026, needs more optimization.
9 108 0.400036531408 Henry Cohn, 2026, needs more optimization.
9 109 0.403046935961 Henry Cohn, 2026, needs more optimization.
9 110 0.405589538421 Henry Cohn, 2026, needs more optimization.
9 111 0.407513804262 Henry Cohn, 2026, needs more optimization.
9 112 0.408810852559 Henry Cohn, 2026, needs more optimization.
9 113 0.411168468293 Henry Cohn, 2026, needs more optimization.
9 114 0.412372934093 Henry Cohn, 2026, needs more optimization.
9 115 0.413458861954 Henry Cohn, 2026, needs more optimization.
9 116 0.414182867517 Henry Cohn, 2026, needs more optimization.
9 117 0.415117235237 Henry Cohn, 2026, needs more optimization.
9 118 0.416412932336 Henry Cohn, 2026, needs more optimization.
9 119 0.416531299820 Henry Cohn, 2026, needs more optimization.
9 120 0.416979319197 Henry Cohn, 2026, needs more optimization.
9 121 0.418412104036 Henry Cohn, 2026, needs more optimization.
9 122 0.419973423986 Henry Cohn, 2026, needs more optimization.
9 123 0.421158319955 Henry Cohn, 2026, needs more optimization.
9 124 0.421769889309 Henry Cohn, 2026, needs more optimization.
9 125 0.422393884634 Henry Cohn, 2026, needs more optimization.
9 126 0.423144673799 Henry Cohn, 2026, needs more optimization.
9 127 0.424066535015 Henry Cohn, 2026, needs more optimization.
9 128 0.426638776724 Henry Cohn, 2026, needs more optimization.
9 129 0.428279423083 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 0.441693515174 Henry Cohn, 2026, needs more optimization.
9 148 0.444822266120 Henry Cohn, 2026, needs more optimization.
9 149 0.448505728271 Henry Cohn, 2026, needs more optimization.
9 150 0.450388211708 Henry Cohn, 2026, needs more optimization.
9 151 0.451763114842 Henry Cohn, 2026, needs more optimization.
9 152 0.453419362542 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 0.459879189440 Henry Cohn, 2026, needs more optimization.
9 168 0.460201817253 Henry Cohn, 2026, needs more optimization.
9 169 0.461739884431 Henry Cohn, 2026, needs more optimization.
9 170 0.461787724445 Henry Cohn, 2026, needs more optimization.
9 171 0.461807277931 Henry Cohn, 2026, needs more optimization.
9 172 0.461944158912 Henry Cohn, 2026, needs more optimization.
9 173 0.462039871565 Henry Cohn, 2026, needs more optimization.
9 174 0.462175701992 Henry Cohn, 2026, needs more optimization.
9 175 0.462222724698 Henry Cohn, 2026, needs more optimization.
9 176 0.462272110706 Henry Cohn, 2026, needs more optimization.
9 177 0.462304953477 Henry Cohn, 2026, needs more optimization.
9 178 0.462321690829 Henry Cohn, 2026, needs more optimization.
9 179 0.462400033559 Henry Cohn, 2026, needs more optimization.
9 180 0.462418617886 Henry Cohn, 2026, needs more optimization.
9 181 0.462513862410 Henry Cohn, 2026, needs more optimization.
9 182 0.463639305092 Henry Cohn, 2026, needs more optimization.
9 183 0.465613591053 Henry Cohn, 2026, needs more optimization.
9 184 0.467349856564 Henry Cohn, 2026, needs more optimization.
9 185 0.469465343520 Henry Cohn, 2026, needs more optimization.
9 186 0.470180947944 Henry Cohn, 2026, needs more optimization.
9 187 0.473143083808 Henry Cohn, 2026, needs more optimization.
9 209 0.475156558223 Henry Cohn, 2026.
103⁢x2−30⁢x−9
9 210 0.478332341741 Henry Cohn, 2026, needs more optimization.
9 211 0.481463808793 Henry Cohn, 2026, needs more optimization.
9 212 0.482325644760 Henry Cohn, 2026, needs more optimization.
9 213 0.485464255730 Henry Cohn, 2026, needs more optimization.
9 214 0.487532683813 Henry Cohn, 2026, needs more optimization.
9 215 0.490142513321 Henry Cohn, 2026, needs more optimization.
9 216 0.491403798253 Henry Cohn, 2026, needs more optimization.
9 217 0.493127200225 Henry Cohn, 2026, needs more optimization.
9 218 0.493634957903 Henry Cohn, 2026, needs more optimization.
9 219 0.494513074471 Henry Cohn, 2026, needs more optimization.
9 220 0.495590770846 Henry Cohn, 2026, needs more optimization.
9 221 0.496589389112 Henry Cohn, 2026, needs more optimization.
9 222 0.497015396784 Henry Cohn, 2026, needs more optimization.
9 223 0.497027454846 Henry Cohn, 2026, needs more optimization.
9 224 0.497088436852 Henry Cohn, 2026, needs more optimization.
9 225 0.497219648461 Henry Cohn, 2026, needs more optimization.
9 226 0.497563507024 Henry Cohn, 2026, needs more optimization.
9 227 0.497581449919 Henry Cohn, 2026, needs more optimization.
9 228 0.498189519652 Henry Cohn, 2026, needs more optimization.
9 229 0.498399758247 Henry Cohn, 2026, needs more optimization.
9 230 0.498515333540 Henry Cohn, 2026, needs more optimization.
9 232 0.498673810781 Henry Cohn, 2026, needs more optimization.
9 233 0.498831492665 Henry Cohn, 2026, needs more optimization.
9 234 0.499106523121 Henry Cohn, 2026, needs more optimization.
9 235 0.499207714403 Henry Cohn, 2026, needs more optimization.
9 236 0.499280692124 Henry Cohn, 2026, needs more optimization.
9 237 0.499328280255 Henry Cohn, 2026, needs more optimization.
9 238 0.499428629625 Henry Cohn, 2026, needs more optimization.
9 239 0.499468858270 Henry Cohn, 2026, needs more optimization.
9 240 0.499545043024 Henry Cohn, 2026, needs more optimization.
9 242 0.499613651737 Henry Cohn, 2026, needs more optimization.
9 243 0.499628881142 Henry Cohn, 2026, needs more optimization.
9 244 0.499684133889 Henry Cohn, 2026, needs more optimization.
9 245 0.499774682947 Henry Cohn, 2026, needs more optimization.
9 246 0.499904013877 Henry Cohn, 2026, needs more optimization.
9 247 0.499922499646 Henry Cohn, 2026, needs more optimization.
9 248 0.499983066299 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 0.517093319398 Henry Cohn, 2026, needs more optimization.
9 308 0.518946168202 Henry Cohn, 2026, needs more optimization.
9 309 0.520879651194 Henry Cohn, 2026, needs more optimization.
9 312 0.521868308188 Henry Cohn, 2026, needs more optimization.
9 330 0.523809523810 Henry Cohn and Ilmari Vahteristo (independently), 2026.
21⁢x−11
9 331 0.528501225185 Henry Cohn, 2026, needs more optimization.
9 332 0.530021402215 Henry Cohn, 2026, needs more optimization.
9 333 0.533339210090 Henry Cohn, 2026, needs more optimization.
9 334 0.534913028854 Henry Cohn, 2026, needs more optimization.
9 335 0.536137442245 Henry Cohn, 2026, needs more optimization.
9 336 0.536269793581 Henry Cohn, 2026, needs more optimization.
9 338 0.536462735144 Henry Cohn, 2026, needs more optimization.
9 339 0.537044670995 Henry Cohn, 2026, needs more optimization.
9 340 0.538018398142 Henry Cohn, 2026, needs more optimization.
9 341 0.538117271569 Henry Cohn, 2026, needs more optimization.
9 342 0.539550817716 Henry Cohn, 2026, needs more optimization.
9 343 0.540110000545 Henry Cohn, 2026, needs more optimization.
9 344 0.540915477698 Henry Cohn, 2026, needs more optimization.
9 346 0.541100708310 Henry Cohn, 2026, needs more optimization.
9 347 0.541622425110 Henry Cohn, 2026, needs more optimization.
9 348 0.542607666971 Henry Cohn, 2026, needs more optimization.
9 349 0.543266803010 Henry Cohn, 2026, needs more optimization.
9 350 0.543439372878 Henry Cohn, 2026, needs more optimization.
9 351 0.543652744144 Henry Cohn, 2026, needs more optimization.
9 354 0.544343041187 Henry Cohn, 2026, needs more optimization.
9 355 0.544502416994 Henry Cohn, 2026, needs more optimization.
9 356 0.544574510388 Henry Cohn, 2026, needs more optimization.
9 357 0.544734049398 Henry Cohn, 2026, needs more optimization.
9 358 0.544901270039 Henry Cohn, 2026, needs more optimization.
9 359 0.546102870579 Henry Cohn, 2026, needs more optimization.
9 360 0.546574744911 Henry Cohn, 2026, needs more optimization.
9 482 0.546918160679 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x2−2⁢x−1
9 483 0.555266742912 Henry Cohn, 2026, needs more optimization.
9 484 0.557694973636 Henry Cohn, 2026, needs more optimization.
9 485 0.562942891843 Henry Cohn, 2026, needs more optimization.
9 486 0.565409247966 Henry Cohn, 2026, needs more optimization.
9 487 0.568339067347 Henry Cohn, 2026, needs more optimization.
9 488 0.569269637239 Henry Cohn, 2026, needs more optimization.
9 489 0.570800842115 Henry Cohn, 2026, needs more optimization.
9 490 0.572441816740 Henry Cohn, 2026, needs more optimization.
9 491 0.574105632459 Henry Cohn, 2026, needs more optimization.
9 492 0.574942285769 Henry Cohn, 2026, needs more optimization.
9 493 0.576347674255 Henry Cohn, 2026, needs more optimization.
9 494 0.578048005537 Henry Cohn, 2026, needs more optimization.
9 495 0.578930605583 Henry Cohn, 2026, needs more optimization.
9 496 0.580091170515 Henry Cohn, 2026, needs more optimization.
9 497 0.580673356448 Henry Cohn, 2026, needs more optimization.
9 498 0.581754065829 Henry Cohn, 2026, needs more optimization.
9 499 0.582996301870 Henry Cohn, 2026, needs more optimization.
9 500 0.583924975049 Henry Cohn, 2026, needs more optimization.
9 501 0.584668800750 Henry Cohn, 2026, needs more optimization.
9 502 0.585626018667 Henry Cohn, 2026, needs more optimization.
9 503 0.586253611397 Henry Cohn, 2026, needs more optimization.
9 504 0.587165992467 Henry Cohn, 2026, needs more optimization.
9 505 0.587234387036 Henry Cohn, 2026, needs more optimization.
9 506 0.588174125628 Henry Cohn, 2026, needs more optimization.
9 507 0.588351701777 Henry Cohn, 2026, needs more optimization.
9 508 0.589115643602 Henry Cohn, 2026, needs more optimization.
9 509 0.590020523243 Henry Cohn, 2026, needs more optimization.
9 510 0.590450863973 Henry Cohn, 2026, needs more optimization.
9 511 0.590827797986 Henry Cohn, 2026, needs more optimization.
9 512 0.591267731698 Henry Cohn, 2026, needs more optimization.
9 513 0.591663798719 Henry Cohn, 2026, needs more optimization.
9 514 0.592129373464 Henry Cohn, 2026, needs more optimization.
9 515 0.592406783643 Henry Cohn, 2026, needs more optimization.
9 516 0.593032336062 Henry Cohn, 2026, needs more optimization.
9 517 0.593288127268 Henry Cohn, 2026, needs more optimization.
9 518 0.593630378830 Henry Cohn, 2026, needs more optimization.
9 519 0.594116271040 Henry Cohn, 2026, needs more optimization.
9 520 0.594438996910 Henry Cohn, 2026, needs more optimization.
9 521 0.594858542274 Henry Cohn, 2026, needs more optimization.
9 522 0.595209298674 Henry Cohn, 2026, needs more optimization.
9 523 0.595529659257 Henry Cohn, 2026, needs more optimization.
9 524 0.595871730738 Henry Cohn, 2026, needs more optimization.
9 525 0.596273838314 Henry Cohn, 2026, needs more optimization.
9 526 0.596596586127 Henry Cohn, 2026, needs more optimization.
9 527 0.596624686130 Henry Cohn, 2026, needs more optimization.
9 528 0.597089159401 Henry Cohn, 2026, needs more optimization.
9 529 0.597198292915 Henry Cohn, 2026, needs more optimization.
9 530 0.597428404684 Henry Cohn, 2026, needs more optimization.
9 531 0.597698224180 Henry Cohn, 2026, needs more optimization.
9 532 0.597842841368 Henry Cohn, 2026, needs more optimization.
9 533 0.598247471701 Henry Cohn, 2026, needs more optimization.
9 534 0.598418579764 Henry Cohn, 2026, needs more optimization.
9 536 0.598653151581 Henry Cohn, 2026, needs more optimization.
9 537 0.598820871122 Henry Cohn, 2026, needs more optimization.
9 538 0.599021784617 Henry Cohn, 2026, needs more optimization.
9 539 0.599461967944 Henry Cohn, 2026, needs more optimization.
9 540 0.599781819766 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 0.605135796423 Henry Cohn, 2026, needs more optimization.
9 616 0.614624448172 Henry Cohn, 2026, needs more optimization.
9 618 0.615839542171 Henry Cohn, 2026, needs more optimization.
9 619 0.615937324784 Henry Cohn, 2026, needs more optimization.
9 620 0.616289147213 Henry Cohn, 2026, needs more optimization.
9 621 0.616354486939 Henry Cohn, 2026, needs more optimization.
9 622 0.616481467026 Henry Cohn, 2026, needs more optimization.
9 623 0.616613713131 Henry Cohn, 2026, needs more optimization.
9 624 0.616829677699 Henry Cohn, 2026, needs more optimization.
9 625 0.617030554511 Henry Cohn, 2026, needs more optimization.
9 626 0.617211481507 Henry Cohn, 2026, needs more optimization.
9 627 0.617274349808 Henry Cohn, 2026, needs more optimization.
9 628 0.617483236076 Henry Cohn, 2026, needs more optimization.
9 629 0.617560316398 Henry Cohn, 2026, needs more optimization.
9 630 0.617632306034 Henry Cohn, 2026, needs more optimization.
9 632 0.617652487577 Henry Cohn, 2026, needs more optimization.
9 633 0.617857502011 Henry Cohn, 2026, needs more optimization.
9 634 0.618033787493 Henry Cohn, 2026, needs more optimization.
9 638 0.618033981339 Henry Cohn, 2026, needs more optimization.
9 640 0.618033987180 Henry Cohn, 2026, needs more optimization.
9 641 0.618033987209 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 0.643192615694 Henry Cohn, 2026, needs more optimization.
9 727 0.643254326513 Henry Cohn, 2026, needs more optimization.
9 728 0.643364522900 Henry Cohn, 2026, 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 0.643829091594 Henry Cohn, 2026, 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 0.644491847785 Henry Cohn, 2026, needs more optimization.
9 737 0.644572945237 Henry Cohn, 2026, needs more optimization.
9 738 0.644585847025 Henry Cohn, 2026, needs more optimization.
9 739 0.644984741360 Henry Cohn, 2026, needs more optimization.
9 740 0.645103875221 Henry Cohn, 2026, needs more optimization.
9 741 0.645112025832 Henry Cohn, 2026, needs more optimization.
9 742 0.645210638002 Henry Cohn, 2026, needs more optimization.
9 743 0.645218013025 Henry Cohn, 2026, 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 0.646444048402 Henry Cohn, 2026, 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 0.647411078840 Henry Cohn, 2026, 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 0.647884854551 Henry Cohn, 2026, 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 0.648174447495 Henry Cohn, 2026, 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 0.648494290795 Henry Cohn, 2026, needs more optimization.
9 770 0.648525378931 Henry Cohn, 2026, needs more optimization.
9 771 0.648975903378 Henry Cohn, 2026, needs more optimization.
9 772 0.648984750198 Henry Cohn, 2026, needs more optimization.
9 773 0.648996089264 Henry Cohn, 2026, 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 0.649381779372 Henry Cohn, 2026, needs more optimization.
9 779 0.649888678000 Henry Cohn, 2026, needs more optimization.
9 780 0.649918271222 Henry Cohn, 2026, needs more optimization.
9 781 0.649981132962 Henry Cohn, 2026, needs more optimization.
9 782 0.650110548272 Henry Cohn, 2026, 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.
9 792 0.651295458782 Henry Cohn, 2026, needs more optimization.
9 793 0.651425839560 Henry Cohn, 2026, needs more optimization.
9 794 0.651526523791 Henry Cohn, 2026, needs more optimization.
9 795 0.651645742881 Henry Cohn, 2026, needs more optimization.
9 796 0.651652620314 Henry Cohn, 2026, 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 0.652211244907 Henry Cohn, 2026, 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 0.652904449306 Henry Cohn, 2026, needs more optimization.
9 808 0.652955833314 Henry Cohn, 2026, needs more optimization.
9 809 0.653149763370 Henry Cohn, 2026, 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 0.653365776787 Henry Cohn, 2026, 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 0.653814047740 Henry Cohn, 2026, 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 0.654217395308 Henry Cohn, 2026, needs more optimization.
9 822 0.654253727399 Henry Cohn, 2026, needs more optimization.
9 823 0.654389441086 Henry Cohn, 2026, needs more optimization.
9 824 0.654464458067 Henry Cohn, 2026, 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 0.655000233184 Henry Cohn, 2026, needs more optimization.
9 829 0.655218926120 Henry Cohn, 2026, needs more optimization.
9 830 0.655438931051 Henry Cohn, 2026, needs more optimization.
9 831 0.655447711869 Henry Cohn, 2026, 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 0.656257811448 Henry Cohn, 2026, 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 0.656560952109 Henry Cohn, 2026, needs more optimization.
9 842 0.656810400690 Henry Cohn, 2026, needs more optimization.
9 843 0.657090999508 Henry Cohn, 2026, needs more optimization.
9 844 0.657093783068 Henry Cohn, 2026, needs more optimization.
9 845 0.657205808161 Henry Cohn, 2026, needs more optimization.
9 846 0.657389995690 Henry Cohn, 2026, needs more optimization.
9 848 0.657413818724 Henry Cohn, 2026, needs more optimization.
9 849 0.657446195721 Henry Cohn, 2026, needs more optimization.
9 850 0.657527383757 Henry Cohn, 2026, needs more optimization.
9 851 0.657746113487 Henry Cohn, 2026, 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 0.658324461754 Henry Cohn, 2026, 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 0.659026804704 Henry Cohn, 2026, needs more optimization.
9 863 0.659042323165 Henry Cohn, 2026, needs more optimization.
9 864 0.659257430573 Henry Cohn, 2026, needs more optimization.
9 865 0.659341722327 Henry Cohn, 2026, needs more optimization.
9 866 0.659351885611 Henry Cohn, 2026, needs more optimization.
9 867 0.659590405341 Henry Cohn, 2026, needs more optimization.
9 868 0.659601517904 Henry Cohn, 2026, needs more optimization.
9 869 0.659628460688 Henry Cohn, 2026, 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 0.660499111506 Henry Cohn, 2026, 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 0.661237629596 Henry Cohn, 2026, needs more optimization.
9 886 0.661241276234 Henry Cohn, 2026, 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 0.662242426748 Henry Cohn, 2026, 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 0.662534066047 Henry Cohn, 2026, needs more optimization.
9 900 0.662630711000 Henry Cohn, 2026, needs more optimization.
9 901 0.662637303247 Henry Cohn, 2026, 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 0.663146923536 Henry Cohn, 2026, needs more optimization.
9 905 0.663184166271 Henry Cohn, 2026, needs more optimization.
9 906 0.663318369274 Henry Cohn, 2026, 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 0.664688921790 Henry Cohn, 2026, needs more optimization.
9 920 0.664707746199 Henry Cohn, 2026, needs more optimization.
9 921 0.664725040664 Henry Cohn, 2026, needs more optimization.
9 922 0.665004959682 Henry Cohn, 2026, 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 0.665651107222 Henry Cohn, 2026, needs more optimization.
9 929 0.665655122760 Henry Cohn, 2026, 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 52 0.230823073590 Henry Cohn, 2026.
10 57 0.231237647788 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
36⁢x2−4⁢x−1
10 58 0.25 Henry Cohn, 2024.
4⁢x−1
10 59 0.253695768464 Henry Cohn, 2024.
10 60 0.254730982571 Henry Cohn, 2026.
10 61 0.255558009805 Henry Cohn, 2026, needs more optimization.
10 63 0.257944905339 Henry Cohn, 2025.
10 64 0.260558293949 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 0.269390887679 Henry Cohn, 2026, needs more optimization.
10 69 0.269775337242 Henry Cohn, 2026, needs more optimization.
10 70 0.271729029622 Henry Cohn, 2026, needs more optimization.
10 71 0.271905044080 Henry Cohn, 2026, needs more optimization.
10 72 0.274448309369 Henry Cohn, 2026, needs more optimization.
10 73 0.275987133320 Henry Cohn, 2025.
10 74 0.279604372367 Henry Cohn, 2026, needs more optimization.
10 75 0.283455182208 Henry Cohn, 2026, needs more optimization.
10 76 0.284096667917 Henry Cohn, 2025.
10 77 0.284910960402 Henry Cohn, 2025.
10 78 0.289756903643 Henry Cohn, 2026, needs more optimization.
10 79 0.295238353835 Henry Cohn, 2026, needs more optimization.
10 80 0.299105344231 Henry Cohn, 2026, needs more optimization.
10 81 0.301759908598 Henry Cohn, 2026, needs more optimization.
10 82 0.304433208409 Henry Cohn, 2026, needs more optimization.
10 83 0.307851642008 Henry Cohn, 2026, needs more optimization.
10 84 0.310848806540 Henry Cohn, 2026, needs more optimization.
10 85 0.318197566143 Henry Cohn, 2026, needs more optimization.
10 86 0.322961934521 Henry Cohn, 2026, needs more optimization.
10 87 0.323578394071 Henry Cohn, 2026, needs more optimization.
10 88 0.324382161722 Henry Cohn, 2026, needs more optimization.
10 89 0.324779864431 Henry Cohn, 2026, needs more optimization.
10 90 0.325389381674 Henry Cohn, 2026, needs more optimization.
10 91 0.326529043496 Henry Cohn, 2026, needs more optimization.
10 92 0.327951650403 Henry Cohn, 2026, needs more optimization.
10 93 0.328644914787 Henry Cohn, 2026, needs more optimization.
10 94 0.329620657087 Henry Cohn, 2026, needs more optimization.
10 95 0.329854854198 Henry Cohn, 2025, needs more optimization.
10 96 0.330315694183 Henry Cohn, 2026, needs more optimization.
10 97 0.330611330468 Henry Cohn, 2026, needs more optimization.
10 98 0.330701964443 Henry Cohn, 2026, needs more optimization.
10 99 0.330884811209 Henry Cohn, 2026, needs more optimization.
10 100 0.331072104458 Henry Cohn, 2026, needs more optimization.
10 101 0.331169613949 Henry Cohn, 2026, needs more optimization.
10 102 0.331364193730 Henry Cohn, 2026, needs more optimization.
10 103 0.333227831929 Henry Cohn, 2026, needs more optimization.
10 104 0.333227864338 Henry Cohn, 2026, needs more optimization.
10 105 0.333275435089 Henry Cohn, 2026, needs more optimization.
10 106 0.333305884528 Henry Cohn, 2026, needs more optimization.
10 107 0.333311277996 Henry Cohn, 2026, needs more optimization.
10 108 0.333316878710 Henry Cohn, 2026, needs more optimization.
10 109 0.335269294266 Henry Cohn, 2026, needs more optimization.
10 110 0.339578695136 Henry Cohn, 2026, needs more optimization.
10 111 0.342183778916 Henry Cohn, 2026, needs more optimization.
10 112 0.344830914496 Henry Cohn, 2026, needs more optimization.
10 113 0.347302148278 Henry Cohn, 2026, needs more optimization.
10 114 0.348285012519 Henry Cohn, 2026, needs more optimization.
10 115 0.352515784788 Henry Cohn, 2026, needs more optimization.
10 116 0.353972588881 Henry Cohn, 2026, needs more optimization.
10 117 0.360088212996 Henry Cohn, 2026, needs more optimization.
10 118 0.362412801166 Henry Cohn, 2026, needs more optimization.
10 119 0.363761710067 Henry Cohn, 2026, needs more optimization.
10 120 0.364675138961 Henry Cohn, 2026, needs more optimization.
10 121 0.365325811601 Henry Cohn, 2026, needs more optimization.
10 122 0.365459215856 Henry Cohn, 2026, needs more optimization.
10 124 0.365550021069 Henry Cohn, 2026, needs more optimization.
10 125 0.365550181481 Henry Cohn, 2026, needs more optimization.
10 126 0.365558732136 Henry Cohn, 2026, needs more optimization.
10 127 0.366035053027 Henry Cohn, 2024.
10 128 0.367843362428 Henry Cohn, 2026, needs more optimization.
10 129 0.370352757639 Henry Cohn, 2026, needs more optimization.
10 130 0.371247320210 Henry Cohn, 2026, needs more optimization.
10 131 0.371343446604 Henry Cohn, 2026, needs more optimization.
10 132 0.371409893582 Henry Cohn, 2026, needs more optimization.
10 133 0.385289992545 Henry Cohn, 2026, needs more optimization.
10 134 0.389768459446 Henry Cohn, 2026, needs more optimization.
10 135 0.392340761166 Henry Cohn, 2026, needs more optimization.
10 136 0.393476979227 Henry Cohn, 2026, needs more optimization.
10 137 0.396212763308 Henry Cohn, 2026, needs more optimization.
10 138 0.398651390972 Henry Cohn, 2026, needs more optimization.
10 139 0.400187109545 Henry Cohn, 2026, needs more optimization.
10 140 0.401787413901 Henry Cohn, 2026, needs more optimization.
10 141 0.403139490787 Henry Cohn, 2026, needs more optimization.
10 142 0.404397831423 Henry Cohn, 2026, needs more optimization.
10 156 0.405827419558 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
11⁢x2−2⁢x−1
10 157 0.413096978622 Henry Cohn, 2026, needs more optimization.
10 158 0.414041442530 Henry Cohn, 2026, needs more optimization.
10 159 0.415042149936 Henry Cohn, 2026, needs more optimization.
10 160 0.416103460329 Henry Cohn, 2026, needs more optimization.
10 161 0.417179338543 Henry Cohn, 2026, needs more optimization.
10 162 0.418538837298 Henry Cohn, 2026, needs more optimization.
10 163 0.419225762338 Henry Cohn, 2026, needs more optimization.
10 164 0.420594116236 Henry Cohn, 2026, needs more optimization.
10 165 0.421680628727 Henry Cohn, 2026, needs more optimization.
10 166 0.422486777012 Henry Cohn, 2026, needs more optimization.
10 167 0.423423740060 Henry Cohn, 2026, needs more optimization.
10 168 0.424374959358 Henry Cohn, 2026, needs more optimization.
10 169 0.425515856893 Henry Cohn, 2026, needs more optimization.
10 170 0.425992960905 Henry Cohn, 2026, needs more optimization.
10 171 0.427021657823 Henry Cohn, 2026, needs more optimization.
10 172 0.428168916140 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 0.438692154355 Henry Cohn, 2026, needs more optimization.
10 196 0.441226110614 Henry Cohn, 2026, needs more optimization.
10 197 0.443967336853 Henry Cohn, 2026, needs more optimization.
10 198 0.445538482333 Henry Cohn, 2026, needs more optimization.
10 199 0.447197360325 Henry Cohn, 2026, needs more optimization.
10 200 0.448240578067 Henry Cohn, 2026, needs more optimization.
10 201 0.449280154702 Henry Cohn, 2026, needs more optimization.
10 202 0.450515978162 Henry Cohn, 2026, needs more optimization.
10 203 0.451663310532 Henry Cohn, 2026, needs more optimization.
10 204 0.452579690897 Henry Cohn, 2026, needs more optimization.
10 205 0.453663103739 Henry Cohn, 2026, needs more optimization.
10 206 0.454684721261 Henry Cohn, 2026, needs more optimization.
10 207 0.454789839686 Henry Cohn, 2026, needs more optimization.
10 208 0.454792506898 Henry Cohn, 2026, needs more optimization.
10 209 0.454942205334 Henry Cohn, 2026, needs more optimization.
10 210 0.454959176598 Henry Cohn, 2026, needs more optimization.
10 211 0.455026958165 Henry Cohn, 2026, needs more optimization.
10 212 0.455067250353 Henry Cohn, 2026, needs more optimization.
10 213 0.455129690122 Henry Cohn, 2026, needs more optimization.
10 214 0.455206539608 Henry Cohn, 2026, needs more optimization.
10 237 0.455341801262 Henry Cohn, 2026.
18⁢x2−6⁢x−1
10 238 0.455725547120 Henry Cohn, 2026, needs more optimization.
10 239 0.456309086187 Henry Cohn, 2026, needs more optimization.
10 240 0.457933074010 Henry Cohn, 2026, needs more optimization.
10 241 0.458084857696 Henry Cohn, 2026, needs more optimization.
10 242 0.458092565744 Henry Cohn, 2026, needs more optimization.
10 243 0.458112843395 Henry Cohn, 2026, needs more optimization.
10 244 0.458196449707 Henry Cohn, 2026, needs more optimization.
10 245 0.459797578115 Henry Cohn, 2026, needs more optimization.
10 246 0.461420454343 Henry Cohn, 2026, needs more optimization.
10 247 0.463346555444 Henry Cohn, 2026, needs more optimization.
10 248 0.464987827868 Henry Cohn, 2026, needs more optimization.
10 249 0.466118677775 Henry Cohn, 2026, needs more optimization.
10 250 0.468072936431 Henry Cohn, 2026, needs more optimization.
10 251 0.468790408515 Henry Cohn, 2026, needs more optimization.
10 252 0.469986187713 Henry Cohn, 2026, needs more optimization.
10 253 0.471234215543 Henry Cohn, 2026, needs more optimization.
10 255 0.471951448920 Henry Cohn, 2026, needs more optimization.
10 256 0.473708100174 Henry Cohn, 2026, needs more optimization.
10 257 0.474340144449 Henry Cohn, 2026, needs more optimization.
10 258 0.474500138504 Henry Cohn, 2026, needs more optimization.
10 259 0.475815998358 Henry Cohn, 2026, needs more optimization.
10 260 0.476169521039 Henry Cohn, 2026, needs more optimization.
10 261 0.476770240565 Henry Cohn, 2026, needs more optimization.
10 262 0.477492252994 Henry Cohn, 2026, needs more optimization.
10 263 0.478648518110 Henry Cohn, 2026, needs more optimization.
10 264 0.478933185231 Henry Cohn, 2026, needs more optimization.
10 265 0.479001789489 Henry Cohn, 2026, needs more optimization.
10 266 0.479065601223 Henry Cohn, 2026, needs more optimization.
10 267 0.479348901620 Henry Cohn, 2026, needs more optimization.
10 268 0.479642049640 Henry Cohn, 2026, needs more optimization.
10 269 0.479830413110 Henry Cohn, 2026, needs more optimization.
10 270 0.480404447675 Henry Cohn, 2026, needs more optimization.
10 271 0.480405776748 Henry Cohn, 2026, needs more optimization.
10 272 0.480448399262 Henry Cohn, 2026, needs more optimization.
10 273 0.480872128260 Henry Cohn, 2026, needs more optimization.
10 274 0.481095579016 Henry Cohn, 2026, needs more optimization.
10 275 0.481141342341 Henry Cohn, 2026, needs more optimization.
10 276 0.481260458263 Henry Cohn, 2026, needs more optimization.
10 277 0.481661113645 Henry Cohn, 2026, needs more optimization.
10 278 0.483364614063 Henry Cohn, 2026, needs more optimization.
10 279 0.483656286940 Henry Cohn, 2026, needs more optimization.
10 280 0.483946534790 Henry Cohn, 2026, needs more optimization.
10 281 0.484331834216 Henry Cohn, 2026, needs more optimization.
10 282 0.484551077794 Henry Cohn, 2026, needs more optimization.
10 283 0.485082429583 Henry Cohn, 2026, needs more optimization.
10 284 0.485372719418 Henry Cohn, 2026, needs more optimization.
10 285 0.485462419809 Henry Cohn, 2026, needs more optimization.
10 286 0.485779544061 Henry Cohn, 2026, needs more optimization.
10 287 0.486087696296 Henry Cohn, 2026, needs more optimization.
10 288 0.486399123136 Henry Cohn, 2026, needs more optimization.
10 289 0.486625467964 Henry Cohn, 2026, needs more optimization.
10 290 0.486765672782 Henry Cohn, 2026, needs more optimization.
10 291 0.487067737970 Henry Cohn, 2026, needs more optimization.
10 292 0.487413669866 Henry Cohn, 2026, needs more optimization.
10 293 0.487590301885 Henry Cohn, 2026, needs more optimization.
10 294 0.488041305999 Henry Cohn, 2026, needs more optimization.
10 295 0.488381322045 Henry Cohn, 2026, needs more optimization.
10 296 0.488513225502 Henry Cohn, 2026, needs more optimization.
10 297 0.488619433298 Henry Cohn, 2026, needs more optimization.
10 298 0.488797152567 Henry Cohn, 2026, needs more optimization.
10 299 0.489130324653 Henry Cohn, 2026, needs more optimization.
10 300 0.489313068243 Henry Cohn, 2026, needs more optimization.
10 301 0.489419790666 Henry Cohn, 2026, needs more optimization.
10 302 0.489535236267 Henry Cohn, 2026, needs more optimization.
10 303 0.489688698067 Henry Cohn, 2026, needs more optimization.
10 304 0.490071710090 Henry Cohn, 2026, needs more optimization.
10 305 0.490443629674 Henry Cohn, 2026, needs more optimization.
10 306 0.490885393224 Henry Cohn, 2026, needs more optimization.
10 307 0.491196462099 Henry Cohn, 2026, needs more optimization.
10 309 0.491227709471 Henry Cohn, 2026, needs more optimization.
10 310 0.491300374276 Henry Cohn, 2026, needs more optimization.
10 311 0.491430058713 Henry Cohn, 2026, needs more optimization.
10 312 0.491608729139 Henry Cohn, 2026, needs more optimization.
10 314 0.492053882420 Henry Cohn, 2026, needs more optimization.
10 315 0.492700232422 Henry Cohn, 2026, needs more optimization.
10 316 0.492795886840 Henry Cohn, 2026, needs more optimization.
10 317 0.493119319883 Henry Cohn, 2026, needs more optimization.
10 318 0.493240660617 Henry Cohn, 2026, needs more optimization.
10 319 0.493915829340 Henry Cohn, 2026, needs more optimization.
10 320 0.494175685056 Henry Cohn, 2026, needs more optimization.
10 321 0.494306351456 Henry Cohn, 2026, needs more optimization.
10 322 0.494520544415 Henry Cohn, 2026, needs more optimization.
10 323 0.494772229367 Henry Cohn, 2026, needs more optimization.
10 324 0.494795789865 Henry Cohn, 2026, needs more optimization.
10 325 0.494869093726 Henry Cohn, 2026, needs more optimization.
10 326 0.495036908003 Henry Cohn, 2026, needs more optimization.
10 327 0.495090275703 Henry Cohn, 2026, needs more optimization.
10 329 0.495096994646 Henry Cohn, 2026, needs more optimization.
10 330 0.495211453486 Henry Cohn, 2026, needs more optimization.
10 331 0.495415202006 Henry Cohn, 2026, needs more optimization.
10 332 0.495459328084 Henry Cohn, 2026, needs more optimization.
10 333 0.495727975331 Henry Cohn, 2026, needs more optimization.
10 334 0.496307200901 Henry Cohn, 2026, needs more optimization.
10 335 0.496424483018 Henry Cohn, 2026, needs more optimization.
10 336 0.496569905043 Henry Cohn, 2026, needs more optimization.
10 337 0.496834634796 Henry Cohn, 2026, needs more optimization.
10 338 0.496946174544 Henry Cohn, 2026, needs more optimization.
10 339 0.497060336581 Henry Cohn, 2026, needs more optimization.
10 340 0.497179501756 Henry Cohn, 2026, needs more optimization.
10 341 0.497313294525 Henry Cohn, 2026, needs more optimization.
10 342 0.497335631110 Henry Cohn, 2026, needs more optimization.
10 343 0.497426052656 Henry Cohn, 2026, needs more optimization.
10 344 0.497456305161 Henry Cohn, 2026, needs more optimization.
10 345 0.497582588315 Henry Cohn, 2026, needs more optimization.
10 346 0.498154224957 Henry Cohn, 2026, needs more optimization.
10 347 0.498290496034 Henry Cohn, 2026, needs more optimization.
10 348 0.498387667525 Henry Cohn, 2026, needs more optimization.
10 349 0.498394445105 Henry Cohn, 2026, needs more optimization.
10 350 0.498556948738 Henry Cohn, 2026, needs more optimization.
10 351 0.498665684447 Henry Cohn, 2026, needs more optimization.
10 352 0.498745912489 Henry Cohn, 2026, needs more optimization.
10 353 0.498783698563 Henry Cohn, 2026, needs more optimization.
10 355 0.498786494159 Henry Cohn, 2026, needs more optimization.
10 356 0.498829419875 Henry Cohn, 2026, needs more optimization.
10 357 0.498868806268 Henry Cohn, 2026, needs more optimization.
10 358 0.499121240302 Henry Cohn, 2026, needs more optimization.
10 360 0.499282891876 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 0.526725298485 Henry Cohn, 2026, needs more optimization.
10 512 0.530003387101 Henry Cohn, 2026, needs more optimization.
10 513 0.532757745031 Henry Cohn, 2026, needs more optimization.
10 514 0.533853448293 Henry Cohn, 2026, needs more optimization.
10 515 0.535039845396 Henry Cohn, 2026, needs more optimization.
10 516 0.536945737919 Henry Cohn, 2026, needs more optimization.
10 517 0.538187727389 Henry Cohn, 2026, needs more optimization.
10 518 0.538859070380 Henry Cohn, 2026, needs more optimization.
10 519 0.540302744031 Henry Cohn, 2026, needs more optimization.
10 520 0.541071908351 Henry Cohn, 2026, needs more optimization.
10 521 0.542228569116 Henry Cohn, 2026, needs more optimization.
10 522 0.543010528978 Henry Cohn, 2026, needs more optimization.
10 523 0.543649227911 Henry Cohn, 2026, needs more optimization.
10 524 0.544358388473 Henry Cohn, 2026, needs more optimization.
10 525 0.545227705280 Henry Cohn, 2026, needs more optimization.
10 526 0.545989564320 Henry Cohn, 2026, needs more optimization.
10 527 0.546338963146 Henry Cohn, 2026, needs more optimization.
10 528 0.547372432522 Henry Cohn, 2026, needs more optimization.
10 529 0.548033329419 Henry Cohn, 2026, needs more optimization.
10 530 0.548761233454 Henry Cohn, 2026, needs more optimization.
10 531 0.549363208238 Henry Cohn, 2026, needs more optimization.
10 532 0.549656959919 Henry Cohn, 2026, needs more optimization.
10 533 0.550240071946 Henry Cohn, 2026, needs more optimization.
10 534 0.550819232347 Henry Cohn, 2026, needs more optimization.
10 535 0.551336285514 Henry Cohn, 2026, needs more optimization.
10 536 0.552034741239 Henry Cohn, 2026, needs more optimization.
10 537 0.552523856804 Henry Cohn, 2026, needs more optimization.
10 538 0.553360527402 Henry Cohn, 2026, needs more optimization.
10 539 0.553516473480 Henry Cohn, 2026, needs more optimization.
10 540 0.554036898676 Henry Cohn, 2026, needs more optimization.
10 541 0.554471607970 Henry Cohn, 2026, needs more optimization.
10 542 0.554891100923 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 0.567879432829 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.
10 777 0.573079317473 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.
10 796 0.580555072386 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.
10 802 0.583466151973 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 0.590879368178 Henry Cohn, 2026, needs more optimization.
10 838 0.590889202762 Henry Cohn, 2026, needs more optimization.
10 839 0.591158199435 Henry Cohn, 2026, needs more optimization.
10 840 0.591171849672 Henry Cohn, 2026, needs more optimization.
10 841 0.591180729796 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.
10 868 0.594857770515 Henry Cohn, 2026, needs more optimization.
10 869 0.594905858672 Henry Cohn, 2026, needs more optimization.
10 870 0.594945140922 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 0.597083676115 Henry Cohn, 2026, needs more optimization.
10 889 0.597120621295 Henry Cohn, 2026, needs more optimization.
10 890 0.597164280831 Henry Cohn, 2026, needs more optimization.
10 891 0.597219301688 Henry Cohn, 2026, needs more optimization.
10 892 0.597246410113 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.
263⁢x8−408⁢x7+27724⁢x6−10136⁢x5−11182⁢x4+5880⁢x3−932⁢x2+56⁢x−1
11 71 0.252457221944 Henry Cohn, 2026, needs more optimization.
11 72 0.253231432637 Henry Cohn, 2026, needs more optimization.
11 73 0.253340784506 Henry Cohn, 2026, needs more optimization.
11 74 0.255282197533 Henry Cohn, 2026, needs more optimization.
11 75 0.256152422493 Henry Cohn, 2026, needs more optimization.
11 76 0.260611780462 Henry Cohn, 2026, needs more optimization.
11 77 0.260658461655 Henry Cohn, 2026, needs more optimization.
11 78 0.260785701795 Henry Cohn, 2026, needs more optimization.
11 79 0.261253438671 Henry Cohn, 2026, needs more optimization.
11 80 0.261310052547 Henry Cohn, 2026, needs more optimization.
11 81 0.262004277165 Henry Cohn, 2026, needs more optimization.
11 82 0.263453239754 Henry Cohn, 2026, needs more optimization.
11 83 0.264193721223 Henry Cohn, 2026, needs more optimization.
11 84 0.265218731030 Henry Cohn, 2026, needs more optimization.
11 85 0.266213158428 Henry Cohn, 2026, needs more optimization.
11 90 0.267191024627 Henry Cohn, 2026.
71⁢x2−4⁢x−4
11 91 0.273036354862 Henry Cohn, 2026, needs more optimization.
11 92 0.280580262154 Henry Cohn, 2026, needs more optimization.
11 93 0.281614171527 Henry Cohn, 2026, needs more optimization.
11 94 0.282805919347 Henry Cohn, 2026, needs more optimization.
11 95 0.283478101923 Henry Cohn, 2026, needs more optimization.
11 96 0.284720067810 Henry Cohn, 2026, needs more optimization.
11 97 0.285922912439 Henry Cohn, 2026, needs more optimization.
11 98 0.287787023425 Henry Cohn, 2026, needs more optimization.
11 99 0.288712383668 Henry Cohn, 2026, needs more optimization.
11 100 0.299860274989 Henry Cohn, 2026, needs more optimization.
11 101 0.302859605288 Henry Cohn, 2026, needs more optimization.
11 102 0.304440333190 Henry Cohn, 2026, needs more optimization.
11 103 0.305710084485 Henry Cohn, 2026, needs more optimization.
11 104 0.306554003777 Henry Cohn, 2026, needs more optimization.
11 105 0.307098294183 Henry Cohn, 2026, needs more optimization.
11 106 0.307735860920 Henry Cohn, 2026, needs more optimization.
11 107 0.310786210597 Henry Cohn, 2026, needs more optimization.
11 108 0.317734319490 Henry Cohn, 2026, needs more optimization.
11 109 0.320353778356 Henry Cohn, 2026, needs more optimization.
11 110 0.321720180383 Henry Cohn, 2026, needs more optimization.
11 111 0.323502843169 Henry Cohn, 2026, needs more optimization.
11 112 0.323965570441 Henry Cohn, 2026, needs more optimization.
11 113 0.324018848818 Henry Cohn, 2026, needs more optimization.
11 114 0.324153803427 Henry Cohn, 2026, needs more optimization.
11 115 0.324268687793 Henry Cohn, 2026, needs more optimization.
11 116 0.324384828714 Henry Cohn, 2026, needs more optimization.
11 117 0.324521235885 Henry Cohn, 2026, needs more optimization.
11 118 0.324910590267 Henry Cohn, 2026, needs more optimization.
11 119 0.325523427682 Henry Cohn, 2026, needs more optimization.
11 120 0.325605721325 Henry Cohn, 2026, needs more optimization.
11 121 0.325805249556 Henry Cohn, 2026, needs more optimization.
11 122 0.325945498909 Henry Cohn, 2026, needs more optimization.
11 123 0.328143225979 Henry Cohn, 2026, needs more optimization.
11 124 0.328653380576 Henry Cohn, 2026, needs more optimization.
11 125 0.332581622644 Henry Cohn, 2026, needs more optimization.
11 126 0.332697765607 Henry Cohn, 2026, needs more optimization.
11 127 0.332760063251 Henry Cohn, 2026, needs more optimization.
11 128 0.332853446705 Henry Cohn, 2026, needs more optimization.
11 129 0.333205451471 Henry Cohn, 2026, needs more optimization.
11 130 0.333241118518 Henry Cohn, 2026, needs more optimization.
11 131 0.333250409433 Henry Cohn, 2026, needs more optimization.
11 132 0.333250507725 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 0.361532791809 Henry Cohn, 2026, needs more optimization.
11 158 0.363876554217 Henry Cohn, 2026, needs more optimization.
11 159 0.368509337849 Henry Cohn, 2026, needs more optimization.
11 160 0.371731338805 Henry Cohn, 2026, needs more optimization.
11 161 0.373132150912 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 0.387092810732 Henry Cohn, 2026, needs more optimization.
11 168 0.389074036366 Henry Cohn, 2026, needs more optimization.
11 169 0.390142038372 Henry Cohn, 2026, needs more optimization.
11 170 0.391448613668 Henry Cohn, 2026, needs more optimization.
11 171 0.391488669495 Henry Cohn, 2026, needs more optimization.
11 172 0.391574217045 Henry Cohn, 2026, needs more optimization.
11 173 0.392069034371 Henry Cohn, 2026, needs more optimization.
11 174 0.392081983066 Henry Cohn, 2026, needs more optimization.
11 175 0.392801675298 Henry Cohn, 2026, needs more optimization.
11 176 0.393604762413 Henry Cohn, 2026, needs more optimization.
11 177 0.393936785272 Henry Cohn, 2026, needs more optimization.
11 178 0.394110351657 Henry Cohn, 2026, needs more optimization.
11 179 0.395181799907 Henry Cohn, 2026, needs more optimization.
11 180 0.395821428432 Henry Cohn, 2026, needs more optimization.
11 181 0.396164961786 Henry Cohn, 2026, needs more optimization.
11 182 0.396845343750 Henry Cohn, 2026, needs more optimization.
11 183 0.397265518908 Henry Cohn, 2026, needs more optimization.
11 184 0.397691692774 Henry Cohn, 2026, needs more optimization.
11 185 0.398484946869 Henry Cohn, 2026, needs more optimization.
11 186 0.399294860625 Henry Cohn, 2026, needs more optimization.
11 187 0.399800831771 Henry Cohn, 2026, needs more optimization.
11 188 0.400248784544 Henry Cohn, 2026, needs more optimization.
11 189 0.400799354770 Henry Cohn, 2026, needs more optimization.
11 190 0.401713205483 Henry Cohn, 2026, needs more optimization.
11 191 0.402667178861 Henry Cohn, 2026, needs more optimization.
11 192 0.403040052120 Henry Cohn, 2026, needs more optimization.
11 193 0.403533594338 Henry Cohn, 2026, needs more optimization.
11 194 0.403787419208 Henry Cohn, 2026, needs more optimization.
11 195 0.404522769385 Henry Cohn, 2026, needs more optimization.
11 196 0.406971728562 Henry Cohn, 2026, needs more optimization.
11 197 0.408055659895 Henry Cohn, 2026, needs more optimization.
11 198 0.409009683292 Henry Cohn, 2026, needs more optimization.
11 199 0.410354056251 Henry Cohn, 2026, needs more optimization.
11 200 0.410532358498 Henry Cohn, 2026, needs more optimization.
11 201 0.411042632322 Henry Cohn, 2026, needs more optimization.
11 202 0.411548296421 Henry Cohn, 2026, needs more optimization.
11 203 0.412155138642 Henry Cohn, 2026, needs more optimization.
11 204 0.412885570122 Henry Cohn, 2026, needs more optimization.
11 205 0.413254500229 Henry Cohn, 2026, needs more optimization.
11 206 0.413868530885 Henry Cohn, 2026, needs more optimization.
11 207 0.413868532449 Henry Cohn, 2026, needs more optimization.
11 208 0.414301132941 Henry Cohn, 2026, needs more optimization.
11 209 0.414793060556 Henry Cohn, 2026, needs more optimization.
11 210 0.415154921717 Henry Cohn, 2026, needs more optimization.
11 211 0.415408610376 Henry Cohn, 2026, needs more optimization.
11 212 0.416172019937 Henry Cohn, 2026, needs more optimization.
11 213 0.416530386359 Henry Cohn, 2026, needs more optimization.
11 214 0.417327484557 Henry Cohn, 2026, needs more optimization.
11 215 0.417860254120 Henry Cohn, 2026, needs more optimization.
11 216 0.418437270769 Henry Cohn, 2026, needs more optimization.
11 217 0.418727098232 Henry Cohn, 2026, needs more optimization.
11 218 0.419764082283 Henry Cohn, 2026, needs more optimization.
11 219 0.420159037373 Henry Cohn, 2026, needs more optimization.
11 220 0.420568652184 Henry Cohn, 2026, needs more optimization.
11 221 0.421089497668 Henry Cohn, 2026, needs more optimization.
11 222 0.421867940536 Henry Cohn, 2026, needs more optimization.
11 223 0.422308147342 Henry Cohn, 2026, needs more optimization.
11 224 0.422960788333 Henry Cohn, 2026, needs more optimization.
11 225 0.423243897640 Henry Cohn, 2026, needs more optimization.
11 226 0.423614036583 Henry Cohn, 2026, needs more optimization.
11 227 0.423771190799 Henry Cohn, 2026, needs more optimization.
11 228 0.424182257069 Henry Cohn, 2026, needs more optimization.
11 229 0.424446979528 Henry Cohn, 2026, needs more optimization.
11 230 0.425093293108 Henry Cohn, 2026, needs more optimization.
11 231 0.425438309453 Henry Cohn, 2026, needs more optimization.
11 232 0.425745160007 Henry Cohn, 2026, needs more optimization.
11 233 0.425938992548 Henry Cohn, 2026, needs more optimization.
11 234 0.426275332462 Henry Cohn, 2026, needs more optimization.
11 235 0.426733272866 Henry Cohn, 2026, needs more optimization.
11 236 0.426950029044 Henry Cohn, 2026, needs more optimization.
11 237 0.427230542448 Henry Cohn, 2026, needs more optimization.
11 238 0.427623336328 Henry Cohn, 2026, needs more optimization.
11 239 0.427811389454 Henry Cohn, 2026, needs more optimization.
11 240 0.428092484035 Henry Cohn, 2026, needs more optimization.
11 241 0.428398825514 Henry Cohn, 2026, needs more optimization.
11 242 0.428618994985 Henry Cohn, 2026, needs more optimization.
11 243 0.429044435057 Henry Cohn, 2026, needs more optimization.
11 244 0.430193485269 Henry Cohn, 2026, needs more optimization.
11 245 0.430431411282 Henry Cohn, 2026, needs more optimization.
11 246 0.430675783815 Henry Cohn, 2026, needs more optimization.
11 247 0.430852071882 Henry Cohn, 2026, needs more optimization.
11 248 0.431483247241 Henry Cohn, 2026, needs more optimization.
11 249 0.432401693112 Henry Cohn, 2026, needs more optimization.
11 250 0.433210622339 Henry Cohn, 2026, needs more optimization.
11 251 0.433556037503 Henry Cohn, 2026, needs more optimization.
11 252 0.434055185527 Henry Cohn, 2026, needs more optimization.
11 253 0.435639580547 Henry Cohn, 2026, needs more optimization.
11 254 0.435935916523 Henry Cohn, 2026, needs more optimization.
11 255 0.436532486065 Henry Cohn, 2026, needs more optimization.
11 256 0.437935553523 Henry Cohn, 2026, needs more optimization.
11 257 0.438603941970 Henry Cohn, 2026, needs more optimization.
11 258 0.438679521065 Henry Cohn, 2026, needs more optimization.
11 259 0.438800842127 Henry Cohn, 2026, needs more optimization.
11 260 0.438855382923 Henry Cohn, 2026, needs more optimization.
11 261 0.438881909559 Henry Cohn, 2026, needs more optimization.
11 262 0.438921208599 Henry Cohn, 2026, needs more optimization.
11 263 0.439031024080 Henry Cohn, 2026, needs more optimization.
11 264 0.439054034165 Henry Cohn, 2026, needs more optimization.
11 265 0.439102073525 Henry Cohn, 2026, needs more optimization.
11 266 0.439298862664 Henry Cohn, 2026, needs more optimization.
11 267 0.439345847702 Henry Cohn, 2026, needs more optimization.
11 268 0.439508698245 Henry Cohn, 2026, needs more optimization.
11 269 0.439610112955 Henry Cohn, 2026, needs more optimization.
11 270 0.439798699111 Henry Cohn, 2026, needs more optimization.
11 271 0.439894081478 Henry Cohn, 2026, needs more optimization.
11 272 0.439967604736 Henry Cohn, 2026, needs more optimization.
11 273 0.440336245460 Henry Cohn, 2026, needs more optimization.
11 274 0.440416932207 Henry Cohn, 2026, needs more optimization.
11 275 0.440523100496 Henry Cohn, 2026, needs more optimization.
11 276 0.440763035973 Henry Cohn, 2026, needs more optimization.
11 277 0.441105995012 Henry Cohn, 2026, needs more optimization.
11 278 0.441368624117 Henry Cohn, 2026, needs more optimization.
11 279 0.441568589633 Henry Cohn, 2026, needs more optimization.
11 280 0.441936166592 Henry Cohn, 2026, needs more optimization.
11 281 0.442408475510 Henry Cohn, 2026, needs more optimization.
11 282 0.442686432208 Henry Cohn, 2026, needs more optimization.
11 283 0.442753865512 Henry Cohn, 2026, needs more optimization.
11 284 0.443024964470 Henry Cohn, 2026, needs more optimization.
11 285 0.443573761215 Henry Cohn, 2026, needs more optimization.
11 286 0.444109086708 Henry Cohn, 2026, needs more optimization.
11 287 0.444196048206 Henry Cohn, 2026, needs more optimization.
11 288 0.444766564813 Henry Cohn, 2026, needs more optimization.
11 289 0.445146520062 Henry Cohn, 2026, needs more optimization.
11 290 0.445398313080 Henry Cohn, 2026, needs more optimization.
11 291 0.446220380102 Henry Cohn, 2026, needs more optimization.
11 292 0.447113833088 Henry Cohn, 2026, needs more optimization.
11 293 0.447786936419 Henry Cohn, 2026, needs more optimization.
11 294 0.448382362660 Henry Cohn, 2026, needs more optimization.
11 295 0.449284580927 Henry Cohn, 2026, needs more optimization.
11 296 0.451322873492 Henry Cohn, 2026, needs more optimization.
11 297 0.452267675043 Henry Cohn, 2026, needs more optimization.
11 298 0.453696173825 Henry Cohn, 2026, needs more optimization.
11 299 0.454253059291 Henry Cohn, 2026, needs more optimization.
11 300 0.455153109224 Henry Cohn, 2026, needs more optimization.
11 301 0.455715154244 Henry Cohn, 2026, needs more optimization.
11 302 0.456183402197 Henry Cohn, 2026, needs more optimization.
11 303 0.457633848860 Henry Cohn, 2026, needs more optimization.
11 304 0.458918832650 Henry Cohn, 2026, needs more optimization.
11 305 0.459787546418 Henry Cohn, 2026, needs more optimization.
11 306 0.460540553547 Henry Cohn, 2026, needs more optimization.
11 307 0.461245825063 Henry Cohn, 2026, needs more optimization.
11 308 0.462097792898 Henry Cohn, 2026, needs more optimization.
11 309 0.462698676168 Henry Cohn, 2026, needs more optimization.
11 310 0.463402936874 Henry Cohn, 2026, needs more optimization.
11 311 0.463584685555 Henry Cohn, 2026, needs more optimization.
11 312 0.464089829779 Henry Cohn, 2026, needs more optimization.
11 313 0.464248996300 Henry Cohn, 2026, needs more optimization.
11 314 0.464725656303 Henry Cohn, 2026, needs more optimization.
11 315 0.464933204414 Henry Cohn, 2026, needs more optimization.
11 316 0.465164623823 Henry Cohn, 2026, needs more optimization.
11 317 0.465649583902 Henry Cohn, 2026, needs more optimization.
11 318 0.465994803355 Henry Cohn, 2026, needs more optimization.
11 319 0.466208011107 Henry Cohn, 2026, needs more optimization.
11 320 0.466389895986 Henry Cohn, 2026, needs more optimization.
11 321 0.466931385668 Henry Cohn, 2026, needs more optimization.
11 322 0.467445098003 Henry Cohn, 2026, needs more optimization.
11 323 0.467783267249 Henry Cohn, 2026, needs more optimization.
11 324 0.468221104126 Henry Cohn, 2026, needs more optimization.
11 325 0.468764847834 Henry Cohn, 2026, needs more optimization.
11 326 0.468908562712 Henry Cohn, 2026, needs more optimization.
11 327 0.469216595836 Henry Cohn, 2026, needs more optimization.
11 328 0.469744445042 Henry Cohn, 2026, needs more optimization.
11 329 0.470053582184 Henry Cohn, 2026, needs more optimization.
11 342 0.470588235295 Henry Cohn, 2026.
17⁢x−8
11 343 0.472339930896 Henry Cohn, 2026, needs more optimization.
11 344 0.473621574787 Henry Cohn, 2026, needs more optimization.
11 345 0.474466376647 Henry Cohn, 2026, needs more optimization.
11 346 0.474892556998 Henry Cohn, 2026, needs more optimization.
11 347 0.475250987447 Henry Cohn, 2026, needs more optimization.
11 348 0.475930980876 Henry Cohn, 2026, needs more optimization.
11 349 0.476440639090 Henry Cohn, 2026, needs more optimization.
11 350 0.476740957288 Henry Cohn, 2026, needs more optimization.
11 351 0.477075007167 Henry Cohn, 2026, needs more optimization.
11 352 0.477386654506 Henry Cohn, 2026, needs more optimization.
11 353 0.477689492273 Henry Cohn, 2026, needs more optimization.
11 354 0.478298483500 Henry Cohn, 2026, needs more optimization.
11 355 0.478654753744 Henry Cohn, 2026, needs more optimization.
11 356 0.478969410559 Henry Cohn, 2026, needs more optimization.
11 357 0.479279559365 Henry Cohn, 2026, needs more optimization.
11 358 0.479810902163 Henry Cohn, 2026, needs more optimization.
11 359 0.480312737342 Henry Cohn, 2026, needs more optimization.
11 360 0.480843272073 Henry Cohn, 2026, needs more optimization.
11 361 0.481192262386 Henry Cohn, 2026, needs more optimization.
11 362 0.481466654594 Henry Cohn, 2026, needs more optimization.
11 363 0.481656793599 Henry Cohn, 2026, needs more optimization.
11 364 0.481773873730 Henry Cohn, 2026, needs more optimization.
11 365 0.481945779037 Henry Cohn, 2026, needs more optimization.
11 366 0.482241129597 Henry Cohn, 2026, needs more optimization.
11 367 0.482504542391 Henry Cohn, 2026, needs more optimization.
11 368 0.482902862395 Henry Cohn, 2026, needs more optimization.
11 369 0.483158955568 Henry Cohn, 2026, needs more optimization.
11 370 0.483365280179 Henry Cohn, 2026, needs more optimization.
11 371 0.483465282997 Henry Cohn, 2026, needs more optimization.
11 372 0.483582708756 Henry Cohn, 2026, needs more optimization.
11 373 0.483703074281 Henry Cohn, 2026, needs more optimization.
11 374 0.483760949578 Henry Cohn, 2026, needs more optimization.
11 375 0.483848368802 Henry Cohn, 2026, needs more optimization.
11 376 0.484108390660 Henry Cohn, 2026, needs more optimization.
11 377 0.484280151896 Henry Cohn, 2026, needs more optimization.
11 378 0.484417504202 Henry Cohn, 2026, needs more optimization.
11 379 0.484581576379 Henry Cohn, 2026, needs more optimization.
11 380 0.484807940158 Henry Cohn, 2026, needs more optimization.
11 381 0.484947771378 Henry Cohn, 2026, needs more optimization.
11 382 0.485180720657 Henry Cohn, 2026, needs more optimization.
11 383 0.485417631335 Henry Cohn, 2026, needs more optimization.
11 384 0.485558551128 Henry Cohn, 2026, needs more optimization.
11 385 0.486022793771 Henry Cohn, 2026, needs more optimization.
11 386 0.486286970619 Henry Cohn, 2026, needs more optimization.
11 387 0.486304114021 Henry Cohn, 2026, needs more optimization.
11 388 0.486337187200 Henry Cohn, 2026, needs more optimization.
11 389 0.486430816835 Henry Cohn, 2026, needs more optimization.
11 390 0.486503521716 Henry Cohn, 2026, needs more optimization.
11 391 0.486568443986 Henry Cohn, 2026, needs more optimization.
11 392 0.486671216286 Henry Cohn, 2026, needs more optimization.
11 393 0.486797798955 Henry Cohn, 2026, needs more optimization.
11 394 0.486879737421 Henry Cohn, 2026, needs more optimization.
11 395 0.486904248336 Henry Cohn, 2026, needs more optimization.
11 396 0.486985674923 Henry Cohn, 2026, needs more optimization.
11 397 0.487051266751 Henry Cohn, 2026, needs more optimization.
11 398 0.487117422405 Henry Cohn, 2026, needs more optimization.
11 399 0.487264299857 Henry Cohn, 2026, needs more optimization.
11 400 0.487462782579 Henry Cohn, 2026, needs more optimization.
11 402 0.487563715216 Henry Cohn, 2026, needs more optimization.
11 403 0.487703781967 Henry Cohn, 2026, needs more optimization.
11 404 0.487753492836 Henry Cohn, 2026, needs more optimization.
11 405 0.488140188650 Henry Cohn, 2026, needs more optimization.
11 407 0.488274978383 Henry Cohn, 2026, needs more optimization.
11 408 0.488518131417 Henry Cohn, 2026, needs more optimization.
11 410 0.488610000100 Henry Cohn, 2026, needs more optimization.
11 411 0.488690847648 Henry Cohn, 2026, needs more optimization.
11 412 0.488833784744 Henry Cohn, 2026, needs more optimization.
11 413 0.488914643364 Henry Cohn, 2026, needs more optimization.
11 414 0.489278711085 Henry Cohn, 2026, needs more optimization.
11 415 0.489344665567 Henry Cohn, 2026, needs more optimization.
11 416 0.489553715751 Henry Cohn, 2026, needs more optimization.
11 417 0.489741119874 Henry Cohn, 2026, needs more optimization.
11 418 0.489860024007 Henry Cohn, 2026, needs more optimization.
11 419 0.489947902855 Henry Cohn, 2026, needs more optimization.
11 420 0.490110720653 Henry Cohn, 2026, needs more optimization.
11 421 0.490267666645 Henry Cohn, 2026, needs more optimization.
11 422 0.490392432059 Henry Cohn, 2026, needs more optimization.
11 423 0.490455392135 Henry Cohn, 2026, needs more optimization.
11 424 0.490567400677 Henry Cohn, 2026, needs more optimization.
11 426 0.490751458992 Henry Cohn, 2026, needs more optimization.
11 427 0.490932145106 Henry Cohn, 2026, needs more optimization.
11 428 0.491164880523 Henry Cohn, 2026, needs more optimization.
11 429 0.491326236767 Henry Cohn, 2026, needs more optimization.
11 430 0.491609232057 Henry Cohn, 2026, needs more optimization.
11 431 0.491857090544 Henry Cohn, 2026, needs more optimization.
11 432 0.491952960521 Henry Cohn, 2026, needs more optimization.
11 433 0.492125078436 Henry Cohn, 2026, needs more optimization.
11 434 0.492303747574 Henry Cohn, 2026, needs more optimization.
11 435 0.492588187372 Henry Cohn, 2026, needs more optimization.
11 436 0.492720371150 Henry Cohn, 2026, needs more optimization.
11 437 0.492823953624 Henry Cohn, 2026, needs more optimization.
11 438 0.492886103075 Henry Cohn, 2026, needs more optimization.
11 439 0.492909571061 Henry Cohn, 2026, needs more optimization.
11 440 0.493021765171 Henry Cohn, 2026, needs more optimization.
11 441 0.493067840478 Henry Cohn, 2026, needs more optimization.
11 442 0.493096216259 Henry Cohn, 2026, needs more optimization.
11 443 0.493128118904 Henry Cohn, 2026, needs more optimization.
11 445 0.493330267596 Henry Cohn, 2026, needs more optimization.
11 446 0.494025800941 Henry Cohn, 2026, needs more optimization.
11 447 0.494463624997 Henry Cohn, 2026, needs more optimization.
11 448 0.494752152747 Henry Cohn, 2026, needs more optimization.
11 449 0.495090439217 Henry Cohn, 2026, needs more optimization.
11 450 0.495297191629 Henry Cohn, 2026, needs more optimization.
11 451 0.495438685875 Henry Cohn, 2026, needs more optimization.
11 452 0.495607575372 Henry Cohn, 2026, needs more optimization.
11 453 0.495662047499 Henry Cohn, 2026, needs more optimization.
11 454 0.495853317247 Henry Cohn, 2026, needs more optimization.
11 455 0.495948284593 Henry Cohn, 2026, needs more optimization.
11 456 0.496209653687 Henry Cohn, 2026, needs more optimization.
11 458 0.496253694124 Henry Cohn, 2026, needs more optimization.
11 459 0.496379229304 Henry Cohn, 2026, needs more optimization.
11 460 0.496715693180 Henry Cohn, 2026, needs more optimization.
11 461 0.497161375065 Henry Cohn, 2026, needs more optimization.
11 462 0.497257888401 Henry Cohn, 2026, needs more optimization.
11 463 0.497334550770 Henry Cohn, 2026, needs more optimization.
11 464 0.497562978466 Henry Cohn, 2026, needs more optimization.
11 465 0.497777642753 Henry Cohn, 2026, needs more optimization.
11 466 0.497860338409 Henry Cohn, 2026, needs more optimization.
11 467 0.498000271599 Henry Cohn, 2026, needs more optimization.
11 468 0.498220629143 Henry Cohn, 2026, needs more optimization.
11 469 0.498247671834 Henry Cohn, 2026, needs more optimization.
11 470 0.498361299827 Henry Cohn, 2026, needs more optimization.
11 471 0.498423959387 Henry Cohn, 2026, needs more optimization.
11 472 0.498744883902 Henry Cohn, 2026, needs more optimization.
11 473 0.498843729302 Henry Cohn, 2026, needs more optimization.
11 474 0.498865816319 Henry Cohn, 2026, needs more optimization.
11 477 0.498926837327 Henry Cohn, 2026, needs more optimization.
11 585 0.499664042007 Henry Cohn, 2026, needs more optimization.
11 586 0.499665774275 Henry Cohn, 2026, needs more optimization.
11 587 0.499967774882 Henry Cohn, 2026, needs more optimization.
11 588 0.499980852733 Henry Cohn, 2026, needs more optimization.
11 589 0.499999441885 Henry Cohn, 2026, needs more optimization.
11 590 0.499999516369 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 0.500141288801 Henry Cohn, 2026, needs more optimization.
11 595 0.500576410746 Henry Cohn, 2026, needs more optimization.
11 596 0.500894540533 Henry Cohn, 2026, needs more optimization.
11 597 0.502760017366 Henry Cohn, 2026, needs more optimization.
11 598 0.504320670565 Henry Cohn, 2026, needs more optimization.
11 599 0.505804457613 Henry Cohn, 2026, needs more optimization.
11 600 0.507055209482 Henry Cohn, 2026, needs more optimization.
11 601 0.507799381254 Henry Cohn, 2026, needs more optimization.
11 602 0.508459156281 Henry Cohn, 2026, needs more optimization.
11 603 0.509205748901 Henry Cohn, 2026, needs more optimization.
11 604 0.510242540478 Henry Cohn, 2026, needs more optimization.
11 605 0.511038576891 Henry Cohn, 2026, needs more optimization.
11 606 0.511418350644 Henry Cohn, 2026, needs more optimization.
11 607 0.512165310119 Henry Cohn, 2026, needs more optimization.
11 608 0.512508559306 Henry Cohn, 2026, needs more optimization.
11 609 0.513097653307 Henry Cohn, 2026, needs more optimization.
11 610 0.513635565978 Henry Cohn, 2026, needs more optimization.
11 611 0.514380665667 Henry Cohn, 2026, needs more optimization.
11 612 0.515195163275 Henry Cohn, 2026, needs more optimization.
11 613 0.515882492920 Henry Cohn, 2026, needs more optimization.
11 614 0.516453933033 Henry Cohn, 2026, needs more optimization.
11 615 0.516859667986 Henry Cohn, 2026, needs more optimization.
11 616 0.517561905410 Henry Cohn, 2026, needs more optimization.
11 617 0.518111906626 Henry Cohn, 2026, needs more optimization.
11 618 0.518471043457 Henry Cohn, 2026, needs more optimization.
11 619 0.518728881056 Henry Cohn, 2026, needs more optimization.
11 620 0.519186911678 Henry Cohn, 2026, needs more optimization.
11 621 0.519645927130 Henry Cohn, 2026, needs more optimization.
11 622 0.519890251658 Henry Cohn, 2026, needs more optimization.
11 623 0.520425877389 Henry Cohn, 2026, needs more optimization.
11 624 0.520941949818 Henry Cohn, 2026, needs more optimization.
11 625 0.521511931799 Henry Cohn, 2026, needs more optimization.
11 626 0.521845367194 Henry Cohn, 2026, needs more optimization.
11 627 0.522451196472 Henry Cohn, 2026, needs more optimization.
11 628 0.522778006158 Henry Cohn, 2026, needs more optimization.
11 629 0.523433699769 Henry Cohn, 2026, needs more optimization.
11 630 0.523970160329 Henry Cohn, 2026, needs more optimization.
11 631 0.524640632114 Henry Cohn, 2026, needs more optimization.
11 632 0.525118208464 Henry Cohn, 2026, needs more optimization.
11 633 0.525560638840 Henry Cohn, 2026, needs more optimization.
11 634 0.525870527873 Henry Cohn, 2026, needs more optimization.
11 635 0.526427414720 Henry Cohn, 2026, needs more optimization.
11 636 0.526760375241 Henry Cohn, 2026, needs more optimization.
11 637 0.526986986801 Henry Cohn, 2026, needs more optimization.
11 638 0.527305712715 Henry Cohn, 2026, needs more optimization.
11 639 0.527724782789 Henry Cohn, 2026, needs more optimization.
11 640 0.528159394046 Henry Cohn, 2026, needs more optimization.
11 643 0.528576384439 Henry Cohn, 2026, needs more optimization.
11 644 0.528661507624 Henry Cohn, 2026, needs more optimization.
11 645 0.528691798829 Henry Cohn, 2026, needs more optimization.
11 652 0.528692975180 Henry Cohn, 2026, needs more optimization.
11 653 0.528700582141 Henry Cohn, 2026, needs more optimization.
11 654 0.529055524939 Henry Cohn, 2026, needs more optimization.
11 655 0.529317692906 Henry Cohn, 2026, needs more optimization.
11 656 0.529905755124 Henry Cohn, 2026, needs more optimization.
11 657 0.530558613240 Henry Cohn, 2026, needs more optimization.
11 658 0.531152335779 Henry Cohn, 2026, needs more optimization.
11 659 0.531657171509 Henry Cohn, 2026, needs more optimization.
11 660 0.532090612629 Henry Cohn, 2026, needs more optimization.
11 661 0.533246969372 Henry Cohn, 2026, needs more optimization.
11 662 0.533714484413 Henry Cohn, 2026, needs more optimization.
11 663 0.534022751834 Henry Cohn, 2026, needs more optimization.
11 664 0.534428721421 Henry Cohn, 2026, needs more optimization.
11 665 0.535028728956 Henry Cohn, 2026, needs more optimization.
11 666 0.535275595083 Henry Cohn, 2026, needs more optimization.
11 667 0.535676792078 Henry Cohn, 2026, needs more optimization.
11 668 0.535993378358 Henry Cohn, 2026, needs more optimization.
11 669 0.536262391722 Henry Cohn, 2026, needs more optimization.
11 670 0.536416380070 Henry Cohn, 2026, needs more optimization.
11 671 0.536721730350 Henry Cohn, 2026, needs more optimization.
11 673 0.536760013077 Henry Cohn, 2026, needs more optimization.
11 674 0.536800876011 Henry Cohn, 2026, needs more optimization.
11 675 0.536942392372 Henry Cohn, 2026, needs more optimization.
11 676 0.537322435885 Henry Cohn, 2026, needs more optimization.
11 677 0.537701225040 Henry Cohn, 2026, needs more optimization.
11 678 0.538195635159 Henry Cohn, 2026, needs more optimization.
11 679 0.538480300355 Henry Cohn, 2026, needs more optimization.
11 680 0.538751755535 Henry Cohn, 2026, needs more optimization.
11 681 0.539056932024 Henry Cohn, 2026, needs more optimization.
11 682 0.539388031573 Henry Cohn, 2026, needs more optimization.
11 683 0.539694303844 Henry Cohn, 2026, needs more optimization.
11 684 0.539969724852 Henry Cohn, 2026, needs more optimization.
11 685 0.540275676976 Henry Cohn, 2026, needs more optimization.
11 686 0.540641903095 Henry Cohn, 2026, needs more optimization.
11 687 0.541005164620 Henry Cohn, 2026, needs more optimization.
11 688 0.541416359863 Henry Cohn, 2026, needs more optimization.
11 689 0.541913907856 Henry Cohn, 2026, needs more optimization.
11 690 0.542295508158 Henry Cohn, 2026, needs more optimization.
11 691 0.542651076337 Henry Cohn, 2026, needs more optimization.
11 692 0.543044829071 Henry Cohn, 2026, needs more optimization.
11 693 0.543227932091 Henry Cohn, 2026, needs more optimization.
11 694 0.543345387128 Henry Cohn, 2026, needs more optimization.
11 695 0.543753318400 Henry Cohn, 2026, needs more optimization.
11 696 0.544177054076 Henry Cohn, 2026, needs more optimization.
11 697 0.544431033527 Henry Cohn, 2026, needs more optimization.
11 698 0.544742047138 Henry Cohn, 2026, needs more optimization.
11 699 0.544991465133 Henry Cohn, 2026, needs more optimization.
11 700 0.545309976280 Henry Cohn, 2026, needs more optimization.
11 701 0.545543034517 Henry Cohn, 2026, needs more optimization.
11 702 0.545826829488 Henry Cohn, 2026, needs more optimization.
11 703 0.546078485053 Henry Cohn, 2026, needs more optimization.
11 704 0.546365651192 Henry Cohn, 2026, needs more optimization.
11 705 0.546637909059 Henry Cohn, 2026, needs more optimization.
11 706 0.546860178470 Henry Cohn, 2026, needs more optimization.
11 707 0.547015378914 Henry Cohn, 2026, needs more optimization.
11 708 0.547270235395 Henry Cohn, 2026, needs more optimization.
11 709 0.547568368921 Henry Cohn, 2026, needs more optimization.
11 710 0.547834529087 Henry Cohn, 2026, needs more optimization.
11 711 0.548045844767 Henry Cohn, 2026, needs more optimization.
11 712 0.548273694150 Henry Cohn, 2026, needs more optimization.
11 713 0.548651056545 Henry Cohn, 2026, needs more optimization.
11 714 0.548939823545 Henry Cohn, 2026, needs more optimization.
11 715 0.549161729906 Henry Cohn, 2026, needs more optimization.
11 716 0.549342406646 Henry Cohn, 2026, needs more optimization.
11 717 0.549673475582 Henry Cohn, 2026, needs more optimization.
11 718 0.549862764499 Henry Cohn, 2026, needs more optimization.
11 719 0.550149185812 Henry Cohn, 2026, needs more optimization.
11 720 0.550434427285 Henry Cohn, 2026, needs more optimization.
11 721 0.550743761730 Henry Cohn, 2026, needs more optimization.
11 722 0.550818398940 Henry Cohn, 2026, needs more optimization.
11 723 0.550984456273 Henry Cohn, 2026, needs more optimization.
11 724 0.551173629779 Henry Cohn, 2026, needs more optimization.
11 725 0.551345530177 Henry Cohn, 2026, needs more optimization.
11 726 0.551573338652 Henry Cohn, 2026, needs more optimization.
11 727 0.551833456623 Henry Cohn, 2026, needs more optimization.
11 728 0.552158882902 Henry Cohn, 2026, needs more optimization.
11 729 0.552344608045 Henry Cohn, 2026, needs more optimization.
11 730 0.552589886261 Henry Cohn, 2026, needs more optimization.
11 731 0.552786719240 Henry Cohn, 2026, needs more optimization.
11 732 0.553066058469 Henry Cohn, 2026, needs more optimization.
11 733 0.553242161332 Henry Cohn, 2026, needs more optimization.
11 734 0.553654625389 Henry Cohn, 2026, needs more optimization.
11 735 0.553803862669 Henry Cohn, 2026, needs more optimization.
11 736 0.554024020425 Henry Cohn, 2026, needs more optimization.
11 737 0.554155784934 Henry Cohn, 2026, needs more optimization.
11 738 0.554317108091 Henry Cohn, 2026, needs more optimization.
11 739 0.554574497050 Henry Cohn, 2026, needs more optimization.
11 740 0.554756405538 Henry Cohn, 2026, needs more optimization.
11 741 0.554942051551 Henry Cohn, 2026, needs more optimization.
11 742 0.555075760625 Henry Cohn, 2026, needs more optimization.
11 743 0.555257918158 Henry Cohn, 2026, needs more optimization.
11 744 0.555444837747 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 0.562767951988 Henry Cohn, 2026, needs more optimization.
11 985 0.563606372646 Henry Cohn, 2026, needs more optimization.
11 986 0.564083619357 Henry Cohn, 2026, needs more optimization.
11 987 0.564358531857 Henry Cohn, 2026, needs more optimization.
11 988 0.564570413127 Henry Cohn, 2026, needs more optimization.
11 989 0.564700692643 Henry Cohn, 2026, needs more optimization.
11 990 0.564809859573 Henry Cohn, 2026, needs more optimization.
11 991 0.564867040904 Henry Cohn, 2026, needs more optimization.
11 992 0.564959118353 Henry Cohn, 2026, needs more optimization.
11 993 0.566290250977 Henry Cohn, 2026, needs more optimization.
11 994 0.566829082455 Henry Cohn, 2026, needs more optimization.
11 995 0.567194979346 Henry Cohn, 2026, needs more optimization.
11 996 0.567467968921 Henry Cohn, 2026, needs more optimization.
11 997 0.568136770249 Henry Cohn, 2026, needs more optimization.
11 998 0.568511075641 Henry Cohn, 2026, needs more optimization.
11 999 0.568923800372 Henry Cohn, 2026, needs more optimization.
11 1000 0.569196667976 Henry Cohn, 2026, needs more optimization.
11 1001 0.569436811957 Henry Cohn, 2026, needs more optimization.
11 1002 0.569690396962 Henry Cohn, 2026, needs more optimization.
11 1003 0.569947334360 Henry Cohn, 2026, needs more optimization.
11 1004 0.570149653486 Henry Cohn, 2026, needs more optimization.
11 1005 0.570349246480 Henry Cohn, 2026, needs more optimization.
11 1006 0.570561108966 Henry Cohn, 2026, needs more optimization.
11 1007 0.570728005119 Henry Cohn, 2026, needs more optimization.
11 1008 0.570864832971 Henry Cohn, 2026, needs more optimization.
11 1009 0.570994874109 Henry Cohn, 2026, needs more optimization.
11 1010 0.571119579686 Henry Cohn, 2026, needs more optimization.
11 1011 0.571366341133 Henry Cohn, 2026, needs more optimization.
11 1012 0.571497230717 Henry Cohn, 2026, needs more optimization.
11 1013 0.571702100155 Henry Cohn, 2026, needs more optimization.
11 1014 0.571858314664 Henry Cohn, 2026, needs more optimization.
11 1015 0.572015155672 Henry Cohn, 2026, needs more optimization.
11 1016 0.572153712758 Henry Cohn, 2026, needs more optimization.
11 1017 0.572246691454 Henry Cohn, 2026, needs more optimization.
11 1018 0.572400553152 Henry Cohn, 2026, needs more optimization.
11 1019 0.572506577941 Henry Cohn, 2026, needs more optimization.
11 1020 0.572640770896 Henry Cohn, 2026, needs more optimization.
11 1021 0.572682298905 Henry Cohn, 2026, needs more optimization.
11 1022 0.572844583207 Henry Cohn, 2026, needs more optimization.
11 1023 0.572943049093 Henry Cohn, 2026, needs more optimization.
11 1024 0.573050364270 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 60 0.193457871625 Henry Cohn, 2026.
3088⁢x4−1184⁢x3−120⁢x2+40⁢x+1
12 61 0.196620537579 Henry Cohn, 2026, needs more optimization.
12 62 0.197162933815 Henry Cohn, 2026.
24⁢x3+92⁢x2−14⁢x−1
12 63 0.207401105190 Henry Cohn, 2026, needs more optimization.
12 64 0.211277513904 Henry Cohn, 2026, needs more optimization.
12 65 0.214410531348 Henry Cohn, 2026, needs more optimization.
12 66 0.215064206330 Henry Cohn, 2026, needs more optimization.
12 67 0.215316773918 Henry Cohn, 2026, needs more optimization.
12 68 0.220678206736 Henry Cohn, 2026, needs more optimization.
12 69 0.225479668014 Henry Cohn, 2026, needs more optimization.
12 70 0.228644883276 Henry Cohn, 2026, needs more optimization.
12 71 0.230996703869 Henry Cohn, 2026, needs more optimization.
12 72 0.232110202880 Henry Cohn, 2026, needs more optimization.
12 73 0.232386126300 Henry Cohn, 2026, needs more optimization.
12 74 0.233373126289 Henry Cohn, 2026, needs more optimization.
12 75 0.236174147784 Henry Cohn, 2026, needs more optimization.
12 76 0.237176010474 Henry Cohn, 2026, needs more optimization.
12 77 0.237968057446 Henry Cohn, 2025.
12 78 0.241648057068 Henry Cohn, 2025.
12 79 0.242863197883 Henry Cohn, 2026, needs more optimization.
12 80 0.247312790707 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 0.255753793422 Henry Cohn, 2026, needs more optimization.
12 83 0.258657191371 Henry Cohn, 2026, needs more optimization.
12 84 0.259074951046 Henry Cohn, 2026, needs more optimization.
12 85 0.260700615912 Henry Cohn, 2026, needs more optimization.
12 86 0.261447398295 Henry Cohn, 2026, needs more optimization.
12 87 0.261666110352 Henry Cohn, 2026, needs more optimization.
12 88 0.261807982271 Henry Cohn, 2026, needs more optimization.
12 89 0.262186145511 Henry Cohn, 2026, needs more optimization.
12 90 0.262662626369 Henry Cohn, 2026, needs more optimization.
12 91 0.263141215405 Henry Cohn, 2026, needs more optimization.
12 92 0.263474205142 Henry Cohn, 2026, needs more optimization.
12 93 0.264133942632 Henry Cohn, 2026, needs more optimization.
12 94 0.264728533633 Henry Cohn, 2026, needs more optimization.
12 95 0.265413634455 Henry Cohn, 2026, needs more optimization.
12 96 0.265971169427 Henry Cohn, 2026, needs more optimization.
12 97 0.266109755644 Henry Cohn, 2026, needs more optimization.
12 98 0.266755943752 Henry Cohn, 2026, needs more optimization.
12 99 0.267074812861 Henry Cohn, 2026, needs more optimization.
12 100 0.267113352298 Henry Cohn, 2026, needs more optimization.
12 101 0.267190932090 Henry Cohn, 2026, needs more optimization.
12 102 0.267190937318 Henry Cohn, 2026, needs more optimization.
12 103 0.269103247691 Henry Cohn, 2026, needs more optimization.
12 104 0.271259754125 Henry Cohn, 2026, needs more optimization.
12 105 0.273322872175 Henry Cohn, 2026, needs more optimization.
12 106 0.274536879631 Henry Cohn, 2026, needs more optimization.
12 107 0.275779018583 Henry Cohn, 2026, needs more optimization.
12 108 0.276805376332 Henry Cohn, 2026, needs more optimization.
12 109 0.277603298647 Henry Cohn, 2026, needs more optimization.
12 110 0.277964024387 Henry Cohn, 2026, needs more optimization.
12 111 0.278766142608 Henry Cohn, 2026, needs more optimization.
12 112 0.279501591769 Henry Cohn, 2026, needs more optimization.
12 113 0.281954415798 Henry Cohn, 2026, needs more optimization.
12 114 0.291572209371 Henry Cohn, 2026, needs more optimization.
12 115 0.291874267820 Henry Cohn, 2026, needs more optimization.
12 116 0.292564160599 Henry Cohn, 2026, needs more optimization.
12 117 0.293349265363 Henry Cohn, 2026, needs more optimization.
12 118 0.293573541873 Henry Cohn, 2026, needs more optimization.
12 121 0.294708984704 Henry Cohn, 2026, needs more optimization.
12 122 0.304154398750 Henry Cohn, 2026, needs more optimization.
12 123 0.305690147796 Henry Cohn, 2026, needs more optimization.
12 124 0.305733445727 Henry Cohn, 2026, needs more optimization.
12 125 0.305882748145 Henry Cohn, 2026, needs more optimization.
12 126 0.306150448061 Henry Cohn, 2026, needs more optimization.
12 127 0.306791570851 Henry Cohn, 2026, needs more optimization.
12 128 0.308118106478 Henry Cohn, 2026, needs more optimization.
12 129 0.309036133415 Henry Cohn, 2026, needs more optimization.
12 130 0.309511014600 Henry Cohn, 2026, needs more optimization.
12 131 0.309520547091 Henry Cohn, 2026, needs more optimization.
12 132 0.309837050243 Henry Cohn, 2026, needs more optimization.
12 133 0.310046116031 Henry Cohn, 2026, needs more optimization.
12 134 0.311214391854 Henry Cohn, 2026, needs more optimization.
12 135 0.312209438698 Henry Cohn, 2026, needs more optimization.
12 136 0.313796241357 Henry Cohn, 2026, needs more optimization.
12 137 0.315198430093 Henry Cohn, 2026, needs more optimization.
12 138 0.317974940937 Henry Cohn, 2026, needs more optimization.
12 139 0.319400033346 Henry Cohn, 2026, needs more optimization.
12 140 0.321962959301 Henry Cohn, 2026, needs more optimization.
12 141 0.322154039001 Henry Cohn, 2026, needs more optimization.
12 142 0.322591367138 Henry Cohn, 2026, needs more optimization.
12 143 0.322964757743 Henry Cohn, 2026, needs more optimization.
12 144 0.323296366475 Henry Cohn, 2026, needs more optimization.
12 145 0.323571904907 Henry Cohn, 2026, needs more optimization.
12 146 0.324013797548 Henry Cohn, 2026, needs more optimization.
12 147 0.324395557159 Henry Cohn, 2026, needs more optimization.
12 148 0.324858407759 Henry Cohn, 2026, needs more optimization.
12 149 0.325299978860 Henry Cohn, 2026, needs more optimization.
12 150 0.325731909098 Henry Cohn, 2026, needs more optimization.
12 151 0.327152193784 Henry Cohn, 2026, needs more optimization.
12 152 0.327599030019 Henry Cohn, 2026, needs more optimization.
12 153 0.328488822279 Henry Cohn, 2026, needs more optimization.
12 154 0.329005168155 Henry Cohn, 2026, needs more optimization.
12 155 0.329446375574 Henry Cohn, 2026, needs more optimization.
12 156 0.329624567488 Henry Cohn, 2026, needs more optimization.
12 157 0.329848058901 Henry Cohn, 2026, needs more optimization.
12 158 0.329987923234 Henry Cohn, 2026, needs more optimization.
12 159 0.329987923235 Henry Cohn, 2026, needs more optimization.
12 160 0.329989755326 Henry Cohn, 2026, needs more optimization.
12 161 0.330001789594 Henry Cohn, 2026, needs more optimization.
12 162 0.330019417922 Henry Cohn, 2026, needs more optimization.
12 163 0.331514886604 Henry Cohn, 2026, needs more optimization.
12 164 0.331670344873 Henry Cohn, 2026, needs more optimization.
12 165 0.332048900767 Henry Cohn, 2026, needs more optimization.
12 166 0.332624220508 Henry Cohn, 2026, needs more optimization.
12 167 0.332815836159 Henry Cohn, 2026, needs more optimization.
12 168 0.332827879001 Henry Cohn, 2026, needs more optimization.
12 169 0.332924539816 Henry Cohn, 2026, needs more optimization.
12 170 0.332996362770 Henry Cohn, 2026, needs more optimization.
12 171 0.333035218755 Henry Cohn, 2026, needs more optimization.
12 172 0.333059090736 Henry Cohn, 2026, needs more optimization.
12 173 0.333103333611 Henry Cohn, 2026, needs more optimization.
12 174 0.333152810136 Henry Cohn, 2026, needs more optimization.
12 175 0.333163020982 Henry Cohn, 2026, needs more optimization.
12 176 0.333193468922 Henry Cohn, 2026, needs more optimization.
12 177 0.333210653101 Henry Cohn, 2026, needs more optimization.
12 178 0.333243475245 Henry Cohn, 2026, needs more optimization.
12 179 0.333357097887 Henry Cohn, 2026, needs more optimization.
12 180 0.336132124803 Henry Cohn, 2026, needs more optimization.
12 181 0.344227906900 Henry Cohn, 2026, needs more optimization.
12 182 0.345968128804 Henry Cohn, 2026, needs more optimization.
12 183 0.349202861813 Henry Cohn, 2026, needs more optimization.
12 184 0.351145635727 Henry Cohn, 2026, needs more optimization.
12 185 0.352294053187 Henry Cohn, 2026, needs more optimization.
12 186 0.353347381367 Henry Cohn, 2026, needs more optimization.
12 187 0.353804004535 Henry Cohn, 2026, needs more optimization.
12 188 0.354982746791 Henry Cohn, 2026, needs more optimization.
12 189 0.355534173913 Henry Cohn, 2026, needs more optimization.
12 190 0.356784381430 Henry Cohn, 2026, needs more optimization.
12 191 0.358023713202 Henry Cohn, 2026, needs more optimization.
12 192 0.359656743708 Henry Cohn, 2026, needs more optimization.
12 193 0.360910156269 Henry Cohn, 2026, needs more optimization.
12 194 0.362078311597 Henry Cohn, 2026, needs more optimization.
12 195 0.363641965674 Henry Cohn, 2026, needs more optimization.
12 196 0.365047103695 Henry Cohn, 2026, needs more optimization.
12 197 0.365613164451 Henry Cohn, 2026, needs more optimization.
12 198 0.366069197214 Henry Cohn, 2026, needs more optimization.
12 199 0.366816690060 Henry Cohn, 2026, needs more optimization.
12 200 0.367146660507 Henry Cohn, 2026, needs more optimization.
12 201 0.368799336986 Henry Cohn, 2026, needs more optimization.
12 202 0.369143842809 Henry Cohn, 2026, needs more optimization.
12 203 0.370088276742 Henry Cohn, 2026, needs more optimization.
12 204 0.370848427237 Henry Cohn, 2026, needs more optimization.
12 205 0.372178758974 Henry Cohn, 2026, needs more optimization.
12 206 0.373165491849 Henry Cohn, 2026, needs more optimization.
12 207 0.374116796300 Henry Cohn, 2026, needs more optimization.
12 208 0.374957663116 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 0.378110870749 Henry Cohn, 2026, needs more optimization.
12 212 0.381048045257 Henry Cohn, 2026, needs more optimization.
12 213 0.381715483943 Henry Cohn, 2026, needs more optimization.
12 214 0.381837370060 Henry Cohn, 2026, needs more optimization.
12 215 0.382879346145 Henry Cohn, 2026, needs more optimization.
12 216 0.384001520877 Henry Cohn, 2026, needs more optimization.
12 217 0.384574977873 Henry Cohn, 2026, needs more optimization.
12 218 0.385469664070 Henry Cohn, 2026, needs more optimization.
12 219 0.386490647429 Henry Cohn, 2026, needs more optimization.
12 220 0.387210676928 Henry Cohn, 2026, needs more optimization.
12 221 0.387727383860 Henry Cohn, 2026, needs more optimization.
12 222 0.388337771495 Henry Cohn, 2026, needs more optimization.
12 223 0.388800389558 Henry Cohn, 2026, needs more optimization.
12 224 0.389489678385 Henry Cohn, 2026, needs more optimization.
12 225 0.390284377471 Henry Cohn, 2026, needs more optimization.
12 226 0.390649601674 Henry Cohn, 2026, needs more optimization.
12 227 0.391277921621 Henry Cohn, 2026, needs more optimization.
12 228 0.391370216930 Henry Cohn, 2026, needs more optimization.
12 229 0.392255302611 Henry Cohn, 2026, needs more optimization.
12 230 0.392405902563 Henry Cohn, 2026, needs more optimization.
12 231 0.392524531830 Henry Cohn, 2026, needs more optimization.
12 232 0.393336514544 Henry Cohn, 2026, needs more optimization.
12 233 0.393443039661 Henry Cohn, 2026, needs more optimization.
12 234 0.393515888204 Henry Cohn, 2026, needs more optimization.
12 235 0.393957399823 Henry Cohn, 2026, needs more optimization.
12 236 0.394077186616 Henry Cohn, 2026, needs more optimization.
12 237 0.396288628199 Henry Cohn, 2026, needs more optimization.
12 238 0.396547465816 Henry Cohn, 2026, needs more optimization.
12 239 0.397323192741 Henry Cohn, 2026, needs more optimization.
12 240 0.398288816868 Henry Cohn, 2026, needs more optimization.
12 241 0.399381566485 Henry Cohn, 2026, needs more optimization.
12 288 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
12 290 0.4 Henry Cohn, 2026.
5⁢x−2
12 291 0.401758592621 Henry Cohn, 2026, needs more optimization.
12 292 0.406638298133 Henry Cohn, 2026, needs more optimization.
12 293 0.409435417602 Henry Cohn, 2026, needs more optimization.
12 294 0.410774353159 Henry Cohn, 2026, needs more optimization.
12 295 0.412741311972 Henry Cohn, 2026, needs more optimization.
12 296 0.414339582569 Henry Cohn, 2026, needs more optimization.
12 297 0.415478345072 Henry Cohn, 2026, needs more optimization.
12 298 0.417387599524 Henry Cohn, 2026, needs more optimization.
12 299 0.418812243139 Henry Cohn, 2026, needs more optimization.
12 300 0.419879782130 Henry Cohn, 2026, needs more optimization.
12 301 0.420859253651 Henry Cohn, 2026, needs more optimization.
12 302 0.422077299398 Henry Cohn, 2026, needs more optimization.
12 303 0.423142317678 Henry Cohn, 2026, needs more optimization.
12 304 0.424154871567 Henry Cohn, 2026, needs more optimization.
12 305 0.425044742810 Henry Cohn, 2026, needs more optimization.
12 306 0.426484368004 Henry Cohn, 2026, needs more optimization.
12 307 0.427433485161 Henry Cohn, 2026, needs more optimization.
12 308 0.428247055911 Henry Cohn, 2026, needs more optimization.
12 309 0.428339580927 Henry Cohn, 2026, needs more optimization.
12 310 0.429336218186 Henry Cohn, 2026, needs more optimization.
12 311 0.430213791689 Henry Cohn, 2026, needs more optimization.
12 312 0.430820606314 Henry Cohn, 2026, needs more optimization.
12 313 0.431232528878 Henry Cohn, 2026, needs more optimization.
12 314 0.431719417934 Henry Cohn, 2026, needs more optimization.
12 315 0.432279798804 Henry Cohn, 2026, needs more optimization.
12 316 0.432675655522 Henry Cohn, 2026, needs more optimization.
12 317 0.433099539678 Henry Cohn, 2026, needs more optimization.
12 318 0.433204439342 Henry Cohn, 2026, needs more optimization.
12 319 0.433591056047 Henry Cohn, 2026, needs more optimization.
12 320 0.434127104569 Henry Cohn, 2026, needs more optimization.
12 321 0.434710396157 Henry Cohn, 2026, needs more optimization.
12 322 0.435146091037 Henry Cohn, 2026, needs more optimization.
12 323 0.435626801663 Henry Cohn, 2026, needs more optimization.
12 324 0.436063867229 Henry Cohn, 2026, needs more optimization.
12 325 0.436612971432 Henry Cohn, 2026, needs more optimization.
12 326 0.437004101733 Henry Cohn, 2026, needs more optimization.
12 327 0.437262322255 Henry Cohn, 2026, needs more optimization.
12 328 0.437697580098 Henry Cohn, 2026, needs more optimization.
12 329 0.438252412813 Henry Cohn, 2026, needs more optimization.
12 330 0.438279275572 Henry Cohn, 2026, needs more optimization.
12 332 0.439101439135 Henry Cohn, 2026, needs more optimization.
12 333 0.439301776179 Henry Cohn, 2026, needs more optimization.
12 334 0.439957587551 Henry Cohn, 2026, needs more optimization.
12 335 0.439966477714 Henry Cohn, 2026, needs more optimization.
12 336 0.440339744087 Henry Cohn, 2026, needs more optimization.
12 337 0.440885396514 Henry Cohn, 2026, needs more optimization.
12 338 0.441031051062 Henry Cohn, 2026, needs more optimization.
12 339 0.441502330226 Henry Cohn, 2026, needs more optimization.
12 340 0.441615259790 Henry Cohn, 2026, needs more optimization.
12 341 0.442053112387 Henry Cohn, 2026, needs more optimization.
12 342 0.442166678186 Henry Cohn, 2026, needs more optimization.
12 343 0.442340279725 Henry Cohn, 2026, needs more optimization.
12 344 0.442592423998 Henry Cohn, 2026, needs more optimization.
12 345 0.443082944159 Henry Cohn, 2026, needs more optimization.
12 346 0.443673376918 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 0.447147073485 Henry Cohn, 2026, needs more optimization.
12 410 0.447929427677 Henry Cohn, 2026, needs more optimization.
12 411 0.448617306124 Henry Cohn, 2026, needs more optimization.
12 412 0.449181905329 Henry Cohn, 2026, needs more optimization.
12 413 0.450252064644 Henry Cohn, 2026, needs more optimization.
12 414 0.450745426410 Henry Cohn, 2026, needs more optimization.
12 415 0.450786028228 Henry Cohn, 2026, needs more optimization.
12 416 0.451181381009 Henry Cohn, 2026, needs more optimization.
12 417 0.451398624771 Henry Cohn, 2026, needs more optimization.
12 418 0.451498145872 Henry Cohn, 2026, needs more optimization.
12 419 0.451849469087 Henry Cohn, 2026, needs more optimization.
12 420 0.452184525253 Henry Cohn, 2026, needs more optimization.
12 421 0.452262848504 Henry Cohn, 2026, needs more optimization.
12 422 0.452320798017 Henry Cohn, 2026, needs more optimization.
12 423 0.452517064422 Henry Cohn, 2026, needs more optimization.
12 424 0.456884871472 Henry Cohn, 2026, needs more optimization.
12 425 0.457293597192 Henry Cohn, 2026, needs more optimization.
12 426 0.458841096535 Henry Cohn, 2026, needs more optimization.
12 428 0.461134007548 Henry Cohn, 2026, needs more optimization.
12 429 0.462352793103 Henry Cohn, 2026, needs more optimization.
12 430 0.462969790235 Henry Cohn, 2026, needs more optimization.
12 431 0.462991692924 Henry Cohn, 2026, needs more optimization.
12 432 0.463017220520 Henry Cohn, 2026, needs more optimization.
12 433 0.463836590941 Henry Cohn, 2026, needs more optimization.
12 434 0.463960173159 Henry Cohn, 2026, needs more optimization.
12 435 0.464574841657 Henry Cohn, 2026, needs more optimization.
12 436 0.464683109233 Henry Cohn, 2026, needs more optimization.
12 437 0.465614373396 Henry Cohn, 2026, needs more optimization.
12 438 0.466374974905 Henry Cohn, 2026, needs more optimization.
12 439 0.466430095206 Henry Cohn, 2026, needs more optimization.
12 440 0.466716702752 Henry Cohn, 2026, needs more optimization.
12 442 0.466842591595 Henry Cohn, 2026, needs more optimization.
12 443 0.467018371925 Henry Cohn, 2026, needs more optimization.
12 444 0.467288063190 Henry Cohn, 2026, needs more optimization.
12 445 0.467547925958 Henry Cohn, 2026, needs more optimization.
12 446 0.467618019440 Henry Cohn, 2026, needs more optimization.
12 447 0.467999049992 Henry Cohn, 2026, needs more optimization.
12 448 0.468426244257 Henry Cohn, 2026, needs more optimization.
12 449 0.468573044821 Henry Cohn, 2026, needs more optimization.
12 450 0.468646877166 Henry Cohn, 2026, needs more optimization.
12 451 0.468805294256 Henry Cohn, 2026, needs more optimization.
12 452 0.469051188429 Henry Cohn, 2026, needs more optimization.
12 453 0.469331529187 Henry Cohn, 2026, needs more optimization.
12 454 0.469608830975 Henry Cohn, 2026, needs more optimization.
12 455 0.469681333812 Henry Cohn, 2026, needs more optimization.
12 456 0.470012493433 Henry Cohn, 2026, needs more optimization.
12 457 0.470415859788 Henry Cohn, 2026, needs more optimization.
12 458 0.470555448479 Henry Cohn, 2026, needs more optimization.
12 459 0.470765859111 Henry Cohn, 2026, needs more optimization.
12 460 0.470862021121 Henry Cohn, 2026, needs more optimization.
12 461 0.471123130350 Henry Cohn, 2026, needs more optimization.
12 462 0.471305480232 Henry Cohn, 2026, needs more optimization.
12 463 0.471405157139 Henry Cohn, 2026, needs more optimization.
12 464 0.471501185282 Henry Cohn, 2026, needs more optimization.
12 465 0.471798523252 Henry Cohn, 2026, needs more optimization.
12 466 0.472035665666 Henry Cohn, 2026, needs more optimization.
12 467 0.472176229167 Henry Cohn, 2026, needs more optimization.
12 468 0.472361558116 Henry Cohn, 2026, needs more optimization.
12 469 0.472508888959 Henry Cohn, 2026, needs more optimization.
12 470 0.472567001063 Henry Cohn, 2026, needs more optimization.
12 471 0.472640592102 Henry Cohn, 2026, needs more optimization.
12 472 0.472852498492 Henry Cohn, 2026, needs more optimization.
12 473 0.472971171139 Henry Cohn, 2026, needs more optimization.
12 474 0.473191245454 Henry Cohn, 2026, needs more optimization.
12 475 0.473311304332 Henry Cohn, 2026, needs more optimization.
12 476 0.473502543705 Henry Cohn, 2026, needs more optimization.
12 477 0.473735136757 Henry Cohn, 2026, needs more optimization.
12 478 0.474002408764 Henry Cohn, 2026, needs more optimization.
12 479 0.474132262698 Henry Cohn, 2026, needs more optimization.
12 480 0.474154325441 Henry Cohn, 2026, needs more optimization.
12 481 0.474559509590 Henry Cohn, 2026, needs more optimization.
12 482 0.474718238671 Henry Cohn, 2026, needs more optimization.
12 483 0.474835387157 Henry Cohn, 2026, needs more optimization.
12 484 0.475024833665 Henry Cohn, 2026, needs more optimization.
12 485 0.475244224205 Henry Cohn, 2026, needs more optimization.
12 486 0.475353038101 Henry Cohn, 2026, needs more optimization.
12 487 0.475667750854 Henry Cohn, 2026, needs more optimization.
12 488 0.475842125274 Henry Cohn, 2026, needs more optimization.
12 489 0.475999720099 Henry Cohn, 2026, needs more optimization.
12 490 0.476041580033 Henry Cohn, 2026, needs more optimization.
12 491 0.476150397056 Henry Cohn, 2026, needs more optimization.
12 492 0.476258535187 Henry Cohn, 2026, needs more optimization.
12 493 0.476402728686 Henry Cohn, 2026, needs more optimization.
12 494 0.476571394211 Henry Cohn, 2026, needs more optimization.
12 495 0.476729555862 Henry Cohn, 2026, needs more optimization.
12 496 0.476773846784 Henry Cohn, 2026, needs more optimization.
12 497 0.476961963243 Henry Cohn, 2026, needs more optimization.
12 498 0.477172008458 Henry Cohn, 2026, needs more optimization.
12 499 0.477481864050 Henry Cohn, 2026, needs more optimization.
12 500 0.477528305927 Henry Cohn, 2026, needs more optimization.
12 501 0.477594032096 Henry Cohn, 2026, needs more optimization.
12 502 0.477722157864 Henry Cohn, 2026, needs more optimization.
12 503 0.477839446449 Henry Cohn, 2026, needs more optimization.
12 504 0.478183432107 Henry Cohn, 2026, needs more optimization.
12 505 0.478495650067 Henry Cohn, 2026, needs more optimization.
12 506 0.478500927528 Henry Cohn, 2026, needs more optimization.
12 507 0.478819113550 Henry Cohn, 2026, needs more optimization.
12 508 0.478909859755 Henry Cohn, 2026, needs more optimization.
12 509 0.479118873860 Henry Cohn, 2026, needs more optimization.
12 511 0.479336451917 Henry Cohn, 2026, needs more optimization.
12 512 0.479559167738 Henry Cohn, 2026, needs more optimization.
12 513 0.479749536792 Henry Cohn, 2026, needs more optimization.
12 514 0.479805731792 Henry Cohn, 2026, needs more optimization.
12 515 0.480126991747 Henry Cohn, 2026, needs more optimization.
12 516 0.480370002458 Henry Cohn, 2026, needs more optimization.
12 517 0.480456959513 Henry Cohn, 2026, needs more optimization.
12 518 0.480662489351 Henry Cohn, 2026, needs more optimization.
12 519 0.480994867117 Henry Cohn, 2026, needs more optimization.
12 520 0.481129185176 Henry Cohn, 2026, needs more optimization.
12 521 0.481162548485 Henry Cohn, 2026, needs more optimization.
12 522 0.481233781161 Henry Cohn, 2026, needs more optimization.
12 523 0.481379805962 Henry Cohn, 2026, needs more optimization.
12 524 0.481453733559 Henry Cohn, 2026, needs more optimization.
12 525 0.481626335443 Henry Cohn, 2026, needs more optimization.
12 526 0.481804290516 Henry Cohn, 2026, needs more optimization.
12 527 0.481893513610 Henry Cohn, 2026, needs more optimization.
12 528 0.482024367389 Henry Cohn, 2026, needs more optimization.
12 529 0.482198482933 Henry Cohn, 2026, needs more optimization.
12 530 0.482387810534 Henry Cohn, 2026, needs more optimization.
12 531 0.482452014850 Henry Cohn, 2026, needs more optimization.
12 532 0.482590383022 Henry Cohn, 2026, needs more optimization.
12 533 0.482722801879 Henry Cohn, 2026, needs more optimization.
12 534 0.482791622718 Henry Cohn, 2026, needs more optimization.
12 535 0.482948344893 Henry Cohn, 2026, needs more optimization.
12 536 0.483068505038 Henry Cohn, 2026, needs more optimization.
12 537 0.483118380933 Henry Cohn, 2026, needs more optimization.
12 538 0.483241119168 Henry Cohn, 2026, needs more optimization.
12 539 0.483419568719 Henry Cohn, 2026, needs more optimization.
12 540 0.483465465077 Henry Cohn, 2026, needs more optimization.
12 541 0.483527313894 Henry Cohn, 2026, needs more optimization.
12 542 0.483676926148 Henry Cohn, 2026, needs more optimization.
12 543 0.483819256933 Henry Cohn, 2026, needs more optimization.
12 544 0.483910506227 Henry Cohn, 2026, needs more optimization.
12 545 0.483979159543 Henry Cohn, 2026, needs more optimization.
12 546 0.484084883576 Henry Cohn, 2026, needs more optimization.
12 547 0.484364686608 Henry Cohn, 2026, needs more optimization.
12 548 0.484616246856 Henry Cohn, 2026, needs more optimization.
12 549 0.484875157928 Henry Cohn, 2026, needs more optimization.
12 550 0.485010611226 Henry Cohn, 2026, needs more optimization.
12 551 0.485190840336 Henry Cohn, 2026, needs more optimization.
12 552 0.485339819710 Henry Cohn, 2026, needs more optimization.
12 553 0.485393348858 Henry Cohn, 2026, needs more optimization.
12 554 0.485612109896 Henry Cohn, 2026, needs more optimization.
12 555 0.485682165502 Henry Cohn, 2026, needs more optimization.
12 556 0.485734800962 Henry Cohn, 2026, needs more optimization.
12 557 0.485842477870 Henry Cohn, 2026, needs more optimization.
12 558 0.485951706408 Henry Cohn, 2026, needs more optimization.
12 559 0.486116183572 Henry Cohn, 2026, needs more optimization.
12 560 0.486233877601 Henry Cohn, 2026, needs more optimization.
12 561 0.486357460506 Henry Cohn, 2026, needs more optimization.
12 562 0.486385962368 Henry Cohn, 2026, needs more optimization.
12 563 0.486552521608 Henry Cohn, 2026, needs more optimization.
12 564 0.486636869676 Henry Cohn, 2026, needs more optimization.
12 565 0.486757033636 Henry Cohn, 2026, needs more optimization.
12 566 0.486842333605 Henry Cohn, 2026, needs more optimization.
12 567 0.486851172350 Henry Cohn, 2026, needs more optimization.
12 568 0.487032875236 Henry Cohn, 2026, needs more optimization.
12 569 0.487133575984 Henry Cohn, 2026, needs more optimization.
12 570 0.487317742110 Henry Cohn, 2026, needs more optimization.
12 571 0.487420574856 Henry Cohn, 2026, needs more optimization.
12 572 0.487551826375 Henry Cohn, 2026, needs more optimization.
12 573 0.487615532271 Henry Cohn, 2026, needs more optimization.
12 574 0.487701838066 Henry Cohn, 2026, needs more optimization.
12 575 0.487794160920 Henry Cohn, 2026, needs more optimization.
12 576 0.487856592420 Henry Cohn, 2026, needs more optimization.
12 577 0.488031281335 Henry Cohn, 2026, needs more optimization.
12 578 0.488252022271 Henry Cohn, 2026, needs more optimization.
12 579 0.488343516291 Henry Cohn, 2026, needs more optimization.
12 580 0.488372078598 Henry Cohn, 2026, needs more optimization.
12 582 0.488480971018 Henry Cohn, 2026, needs more optimization.
12 584 0.488584002191 Henry Cohn, 2026, needs more optimization.
12 585 0.488670046213 Henry Cohn, 2026, needs more optimization.
12 586 0.488782045808 Henry Cohn, 2026, needs more optimization.
12 587 0.488846951757 Henry Cohn, 2026, needs more optimization.
12 588 0.488973228045 Henry Cohn, 2026, needs more optimization.
12 589 0.489025288853 Henry Cohn, 2026, needs more optimization.
12 590 0.489179775006 Henry Cohn, 2026, needs more optimization.
12 591 0.489256637365 Henry Cohn, 2026, needs more optimization.
12 592 0.489348849697 Henry Cohn, 2026, needs more optimization.
12 593 0.489406407305 Henry Cohn, 2026, needs more optimization.
12 594 0.489463027668 Henry Cohn, 2026, needs more optimization.
12 595 0.489622523068 Henry Cohn, 2026, needs more optimization.
12 596 0.489664946098 Henry Cohn, 2026, needs more optimization.
12 597 0.489695290988 Henry Cohn, 2026, needs more optimization.
12 598 0.489802454840 Henry Cohn, 2026, needs more optimization.
12 600 0.489888782229 Henry Cohn, 2026, needs more optimization.
12 601 0.489982578517 Henry Cohn, 2026, needs more optimization.
12 602 0.490039622109 Henry Cohn, 2026, needs more optimization.
12 603 0.490185664129 Henry Cohn, 2026, needs more optimization.
12 604 0.490323599970 Henry Cohn, 2026, needs more optimization.
12 605 0.490348123989 Henry Cohn, 2026, needs more optimization.
12 606 0.490441511577 Henry Cohn, 2026, needs more optimization.
12 607 0.490614687765 Henry Cohn, 2026, needs more optimization.
12 608 0.490746821454 Henry Cohn, 2026, needs more optimization.
12 612 0.490827031497 Henry Cohn, 2026, needs more optimization.
12 613 0.491018864232 Henry Cohn, 2026, needs more optimization.
12 615 0.491131302118 Henry Cohn, 2026, needs more optimization.
12 616 0.491309944162 Henry Cohn, 2026, needs more optimization.
12 617 0.491424305721 Henry Cohn, 2026, needs more optimization.
12 618 0.491487756475 Henry Cohn, 2026, needs more optimization.
12 619 0.491537084405 Henry Cohn, 2026, needs more optimization.
12 620 0.491734381253 Henry Cohn, 2026, needs more optimization.
12 621 0.491746070883 Henry Cohn, 2026, needs more optimization.
12 622 0.491864694768 Henry Cohn, 2026, needs more optimization.
12 624 0.491890952457 Henry Cohn, 2026, needs more optimization.
12 625 0.491924751822 Henry Cohn, 2026, needs more optimization.
12 626 0.492030052022 Henry Cohn, 2026, needs more optimization.
12 627 0.492086019728 Henry Cohn, 2026, needs more optimization.
12 628 0.492121858700 Henry Cohn, 2026, needs more optimization.
12 629 0.492223268491 Henry Cohn, 2026, needs more optimization.
12 630 0.492293769265 Henry Cohn, 2026, needs more optimization.
12 631 0.492355588599 Henry Cohn, 2026, needs more optimization.
12 633 0.492491004040 Henry Cohn, 2026, needs more optimization.
12 635 0.492555551983 Henry Cohn, 2026, needs more optimization.
12 636 0.492730433116 Henry Cohn, 2026, needs more optimization.
12 637 0.492742738336 Henry Cohn, 2026, needs more optimization.
12 638 0.492879866892 Henry Cohn, 2026, needs more optimization.
12 639 0.492914944198 Henry Cohn, 2026, needs more optimization.
12 640 0.493044962624 Henry Cohn, 2026, needs more optimization.
12 641 0.493109239481 Henry Cohn, 2026, needs more optimization.
12 642 0.493191561270 Henry Cohn, 2026, needs more optimization.
12 643 0.493263069080 Henry Cohn, 2026, needs more optimization.
12 644 0.493310150574 Henry Cohn, 2026, needs more optimization.
12 645 0.493366648029 Henry Cohn, 2026, needs more optimization.
12 646 0.493482668161 Henry Cohn, 2026, needs more optimization.
12 652 0.493555189269 Henry Cohn, 2026, needs more optimization.
12 653 0.493656964634 Henry Cohn, 2026, needs more optimization.
12 654 0.493684241732 Henry Cohn, 2026, needs more optimization.
12 655 0.493770346947 Henry Cohn, 2026, needs more optimization.
12 656 0.493774382963 Henry Cohn, 2026, needs more optimization.
12 657 0.493900977657 Henry Cohn, 2026, needs more optimization.
12 658 0.493981022403 Henry Cohn, 2026, needs more optimization.
12 660 0.494052152480 Henry Cohn, 2026, needs more optimization.
12 662 0.494081005121 Henry Cohn, 2026, needs more optimization.
12 663 0.494128496542 Henry Cohn, 2026, needs more optimization.
12 664 0.494291410152 Henry Cohn, 2026, needs more optimization.
12 665 0.494373419128 Henry Cohn, 2026, needs more optimization.
12 666 0.494396456303 Henry Cohn, 2026, needs more optimization.
12 667 0.494465453159 Henry Cohn, 2026, needs more optimization.
12 669 0.494597057381 Henry Cohn, 2026, needs more optimization.
12 670 0.494718633199 Henry Cohn, 2026, needs more optimization.
12 671 0.494724014252 Henry Cohn, 2026, needs more optimization.
12 673 0.494810829521 Henry Cohn, 2026, needs more optimization.
12 674 0.494844156798 Henry Cohn, 2026, needs more optimization.
12 675 0.494879244321 Henry Cohn, 2026, needs more optimization.
12 677 0.494950443218 Henry Cohn, 2026, needs more optimization.
12 679 0.495033298252 Henry Cohn, 2026, needs more optimization.
12 681 0.495103905099 Henry Cohn, 2026, needs more optimization.
12 682 0.495135365549 Henry Cohn, 2026, needs more optimization.
12 683 0.495237062418 Henry Cohn, 2026, needs more optimization.
12 684 0.495257721251 Henry Cohn, 2026, needs more optimization.
12 686 0.495273079934 Henry Cohn, 2026, needs more optimization.
12 687 0.495370851901 Henry Cohn, 2026, needs more optimization.
12 688 0.495389933405 Henry Cohn, 2026, needs more optimization.
12 689 0.495471267559 Henry Cohn, 2026, needs more optimization.
12 690 0.495578520389 Henry Cohn, 2026, needs more optimization.
12 691 0.495609478220 Henry Cohn, 2026, needs more optimization.
12 694 0.495687791466 Henry Cohn, 2026, needs more optimization.
12 696 0.495710621058 Henry Cohn, 2026, needs more optimization.
12 697 0.495773310311 Henry Cohn, 2026, needs more optimization.
12 698 0.495805510473 Henry Cohn, 2026, needs more optimization.
12 699 0.495901115606 Henry Cohn, 2026, needs more optimization.
12 700 0.495933833652 Henry Cohn, 2026, needs more optimization.
12 701 0.495956390800 Henry Cohn, 2026, needs more optimization.
12 702 0.496047294623 Henry Cohn, 2026, needs more optimization.
12 703 0.496061439894 Henry Cohn, 2026, needs more optimization.
12 704 0.496061757771 Henry Cohn, 2026, needs more optimization.
12 705 0.496144360798 Henry Cohn, 2026, needs more optimization.
12 706 0.496207453397 Henry Cohn, 2026, needs more optimization.
12 707 0.496214981831 Henry Cohn, 2026, needs more optimization.
12 708 0.496259931434 Henry Cohn, 2026, needs more optimization.
12 709 0.496314053563 Henry Cohn, 2026, needs more optimization.
12 711 0.496373983072 Henry Cohn, 2026, needs more optimization.
12 712 0.496393448006 Henry Cohn, 2026, needs more optimization.
12 713 0.496474864692 Henry Cohn, 2026, needs more optimization.
12 714 0.496480523282 Henry Cohn, 2026, needs more optimization.
12 715 0.496492690676 Henry Cohn, 2026, needs more optimization.
12 716 0.496497328262 Henry Cohn, 2026, needs more optimization.
12 717 0.496525637876 Henry Cohn, 2026, needs more optimization.
12 719 0.496565020417 Henry Cohn, 2026, needs more optimization.
12 720 0.496600340707 Henry Cohn, 2026, needs more optimization.
12 721 0.496668844018 Henry Cohn, 2026, needs more optimization.
12 723 0.496725865998 Henry Cohn, 2026, needs more optimization.
12 724 0.496761977491 Henry Cohn, 2026, needs more optimization.
12 725 0.496853468434 Henry Cohn, 2026, needs more optimization.
12 726 0.496882162750 Henry Cohn, 2026, needs more optimization.
12 743 0.496902983196 Henry Cohn, 2026, needs more optimization.
12 745 0.496904373124 Henry Cohn, 2026, needs more optimization.
12 746 0.496968159806 Henry Cohn, 2026, needs more optimization.
12 747 0.496992888575 Henry Cohn, 2026, needs more optimization.
12 748 0.497031390151 Henry Cohn, 2026, needs more optimization.
12 749 0.497035555065 Henry Cohn, 2026, needs more optimization.
12 751 0.497053309283 Henry Cohn, 2026, needs more optimization.
12 755 0.497097018280 Henry Cohn, 2026, needs more optimization.
12 756 0.497261404575 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.
12 757 0.498423313703 Henry Cohn, 2026, needs more 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 0.510889066593 Henry Cohn, 2026, needs more optimization.
12 842 0.515164242235 Henry Cohn, 2026, needs more optimization.
12 843 0.515726314633 Henry Cohn, 2026, needs more optimization.
12 844 0.516736569536 Henry Cohn, 2026, needs more optimization.
12 845 0.516781708412 Henry Cohn, 2026, needs more optimization.
12 846 0.517042876826 Henry Cohn, 2026, needs more optimization.
12 847 0.517344433184 Henry Cohn, 2026, needs more optimization.
12 848 0.517723343205 Henry Cohn, 2026, needs more optimization.
12 849 0.518051904692 Henry Cohn, 2026, needs more optimization.
12 850 0.518746109590 Henry Cohn, 2026, needs more optimization.
12 851 0.518996140412 Henry Cohn, 2026, needs more optimization.
12 852 0.519407575683 Henry Cohn, 2026, needs more optimization.
12 853 0.519718436820 Henry Cohn, 2026, needs more optimization.
12 854 0.520123923667 Henry Cohn, 2026, needs more optimization.
12 855 0.520383367102 Henry Cohn, 2026, needs more optimization.
12 856 0.520811052038 Henry Cohn, 2026, needs more optimization.
12 857 0.521091416673 Henry Cohn, 2026, needs more optimization.
12 858 0.521427788830 Henry Cohn, 2026, needs more optimization.
12 859 0.522009022715 Henry Cohn, 2026, needs more optimization.
12 860 0.522338747010 Henry Cohn, 2026, needs more optimization.
12 861 0.522629741145 Henry Cohn, 2026, needs more optimization.
12 862 0.522877661608 Henry Cohn, 2026, needs more optimization.
12 863 0.523071901596 Henry Cohn, 2026, needs more optimization.
12 864 0.523314229810 Henry Cohn, 2026, needs more optimization.
12 865 0.523736598057 Henry Cohn, 2026, needs more optimization.
12 866 0.524033652802 Henry Cohn, 2026, needs more optimization.
12 867 0.524218288054 Henry Cohn, 2026, needs more optimization.
12 868 0.524364278717 Henry Cohn, 2026, needs more optimization.
12 869 0.524669605169 Henry Cohn, 2026, needs more optimization.
12 870 0.524859973840 Henry Cohn, 2026, needs more optimization.
12 871 0.525060947757 Henry Cohn, 2026, needs more optimization.
12 872 0.525560615671 Henry Cohn, 2026, needs more optimization.
12 873 0.525818597523 Henry Cohn, 2026, needs more optimization.
12 874 0.526184471481 Henry Cohn, 2026, needs more optimization.
12 875 0.526370027965 Henry Cohn, 2026, needs more optimization.
12 876 0.526642033755 Henry Cohn, 2026, needs more optimization.
12 877 0.526877987620 Henry Cohn, 2026, needs more optimization.
12 878 0.527182175616 Henry Cohn, 2026, needs more optimization.
12 879 0.527406989117 Henry Cohn, 2026, needs more optimization.
12 880 0.527644622258 Henry Cohn, 2026, needs more optimization.
12 881 0.527887024384 Henry Cohn, 2026, needs more optimization.
12 882 0.528212703938 Henry Cohn, 2026, needs more optimization.
12 883 0.528452519785 Henry Cohn, 2026, needs more optimization.
12 884 0.528810112617 Henry Cohn, 2026, needs more optimization.
12 885 0.529018865546 Henry Cohn, 2026, needs more optimization.
12 886 0.529186217004 Henry Cohn, 2026, needs more optimization.
12 887 0.529469017165 Henry Cohn, 2026, needs more optimization.
12 888 0.529715006676 Henry Cohn, 2026, needs more optimization.
12 889 0.530303880185 Henry Cohn, 2026, needs more optimization.
12 890 0.530504778235 Henry Cohn, 2026, needs more optimization.
12 891 0.530654903156 Henry Cohn, 2026, needs more optimization.
12 892 0.530934800344 Henry Cohn, 2026, needs more optimization.
12 893 0.531121175952 Henry Cohn, 2026, needs more optimization.
12 894 0.531349608600 Henry Cohn, 2026, needs more optimization.
12 895 0.531686204846 Henry Cohn, 2026, needs more optimization.
12 896 0.531905793172 Henry Cohn, 2026, needs more optimization.
12 897 0.532202093934 Henry Cohn, 2026, needs more optimization.
12 898 0.532348403448 Henry Cohn, 2026, needs more optimization.
12 899 0.532539387740 Henry Cohn, 2026, needs more optimization.
12 900 0.532671631587 Henry Cohn, 2026, needs more optimization.
12 901 0.532854353042 Henry Cohn, 2026, needs more optimization.
12 902 0.533070736740 Henry Cohn, 2026, needs more optimization.
12 903 0.533241964293 Henry Cohn, 2026, needs more optimization.
12 904 0.533507893660 Henry Cohn, 2026, needs more optimization.
12 905 0.533714008052 Henry Cohn, 2026, needs more optimization.
12 906 0.533946563838 Henry Cohn, 2026, needs more optimization.
12 907 0.534109536067 Henry Cohn, 2026, needs more optimization.
12 908 0.534369890714 Henry Cohn, 2026, needs more optimization.
12 909 0.534476422588 Henry Cohn, 2026, needs more optimization.
12 910 0.534671830317 Henry Cohn, 2026, needs more optimization.
12 911 0.534890059491 Henry Cohn, 2026, needs more optimization.
12 912 0.535102840342 Henry Cohn, 2026, needs more optimization.
12 913 0.535299758284 Henry Cohn, 2026, needs more optimization.
12 914 0.535544034233 Henry Cohn, 2026, needs more optimization.
12 915 0.535886788787 Henry Cohn, 2026, needs more optimization.
12 916 0.536098869442 Henry Cohn, 2026, needs more optimization.
12 917 0.536246900934 Henry Cohn, 2026, needs more optimization.
12 918 0.536612216869 Henry Cohn, 2026, needs more optimization.
12 919 0.536852935008 Henry Cohn, 2026, needs more optimization.
12 920 0.537072252161 Henry Cohn, 2026, needs more optimization.
12 921 0.537271113113 Henry Cohn, 2026, needs more optimization.
12 922 0.537424727162 Henry Cohn, 2026, needs more optimization.
12 923 0.537575524996 Henry Cohn, 2026, needs more optimization.
12 924 0.537793290890 Henry Cohn, 2026, needs more optimization.
12 925 0.537901575222 Henry Cohn, 2026, needs more optimization.
12 926 0.538141751881 Henry Cohn, 2026, needs more optimization.
12 927 0.538275735828 Henry Cohn, 2026, needs more optimization.
12 928 0.538412888889 Henry Cohn, 2026, needs more optimization.
12 929 0.538596017952 Henry Cohn, 2026, needs more optimization.
12 930 0.538762587375 Henry Cohn, 2026, needs more optimization.
12 931 0.539019554318 Henry Cohn, 2026, needs more optimization.
12 932 0.539193868067 Henry Cohn, 2026, needs more optimization.
12 933 0.539366412921 Henry Cohn, 2026, needs more optimization.
12 934 0.539542182114 Henry Cohn, 2026, needs more optimization.
12 935 0.539748038462 Henry Cohn, 2026, needs more optimization.
12 936 0.539911194491 Henry Cohn, 2026, needs more optimization.
12 937 0.540122386264 Henry Cohn, 2026, needs more optimization.
12 938 0.540321199223 Henry Cohn, 2026, needs more optimization.
12 939 0.540564925259 Henry Cohn, 2026, needs more optimization.
12 940 0.540720677343 Henry Cohn, 2026, needs more optimization.
12 941 0.540961772921 Henry Cohn, 2026, needs more optimization.
12 942 0.541100724183 Henry Cohn, 2026, needs more optimization.
12 943 0.541191048951 Henry Cohn, 2026, needs more optimization.
12 944 0.541360971412 Henry Cohn, 2026, needs more optimization.
12 945 0.541571411520 Henry Cohn, 2026, needs more optimization.
12 946 0.541717576978 Henry Cohn, 2026, needs more optimization.
12 947 0.542026585209 Henry Cohn, 2026, needs more optimization.
12 948 0.542216292151 Henry Cohn, 2026, needs more optimization.
12 949 0.542322343174 Henry Cohn, 2026, needs more optimization.
12 950 0.542462852871 Henry Cohn, 2026, needs more optimization.
12 951 0.542597280815 Henry Cohn, 2026, needs more optimization.
12 952 0.542808298332 Henry Cohn, 2026, needs more optimization.
12 953 0.543094782958 Henry Cohn, 2026, needs more optimization.
12 954 0.543242714594 Henry Cohn, 2026, needs more optimization.
12 955 0.543492045604 Henry Cohn, 2026, needs more optimization.
12 956 0.543602403021 Henry Cohn, 2026, needs more optimization.
12 957 0.543823136461 Henry Cohn, 2026, needs more optimization.
12 958 0.543935940247 Henry Cohn, 2026, needs more optimization.
12 959 0.544055494811 Henry Cohn, 2026, needs more optimization.
12 960 0.544198976512 Henry Cohn, 2026, needs more optimization.
12 961 0.544312814517 Henry Cohn, 2026, needs more optimization.
12 962 0.544513919679 Henry Cohn, 2026, needs more optimization.
12 963 0.544622832558 Henry Cohn, 2026, needs more optimization.
12 964 0.544784529922 Henry Cohn, 2026, needs more optimization.
12 965 0.544893087574 Henry Cohn, 2026, needs more optimization.
12 966 0.545015691514 Henry Cohn, 2026, needs more optimization.
12 967 0.545178711577 Henry Cohn, 2026, needs more optimization.
12 968 0.545317946551 Henry Cohn, 2026, needs more optimization.
12 969 0.545528301616 Henry Cohn, 2026, needs more optimization.
12 970 0.545595178706 Henry Cohn, 2026, needs more optimization.
12 971 0.545703028542 Henry Cohn, 2026, needs more optimization.
12 972 0.545827641149 Henry Cohn, 2026, needs more optimization.
12 973 0.546033027134 Henry Cohn, 2026, needs more optimization.
12 974 0.546186039303 Henry Cohn, 2026, needs more optimization.
12 975 0.546338212352 Henry Cohn, 2026, needs more optimization.
12 976 0.546476898417 Henry Cohn, 2026, needs more optimization.
12 977 0.546633220562 Henry Cohn, 2026, needs more optimization.
12 978 0.546749737350 Henry Cohn, 2026, needs more optimization.
12 979 0.546899786485 Henry Cohn, 2026, needs more optimization.
12 980 0.546982139562 Henry Cohn, 2026, needs more optimization.
12 981 0.547143992063 Henry Cohn, 2026, needs more optimization.
12 982 0.547208846803 Henry Cohn, 2026, needs more optimization.
12 983 0.547362031643 Henry Cohn, 2026, needs more optimization.
12 984 0.547521391790 Henry Cohn, 2026, needs more optimization.
12 985 0.547678640406 Henry Cohn, 2026, needs more optimization.
12 986 0.547811544812 Henry Cohn, 2026, needs more optimization.
12 987 0.547931371434 Henry Cohn, 2026, needs more optimization.
12 988 0.548037765122 Henry Cohn, 2026, needs more optimization.
12 989 0.548157568397 Henry Cohn, 2026, needs more optimization.
12 990 0.548244372929 Henry Cohn, 2026, needs more optimization.
12 991 0.548324612731 Henry Cohn, 2026, needs more optimization.
12 992 0.548431861222 Henry Cohn, 2026, needs more optimization.
12 993 0.548557552078 Henry Cohn, 2026, needs more optimization.
12 994 0.548760800607 Henry Cohn, 2026, needs more optimization.
12 995 0.548842385549 Henry Cohn, 2026, needs more optimization.
12 996 0.549043018783 Henry Cohn, 2026, needs more optimization.
12 997 0.549168959459 Henry Cohn, 2026, needs more optimization.
12 998 0.549294968069 Henry Cohn, 2026, needs more optimization.
12 999 0.549500138852 Henry Cohn, 2026, needs more optimization.
12 1000 0.549721885590 Henry Cohn, 2026, needs more optimization.
12 1001 0.549867777972 Henry Cohn, 2026, needs more optimization.
12 1002 0.550016003548 Henry Cohn, 2026, needs more optimization.
12 1003 0.550090664557 Henry Cohn, 2026, needs more optimization.
12 1004 0.550285308903 Henry Cohn, 2026, needs more optimization.
12 1005 0.550413045773 Henry Cohn, 2026, needs more optimization.
12 1006 0.550473698493 Henry Cohn, 2026, needs more optimization.
12 1007 0.550592999942 Henry Cohn, 2026, needs more optimization.
12 1008 0.550731946322 Henry Cohn, 2026, needs more optimization.
12 1009 0.550860817878 Henry Cohn, 2026, needs more optimization.
12 1010 0.551051950785 Henry Cohn, 2026, needs more optimization.
12 1011 0.551165730840 Henry Cohn, 2026, needs more optimization.
12 1012 0.551255966319 Henry Cohn, 2026, needs more optimization.
12 1013 0.551402110767 Henry Cohn, 2026, needs more optimization.
12 1014 0.551479668516 Henry Cohn, 2026, needs more optimization.
12 1015 0.551549891283 Henry Cohn, 2026, needs more optimization.
12 1016 0.551784584748 Henry Cohn, 2026, needs more optimization.
12 1017 0.551859923907 Henry Cohn, 2026, needs more optimization.
12 1018 0.551970544040 Henry Cohn, 2026, needs more optimization.
12 1019 0.552208183471 Henry Cohn, 2026, needs more optimization.
12 1020 0.552323898499 Henry Cohn, 2026, needs more optimization.
12 1021 0.552438011435 Henry Cohn, 2026, needs more optimization.
12 1022 0.552527888210 Henry Cohn, 2026, needs more optimization.
12 1023 0.552673334471 Henry Cohn, 2026, needs more optimization.
12 1024 0.552791951280 Henry Cohn, 2026, needs more optimization.
13 27 0.057072523783 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
1573⁢x3−169⁢x2−13⁢x+1
13 28 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
15⁢x−1
13 29 0.068098609479 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
2576⁢x4−640⁢x3−184⁢x2+1
13 30 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 31 0.071714034728 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
55⁢x2+10⁢x−1
13 32 0.071714034728 N. J. A. Sloane, with the collaboration of R. H. Hardin, W. D. Smith, and others, Tables of spherical codes, 1994–1996.
55⁢x2+10⁢x−1
13 33 0.089833578043 Henry Cohn, 2026.
13 34 0.090095382331 Henry Cohn, 2023.
13 36 0.092610094433 H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
95⁢x2+2⁢x−1
13 37 0.111409136725 Henry Cohn, 2023.
13 38 0.112004618870 Henry Cohn, 2023.
44⁢x2+4⁢x−1
13 39 0.116893063508 Henry Cohn, 2024.
13 40 0.121353571480 Henry Cohn, 2026.
13 42 0.125 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
8⁢x−1
13 44 0.126079252818 Henry Cohn, 2025.
6095⁢x2−126⁢x−81
13 48 0.126131983623 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2+2⁢x−1
13 49 0.141095436175 Henry Cohn, 2025.
13 50 0.142459427551 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 51 0.145120831484 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
13 52 0.147159522238 Henry Cohn, 2023.
613567⁢x7+96585⁢x6−98333⁢x5−8219⁢x4+381⁢x3+539⁢x2+33⁢x−9
13 53 0.147908234060 Henry Cohn, 2024.
13 54 0.148576022240 Henry Cohn, 2025.
13 55 0.148805252884 Henry Cohn, 2024.
13 56 0.148975682089 Henry Cohn, 2023.
13 57 0.166162190421 Henry Cohn, 2024.
13 58 0.173474302723 Henry Cohn, 2023.
13 59 0.180540658957 Henry Cohn, 2024.
13 60 0.184417827015 Henry Cohn, 2026, needs more optimization.
13 61 0.189133285958 Henry Cohn, 2026, needs more optimization.
13 62 0.189939244395 Henry Cohn, 2026.
13 63 0.193274783328 Henry Cohn, 2026.
13 64 0.194851455955 Henry Cohn, 2026, needs more optimization.
13 65 0.198938999892 Henry Cohn, 2026, needs more optimization.
13 66 0.201500079720 Henry Cohn, 2026, needs more optimization.
13 67 0.204060485651 Henry Cohn, 2026, needs more optimization.
13 68 0.207237119776 Henry Cohn, 2026, needs more optimization.
13 69 0.208427075365 Henry Cohn, 2025.
13 70 0.210762897379 Henry Cohn, 2026, needs more optimization.
13 71 0.212574330623 Henry Cohn, 2025.
13 72 0.214183844238 Henry Cohn, 2025.
13 73 0.216144703189 Henry Cohn, 2026, needs more optimization.
13 74 0.217555077772 Henry Cohn, 2026, needs more optimization.
13 75 0.219796325248 Henry Cohn, 2026, needs more optimization.
13 76 0.222090008830 Henry Cohn, 2026, needs more optimization.
13 77 0.224126205712 Henry Cohn, 2026, needs more optimization.
13 78 0.226253188927 Henry Cohn, 2026, needs more optimization.
13 79 0.228139500109 Henry Cohn, 2026, needs more optimization.
13 80 0.230720126969 Henry Cohn, 2026, needs more optimization.
13 81 0.232720216127 Henry Cohn, 2024, needs more optimization.
13 82 0.234406900251 Henry Cohn, 2026, needs more optimization.
13 83 0.236560164014 Henry Cohn, 2026, needs more optimization.
13 84 0.238093292153 Henry Cohn, 2026, needs more optimization.
13 85 0.239148109907 Henry Cohn, 2026, needs more optimization.
13 86 0.240112147390 Henry Cohn, 2026, needs more optimization.
13 87 0.241034848687 Henry Cohn, 2026, needs more optimization.
13 88 0.242148839888 Henry Cohn, 2026, needs more optimization.
13 89 0.243767059733 Henry Cohn, 2026, needs more optimization.
13 90 0.244053098370 Henry Cohn, 2026, needs more optimization.
13 91 0.244053162699 Henry Cohn, 2026, needs more optimization.
13 92 0.244060792684 Henry Cohn, 2026, needs more optimization.
13 93 0.244060811292 Henry Cohn, 2026, needs more optimization.
13 94 0.244143161935 Henry Cohn, 2026, needs more optimization.
13 95 0.244232299465 Henry Cohn, 2026, needs more optimization.
13 96 0.244334788816 Henry Cohn, 2026, needs more optimization.
13 97 0.244403643906 Henry Cohn, 2026, needs more optimization.
13 98 0.244475717847 Henry Cohn, 2026, needs more optimization.
13 99 0.246245169443 Henry Cohn, 2026, needs more optimization.
13 100 0.246937484624 Henry Cohn, 2026, needs more optimization.
13 101 0.249341456819 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 0.257876424884 Henry Cohn, 2026, needs more optimization.
13 108 0.258372340623 Henry Cohn, 2026, needs more optimization.
13 109 0.258970157362 Henry Cohn, 2026, needs more optimization.
13 110 0.259445982094 Henry Cohn, 2026, needs more optimization.
13 111 0.259780906598 Henry Cohn, 2026, needs more optimization.
13 112 0.261427280669 Henry Cohn, 2026, needs more optimization.
13 113 0.263326646488 Henry Cohn, 2026, needs more optimization.
13 114 0.263585274774 Henry Cohn, 2026, needs more optimization.
13 115 0.264241092180 Henry Cohn, 2026, needs more optimization.
13 116 0.266807071362 Henry Cohn, 2026, needs more optimization.
13 117 0.270013270641 Henry Cohn, 2026, needs more optimization.
13 118 0.271262797457 Henry Cohn, 2026, needs more optimization.
13 119 0.271262827569 Henry Cohn, 2026, needs more optimization.
13 120 0.271264874098 Henry Cohn, 2026, needs more optimization.
13 121 0.272601630905 Henry Cohn, 2026, needs more optimization.
13 122 0.274060948987 Henry Cohn, 2026, needs more optimization.
13 123 0.274912625356 Henry Cohn, 2026, needs more optimization.
13 124 0.275841579023 Henry Cohn, 2026, needs more optimization.
13 125 0.276039740471 Henry Cohn, 2026, needs more optimization.
13 126 0.277980964213 Henry Cohn, 2026, needs more optimization.
13 127 0.279716989595 Henry Cohn, 2026, needs more optimization.
13 128 0.281348786590 Henry Cohn, 2026, needs more optimization.
13 129 0.283887393750 Henry Cohn, 2026, needs more optimization.
13 130 0.284588899340 Henry Cohn, 2026, needs more optimization.
13 131 0.286727918817 Henry Cohn, 2026, needs more optimization.
13 132 0.287428506366 Henry Cohn, 2026, needs more optimization.
13 133 0.287810008183 Henry Cohn, 2026, needs more optimization.
13 134 0.288953664620 Henry Cohn, 2026, needs more optimization.
13 135 0.289393621937 Henry Cohn, 2026, needs more optimization.
13 136 0.291030675434 Henry Cohn, 2026, needs more optimization.
13 137 0.292469113809 Henry Cohn, 2026, needs more optimization.
13 138 0.294586372646 Henry Cohn, 2026, needs more optimization.
13 139 0.296161122025 Henry Cohn, 2026, needs more optimization.
13 140 0.296843199697 Henry Cohn, 2026, needs more optimization.
13 141 0.297532501639 Henry Cohn, 2026, needs more optimization.
13 142 0.297532510834 Henry Cohn, 2026, needs more optimization.
13 143 0.297669979454 Henry Cohn, 2026, needs more optimization.
13 144 0.299293367094 Henry Cohn, 2026, needs more optimization.
13 145 0.300763460201 Henry Cohn, 2026, needs more optimization.
13 146 0.300803660975 Henry Cohn, 2026, needs more optimization.
13 147 0.300835826914 Henry Cohn, 2026, needs more optimization.
13 148 0.300835851108 Henry Cohn, 2026, needs more optimization.
13 149 0.300899414266 Henry Cohn, 2026, needs more optimization.
13 150 0.300977858076 Henry Cohn, 2026, needs more optimization.
13 151 0.301155400564 Henry Cohn, 2026, needs more optimization.
13 152 0.303732674832 Henry Cohn, 2026, needs more optimization.
13 153 0.304977527831 Henry Cohn, 2026, needs more optimization.
13 154 0.306302349494 Henry Cohn, 2026, needs more optimization.
13 155 0.307516584950 Henry Cohn, 2026, needs more optimization.
13 156 0.308514893182 Henry Cohn, 2026, needs more optimization.
13 157 0.309423462836 Henry Cohn, 2026, needs more optimization.
13 158 0.310599036183 Henry Cohn, 2026, needs more optimization.
13 159 0.311409127223 Henry Cohn, 2026, needs more optimization.
13 160 0.311847196740 Henry Cohn, 2026, needs more optimization.
13 161 0.312525578737 Henry Cohn, 2026, needs more optimization.
13 162 0.313684323701 Henry Cohn, 2026, needs more optimization.
13 163 0.314512879833 Henry Cohn, 2026, needs more optimization.
13 164 0.315558077114 Henry Cohn, 2026, needs more optimization.
13 165 0.315905742491 Henry Cohn, 2026, needs more optimization.
13 166 0.316298670495 Henry Cohn, 2026, needs more optimization.
13 167 0.317162778330 Henry Cohn, 2026, needs more optimization.
13 168 0.317685191539 Henry Cohn, 2026, needs more optimization.
13 169 0.318110247253 Henry Cohn, 2026, needs more optimization.
13 170 0.319134996362 Henry Cohn, 2026, needs more optimization.
13 171 0.319632412208 Henry Cohn, 2026, needs more optimization.
13 172 0.319861331135 Henry Cohn, 2026, needs more optimization.
13 173 0.320597577978 Henry Cohn, 2026, needs more optimization.
13 174 0.320601519363 Henry Cohn, 2026, needs more optimization.
13 175 0.320884125347 Henry Cohn, 2026, needs more optimization.
13 176 0.321171222932 Henry Cohn, 2026, needs more optimization.
13 177 0.321753760049 Henry Cohn, 2026, needs more optimization.
13 178 0.322277073240 Henry Cohn, 2026, needs more optimization.
13 179 0.322691855341 Henry Cohn, 2026, needs more optimization.
13 180 0.323178241167 Henry Cohn, 2026, needs more optimization.
13 181 0.323555451521 Henry Cohn, 2026, needs more optimization.
13 182 0.324060683423 Henry Cohn, 2026, needs more optimization.
13 183 0.324675648895 Henry Cohn, 2026, needs more optimization.
13 184 0.324852421051 Henry Cohn, 2026, needs more optimization.
13 185 0.325422980566 Henry Cohn, 2026, needs more optimization.
13 186 0.326220945626 Henry Cohn, 2026, needs more optimization.
13 187 0.326420264628 Henry Cohn, 2026, needs more optimization.
13 188 0.326750227887 Henry Cohn, 2026, needs more optimization.
13 189 0.326984436333 Henry Cohn, 2026, needs more optimization.
13 190 0.327311170944 Henry Cohn, 2026, needs more optimization.
13 191 0.327714807448 Henry Cohn, 2026, needs more optimization.
13 192 0.328096938285 Henry Cohn, 2026, needs more optimization.
13 193 0.328119134865 Henry Cohn, 2026, needs more optimization.
13 194 0.328300601175 Henry Cohn, 2026, needs more optimization.
13 195 0.328491274013 Henry Cohn, 2026, needs more optimization.
13 196 0.328736808652 Henry Cohn, 2026, needs more optimization.
13 197 0.328876781470 Henry Cohn, 2026, needs more optimization.
13 198 0.329030062996 Henry Cohn, 2026, needs more optimization.
13 199 0.329144459104 Henry Cohn, 2026, needs more optimization.
13 200 0.329342398496 Henry Cohn, 2026, needs more optimization.
13 201 0.329522676576 Henry Cohn, 2026, needs more optimization.
13 202 0.329690749783 Henry Cohn, 2026, needs more optimization.
13 203 0.332322805564 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 0.350454981791 Henry Cohn, 2026, needs more optimization.
13 210 0.351580183348 Henry Cohn, 2026, needs more optimization.
13 211 0.352249768809 Henry Cohn, 2026, needs more optimization.
13 212 0.352778178967 Henry Cohn, 2026, needs more optimization.
13 213 0.353908968891 Henry Cohn, 2026, needs more optimization.
13 214 0.354466062748 Henry Cohn, 2026, needs more optimization.
13 215 0.355369398554 Henry Cohn, 2026, needs more optimization.
13 216 0.355724894873 Henry Cohn, 2026, needs more optimization.
13 217 0.356435440078 Henry Cohn, 2026, needs more optimization.
13 218 0.357592618572 Henry Cohn, 2026, needs more optimization.
13 219 0.358097921751 Henry Cohn, 2026, needs more optimization.
13 220 0.358852636145 Henry Cohn, 2026, needs more optimization.
13 221 0.359893497223 Henry Cohn, 2026, needs more optimization.
13 222 0.360502741409 Henry Cohn, 2026, needs more optimization.
13 223 0.361604733877 Henry Cohn, 2026, needs more optimization.
13 224 0.362377899749 Henry Cohn, 2026, needs more optimization.
13 225 0.363360940064 Henry Cohn, 2026, needs more optimization.
13 226 0.364025150140 Henry Cohn, 2026, needs more optimization.
13 227 0.364774605012 Henry Cohn, 2026, needs more optimization.
13 228 0.365434943661 Henry Cohn, 2026, needs more optimization.
13 229 0.366367041513 Henry Cohn, 2026, needs more optimization.
13 230 0.366888670746 Henry Cohn, 2026, needs more optimization.
13 231 0.367686462590 Henry Cohn, 2026, needs more optimization.
13 232 0.368704853083 Henry Cohn, 2026, needs more optimization.
13 233 0.369233038656 Henry Cohn, 2026, needs more optimization.
13 234 0.369992288088 Henry Cohn, 2026, needs more optimization.
13 235 0.371065292340 Henry Cohn, 2026, needs more optimization.
13 236 0.371367533272 Henry Cohn, 2026, needs more optimization.
13 237 0.372099764028 Henry Cohn, 2026, needs more optimization.
13 238 0.372912056693 Henry Cohn, 2026, needs more optimization.
13 239 0.373572070875 Henry Cohn, 2026, needs more optimization.
13 240 0.374220159380 Henry Cohn, 2026, needs more optimization.
13 241 0.374812171075 Henry Cohn, 2026, needs more optimization.
13 242 0.375602005881 Henry Cohn, 2026, needs more optimization.
13 243 0.376259684839 Henry Cohn, 2026, needs more optimization.
13 244 0.376709503620 Henry Cohn, 2026, needs more optimization.
13 245 0.377633413916 Henry Cohn, 2026, needs more optimization.
13 246 0.378272265949 Henry Cohn, 2026, needs more optimization.
13 247 0.378820680104 Henry Cohn, 2026, needs more optimization.
13 248 0.379276158080 Henry Cohn, 2026, needs more optimization.
13 249 0.380069447711 Henry Cohn, 2026, needs more optimization.
13 250 0.380763937318 Henry Cohn, 2026, needs more optimization.
13 251 0.381485143419 Henry Cohn, 2026, needs more optimization.
13 252 0.381924746742 Henry Cohn, 2026, needs more optimization.
13 266 0.382352941177 Henry Cohn, 2026.
34⁢x−13
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 0.389821451534 Henry Cohn, 2026, needs more optimization.
13 315 0.391824858424 Henry Cohn, 2026, needs more optimization.
13 316 0.395718954832 Henry Cohn, 2026, needs more optimization.
13 317 0.397925205955 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 0.4 Henry Cohn, 2026.
5⁢x−2
13 338 0.400301613389 Henry Cohn, 2026, needs more optimization.
13 339 0.402100061242 Henry Cohn, 2026, needs more optimization.
13 340 0.406063465172 Henry Cohn, 2026, needs more optimization.
13 341 0.407425092427 Henry Cohn, 2026, needs more optimization.
13 342 0.407707477508 Henry Cohn, 2026, needs more optimization.
13 343 0.407830534916 Henry Cohn, 2026, needs more optimization.
13 344 0.408195385980 Henry Cohn, 2026, needs more optimization.
13 345 0.408411883535 Henry Cohn, 2026, needs more optimization.
13 346 0.408777965200 Henry Cohn, 2026, needs more optimization.
13 347 0.409584154800 Henry Cohn, 2026, needs more optimization.
13 348 0.410352841423 Henry Cohn, 2026, needs more optimization.
13 349 0.411015052259 Henry Cohn, 2026, needs more optimization.
13 350 0.411511159177 Henry Cohn, 2026, needs more optimization.
13 351 0.412109539701 Henry Cohn, 2026, needs more optimization.
13 352 0.412740957824 Henry Cohn, 2026, needs more optimization.
13 353 0.413431570669 Henry Cohn, 2026, needs more optimization.
13 354 0.414043285914 Henry Cohn, 2026, needs more optimization.
13 355 0.414618967976 Henry Cohn, 2026, needs more optimization.
13 356 0.414992637726 Henry Cohn, 2026, needs more optimization.
13 357 0.415241692336 Henry Cohn, 2026, needs more optimization.
13 358 0.415708001040 Henry Cohn, 2026, needs more optimization.
13 359 0.416146372630 Henry Cohn, 2026, needs more optimization.
13 383 0.416666666667 Henry Cohn, 2026.
12⁢x−5
13 384 0.419654923330 Henry Cohn, 2026, needs more optimization.
13 385 0.420799940105 Henry Cohn, 2026, needs more optimization.
13 386 0.421225067541 Henry Cohn, 2026, needs more optimization.
13 387 0.422565531479 Henry Cohn, 2026, needs more optimization.
13 388 0.423120361131 Henry Cohn, 2026, needs more optimization.
13 389 0.423848628180 Henry Cohn, 2026, needs more optimization.
13 390 0.424439168899 Henry Cohn, 2026, needs more optimization.
13 391 0.424766631801 Henry Cohn, 2026, needs more optimization.
13 392 0.425263581363 Henry Cohn, 2026, needs more optimization.
13 393 0.426014251827 Henry Cohn, 2026, needs more optimization.
13 394 0.426570505856 Henry Cohn, 2026, needs more optimization.
13 395 0.427264974161 Henry Cohn, 2026, needs more optimization.
13 396 0.428427948101 Henry Cohn, 2026, needs more optimization.
13 416 0.428571428572 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−3
13 492 0.428571428572 M. Ganzhinov and P. R. J. Östergård, Spherical codes with prescribed signed permutation automorphisms inside shells of low-dimensional integer lattices, IEEE Trans. Inform. Theory 70 (2024), 8669–8674, doi:10.1109/tit.2024.3462593, arXiv:2403.04330.
7⁢x−3
13 498 0.428571428572 Henry Cohn, 2026.
7⁢x−3
13 499 0.428809542267 Henry Cohn, 2026, needs more optimization.
13 500 0.429498182135 Henry Cohn, 2026, needs more optimization.
13 501 0.429606297931 Henry Cohn, 2026, needs more optimization.
13 502 0.429680768816 Henry Cohn, 2026, needs more optimization.
13 503 0.429687738251 Henry Cohn, 2026, needs more optimization.
13 504 0.429714303458 Henry Cohn, 2026, needs more optimization.
13 505 0.436922930089 Henry Cohn, 2026, needs more optimization.
13 506 0.439544232648 Henry Cohn, 2026, needs more optimization.
13 507 0.441393316697 Henry Cohn, 2026, needs more optimization.
13 508 0.443045073237 Henry Cohn, 2026, needs more optimization.
13 511 0.443755500151 Henry Cohn, 2026, needs more optimization.
13 512 0.444842783684 Henry Cohn, 2026, needs more optimization.
13 513 0.445185189012 Henry Cohn, 2026, needs more optimization.
13 515 0.445755148753 Henry Cohn, 2026, needs more optimization.
13 516 0.446194659153 Henry Cohn, 2026, needs more optimization.
13 518 0.446609446147 Henry Cohn, 2026, needs more optimization.
13 520 0.446618541345 Henry Cohn, 2026, needs more optimization.
13 521 0.447139055093 Henry Cohn, 2026, needs more optimization.
13 522 0.447232623080 Henry Cohn, 2026, needs more optimization.
13 523 0.447266161995 Henry Cohn, 2026, needs more optimization.
13 526 0.447273243852 Henry Cohn, 2026, needs more optimization.
13 528 0.447299749018 Henry Cohn, 2026, needs more optimization.
13 529 0.447445870339 Henry Cohn, 2026, needs more optimization.
13 530 0.447544486175 Henry Cohn, 2026, needs more optimization.
13 531 0.447578449290 Henry Cohn, 2026, needs more optimization.
13 533 0.447720514037 Henry Cohn, 2026, needs more optimization.
13 534 0.447832743944 Henry Cohn, 2026, needs more optimization.
13 535 0.448055815227 Henry Cohn, 2026, needs more optimization.
13 536 0.448240501027 Henry Cohn, 2026, needs more optimization.
13 537 0.448513012060 Henry Cohn, 2026, needs more optimization.
13 538 0.448616009292 Henry Cohn, 2026, needs more optimization.
13 539 0.448896396505 Henry Cohn, 2026, needs more optimization.
13 540 0.449279186101 Henry Cohn, 2026, needs more optimization.
13 541 0.449423540662 Henry Cohn, 2026, needs more optimization.
13 542 0.449519982656 Henry Cohn, 2026, needs more optimization.
13 545 0.449882927905 Henry Cohn, 2026, needs more optimization.
13 546 0.449937721976 Henry Cohn, 2026, needs more optimization.
13 547 0.450495049745 Henry Cohn, 2026, needs more optimization.
13 549 0.450839936788 Henry Cohn, 2026, needs more optimization.
13 551 0.450905958323 Henry Cohn, 2026, needs more optimization.
13 552 0.450964514184 Henry Cohn, 2026, needs more optimization.
13 553 0.451241859440 Henry Cohn, 2026, needs more optimization.
13 554 0.451521659629 Henry Cohn, 2026, needs more optimization.
13 555 0.451752238371 Henry Cohn, 2026, needs more optimization.
13 556 0.451904297217 Henry Cohn, 2026, needs more optimization.
13 557 0.452021295697 Henry Cohn, 2026, needs more optimization.
13 558 0.452273587002 Henry Cohn, 2026, needs more optimization.
13 559 0.452623814777 Henry Cohn, 2026, needs more optimization.
13 560 0.453071673934 Henry Cohn, 2026, needs more optimization.
13 561 0.453347211408 Henry Cohn, 2026, needs more optimization.
13 562 0.453553262376 Henry Cohn, 2026, needs more optimization.
13 563 0.454008601481 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 0.459815213493 Henry Cohn, 2026, needs more optimization.
13 580 0.460956197651 Henry Cohn, 2026, needs more optimization.
13 581 0.461747305967 Henry Cohn, 2026, needs more optimization.
13 582 0.462475698169 Henry Cohn, 2026, needs more optimization.
13 583 0.463040194319 Henry Cohn, 2026, needs more optimization.
13 584 0.463605030831 Henry Cohn, 2026, needs more optimization.
13 585 0.463957730224 Henry Cohn, 2026, needs more optimization.
13 586 0.464258540960 Henry Cohn, 2026, needs more optimization.
13 587 0.464659754147 Henry Cohn, 2026, needs more optimization.
13 589 0.464691425969 Henry Cohn, 2026, needs more optimization.
13 590 0.464793001017 Henry Cohn, 2026, needs more optimization.
13 591 0.465038535626 Henry Cohn, 2026, needs more optimization.
13 592 0.465139805017 Henry Cohn, 2026, needs more optimization.
13 593 0.465147825619 Henry Cohn, 2026, needs more optimization.
13 594 0.465457725132 Henry Cohn, 2026, needs more optimization.
13 595 0.465529385602 Henry Cohn, 2026, needs more optimization.
13 596 0.465617195107 Henry Cohn, 2026, needs more optimization.
13 597 0.465723814195 Henry Cohn, 2026, needs more optimization.
13 598 0.465867337475 Henry Cohn, 2026, needs more optimization.
13 599 0.465929977849 Henry Cohn, 2026, needs more optimization.
13 600 0.466041292768 Henry Cohn, 2026, needs more optimization.
13 601 0.466164322651 Henry Cohn, 2026, needs more optimization.
13 602 0.466256420724 Henry Cohn, 2026, needs more optimization.
13 603 0.466283040379 Henry Cohn, 2026, needs more optimization.
13 604 0.466308732553 Henry Cohn, 2026, needs more optimization.
13 605 0.466397855691 Henry Cohn, 2026, needs more optimization.
13 606 0.466465400794 Henry Cohn, 2026, needs more optimization.
13 607 0.466491285655 Henry Cohn, 2026, needs more optimization.
13 608 0.466552795072 Henry Cohn, 2026, needs more optimization.
13 609 0.466562927295 Henry Cohn, 2026, needs more optimization.
13 611 0.466571743973 Henry Cohn, 2026, needs more optimization.
13 612 0.466584529888 Henry Cohn, 2026, needs more optimization.
13 613 0.466654087906 Henry Cohn, 2026, needs more optimization.
13 614 0.466741433355 Henry Cohn, 2026, needs more optimization.
13 615 0.466865281507 Henry Cohn, 2026, needs more optimization.
13 616 0.466961139226 Henry Cohn, 2026, needs more optimization.
13 617 0.466984791777 Henry Cohn, 2026, needs more optimization.
13 618 0.467066670714 Henry Cohn, 2026, needs more optimization.
13 619 0.467091944061 Henry Cohn, 2026, needs more optimization.
13 620 0.467164341682 Henry Cohn, 2026, needs more optimization.
13 621 0.467216332951 Henry Cohn, 2026, needs more optimization.
13 622 0.467249629851 Henry Cohn, 2026, needs more optimization.
13 624 0.467306437318 Henry Cohn, 2026, needs more optimization.
13 625 0.467371492657 Henry Cohn, 2026, needs more optimization.
13 626 0.467400818369 Henry Cohn, 2026, needs more optimization.
13 627 0.467476413076 Henry Cohn, 2026, needs more optimization.
13 628 0.467569974410 Henry Cohn, 2026, needs more optimization.
13 630 0.467694999090 Henry Cohn, 2026, needs more optimization.
13 631 0.469231720104 Henry Cohn, 2026, needs more optimization.
13 632 0.469503526951 Henry Cohn, 2026, needs more optimization.
13 633 0.470316826439 Henry Cohn, 2026, needs more optimization.
13 634 0.470999596066 Henry Cohn, 2026, needs more optimization.
13 635 0.471596898492 Henry Cohn, 2026, needs more optimization.
13 636 0.472073526747 Henry Cohn, 2026, needs more optimization.
13 637 0.472525868779 Henry Cohn, 2026, needs more optimization.
13 638 0.473157183057 Henry Cohn, 2026, needs more optimization.
13 639 0.473604221491 Henry Cohn, 2026, needs more optimization.
13 640 0.474115417788 Henry Cohn, 2026, needs more optimization.
13 641 0.474365898033 Henry Cohn, 2026, needs more optimization.
13 642 0.474909818721 Henry Cohn, 2026, needs more optimization.
13 644 0.475 Henry Cohn, 2026.
40⁢x−19
13 645 0.476048287672 Henry Cohn, 2026, needs more optimization.
13 646 0.476935491825 Henry Cohn, 2026, needs more optimization.
13 647 0.477167322555 Henry Cohn, 2026, needs more optimization.
13 648 0.477640683006 Henry Cohn, 2026, needs more optimization.
13 649 0.478068712712 Henry Cohn, 2026, needs more optimization.
13 650 0.478269515189 Henry Cohn, 2026, needs more optimization.
13 651 0.478622900370 Henry Cohn, 2026, needs more optimization.
13 652 0.478856464367 Henry Cohn, 2026, needs more optimization.
13 654 0.479035728245 Henry Cohn, 2026, needs more optimization.
13 655 0.479188858390 Henry Cohn, 2026, needs more optimization.
13 656 0.479328073763 Henry Cohn, 2026, needs more optimization.
13 657 0.479498028101 Henry Cohn, 2026, needs more optimization.
13 658 0.479685947764 Henry Cohn, 2026, needs more optimization.
13 659 0.479722294464 Henry Cohn, 2026, needs more optimization.
13 660 0.479846030786 Henry Cohn, 2026, needs more optimization.
13 661 0.480045996975 Henry Cohn, 2026, needs more optimization.
13 662 0.480211407504 Henry Cohn, 2026, needs more optimization.
13 663 0.480328167292 Henry Cohn, 2026, needs more optimization.
13 664 0.480383029621 Henry Cohn, 2026, needs more optimization.
13 665 0.480583065577 Henry Cohn, 2026, needs more optimization.
13 666 0.480727925625 Henry Cohn, 2026, needs more optimization.
13 667 0.480782573942 Henry Cohn, 2026, needs more optimization.
13 668 0.480831213922 Henry Cohn, 2026, needs more optimization.
13 669 0.480849028199 Henry Cohn, 2026, needs more optimization.
13 670 0.480884443442 Henry Cohn, 2026, needs more optimization.
13 671 0.480933408970 Henry Cohn, 2026, needs more optimization.
13 672 0.481093054489 Henry Cohn, 2026, needs more optimization.
13 673 0.481224083459 Henry Cohn, 2026, needs more optimization.
13 674 0.481284347723 Henry Cohn, 2026, needs more optimization.
13 675 0.481459653973 Henry Cohn, 2026, needs more optimization.
13 676 0.481711856047 Henry Cohn, 2026, needs more optimization.
13 677 0.481767445496 Henry Cohn, 2026, needs more optimization.
13 678 0.481833814115 Henry Cohn, 2026, needs more optimization.
13 679 0.482087760191 Henry Cohn, 2026, needs more optimization.
13 680 0.482154819163 Henry Cohn, 2026, needs more optimization.
13 681 0.482163098858 Henry Cohn, 2026, needs more optimization.
13 682 0.482356421795 Henry Cohn, 2026, needs more optimization.
13 684 0.482466641390 Henry Cohn, 2026, needs more optimization.
13 685 0.482519622360 Henry Cohn, 2026, needs more optimization.
13 686 0.482696484698 Henry Cohn, 2026, needs more optimization.
13 687 0.482718905250 Henry Cohn, 2026, needs more optimization.
13 688 0.482828202893 Henry Cohn, 2026, needs more optimization.
13 689 0.482892778160 Henry Cohn, 2026, needs more optimization.
13 691 0.482929394381 Henry Cohn, 2026, needs more optimization.
13 692 0.482980897204 Henry Cohn, 2026, needs more optimization.
13 693 0.483094263278 Henry Cohn, 2026, needs more optimization.
13 694 0.483243922247 Henry Cohn, 2026, needs more optimization.
13 695 0.483378790789 Henry Cohn, 2026, needs more optimization.
13 696 0.483506940779 Henry Cohn, 2026, needs more optimization.
13 697 0.483622615445 Henry Cohn, 2026, needs more optimization.
13 698 0.483858306706 Henry Cohn, 2026, needs more optimization.
13 699 0.484008706867 Henry Cohn, 2026, needs more optimization.
13 700 0.484139263168 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 0.484349594283 Henry Cohn, 2026, needs more optimization.
13 706 0.484435125173 Henry Cohn, 2026, needs more optimization.
13 707 0.484524894764 Henry Cohn, 2026, needs more optimization.
13 708 0.484623416689 Henry Cohn, 2026, needs more optimization.
13 709 0.484789996817 Henry Cohn, 2026, needs more optimization.
13 710 0.484860565535 Henry Cohn, 2026, needs more optimization.
13 712 0.484958005879 Henry Cohn, 2026, needs more optimization.
13 713 0.484986946592 Henry Cohn, 2026, needs more optimization.
13 714 0.485047437775 Henry Cohn, 2026, needs more optimization.
13 715 0.485095006967 Henry Cohn, 2026, needs more optimization.
13 716 0.485152870254 Henry Cohn, 2026, needs more optimization.
13 717 0.485184628741 Henry Cohn, 2026, needs more optimization.
13 718 0.485220740896 Henry Cohn, 2026, needs more optimization.
13 719 0.485266339722 Henry Cohn, 2026, needs more optimization.
13 720 0.485315882467 Henry Cohn, 2026, needs more optimization.
13 721 0.485361820088 Henry Cohn, 2026, needs more optimization.
13 722 0.485399753361 Henry Cohn, 2026, needs more optimization.
13 723 0.485428053745 Henry Cohn, 2026, needs more optimization.
13 724 0.485498631248 Henry Cohn, 2026, needs more optimization.
13 725 0.485575663182 Henry Cohn, 2026, needs more optimization.
13 726 0.485636077044 Henry Cohn, 2026, needs more optimization.
13 727 0.485645631221 Henry Cohn, 2026, needs more optimization.
13 728 0.485720573568 Henry Cohn, 2026, needs more optimization.
13 729 0.485782743136 Henry Cohn, 2026, needs more optimization.
13 730 0.485878934114 Henry Cohn, 2026, needs more optimization.
13 731 0.485885060888 Henry Cohn, 2026, needs more optimization.
13 732 0.485928134067 Henry Cohn, 2026, needs more optimization.
13 733 0.486030010636 Henry Cohn, 2026, needs more optimization.
13 734 0.486075718162 Henry Cohn, 2026, needs more optimization.
13 735 0.486184324750 Henry Cohn, 2026, needs more optimization.
13 736 0.486243913184 Henry Cohn, 2026, needs more optimization.
13 737 0.486308485677 Henry Cohn, 2026, needs more optimization.
13 738 0.486360574772 Henry Cohn, 2026, needs more optimization.
13 739 0.486437073735 Henry Cohn, 2026, needs more optimization.
13 740 0.486489798734 Henry Cohn, 2026, needs more optimization.
13 742 0.486524531889 Henry Cohn, 2026, needs more optimization.
13 743 0.486621291364 Henry Cohn, 2026, needs more optimization.
13 744 0.486702584669 Henry Cohn, 2026, needs more optimization.
13 746 0.486761049284 Henry Cohn, 2026, needs more optimization.
13 747 0.486844773695 Henry Cohn, 2026, needs more optimization.
13 748 0.486849032614 Henry Cohn, 2026, needs more optimization.
13 749 0.486873266067 Henry Cohn, 2026, needs more optimization.
13 750 0.486927771218 Henry Cohn, 2026, needs more optimization.
13 751 0.486997138732 Henry Cohn, 2026, needs more optimization.
13 752 0.487130250604 Henry Cohn, 2026, needs more optimization.
13 753 0.487218673028 Henry Cohn, 2026, needs more optimization.
13 754 0.487289303258 Henry Cohn, 2026, needs more optimization.
13 755 0.487300078855 Henry Cohn, 2026, needs more optimization.
13 756 0.487325374018 Henry Cohn, 2026, needs more optimization.
13 757 0.487380642818 Henry Cohn, 2026, needs more optimization.
13 758 0.487451867723 Henry Cohn, 2026, needs more optimization.
13 759 0.487528467417 Henry Cohn, 2026, needs more optimization.
13 760 0.487576511697 Henry Cohn, 2026, needs more optimization.
13 761 0.487660088812 Henry Cohn, 2026, needs more optimization.
13 762 0.487725320417 Henry Cohn, 2026, needs more optimization.
13 764 0.487815259315 Henry Cohn, 2026, needs more optimization.
13 765 0.487876447301 Henry Cohn, 2026, needs more optimization.
13 766 0.487902492684 Henry Cohn, 2026, needs more optimization.
13 767 0.488007464738 Henry Cohn, 2026, needs more optimization.
13 768 0.488046007744 Henry Cohn, 2026, needs more optimization.
13 769 0.488088293862 Henry Cohn, 2026, needs more optimization.
13 770 0.488143227135 Henry Cohn, 2026, needs more optimization.
13 771 0.488222081150 Henry Cohn, 2026, needs more optimization.
13 773 0.488227284150 Henry Cohn, 2026, needs more optimization.
13 774 0.488259305254 Henry Cohn, 2026, needs more optimization.
13 775 0.488309755427 Henry Cohn, 2026, needs more optimization.
13 776 0.488324468067 Henry Cohn, 2026, needs more optimization.
13 777 0.488379402322 Henry Cohn, 2026, needs more optimization.
13 778 0.488527319595 Henry Cohn, 2026, needs more optimization.
13 779 0.488537152259 Henry Cohn, 2026, needs more optimization.
13 780 0.488605671128 Henry Cohn, 2026, needs more optimization.
13 781 0.488633481398 Henry Cohn, 2026, needs more optimization.
13 782 0.488713244600 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 0.488874469847 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 0.489183536064 Henry Cohn, 2026, needs more optimization.
13 792 0.489186890019 Henry Cohn, 2026, needs more optimization.
13 793 0.489323213786 Henry Cohn, 2026, needs more optimization.
13 794 0.489391063718 Henry Cohn, 2026, needs more optimization.
13 795 0.489469081627 Henry Cohn, 2026, needs more optimization.
13 799 0.489507654698 Henry Cohn, 2026, needs more optimization.
13 800 0.489534539303 Henry Cohn, 2026, needs more optimization.
13 801 0.489621084053 Henry Cohn, 2026, needs more optimization.
13 803 0.489646459498 Henry Cohn, 2026, needs more optimization.
13 804 0.489681213804 Henry Cohn, 2026, needs more optimization.
13 805 0.489742051851 Henry Cohn, 2026, needs more optimization.
13 806 0.489833162284 Henry Cohn, 2026, needs more optimization.
13 807 0.489846081439 Henry Cohn, 2026, needs more optimization.
13 808 0.489958203020 Henry Cohn, 2026, needs more optimization.
13 809 0.490024269142 Henry Cohn, 2026, needs more optimization.
13 810 0.490073562056 Henry Cohn, 2026, needs more optimization.
13 811 0.490097127167 Henry Cohn, 2026, needs more optimization.
13 812 0.490158822945 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 0.490372306751 Henry Cohn, 2026, needs more optimization.
13 818 0.490539777327 Henry Cohn, 2026, needs more optimization.
13 819 0.490646005447 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 0.491010447836 Henry Cohn, 2026, needs more optimization.
13 824 0.491066127525 Henry Cohn, 2026, needs more optimization.
13 826 0.491069901968 Henry Cohn, 2026, needs more optimization.
13 827 0.491075529378 Henry Cohn, 2026, needs more optimization.
13 828 0.491120645013 Henry Cohn, 2026, needs more optimization.
13 829 0.491327843480 Henry Cohn, 2026, needs more optimization.
13 830 0.491395703869 Henry Cohn, 2026, needs more optimization.
13 831 0.491426925852 Henry Cohn, 2026, needs more optimization.
13 832 0.491469338306 Henry Cohn, 2026, needs more optimization.
13 833 0.491542519062 Henry Cohn, 2026, needs more optimization.
13 834 0.491609134737 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.
13 840 0.491752230932 Henry Cohn, 2026, needs more optimization.
13 841 0.491792199431 Henry Cohn, 2026, needs more optimization.
13 842 0.491804283717 Henry Cohn, 2026, needs more optimization.
13 843 0.492009090739 Henry Cohn, 2026, needs more optimization.
13 844 0.492134401387 Henry Cohn, 2026, needs more optimization.
13 846 0.492163756395 Henry Cohn, 2026, needs more optimization.
13 847 0.492313355362 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 0.492694319899 Henry Cohn, 2026, needs more optimization.
13 851 0.492905636222 Henry Cohn, 2026, needs more optimization.
13 852 0.492999883619 Henry Cohn, 2026, needs more optimization.
13 853 0.493124147263 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 0.493724237538 Henry Cohn, 2026, needs more optimization.
13 858 0.493915595949 Henry Cohn, 2026, needs more optimization.
13 859 0.494129476778 Henry Cohn, 2026, needs more optimization.
13 860 0.494278390579 Henry Cohn, 2026, needs more optimization.
13 861 0.494346204877 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 0.494769024437 Henry Cohn, 2026, needs more optimization.
13 865 0.494916035380 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 0.495400074181 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 0.495915909541 Henry Cohn, 2026, needs more optimization.
13 872 0.496018345558 Henry Cohn, 2026, needs more optimization.
13 874 0.496193550626 Henry Cohn, 2026, needs more optimization.
13 875 0.496339138306 Henry Cohn, 2026, needs more optimization.
13 876 0.496397996437 Henry Cohn, 2026, needs more optimization.
13 877 0.496635120526 Henry Cohn, 2026, needs more optimization.
13 878 0.496740501219 Henry Cohn, 2026, needs more optimization.
13 879 0.497009453323 Henry Cohn, 2026, needs more optimization.
13 880 0.497148156733 Henry Cohn, 2026, needs more optimization.
13 881 0.497279111189 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 0.498891722689 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 0.180979116725 Henry Cohn, 2026, needs more optimization.
14 73 0.184667025692 Henry Cohn, 2026, needs more optimization.
14 75 0.185110498562 Henry Cohn, 2026, needs more optimization.
14 76 0.189883320249 Henry Cohn, 2026, needs more optimization.
14 77 0.190266040190 Henry Cohn, 2026, needs more optimization.
14 78 0.191441908798 Henry Cohn, 2026, needs more optimization.
14 79 0.193295826526 Henry Cohn, 2026, needs more optimization.
14 80 0.195567887108 Henry Cohn, 2026, needs more optimization.
14 81 0.198109449654 Henry Cohn, 2026, needs more optimization.
14 82 0.198235129158 Henry Cohn, 2026, needs more optimization.
14 83 0.198270171611 Henry Cohn, 2026, needs more optimization.
14 84 0.198299756820 Henry Cohn, 2026, needs more optimization.
14 85 0.198385443669 Henry Cohn, 2026, needs more optimization.
14 86 0.198455621150 Henry Cohn, 2026, needs more optimization.
14 87 0.198500455261 Henry Cohn, 2026, needs more optimization.
14 88 0.198573144765 Henry Cohn, 2026, needs more optimization.
14 89 0.198677096726 Henry Cohn, 2026, needs more optimization.
14 90 0.198771632430 Henry Cohn, 2026, needs more optimization.
14 91 0.198843416030 Henry Cohn, 2026, needs more optimization.
14 92 0.208456809641 Henry Cohn, 2026, needs more optimization.
14 93 0.211749206685 Henry Cohn, 2026, needs more optimization.
14 94 0.211903259023 Henry Cohn, 2026, needs more optimization.
14 95 0.212184025107 Henry Cohn, 2026, needs more optimization.
14 96 0.212295215604 Henry Cohn, 2026, needs more optimization.
14 97 0.212297015495 Henry Cohn, 2026, needs more optimization.
14 98 0.212297015496 Henry Cohn, 2026, needs more optimization.
14 99 0.220526964708 Henry Cohn, 2026, needs more optimization.
14 100 0.223682381813 Henry Cohn, 2026, needs more optimization.
14 101 0.225613148985 Henry Cohn, 2026, needs more optimization.
14 102 0.228290445901 Henry Cohn, 2026, needs more optimization.
14 112 0.229910395528 Henry Cohn, 2026, needs more optimization.
14 113 0.234902627893 Henry Cohn, 2026, needs more optimization.
14 114 0.237359837687 Henry Cohn, 2026, needs more optimization.
14 115 0.239305162774 Henry Cohn, 2026, needs more optimization.
14 116 0.240927683446 Henry Cohn, 2026, needs more optimization.
14 117 0.242363536881 Henry Cohn, 2026, needs more optimization.
14 118 0.244005874203 Henry Cohn, 2026, needs more optimization.
14 119 0.244891424842 Henry Cohn, 2026, needs more optimization.
14 120 0.245340349030 Henry Cohn, 2026, needs more optimization.
14 121 0.245811136405 Henry Cohn, 2026, needs more optimization.
14 122 0.249217889356 Henry Cohn, 2026, needs more optimization.
14 123 0.250352159837 Henry Cohn, 2026, needs more optimization.
14 124 0.251242938893 Henry Cohn, 2026, needs more optimization.
14 125 0.252284925644 Henry Cohn, 2026, needs more optimization.
14 126 0.253277127558 Henry Cohn, 2026, needs more optimization.
14 127 0.254058651002 Henry Cohn, 2026, needs more optimization.
14 128 0.254656731743 Henry Cohn, 2026, needs more optimization.
14 129 0.255353344739 Henry Cohn, 2026, needs more optimization.
14 130 0.256004047205 Henry Cohn, 2026, needs more optimization.
14 131 0.258382739285 Henry Cohn, 2026, needs more optimization.
14 132 0.261625264451 Henry Cohn, 2026, needs more optimization.
14 133 0.262928314390 Henry Cohn, 2026, needs more optimization.
14 134 0.264469963236 Henry Cohn, 2026, needs more optimization.
14 135 0.265740345783 Henry Cohn, 2026, needs more optimization.
14 136 0.266894239560 Henry Cohn, 2026, needs more optimization.
14 137 0.268289839241 Henry Cohn, 2026, needs more optimization.
14 138 0.269360778121 Henry Cohn, 2026, needs more optimization.
14 139 0.269360778123 Henry Cohn, 2026, needs more optimization.
14 140 0.269363487453 Henry Cohn, 2026, needs more optimization.
14 141 0.269364653587 Henry Cohn, 2026, needs more optimization.
14 142 0.269374502321 Henry Cohn, 2026, needs more optimization.
14 143 0.269376035718 Henry Cohn, 2026, needs more optimization.
14 144 0.269378581522 Henry Cohn, 2026, needs more optimization.
14 145 0.269385057223 Henry Cohn, 2026, needs more optimization.
14 146 0.269391352219 Henry Cohn, 2026, needs more optimization.
14 147 0.269406350518 Henry Cohn, 2026, needs more optimization.
14 148 0.269435946677 Henry Cohn, 2026, needs more optimization.
14 149 0.269470068873 Henry Cohn, 2026, needs more optimization.
14 150 0.269510622525 Henry Cohn, 2026, needs more optimization.
14 151 0.269752154367 Henry Cohn, 2026, needs more optimization.
14 152 0.269752156057 Henry Cohn, 2026, needs more optimization.
14 153 0.273185531222 Henry Cohn, 2026, needs more optimization.
14 154 0.273861278753 Henry Cohn, 2026.
40⁢x2−3
14 156 0.276328142308 Henry Cohn, 2026, needs more optimization.
14 157 0.276372455325 Henry Cohn, 2026, needs more optimization.
14 158 0.276419044697 Henry Cohn, 2026, needs more optimization.
14 159 0.276645025935 Henry Cohn, 2026, needs more optimization.
14 160 0.277045384070 Henry Cohn, 2026, needs more optimization.
14 161 0.277462604715 Henry Cohn, 2026, needs more optimization.
14 162 0.277837064330 Henry Cohn, 2026, needs more optimization.
14 163 0.278239418944 Henry Cohn, 2026, needs more optimization.
14 164 0.278745365039 Henry Cohn, 2026, needs more optimization.
14 165 0.279342784948 Henry Cohn, 2026, needs more optimization.
14 166 0.280063079944 Henry Cohn, 2026, needs more optimization.
14 167 0.284424966767 Henry Cohn, 2026, needs more optimization.
14 168 0.286574094053 Henry Cohn, 2026, needs more optimization.
14 169 0.287941681168 Henry Cohn, 2026, needs more optimization.
14 170 0.289219118809 Henry Cohn, 2026, needs more optimization.
14 171 0.290633207397 Henry Cohn, 2026, needs more optimization.
14 172 0.290743918244 Henry Cohn, 2026, needs more optimization.
14 173 0.291356340107 Henry Cohn, 2026, needs more optimization.
14 174 0.292124438244 Henry Cohn, 2026, needs more optimization.
14 175 0.293051049319 Henry Cohn, 2026, needs more optimization.
14 176 0.293772607889 Henry Cohn, 2026, needs more optimization.
14 177 0.294410411778 Henry Cohn, 2026, needs more optimization.
14 178 0.295415354468 Henry Cohn, 2026, needs more optimization.
14 179 0.295985242939 Henry Cohn, 2026, needs more optimization.
14 180 0.296647667521 Henry Cohn, 2026, needs more optimization.
14 181 0.297697534392 Henry Cohn, 2026, needs more optimization.
14 182 0.297711417623 Henry Cohn, 2026, needs more optimization.
14 183 0.297832444430 Henry Cohn, 2026, needs more optimization.
14 184 0.298059362116 Henry Cohn, 2026, needs more optimization.
14 185 0.298566407087 Henry Cohn, 2026, needs more optimization.
14 186 0.299330294294 Henry Cohn, 2026, needs more optimization.
14 187 0.299781979624 Henry Cohn, 2026, needs more optimization.
14 188 0.300677814401 Henry Cohn, 2026, needs more optimization.
14 189 0.301687673066 Henry Cohn, 2026, needs more optimization.
14 190 0.301802297823 Henry Cohn, 2026, needs more optimization.
14 191 0.302343409478 Henry Cohn, 2026, needs more optimization.
14 192 0.303612038963 Henry Cohn, 2026, needs more optimization.
14 193 0.304411329640 Henry Cohn, 2026, needs more optimization.
14 194 0.305386034329 Henry Cohn, 2026, needs more optimization.
14 195 0.306540276178 Henry Cohn, 2026, needs more optimization.
14 196 0.307923647129 Henry Cohn, 2026, needs more optimization.
14 197 0.308922654317 Henry Cohn, 2026, needs more optimization.
14 198 0.310108064412 Henry Cohn, 2026, needs more optimization.
14 199 0.310675176432 Henry Cohn, 2026, needs more optimization.
14 200 0.311235878990 Henry Cohn, 2026, needs more optimization.
14 201 0.312453273428 Henry Cohn, 2026, needs more optimization.
14 202 0.313545758001 Henry Cohn, 2026, needs more optimization.
14 203 0.313797242019 Henry Cohn, 2026, needs more optimization.
14 204 0.313845216971 Henry Cohn, 2026, needs more optimization.
14 205 0.314071149768 Henry Cohn, 2026, needs more optimization.
14 206 0.314289078427 Henry Cohn, 2026, needs more optimization.
14 207 0.314610013542 Henry Cohn, 2026, needs more optimization.
14 208 0.315016941224 Henry Cohn, 2026, needs more optimization.
14 209 0.315343997471 Henry Cohn, 2026, needs more optimization.
14 210 0.315611123572 Henry Cohn, 2026, needs more optimization.
14 211 0.315977918085 Henry Cohn, 2026, needs more optimization.
14 212 0.316396455227 Henry Cohn, 2026, needs more optimization.
14 213 0.317118881413 Henry Cohn, 2026, needs more optimization.
14 214 0.317716061292 Henry Cohn, 2026, needs more optimization.
14 215 0.318315584823 Henry Cohn, 2026, needs more optimization.
14 216 0.318932945028 Henry Cohn, 2026, needs more optimization.
14 217 0.319500005859 Henry Cohn, 2026, needs more optimization.
14 218 0.320060770450 Henry Cohn, 2026, needs more optimization.
14 219 0.320688266752 Henry Cohn, 2026, needs more optimization.
14 220 0.321047402735 Henry Cohn, 2026, needs more optimization.
14 221 0.321571228204 Henry Cohn, 2026, needs more optimization.
14 222 0.322177431064 Henry Cohn, 2026, needs more optimization.
14 223 0.322714979606 Henry Cohn, 2026, needs more optimization.
14 224 0.322800428213 Henry Cohn, 2026, needs more optimization.
14 225 0.323284697984 Henry Cohn, 2026, needs more optimization.
14 226 0.324473565639 Henry Cohn, 2026, needs more optimization.
14 227 0.324797674334 Henry Cohn, 2026, needs more optimization.
14 228 0.325283314888 Henry Cohn, 2026, needs more optimization.
14 229 0.325859471881 Henry Cohn, 2026, needs more optimization.
14 230 0.326457746643 Henry Cohn, 2026, needs more optimization.
14 231 0.326901354854 Henry Cohn, 2026, needs more optimization.
14 232 0.327623957314 Henry Cohn, 2026, needs more optimization.
14 233 0.328696135634 Henry Cohn, 2026, needs more optimization.
14 234 0.329429684628 Henry Cohn, 2026, needs more optimization.
14 235 0.330548710841 Henry Cohn, 2026, needs more optimization.
14 236 0.331742174093 Henry Cohn, 2026, needs more optimization.
14 237 0.333113714522 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 0.346775847829 Henry Cohn, 2026, needs more optimization.
14 254 0.346783478747 Henry Cohn, 2026, needs more optimization.
14 255 0.346792969361 Henry Cohn, 2026, needs more optimization.
14 256 0.346912221588 Henry Cohn, 2026, needs more optimization.
14 257 0.347047933364 Henry Cohn, 2026, needs more optimization.
14 258 0.347243699365 Henry Cohn, 2026, needs more optimization.
14 259 0.347258884595 Henry Cohn, 2026, needs more optimization.
14 260 0.347325597157 Henry Cohn, 2026, needs more optimization.
14 261 0.347392286786 Henry Cohn, 2026, needs more optimization.
14 262 0.347549678238 Henry Cohn, 2026, needs more optimization.
14 263 0.347780001983 Henry Cohn, 2026, needs more optimization.
14 264 0.348086610872 Henry Cohn, 2026, needs more optimization.
14 265 0.348218214593 Henry Cohn, 2026, needs more optimization.
14 266 0.348685341410 Henry Cohn, 2026, needs more optimization.
14 267 0.349032975340 Henry Cohn, 2026, needs more optimization.
14 268 0.349149091640 Henry Cohn, 2026, needs more optimization.
14 269 0.349227661624 Henry Cohn, 2026, needs more optimization.
14 270 0.349535648805 Henry Cohn, 2026, needs more optimization.
14 271 0.350125403419 Henry Cohn, 2026, needs more optimization.
14 272 0.350637011024 Henry Cohn, 2026, needs more optimization.
14 273 0.351186119832 Henry Cohn, 2026, needs more optimization.
14 274 0.351408667545 Henry Cohn, 2026, needs more optimization.
14 275 0.351722641993 Henry Cohn, 2026, needs more optimization.
14 276 0.352046605559 Henry Cohn, 2026, needs more optimization.
14 277 0.352287428077 Henry Cohn, 2026, needs more optimization.
14 278 0.352389354319 Henry Cohn, 2026, needs more optimization.
14 279 0.352631360352 Henry Cohn, 2026, needs more optimization.
14 280 0.352754627847 Henry Cohn, 2026, needs more optimization.
14 281 0.353074887525 Henry Cohn, 2026, needs more optimization.
14 282 0.353372611699 Henry Cohn, 2026, needs more optimization.
14 283 0.353612315466 Henry Cohn, 2026, needs more optimization.
14 284 0.353885795218 Henry Cohn, 2026, needs more optimization.
14 285 0.353936384811 Henry Cohn, 2026, needs more optimization.
14 286 0.354095507613 Henry Cohn, 2026, needs more optimization.
14 287 0.354181944093 Henry Cohn, 2026, needs more optimization.
14 288 0.354497030864 Henry Cohn, 2026, needs more optimization.
14 289 0.354574286616 Henry Cohn, 2026, needs more optimization.
14 290 0.354601778652 Henry Cohn, 2026, needs more optimization.
14 291 0.354614461137 Henry Cohn, 2026, needs more optimization.
14 292 0.354617120674 Henry Cohn, 2026, needs more optimization.
14 293 0.354702857371 Henry Cohn, 2026, needs more optimization.
14 294 0.354727035972 Henry Cohn, 2026, needs more optimization.
14 295 0.354883219360 Henry Cohn, 2026, needs more optimization.
14 296 0.354990842381 Henry Cohn, 2026, needs more optimization.
14 297 0.355078827749 Henry Cohn, 2026, needs more optimization.
14 298 0.355158629121 Henry Cohn, 2026, needs more optimization.
14 299 0.355168740487 Henry Cohn, 2026, needs more optimization.
14 300 0.355168934736 Henry Cohn, 2026, needs more optimization.
14 301 0.355170241297 Henry Cohn, 2026, needs more optimization.
14 302 0.355170839871 Henry Cohn, 2026, needs more optimization.
14 303 0.355171165403 Henry Cohn, 2026, needs more optimization.
14 304 0.355171924739 Henry Cohn, 2026, needs more optimization.
14 305 0.355172031563 Henry Cohn, 2026, needs more optimization.
14 306 0.355172043103 Henry Cohn, 2026, needs more optimization.
14 307 0.355172053260 Henry Cohn, 2026, needs more optimization.
14 308 0.355172065434 Henry Cohn, 2026, needs more optimization.
14 309 0.355172081494 Henry Cohn, 2026, needs more optimization.
14 310 0.355175860892 Henry Cohn, 2026, needs more optimization.
14 311 0.355175871108 Henry Cohn, 2026, needs more optimization.
14 312 0.355175880723 Henry Cohn, 2026, needs more optimization.
14 313 0.355175891322 Henry Cohn, 2026, needs more optimization.
14 314 0.355175909096 Henry Cohn, 2026, needs more optimization.
14 315 0.355175924463 Henry Cohn, 2026, needs more optimization.
14 316 0.355175938407 Henry Cohn, 2026, needs more optimization.
14 317 0.355175947529 Henry Cohn, 2026, needs more optimization.
14 318 0.355175957438 Henry Cohn, 2026, needs more optimization.
14 319 0.355175963092 Henry Cohn, 2026, needs more optimization.
14 320 0.355175974345 Henry Cohn, 2026, needs more optimization.
14 321 0.355175986005 Henry Cohn, 2026, needs more optimization.
14 322 0.355176004087 Henry Cohn, 2026, needs more optimization.
14 323 0.355176010923 Henry Cohn, 2026, needs more optimization.
14 324 0.355176019350 Henry Cohn, 2026, needs more optimization.
14 325 0.355176035350 Henry Cohn, 2026, needs more optimization.
14 326 0.355176040441 Henry Cohn, 2026, needs more optimization.
14 327 0.355176049557 Henry Cohn, 2026, needs more optimization.
14 328 0.355176060107 Henry Cohn, 2026, needs more optimization.
14 329 0.355176070309 Henry Cohn, 2026, needs more optimization.
14 330 0.355176087415 Henry Cohn, 2026, needs more optimization.
14 331 0.355176102092 Henry Cohn, 2026, needs more optimization.
14 332 0.355176119492 Henry Cohn, 2026, needs more optimization.
14 333 0.355176135665 Henry Cohn, 2026, needs more optimization.
14 334 0.355176159589 Henry Cohn, 2026, needs more optimization.
14 335 0.355176186675 Henry Cohn, 2026, needs more optimization.
14 336 0.355176212624 Henry Cohn, 2026, needs more optimization.
14 337 0.355176228761 Henry Cohn, 2026, needs more optimization.
14 338 0.355366939097 Henry Cohn, 2026, needs more optimization.
14 339 0.356049481767 Henry Cohn, 2026, needs more optimization.
14 340 0.357691780621 Henry Cohn, 2026, needs more optimization.
14 341 0.358566785701 Henry Cohn, 2026, needs more optimization.
14 342 0.358604133779 Henry Cohn, 2026, needs more optimization.
14 343 0.358665375035 Henry Cohn, 2026, needs more optimization.
14 344 0.360295606082 Henry Cohn, 2026, needs more optimization.
14 345 0.360799969158 Henry Cohn, 2026, needs more optimization.
14 346 0.363064489869 Henry Cohn, 2026, needs more optimization.
14 347 0.365302957241 Henry Cohn, 2026, needs more optimization.
14 348 0.365982596579 Henry Cohn, 2026, needs more optimization.
14 349 0.366748966151 Henry Cohn, 2026, needs more optimization.
14 350 0.367183589829 Henry Cohn, 2026, needs more optimization.
14 351 0.367288676265 Henry Cohn, 2026, needs more optimization.
14 352 0.367375067158 Henry Cohn, 2026, needs more optimization.
14 353 0.368924583459 Henry Cohn, 2026, needs more optimization.
14 354 0.369713028598 Henry Cohn, 2026, needs more optimization.
14 355 0.370613867235 Henry Cohn, 2026, needs more optimization.
14 356 0.372940605605 Henry Cohn, 2026, needs more optimization.
14 357 0.374169424078 Henry Cohn, 2026, needs more optimization.
14 358 0.374187748304 Henry Cohn, 2026, needs more optimization.
14 359 0.374896069434 Henry Cohn, 2026, needs more optimization.
14 360 0.375531890851 Henry Cohn, 2026, needs more optimization.
14 362 0.377676924800 Henry Cohn, 2026, needs more optimization.
14 364 0.377687067360 Henry Cohn, 2026, needs more optimization.
14 365 0.378169601663 Henry Cohn, 2026, needs more optimization.
14 367 0.378189199711 Henry Cohn, 2026, needs more optimization.
14 370 0.378375859724 Henry Cohn, 2026, needs more optimization.
14 371 0.379228230207 Henry Cohn, 2026, needs more optimization.
14 372 0.379407709008 Henry Cohn, 2026, needs more optimization.
14 373 0.379414296353 Henry Cohn, 2026, needs more optimization.
14 375 0.379418252216 Henry Cohn, 2026, needs more optimization.
14 376 0.379428103994 Henry Cohn, 2026, needs more optimization.
14 382 0.381699399131 Henry Cohn, 2026, needs more optimization.
14 384 0.381708236659 Henry Cohn, 2026, needs more optimization.
14 385 0.381804112720 Henry Cohn, 2026, needs more optimization.
14 386 0.381821889554 Henry Cohn, 2026, needs more optimization.
14 387 0.382344946803 Henry Cohn, 2026, needs more optimization.
14 388 0.383685908677 Henry Cohn, 2026, needs more optimization.
14 389 0.384424553280 Henry Cohn, 2026, needs more optimization.
14 390 0.384813227412 Henry Cohn, 2026, needs more optimization.
14 391 0.385559973465 Henry Cohn, 2026, needs more optimization.
14 396 0.385863136144 Henry Cohn, 2026, needs more optimization.
14 398 0.386851800985 Henry Cohn, 2026, needs more optimization.
14 399 0.387847661129 Henry Cohn, 2026, needs more optimization.
14 401 0.387939172669 Henry Cohn, 2026, needs more optimization.
14 402 0.388796287512 Henry Cohn, 2026, needs more optimization.
14 403 0.389276729286 Henry Cohn, 2026, needs more optimization.
14 404 0.389660543025 Henry Cohn, 2026, needs more optimization.
14 405 0.389813293737 Henry Cohn, 2026, needs more optimization.
14 406 0.390141417355 Henry Cohn, 2026, needs more optimization.
14 407 0.390328107686 Henry Cohn, 2026, needs more optimization.
14 409 0.390524882198 Henry Cohn, 2026, needs more optimization.
14 410 0.390706151872 Henry Cohn, 2026, needs more optimization.
14 414 0.390870678686 Henry Cohn, 2026, needs more optimization.
14 415 0.391049157310 Henry Cohn, 2026, needs more optimization.
14 435 0.391891891892 Henry Cohn, 2026.
74⁢x−29
14 436 0.394835395384 Henry Cohn, 2026, needs more optimization.
14 437 0.395907785510 Henry Cohn, 2026, needs more optimization.
14 438 0.396551713013 Henry Cohn, 2026, needs more optimization.
14 439 0.396990626262 Henry Cohn, 2026, needs more optimization.
14 440 0.397346809347 Henry Cohn, 2026, needs more optimization.
14 441 0.397630186161 Henry Cohn, 2026, needs more optimization.
14 442 0.398093258442 Henry Cohn, 2026, needs more optimization.
14 443 0.398793259888 Henry Cohn, 2026, needs more optimization.
14 444 0.399267570342 Henry Cohn, 2026, needs more optimization.
14 445 0.399602601157 Henry Cohn, 2026, needs more optimization.
14 466 0.4 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−2
14 492 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 0.402330459939 Henry Cohn, 2026, needs more optimization.
14 494 0.402332502198 Henry Cohn, 2026, needs more optimization.
14 495 0.403221891855 Henry Cohn, 2026, needs more optimization.
14 496 0.404856098789 Henry Cohn, 2026, needs more optimization.
14 497 0.407599640922 Henry Cohn, 2026, needs more optimization.
14 498 0.408804173402 Henry Cohn, 2026, needs more optimization.
14 500 0.409199447420 Henry Cohn, 2026, needs more optimization.
14 501 0.409647396576 Henry Cohn, 2026, needs more optimization.
14 502 0.410585583685 Henry Cohn, 2026, needs more optimization.
14 503 0.412611990386 Henry Cohn, 2026, needs more optimization.
14 504 0.414215596761 Henry Cohn, 2026, needs more optimization.
14 505 0.414859941034 Henry Cohn, 2026, needs more optimization.
14 506 0.416113388590 Henry Cohn, 2026, needs more optimization.
14 507 0.417918634881 Henry Cohn, 2026, needs more optimization.
14 508 0.418505635050 Henry Cohn, 2026, needs more optimization.
14 509 0.419515651193 Henry Cohn, 2026, needs more optimization.
14 510 0.419698729124 Henry Cohn, 2026, needs more optimization.
14 511 0.420929534720 Henry Cohn, 2026, needs more optimization.
14 512 0.421056197787 Henry Cohn, 2026, needs more optimization.
14 513 0.421223138273 Henry Cohn, 2026, needs more optimization.
14 514 0.421733301195 Henry Cohn, 2026, needs more optimization.
14 515 0.422312880269 Henry Cohn, 2026, needs more optimization.
14 516 0.422501721133 Henry Cohn, 2026, needs more optimization.
14 517 0.423004281192 Henry Cohn, 2026, needs more optimization.
14 555 0.423076923077 Henry Cohn, 2026.
26⁢x−11
14 556 0.425788721707 Henry Cohn, 2026, needs more optimization.
14 557 0.426026837615 Henry Cohn, 2026, needs more optimization.
14 558 0.426727403830 Henry Cohn, 2026, needs more optimization.
14 559 0.427457061752 Henry Cohn, 2026, needs more optimization.
14 560 0.428000469015 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 0.429748171332 Henry Cohn, 2026, needs more optimization.
14 602 0.430061691398 Henry Cohn, 2026, needs more optimization.
14 603 0.430238583748 Henry Cohn, 2026, needs more optimization.
14 604 0.430605377846 Henry Cohn, 2026, needs more optimization.
14 605 0.431008392471 Henry Cohn, 2026, needs more optimization.
14 606 0.431141998946 Henry Cohn, 2026, needs more optimization.
14 607 0.431203582142 Henry Cohn, 2026, needs more optimization.
14 608 0.431365482112 Henry Cohn, 2026, needs more optimization.
14 609 0.431521336610 Henry Cohn, 2026, needs more optimization.
14 610 0.431618317871 Henry Cohn, 2026, needs more optimization.
14 611 0.431633524007 Henry Cohn, 2026, needs more optimization.
14 612 0.432139599736 Henry Cohn, 2026, needs more optimization.
14 613 0.432246594035 Henry Cohn, 2026, needs more optimization.
14 614 0.432335371455 Henry Cohn, 2026, needs more optimization.
14 615 0.432823670217 Henry Cohn, 2026, needs more optimization.
14 617 0.432883655585 Henry Cohn, 2026, needs more optimization.
14 618 0.432929238509 Henry Cohn, 2026, needs more optimization.
14 619 0.432967732001 Henry Cohn, 2026, needs more optimization.
14 621 0.432996030076 Henry Cohn, 2026, needs more optimization.
14 622 0.433031058933 Henry Cohn, 2026, needs more optimization.
14 623 0.433104672323 Henry Cohn, 2026, needs more optimization.
14 624 0.433113239737 Henry Cohn, 2026, needs more optimization.
14 625 0.433182191224 Henry Cohn, 2026, needs more optimization.
14 626 0.433205027227 Henry Cohn, 2026, needs more optimization.
14 627 0.433255006911 Henry Cohn, 2026, needs more optimization.
14 628 0.433543182689 Henry Cohn, 2026, needs more optimization.
14 629 0.433562790708 Henry Cohn, 2026, needs more optimization.
14 630 0.433603423588 Henry Cohn, 2026, needs more optimization.
14 631 0.433676864607 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 0.433894718763 Henry Cohn, 2026, needs more optimization.
14 638 0.433931402932 Henry Cohn, 2026, needs more optimization.
14 639 0.433949108269 Henry Cohn, 2026, 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 0.451559037381 Henry Cohn, 2026, needs more optimization.
14 651 0.451650567060 Henry Cohn, 2026, needs more optimization.
14 653 0.451658069755 Henry Cohn, 2026, needs more optimization.
14 654 0.451682985488 Henry Cohn, 2026, needs more optimization.
14 655 0.451751699793 Henry Cohn, 2026, needs more optimization.
14 656 0.451788208457 Henry Cohn, 2026, needs more optimization.
14 662 0.451892553323 Henry Cohn, 2026, needs more optimization.
14 664 0.451962032127 Henry Cohn, 2026, needs more optimization.
14 665 0.452006338552 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 0.452341236848 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 0.453193619750 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 0.454719228542 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.
14 924 0.455349171804 Henry Cohn, 2026, needs more optimization.
14 925 0.455351537723 Henry Cohn, 2026, needs more optimization.
14 926 0.455358896413 Henry Cohn, 2026, needs more optimization.
14 927 0.455366453145 Henry Cohn, 2026, needs more optimization.
14 928 0.455369387330 Henry Cohn, 2026, needs more optimization.
14 929 0.455374081578 Henry Cohn, 2026, needs more optimization.
14 930 0.455378882411 Henry Cohn, 2026, needs more optimization.
14 931 0.455380847317 Henry Cohn, 2026, needs more optimization.
14 932 0.455388143438 Henry Cohn, 2026, needs more optimization.
14 933 0.455393806318 Henry Cohn, 2026, needs more optimization.
14 934 0.455395236754 Henry Cohn, 2026, needs more optimization.
14 935 0.455397379524 Henry Cohn, 2026, needs more optimization.
14 936 0.455402841336 Henry Cohn, 2026, needs more optimization.
14 937 0.455408675534 Henry Cohn, 2026, needs more optimization.
14 938 0.455413257812 Henry Cohn, 2026, needs more optimization.
14 939 0.455419313207 Henry Cohn, 2026, needs more optimization.
14 940 0.455425118727 Henry Cohn, 2026, needs more optimization.
14 941 0.455429276027 Henry Cohn, 2026, needs more optimization.
14 942 0.455435411346 Henry Cohn, 2026, needs more optimization.
14 943 0.455440550119 Henry Cohn, 2026, needs more optimization.
14 944 0.455446818148 Henry Cohn, 2026, needs more optimization.
14 945 0.455450900106 Henry Cohn, 2026, needs more optimization.
14 946 0.455457025616 Henry Cohn, 2026, needs more optimization.
14 947 0.455459871696 Henry Cohn, 2026, needs more optimization.
14 948 0.455469386987 Henry Cohn, 2026, needs more optimization.
14 949 0.455473216803 Henry Cohn, 2026, needs more optimization.
14 950 0.455477645768 Henry Cohn, 2026, needs more optimization.
14 951 0.455486008927 Henry Cohn, 2026, needs more optimization.
14 952 0.455493218185 Henry Cohn, 2026, needs more optimization.
14 953 0.455498726210 Henry Cohn, 2026, needs more optimization.
14 954 0.455509117681 Henry Cohn, 2026, needs more optimization.
14 955 0.455512657812 Henry Cohn, 2026, needs more optimization.
14 956 0.455534335290 Henry Cohn, 2026, needs more optimization.
14 957 0.455540241388 Henry Cohn, 2026, needs more optimization.
14 958 0.455546639329 Henry Cohn, 2026, needs more optimization.
14 959 0.455553967478 Henry Cohn, 2026, needs more optimization.
14 960 0.455557205263 Henry Cohn, 2026, needs more optimization.
14 961 0.455563237992 Henry Cohn, 2026, needs more optimization.
14 962 0.455568083544 Henry Cohn, 2026, needs more optimization.
14 963 0.455577354830 Henry Cohn, 2026, needs more optimization.
14 964 0.455585771683 Henry Cohn, 2026, needs more optimization.
14 965 0.455592710913 Henry Cohn, 2026, needs more optimization.
14 966 0.455598891046 Henry Cohn, 2026, needs more optimization.
14 967 0.455603819071 Henry Cohn, 2026, needs more optimization.
14 968 0.455610032057 Henry Cohn, 2026, needs more optimization.
14 969 0.455612698212 Henry Cohn, 2026, needs more optimization.
14 970 0.455616300651 Henry Cohn, 2026, needs more optimization.
14 971 0.455626379572 Henry Cohn, 2026, needs more optimization.
14 972 0.455632026554 Henry Cohn, 2026, needs more optimization.
14 973 0.455636034266 Henry Cohn, 2026, needs more optimization.
14 974 0.455640320563 Henry Cohn, 2026, needs more optimization.
14 975 0.455647040535 Henry Cohn, 2026, needs more optimization.
14 976 0.455654548525 Henry Cohn, 2026, needs more optimization.
14 994 0.457506761608 Henry Cohn, 2026, needs more optimization.
14 995 0.457506761658 Henry Cohn, 2026, needs more optimization.
14 996 0.457506761708 Henry Cohn, 2026, needs more optimization.
14 997 0.457506761739 Henry Cohn, 2026, needs more optimization.
14 998 0.457506761749 Henry Cohn, 2026, needs more optimization.
14 999 0.457506761815 Henry Cohn, 2026, needs more optimization.
14 1002 0.457506761859 Henry Cohn, 2026, needs more optimization.
14 1003 0.457506761869 Henry Cohn, 2026, needs more optimization.
14 1004 0.457506761907 Henry Cohn, 2026, needs more optimization.
14 1005 0.457506761949 Henry Cohn, 2026, needs more optimization.
14 1006 0.457506761953 Henry Cohn, 2026, needs more optimization.
14 1007 0.457506762000 Henry Cohn, 2026, needs more optimization.
14 1008 0.457509336271 Henry Cohn, 2026, needs more optimization.
14 1009 0.457511789262 Henry Cohn, 2026, needs more optimization.
14 1010 0.457514623947 Henry Cohn, 2026, needs more optimization.
14 1011 0.457520168291 Henry Cohn, 2026, needs more optimization.
14 1012 0.457525527288 Henry Cohn, 2026, needs more optimization.
14 1013 0.457527938893 Henry Cohn, 2026, needs more optimization.
14 1014 0.457534635857 Henry Cohn, 2026, needs more optimization.
14 1015 0.457544917772 Henry Cohn, 2026, needs more optimization.
14 1016 0.457549967733 Henry Cohn, 2026, needs more optimization.
14 1017 0.457552363580 Henry Cohn, 2026, needs more optimization.
14 1018 0.457554380023 Henry Cohn, 2026, needs more optimization.
14 1019 0.457559618085 Henry Cohn, 2026, needs more optimization.
14 1020 0.457566402411 Henry Cohn, 2026, needs more optimization.
14 1021 0.457575374184 Henry Cohn, 2026, needs more optimization.
14 1022 0.457582487453 Henry Cohn, 2026, needs more optimization.
14 1023 0.457587190989 Henry Cohn, 2026, needs more optimization.
14 1024 0.457591858549 Henry Cohn, 2026, needs more optimization.
15 31 0.050237120373 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
2535⁢x3−225⁢x2−15⁢x+1
15 32 0.058900808489 H. Cohn, Small spherical and projective codes, data set, 2022, DSpace@MIT, https://hdl.handle.net/1721.1/142661.
15 33 0.062706770083 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
15 34 0.066570393658 Henry Cohn, 2025.
15 35 0.070509992992 Henry Cohn, 2023.
15 36 0.070779968044 Henry Cohn, 2023.
5937⁢x4+412⁢x3−202⁢x2−4⁢x+1
15 37 0.078785666352 Henry Cohn, 2025.
15 38 0.079970260232 Henry Cohn, 2026.
15 39 0.082681671944 Henry Cohn, 2023.
347087⁢x8+1080416⁢x7+305012⁢x6+3648⁢x5−20054⁢x4−160⁢x3+276⁢x2−1
15 40 0.086159367074 Henry Cohn, 2023.
15 41 0.093058708471 Henry Cohn, 2026.
15 42 0.096809796022 Henry Cohn, 2023.
15 43 0.099863843733 Henry Cohn, 2025.
15 44 0.099976426707 Henry Cohn, 2025.
15 45 0.102626460761 Henry Cohn, 2026.
15 46 0.110795000982 Henry Cohn, 2025.
15 47 0.111165028345 Henry Cohn, 2026.
15 48 0.112519700675 Henry Cohn, 2026.
15 52 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
15 57 0.115470053838 Henry Cohn, 2024.
75⁢x2−1
15 58 0.119568772343 Henry Cohn, 2025.
15 61 0.128458591981 Henry Cohn, 2025.
263⁢x2−26⁢x−1
15 62 0.129608604602 Henry Cohn, 2026, 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 73 0.161462093425 Henry Cohn, 2026.
15 76 0.168269539561 Henry Cohn, 2026, needs more optimization.
15 78 0.168276949824 Henry Cohn, 2026, needs more optimization.
15 92 0.168685175113 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
47⁢x2−2⁢x−1
15 93 0.169916676995 Henry Cohn, 2025.
169⁢x4−56⁢x3−30⁢x2+1
15 94 0.186858652290 Henry Cohn, 2026, needs more optimization.
15 95 0.187077042680 Henry Cohn, 2026, needs more optimization.
15 96 0.187887288776 Henry Cohn, 2026, needs more optimization.
15 98 0.188666328568 Henry Cohn, 2026, needs more optimization.
15 99 0.188666328574 Henry Cohn, 2026, needs more optimization.
15 100 0.189750003541 Henry Cohn, 2026, needs more optimization.
15 101 0.197672143282 Henry Cohn, 2026, needs more optimization.
15 108 0.199301661815 Henry Cohn, 2026.
347⁢x2−24⁢x−9
15 128 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
15 129 0.209693852047 Henry Cohn, 2026, needs more optimization.
15 130 0.216450091134 Henry Cohn, 2026, needs more optimization.
15 131 0.219825247061 Henry Cohn, 2026, needs more optimization.
15 132 0.221692066424 Henry Cohn, 2026, needs more optimization.
15 135 0.223068626266 Henry Cohn, 2026, needs more optimization.
15 136 0.225990151252 Henry Cohn, 2026, needs more optimization.
15 137 0.226886840485 Henry Cohn, 2026, needs more optimization.
15 142 0.227160244714 Henry Cohn, 2026, needs more optimization.
15 143 0.232254931356 Henry Cohn, 2026, needs more optimization.
15 144 0.235179709766 Henry Cohn, 2026, needs more optimization.
15 145 0.237561438421 Henry Cohn, 2026, needs more optimization.
15 146 0.238721219437 Henry Cohn, 2026, needs more optimization.
15 147 0.238762614057 Henry Cohn, 2026, needs more optimization.
15 148 0.239558562305 Henry Cohn, 2026, needs more optimization.
15 149 0.239558597601 Henry Cohn, 2026, needs more optimization.
15 150 0.239558871952 Henry Cohn, 2026, needs more optimization.
15 151 0.239559227709 Henry Cohn, 2026, needs more optimization.
15 152 0.244616813223 Henry Cohn, 2026, needs more optimization.
15 153 0.245479445825 Henry Cohn, 2026, needs more optimization.
15 156 0.248124762896 Henry Cohn, 2026, needs more optimization.
15 157 0.249069470433 Henry Cohn, 2026.
15 158 0.253987633701 Henry Cohn, 2026, needs more optimization.
15 159 0.254474464845 Henry Cohn, 2026, needs more optimization.
15 160 0.254877441918 Henry Cohn, 2026, needs more optimization.
15 161 0.255435868248 Henry Cohn, 2026, needs more optimization.
15 162 0.256445827580 Henry Cohn, 2026, needs more optimization.
15 163 0.257094873205 Henry Cohn, 2026, needs more optimization.
15 164 0.257359308774 Henry Cohn, 2026, needs more optimization.
15 165 0.257391616061 Henry Cohn, 2026, needs more optimization.
15 166 0.257476235366 Henry Cohn, 2026, needs more optimization.
15 167 0.257676625355 Henry Cohn, 2026, needs more optimization.
15 168 0.257853480086 Henry Cohn, 2026, needs more optimization.
15 169 0.258096235294 Henry Cohn, 2026, needs more optimization.
15 170 0.258179090726 Henry Cohn, 2026, needs more optimization.
15 171 0.258378495379 Henry Cohn, 2026, needs more optimization.
15 172 0.258514350067 Henry Cohn, 2026, needs more optimization.
15 173 0.258642110145 Henry Cohn, 2026, needs more optimization.
15 174 0.258728233010 Henry Cohn, 2026, needs more optimization.
15 175 0.259111087680 Henry Cohn, 2026, needs more optimization.
15 176 0.259187685513 Henry Cohn, 2026, needs more optimization.
15 177 0.259700824040 Henry Cohn, 2026, needs more optimization.
15 178 0.259958289957 Henry Cohn, 2026, needs more optimization.
15 179 0.260069112452 Henry Cohn, 2026, needs more optimization.
15 180 0.260071738767 Henry Cohn, 2026, needs more optimization.
15 181 0.260078826482 Henry Cohn, 2026, needs more optimization.
15 182 0.260107832057 Henry Cohn, 2026, needs more optimization.
15 183 0.260128334592 Henry Cohn, 2026, needs more optimization.
15 184 0.260236772722 Henry Cohn, 2026, needs more optimization.
15 185 0.260320202562 Henry Cohn, 2026, needs more optimization.
15 186 0.260378067225 Henry Cohn, 2026, needs more optimization.
15 187 0.260799388304 Henry Cohn, 2026, needs more optimization.
15 188 0.261524822205 Henry Cohn, 2026, needs more optimization.
15 189 0.261958685146 Henry Cohn, 2026, needs more optimization.
15 190 0.262366848503 Henry Cohn, 2026, needs more optimization.
15 191 0.262528959872 Henry Cohn, 2026, needs more optimization.
15 192 0.262930705652 Henry Cohn, 2026, needs more optimization.
15 193 0.263167012146 Henry Cohn, 2026, needs more optimization.
15 194 0.263494519984 Henry Cohn, 2026, needs more optimization.
15 195 0.263757355657 Henry Cohn, 2026, needs more optimization.
15 196 0.263988368593 Henry Cohn, 2026, needs more optimization.
15 197 0.264167030892 Henry Cohn, 2026, needs more optimization.
15 198 0.264287815124 Henry Cohn, 2026, needs more optimization.
15 199 0.264393230582 Henry Cohn, 2026, needs more optimization.
15 200 0.264512055045 Henry Cohn, 2026, needs more optimization.
15 201 0.264679604070 Henry Cohn, 2026, needs more optimization.
15 202 0.264862838266 Henry Cohn, 2026, needs more optimization.
15 203 0.264984728968 Henry Cohn, 2026, needs more optimization.
15 204 0.265129163684 Henry Cohn, 2026, needs more optimization.
15 205 0.265251543999 Henry Cohn, 2026, needs more optimization.
15 206 0.265354276627 Henry Cohn, 2026, needs more optimization.
15 207 0.265450291555 Henry Cohn, 2026, needs more optimization.
15 208 0.265531313478 Henry Cohn, 2026, needs more optimization.
15 209 0.265670383097 Henry Cohn, 2026, needs more optimization.
15 210 0.265783974255 Henry Cohn, 2026, needs more optimization.
15 211 0.265951552753 Henry Cohn, 2026, needs more optimization.
15 212 0.265981663211 Henry Cohn, 2026, needs more optimization.
15 213 0.266095931907 Henry Cohn, 2026, needs more optimization.
15 214 0.266230466933 Henry Cohn, 2026, needs more optimization.
15 215 0.266322309599 Henry Cohn, 2026, needs more optimization.
15 217 0.266362814742 Henry Cohn, 2026, needs more optimization.
15 218 0.266362814744 Henry Cohn, 2026, needs more optimization.
15 219 0.266440928116 Henry Cohn, 2026, needs more optimization.
15 220 0.266583431142 Henry Cohn, 2026, needs more optimization.
15 221 0.273150769639 Henry Cohn, 2026, needs more optimization.
15 222 0.284150518497 Henry Cohn, 2026, needs more optimization.
15 223 0.284251933118 Henry Cohn, 2026, needs more optimization.
15 224 0.284364410383 Henry Cohn, 2026, needs more optimization.
15 225 0.285452823320 Henry Cohn, 2026, needs more optimization.
15 226 0.285515694808 Henry Cohn, 2026, needs more optimization.
15 227 0.285515695953 Henry Cohn, 2026, needs more optimization.
15 228 0.285515697640 Henry Cohn, 2026, needs more optimization.
15 229 0.285521859150 Henry Cohn, 2026, needs more optimization.
15 230 0.285521870190 Henry Cohn, 2026, needs more optimization.
15 231 0.285525146445 Henry Cohn, 2026, needs more optimization.
15 232 0.285531264973 Henry Cohn, 2026, needs more optimization.
15 233 0.285536309272 Henry Cohn, 2026, needs more optimization.
15 234 0.285542915076 Henry Cohn, 2026, needs more optimization.
15 235 0.285560677193 Henry Cohn, 2026, needs more optimization.
15 236 0.285572449536 Henry Cohn, 2026, needs more optimization.
15 237 0.285583482535 Henry Cohn, 2026, needs more optimization.
15 238 0.285593497710 Henry Cohn, 2026, needs more optimization.
15 239 0.285607662559 Henry Cohn, 2026, needs more optimization.
15 240 0.285631201317 Henry Cohn, 2026, needs more optimization.
15 241 0.285658940997 Henry Cohn, 2026, needs more optimization.
15 242 0.285672695620 Henry Cohn, 2026, needs more optimization.
15 243 0.286368647233 Henry Cohn, 2026, needs more optimization.
15 244 0.286935827711 Henry Cohn, 2026, needs more optimization.
15 245 0.287258072725 Henry Cohn, 2026, needs more optimization.
15 246 0.287706774243 Henry Cohn, 2026, needs more optimization.
15 247 0.288090813571 Henry Cohn, 2026, needs more optimization.
15 248 0.288361312607 Henry Cohn, 2026, needs more optimization.
15 249 0.291752699197 Henry Cohn, 2026, needs more optimization.
15 250 0.294425817098 Henry Cohn, 2026, needs more optimization.
15 251 0.297313697436 Henry Cohn, 2026, needs more optimization.
15 252 0.297805885600 Henry Cohn, 2026, needs more optimization.
15 253 0.297826741256 Henry Cohn, 2026, needs more optimization.
15 254 0.297925421026 Henry Cohn, 2026, needs more optimization.
15 256 0.297926304913 Henry Cohn, 2026, needs more optimization.
15 257 0.302591860530 Henry Cohn, 2026, needs more optimization.
15 258 0.304745123433 Henry Cohn, 2026, needs more optimization.
15 259 0.305963604814 Henry Cohn, 2026, needs more optimization.
15 260 0.307183763306 Henry Cohn, 2026, needs more optimization.
15 261 0.308190960755 Henry Cohn, 2026, needs more optimization.
15 262 0.309418185500 Henry Cohn, 2026, needs more optimization.
15 263 0.309494742428 Henry Cohn, 2026, needs more optimization.
15 264 0.309633719394 Henry Cohn, 2026, needs more optimization.
15 265 0.312022730177 Henry Cohn, 2026, needs more optimization.
15 266 0.313595120620 Henry Cohn, 2026, needs more optimization.
15 267 0.315079097326 Henry Cohn, 2026, needs more optimization.
15 268 0.316238130518 Henry Cohn, 2026, needs more optimization.
15 269 0.316301144608 Henry Cohn, 2026, needs more optimization.
15 270 0.316564747477 Henry Cohn, 2026, needs more optimization.
15 271 0.319241988593 Henry Cohn, 2026, needs more optimization.
15 272 0.321156395971 Henry Cohn, 2026, needs more optimization.
15 273 0.323517749444 Henry Cohn, 2026, needs more optimization.
15 274 0.324908252826 Henry Cohn, 2026, needs more optimization.
15 275 0.326691929895 Henry Cohn, 2026, needs more optimization.
15 276 0.328606373280 Henry Cohn, 2026, needs more optimization.
15 277 0.330223807357 Henry Cohn, 2026, needs more optimization.
15 278 0.331404363040 Henry Cohn, 2026, needs more optimization.
15 279 0.332709973693 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 0.339361252811 Henry Cohn, 2026, needs more optimization.
15 322 0.340377077518 Henry Cohn, 2026, needs more optimization.
15 323 0.341307855976 Henry Cohn, 2026, needs more optimization.
15 324 0.341889515360 Henry Cohn, 2026, needs more optimization.
15 325 0.342383366049 Henry Cohn, 2026, needs more optimization.
15 326 0.342763673552 Henry Cohn, 2026, needs more optimization.
15 327 0.343118318470 Henry Cohn, 2026, needs more optimization.
15 328 0.343554794130 Henry Cohn, 2026, needs more optimization.
15 329 0.343822941458 Henry Cohn, 2026, needs more optimization.
15 330 0.344499360991 Henry Cohn, 2026, needs more optimization.
15 331 0.345419436857 Henry Cohn, 2026, needs more optimization.
15 332 0.345751013657 Henry Cohn, 2026, needs more optimization.
15 333 0.346533424336 Henry Cohn, 2026, needs more optimization.
15 334 0.347033773774 Henry Cohn, 2026, needs more optimization.
15 335 0.347224820952 Henry Cohn, 2026, needs more optimization.
15 336 0.347486773553 Henry Cohn, 2026, needs more optimization.
15 337 0.347854897217 Henry Cohn, 2026, needs more optimization.
15 338 0.348007618236 Henry Cohn, 2026, needs more optimization.
15 339 0.348174975849 Henry Cohn, 2026, needs more optimization.
15 340 0.348380995916 Henry Cohn, 2026, needs more optimization.
15 341 0.348558749721 Henry Cohn, 2026, needs more optimization.
15 342 0.348841531391 Henry Cohn, 2026, needs more optimization.
15 343 0.349075526161 Henry Cohn, 2026, needs more optimization.
15 344 0.349245199751 Henry Cohn, 2026, needs more optimization.
15 345 0.349405267847 Henry Cohn, 2026, needs more optimization.
15 346 0.349620761829 Henry Cohn, 2026, needs more optimization.
15 347 0.350157600631 Henry Cohn, 2026, needs more optimization.
15 348 0.350514256101 Henry Cohn, 2026, needs more optimization.
15 349 0.350851324563 Henry Cohn, 2026, needs more optimization.
15 350 0.351117165243 Henry Cohn, 2026, needs more optimization.
15 351 0.351310136345 Henry Cohn, 2026, needs more optimization.
15 352 0.351656762322 Henry Cohn, 2026, needs more optimization.
15 353 0.352033944887 Henry Cohn, 2026, needs more optimization.
15 354 0.352280863875 Henry Cohn, 2026, needs more optimization.
15 355 0.352554223945 Henry Cohn, 2026, needs more optimization.
15 356 0.352751866224 Henry Cohn, 2026, needs more optimization.
15 357 0.352954018039 Henry Cohn, 2026, needs more optimization.
15 358 0.353284892619 Henry Cohn, 2026, needs more optimization.
15 359 0.353531040378 Henry Cohn, 2026, needs more optimization.
15 360 0.353755739276 Henry Cohn, 2026, needs more optimization.
15 361 0.355596990359 Henry Cohn, 2026, needs more optimization.
15 362 0.355605621768 Henry Cohn, 2026, needs more optimization.
15 363 0.355615037418 Henry Cohn, 2026, needs more optimization.
15 364 0.355616358544 Henry Cohn, 2026, needs more optimization.
15 365 0.355623189261 Henry Cohn, 2026, needs more optimization.
15 366 0.355665489612 Henry Cohn, 2026, needs more optimization.
15 367 0.355676936199 Henry Cohn, 2026, needs more optimization.
15 368 0.355701839361 Henry Cohn, 2026, needs more optimization.
15 369 0.355722545765 Henry Cohn, 2026, needs more optimization.
15 370 0.355770109950 Henry Cohn, 2026, needs more optimization.
15 372 0.355812587682 Henry Cohn, 2026, needs more optimization.
15 373 0.356650480991 Henry Cohn, 2026, needs more optimization.
15 374 0.356893532908 Henry Cohn, 2026, needs more optimization.
15 375 0.356940341465 Henry Cohn, 2026, needs more optimization.
15 376 0.359361544429 Henry Cohn, 2026, needs more optimization.
15 377 0.359383451259 Henry Cohn, 2026, needs more optimization.
15 378 0.359434257125 Henry Cohn, 2026, needs more optimization.
15 379 0.359824912710 Henry Cohn, 2026, needs more optimization.
15 380 0.360555304356 Henry Cohn, 2026, needs more optimization.
15 381 0.360791960602 Henry Cohn, 2026, needs more optimization.
15 382 0.360793410233 Henry Cohn, 2026, needs more optimization.
15 383 0.361531155438 Henry Cohn, 2026, needs more optimization.
15 384 0.362842898211 Henry Cohn, 2026, needs more optimization.
15 385 0.363094403308 Henry Cohn, 2026, needs more optimization.
15 386 0.363947452961 Henry Cohn, 2026, needs more optimization.
15 387 0.365232338758 Henry Cohn, 2026, needs more optimization.
15 388 0.365682282651 Henry Cohn, 2026, needs more optimization.
15 424 0.370431040067 Henry Cohn, 2026.
287⁢x2−190⁢x+31
15 425 0.371522446824 Henry Cohn, 2026, needs more optimization.
15 426 0.373114250712 Henry Cohn, 2026, needs more optimization.
15 427 0.373374303487 Henry Cohn, 2026, needs more optimization.
15 429 0.374924690520 Henry Cohn, 2026, needs more optimization.
15 431 0.374925244319 Henry Cohn, 2026, needs more optimization.
15 432 0.374926734567 Henry Cohn, 2026, needs more optimization.
15 434 0.374967718835 Henry Cohn, 2026, needs more optimization.
15 438 0.376562097730 Henry Cohn, 2026, needs more optimization.
15 439 0.376570136263 Henry Cohn, 2026, needs more optimization.
15 443 0.376578358997 Henry Cohn, 2026, needs more optimization.
15 446 0.376580722575 Henry Cohn, 2026, needs more optimization.
15 447 0.376585950337 Henry Cohn, 2026, needs more optimization.
15 448 0.377002140694 Henry Cohn, 2026, needs more optimization.
15 452 0.377115462685 Henry Cohn, 2026, needs more optimization.
15 453 0.386255074906 Henry Cohn, 2026, needs more optimization.
15 454 0.386326547340 Henry Cohn, 2026, needs more optimization.
15 455 0.386356878729 Henry Cohn, 2026, needs more optimization.
15 456 0.386357383970 Henry Cohn, 2026, needs more optimization.
15 457 0.386366106586 Henry Cohn, 2026, needs more optimization.
15 458 0.386374515746 Henry Cohn, 2026, needs more optimization.
15 462 0.386374631885 Henry Cohn, 2026, needs more optimization.
15 463 0.386380274108 Henry Cohn, 2026, needs more optimization.
15 480 0.387504105641 Henry Cohn, 2026, needs more optimization.
15 481 0.390769831115 Henry Cohn, 2026, needs more optimization.
15 487 0.392879517762 Henry Cohn, 2026, needs more optimization.
15 488 0.392910249680 Henry Cohn, 2026, needs more optimization.
15 489 0.392928042142 Henry Cohn, 2026, needs more optimization.
15 490 0.393062310581 Henry Cohn, 2026, needs more optimization.
15 491 0.393071791173 Henry Cohn, 2026, needs more optimization.
15 492 0.393144968748 Henry Cohn, 2026, needs more optimization.
15 493 0.393213216010 Henry Cohn, 2026, needs more optimization.
15 495 0.393248805538 Henry Cohn, 2026, needs more optimization.
15 496 0.393326058549 Henry Cohn, 2026, needs more optimization.
15 497 0.393424150047 Henry Cohn, 2026, needs more optimization.
15 498 0.393431886361 Henry Cohn, 2026, needs more optimization.
15 499 0.393456866253 Henry Cohn, 2026, needs more optimization.
15 500 0.393467874373 Henry Cohn, 2026, needs more optimization.
15 501 0.393487909579 Henry Cohn, 2026, needs more optimization.
15 503 0.393539465984 Henry Cohn, 2026, needs more optimization.
15 504 0.393558873418 Henry Cohn, 2026, needs more optimization.
15 505 0.393589747046 Henry Cohn, 2026, needs more optimization.
15 506 0.393718484167 Henry Cohn, 2026, needs more optimization.
15 507 0.393803138352 Henry Cohn, 2026, needs more optimization.
15 508 0.393883397204 Henry Cohn, 2026, needs more optimization.
15 509 0.394254633116 Henry Cohn, 2026, needs more optimization.
15 510 0.394640380440 Henry Cohn, 2026, needs more optimization.
15 511 0.394970204048 Henry Cohn, 2026, needs more optimization.
15 512 0.394988017510 Henry Cohn, 2026, needs more optimization.
15 513 0.395198819637 Henry Cohn, 2026, needs more optimization.
15 514 0.395542556791 Henry Cohn, 2026, needs more optimization.
15 516 0.395658087743 Henry Cohn, 2026, needs more optimization.
15 517 0.396052728473 Henry Cohn, 2026, needs more optimization.
15 519 0.396486052283 Henry Cohn, 2026, needs more optimization.
15 520 0.396604079656 Henry Cohn, 2026, needs more optimization.
15 521 0.396880691283 Henry Cohn, 2026, needs more optimization.
15 522 0.397112448874 Henry Cohn, 2026, needs more optimization.
15 523 0.397420704066 Henry Cohn, 2026, needs more optimization.
15 524 0.397604123942 Henry Cohn, 2026, needs more optimization.
15 525 0.397698759035 Henry Cohn, 2026, needs more optimization.
15 527 0.397834952012 Henry Cohn, 2026, needs more optimization.
15 528 0.398017630664 Henry Cohn, 2026, needs more optimization.
15 529 0.398198985092 Henry Cohn, 2026, needs more optimization.
15 530 0.398307812016 Henry Cohn, 2026, needs more optimization.
15 532 0.398316974606 Henry Cohn, 2026, needs more optimization.
15 533 0.398479021818 Henry Cohn, 2026, needs more optimization.
15 534 0.398715923933 Henry Cohn, 2026, needs more optimization.
15 535 0.398854205752 Henry Cohn, 2026, needs more optimization.
15 536 0.398946223317 Henry Cohn, 2026, needs more optimization.
15 539 0.399215273864 Henry Cohn, 2026, needs more optimization.
15 540 0.399255048795 Henry Cohn, 2026, needs more optimization.
15 541 0.399505120587 Henry Cohn, 2026, needs more optimization.
15 542 0.399628529381 Henry Cohn, 2026, needs more optimization.
15 543 0.399837245024 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.
15 695 0.416525575215 Henry Cohn, 2026, needs more optimization.
15 696 0.416612628147 Henry Cohn, 2026, needs more optimization.
15 697 0.417712834616 Henry Cohn, 2026, needs more optimization.
15 699 0.417972167094 Henry Cohn, 2026, needs more optimization.
15 700 0.418185067631 Henry Cohn, 2026, needs more optimization.
15 701 0.418558108426 Henry Cohn, 2026, needs more optimization.
15 702 0.418977389206 Henry Cohn, 2026, needs more optimization.
15 703 0.419382685371 Henry Cohn, 2026, needs more optimization.
15 705 0.419426555604 Henry Cohn, 2026, needs more optimization.
15 706 0.420299806075 Henry Cohn, 2026, needs more optimization.
15 707 0.421218597004 Henry Cohn, 2026, needs more optimization.
15 708 0.421320931869 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 0.112902768077 Henry Cohn, 2026, needs more optimization.
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 0.115470290140 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 0.142353045267 Henry Cohn, 2026, needs more optimization.
16 76 0.155973841389 Henry Cohn, 2026, needs more optimization.
16 77 0.156184626209 Henry Cohn, 2026, needs more optimization.
16 78 0.156332941369 Henry Cohn, 2026, needs more optimization.
16 79 0.156685164565 Henry Cohn, 2026, needs more optimization.
16 80 0.156933594050 Henry Cohn, 2026, needs more optimization.
16 81 0.157231031352 Henry Cohn, 2026, needs more optimization.
16 82 0.158312309845 Henry Cohn, 2026, needs more optimization.
16 83 0.158831583919 Henry Cohn, 2026, needs more optimization.
16 84 0.159473252852 Henry Cohn, 2026, needs more optimization.
16 85 0.161143874706 Henry Cohn, 2026, needs more optimization.
16 88 0.168668499420 Henry Cohn, 2025, needs more optimization.
16 89 0.168683597982 Henry Cohn, 2026, needs more optimization.
16 90 0.168684111462 Henry Cohn, 2026, needs more optimization.
16 92 0.168684604646 Henry Cohn, 2025, needs more optimization.
16 94 0.168684943107 Henry Cohn, 2025, needs more optimization.
16 95 0.168685647441 Henry Cohn, 2026, needs more optimization.
16 96 0.168685666299 Henry Cohn, 2026, needs more optimization.
16 97 0.169880683941 Henry Cohn, 2026, needs more optimization.
16 102 0.170753175474 Henry Cohn, 2026.
128⁢x2−16⁢x−1
16 103 0.174178397911 Henry Cohn, 2026, needs more optimization.
16 104 0.179209765388 Henry Cohn, 2026, needs more optimization.
16 105 0.183420406779 Henry Cohn, 2026, needs more optimization.
16 106 0.185874805614 Henry Cohn, 2026, needs more optimization.
16 107 0.188007787992 Henry Cohn, 2026, needs more optimization.
16 108 0.191292637372 Henry Cohn, 2026, needs more optimization.
16 109 0.191602552374 Henry Cohn, 2026, needs more optimization.
16 110 0.192362602345 Henry Cohn, 2026, needs more optimization.
16 111 0.192383845859 Henry Cohn, 2026, needs more optimization.
16 117 0.192450089730 Henry Cohn, 2026.
27⁢x2−1
16 118 0.192450185263 Henry Cohn, 2026, needs more optimization.
16 119 0.198884094973 Henry Cohn, 2026, needs more optimization.
16 120 0.199966090992 Henry Cohn, 2026, needs more optimization.
16 122 0.199966090996 Henry Cohn, 2026, needs more optimization.
16 123 0.199988971320 Henry Cohn, 2026, needs more optimization.
16 124 0.199989165732 Henry Cohn, 2026, needs more optimization.
16 125 0.199994688491 Henry Cohn, 2026, needs more optimization.
16 126 0.199994689891 Henry Cohn, 2026, needs more optimization.
16 127 0.199995845425 Henry Cohn, 2025, needs more optimization.
16 130 0.199999918321 Henry Cohn, 2025, needs more optimization.
16 159 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 0.204975404608 Henry Cohn, 2026, needs more optimization.
16 161 0.221703250952 Henry Cohn, 2026, needs more optimization.
16 162 0.229553508920 Henry Cohn, 2026, needs more optimization.
16 163 0.233423687584 Henry Cohn, 2026, needs more optimization.
16 164 0.236099339164 Henry Cohn, 2026, needs more optimization.
16 165 0.237943434745 Henry Cohn, 2026, needs more optimization.
16 166 0.239559472920 Henry Cohn, 2026, needs more optimization.
16 167 0.240782278588 Henry Cohn, 2026, needs more optimization.
16 168 0.242156927485 Henry Cohn, 2026, needs more optimization.
16 169 0.242983890500 Henry Cohn, 2026, needs more optimization.
16 170 0.243675075094 Henry Cohn, 2026, needs more optimization.
16 171 0.243676073622 Henry Cohn, 2026, needs more optimization.
16 172 0.243779912382 Henry Cohn, 2026, needs more optimization.
16 173 0.244215492206 Henry Cohn, 2026, needs more optimization.
16 174 0.245066648987 Henry Cohn, 2026, needs more optimization.
16 175 0.245779136582 Henry Cohn, 2026, needs more optimization.
16 176 0.246311238329 Henry Cohn, 2026, needs more optimization.
16 177 0.246660272787 Henry Cohn, 2026, needs more optimization.
16 178 0.247133710003 Henry Cohn, 2026, needs more optimization.
16 179 0.247496633298 Henry Cohn, 2026, needs more optimization.
16 180 0.248255814771 Henry Cohn, 2026, needs more optimization.
16 181 0.248714274356 Henry Cohn, 2026, needs more optimization.
16 182 0.248846518954 Henry Cohn, 2026, needs more optimization.
16 183 0.249103990267 Henry Cohn, 2026, needs more optimization.
16 184 0.249247558594 Henry Cohn, 2026, needs more optimization.
16 185 0.249467081842 Henry Cohn, 2026, needs more optimization.
16 186 0.249492134643 Henry Cohn, 2026, needs more optimization.
16 187 0.249494785371 Henry Cohn, 2026, needs more optimization.
16 188 0.249530407021 Henry Cohn, 2026, needs more optimization.
16 189 0.249715909278 Henry Cohn, 2026, needs more optimization.
16 190 0.249821927569 Henry Cohn, 2026, needs more optimization.
16 191 0.249834580814 Henry Cohn, 2026, needs more optimization.
16 192 0.249860495629 Henry Cohn, 2026, needs more optimization.
16 193 0.249876367181 Henry Cohn, 2026, needs more optimization.
16 194 0.249897565149 Henry Cohn, 2026, needs more optimization.
16 195 0.249902387437 Henry Cohn, 2026, needs more optimization.
16 196 0.249928286475 Henry Cohn, 2026, needs more optimization.
16 197 0.249964843633 Henry Cohn, 2026, needs more optimization.
16 198 0.249972139166 Henry Cohn, 2026, needs more optimization.
16 199 0.249979888452 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 0.286369435353 Henry Cohn, 2026, needs more optimization.
16 290 0.292106714791 Henry Cohn, 2026, needs more optimization.
16 291 0.296363207760 Henry Cohn, 2026, needs more optimization.
16 292 0.297880615452 Henry Cohn, 2026, needs more optimization.
16 293 0.299933227461 Henry Cohn, 2026, needs more optimization.
16 294 0.302149227902 Henry Cohn, 2026, needs more optimization.
16 295 0.304873159269 Henry Cohn, 2026, needs more optimization.
16 296 0.306639141515 Henry Cohn, 2026, needs more optimization.
16 297 0.308192766194 Henry Cohn, 2026, needs more optimization.
16 298 0.309533555208 Henry Cohn, 2026, needs more optimization.
16 299 0.311039464542 Henry Cohn, 2026, needs more optimization.
16 300 0.312031499748 Henry Cohn, 2026, needs more optimization.
16 301 0.313924849394 Henry Cohn, 2026, needs more optimization.
16 302 0.315076176508 Henry Cohn, 2026, needs more optimization.
16 303 0.316349821304 Henry Cohn, 2026, needs more optimization.
16 304 0.317542825641 Henry Cohn, 2026, needs more optimization.
16 305 0.318706616682 Henry Cohn, 2026, needs more optimization.
16 306 0.319662426306 Henry Cohn, 2026, needs more optimization.
16 307 0.320744482736 Henry Cohn, 2026, needs more optimization.
16 308 0.321752291424 Henry Cohn, 2026, needs more optimization.
16 309 0.323026107023 Henry Cohn, 2026, needs more optimization.
16 310 0.323637146297 Henry Cohn, 2026, needs more optimization.
16 311 0.324570494391 Henry Cohn, 2026, needs more optimization.
16 312 0.325098027509 Henry Cohn, 2026, needs more optimization.
16 313 0.325967772352 Henry Cohn, 2026, needs more optimization.
16 314 0.326790216037 Henry Cohn, 2026, needs more optimization.
16 315 0.327161333863 Henry Cohn, 2026, needs more optimization.
16 316 0.327214016090 Henry Cohn, 2026, needs more optimization.
16 317 0.327467859458 Henry Cohn, 2026, needs more optimization.
16 318 0.327488664119 Henry Cohn, 2026, needs more optimization.
16 319 0.327520460663 Henry Cohn, 2026, needs more optimization.
16 320 0.327558454411 Henry Cohn, 2026, needs more optimization.
16 321 0.327678441723 Henry Cohn, 2026, needs more optimization.
16 322 0.327756450257 Henry Cohn, 2026, needs more optimization.
16 323 0.328032728903 Henry Cohn, 2026, needs more optimization.
16 324 0.328131098756 Henry Cohn, 2026, needs more optimization.
16 325 0.328366421429 Henry Cohn, 2026, needs more optimization.
16 326 0.328410550008 Henry Cohn, 2026, needs more optimization.
16 327 0.328652093236 Henry Cohn, 2026, needs more optimization.
16 328 0.328691876025 Henry Cohn, 2026, needs more optimization.
16 329 0.328816042263 Henry Cohn, 2026, needs more optimization.
16 330 0.328866372367 Henry Cohn, 2026, needs more optimization.
16 340 0.328947368422 Henry Cohn, 2026.
76⁢x−25
16 341 0.330389642231 Henry Cohn, 2026, needs more optimization.
16 342 0.330478804974 Henry Cohn, 2026, needs more optimization.
16 343 0.330519828971 Henry Cohn, 2026, needs more optimization.
16 344 0.330698894644 Henry Cohn, 2026, needs more optimization.
16 345 0.330773446853 Henry Cohn, 2026, needs more optimization.
16 346 0.330856889773 Henry Cohn, 2026, needs more optimization.
16 347 0.330905109126 Henry Cohn, 2026, needs more optimization.
16 348 0.330947629242 Henry Cohn, 2026, needs more optimization.
16 349 0.331092108596 Henry Cohn, 2026, needs more optimization.
16 350 0.331150257193 Henry Cohn, 2026, needs more optimization.
16 351 0.331180561048 Henry Cohn, 2026, needs more optimization.
16 352 0.331402969927 Henry Cohn, 2026, needs more optimization.
16 353 0.331444571485 Henry Cohn, 2026, needs more optimization.
16 354 0.331582321233 Henry Cohn, 2026, needs more optimization.
16 355 0.331723614753 Henry Cohn, 2026, needs more optimization.
16 356 0.331849806866 Henry Cohn, 2026, needs more optimization.
16 357 0.332029330144 Henry Cohn, 2026, needs more optimization.
16 358 0.332154195376 Henry Cohn, 2026, needs more optimization.
16 359 0.332155537889 Henry Cohn, 2026, needs more optimization.
16 360 0.332336677651 Henry Cohn, 2026, needs more optimization.
16 362 0.332608712989 Henry Cohn, 2026, needs more optimization.
16 363 0.332769981983 Henry Cohn, 2026, needs more optimization.
16 364 0.332814265466 Henry Cohn, 2026, needs more optimization.
16 365 0.332971128369 Henry Cohn, 2026, needs more optimization.
16 366 0.333054436985 Henry Cohn, 2026, needs more optimization.
16 367 0.333065746954 Henry Cohn, 2026, needs more optimization.
16 368 0.333087248194 Henry Cohn, 2026, needs more optimization.
16 369 0.333210369757 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 0.350817260470 Henry Cohn, 2026, needs more optimization.
16 514 0.351251440933 Henry Cohn, 2026, needs more optimization.
16 515 0.352957058017 Henry Cohn, 2026, needs more optimization.
16 516 0.356589364614 Henry Cohn, 2026, needs more optimization.
16 517 0.357875132411 Henry Cohn, 2026, needs more optimization.
16 518 0.358537212386 Henry Cohn, 2026, needs more optimization.
16 519 0.358907812510 Henry Cohn, 2026, needs more optimization.
16 520 0.359971324298 Henry Cohn, 2026, needs more optimization.
16 521 0.360699849584 Henry Cohn, 2026, needs more optimization.
16 522 0.360866934729 Henry Cohn, 2026, needs more optimization.
16 523 0.361265013397 Henry Cohn, 2026, needs more optimization.
16 524 0.362589735422 Henry Cohn, 2026, needs more optimization.
16 525 0.363017183747 Henry Cohn, 2026, needs more optimization.
16 526 0.363491770565 Henry Cohn, 2026, needs more optimization.
16 527 0.364021708931 Henry Cohn, 2026, needs more optimization.
16 528 0.364565717069 Henry Cohn, 2026, needs more optimization.
16 529 0.365221635583 Henry Cohn, 2026, needs more optimization.
16 530 0.365521476847 Henry Cohn, 2026, needs more optimization.
16 531 0.365852748580 Henry Cohn, 2026, needs more optimization.
16 532 0.366446727385 Henry Cohn, 2026, needs more optimization.
16 533 0.366988724442 Henry Cohn, 2026, needs more optimization.
16 534 0.367440478285 Henry Cohn, 2026, needs more optimization.
16 535 0.367833381571 Henry Cohn, 2026, needs more optimization.
16 536 0.368181686116 Henry Cohn, 2026, needs more optimization.
16 537 0.368749069587 Henry Cohn, 2026, needs more optimization.
16 538 0.369144186787 Henry Cohn, 2026, needs more optimization.
16 567 0.369248411466 Henry Cohn, 2026.
29⁢x2−8⁢x−1
16 568 0.379720648148 Henry Cohn, 2026, needs more optimization.
16 569 0.383122193529 Henry Cohn, 2026, needs more optimization.
16 570 0.384429149903 Henry Cohn, 2026, needs more optimization.
16 571 0.385323775002 Henry Cohn, 2026, needs more optimization.
16 572 0.386108295913 Henry Cohn, 2026, needs more optimization.
16 573 0.387055504561 Henry Cohn, 2026, needs more optimization.
16 574 0.387707517722 Henry Cohn, 2026, needs more optimization.
16 575 0.388309062135 Henry Cohn, 2026, needs more optimization.
16 576 0.389202905406 Henry Cohn, 2026, needs more optimization.
16 577 0.389675240659 Henry Cohn, 2026, needs more optimization.
16 578 0.389791398311 Henry Cohn, 2026, needs more optimization.
16 579 0.390386956834 Henry Cohn, 2026, needs more optimization.
16 580 0.390984500672 Henry Cohn, 2026, needs more optimization.
16 581 0.391437116611 Henry Cohn, 2026, needs more optimization.
16 582 0.391769961381 Henry Cohn, 2026, needs more optimization.
16 583 0.392170375377 Henry Cohn, 2026, needs more optimization.
16 680 0.392857142858 Henry Cohn, 2026.
28⁢x−11
16 681 0.394879810380 Henry Cohn, 2026, needs more optimization.
16 682 0.395908841824 Henry Cohn, 2026, needs more optimization.
16 683 0.396409081553 Henry Cohn, 2026, needs more optimization.
16 684 0.396851567743 Henry Cohn, 2026, needs more optimization.
16 685 0.397222565826 Henry Cohn, 2026, needs more optimization.
16 686 0.397563982390 Henry Cohn, 2026, needs more optimization.
16 687 0.397747863121 Henry Cohn, 2026, needs more optimization.
16 688 0.397923966542 Henry Cohn, 2026, needs more optimization.
16 689 0.398220721469 Henry Cohn, 2026, needs more optimization.
16 690 0.398419642600 Henry Cohn, 2026, needs more optimization.
16 691 0.398594711610 Henry Cohn, 2026, needs more optimization.
16 692 0.398778731937 Henry Cohn, 2026, needs more optimization.
16 693 0.398945069374 Henry Cohn, 2026, needs more optimization.
16 694 0.399115856241 Henry Cohn, 2026, needs more optimization.
16 695 0.399383851977 Henry Cohn, 2026, needs more optimization.
16 696 0.399592402525 Henry Cohn, 2026, needs more optimization.
16 697 0.399709521658 Henry Cohn, 2026, needs more optimization.
16 698 0.399787172546 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.
16 801 0.413043478261 Henry Cohn, 2026.
46⁢x−19
16 832 0.416843914680 Henry Cohn, 2026.
71⁢x2−20⁢x−4
16 833 0.417553459284 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.
16 877 0.423728813560 Henry Cohn, 2026.
59⁢x−25
16 878 0.425519981495 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 0.099686435548 Henry Cohn, 2026.
153⁢x4+480⁢x3−150⁢x2+1
17 56 0.102993455487 Henry Cohn, 2026.
17 64 0.111111111112 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
17 65 0.120840303592 Henry Cohn, 2026, needs more optimization.
17 66 0.124823812492 Henry Cohn, 2026, needs more optimization.
17 67 0.127102475016 Henry Cohn, 2026, needs more optimization.
17 68 0.127214003590 Henry Cohn, 2026, needs more optimization.
17 69 0.127247521203 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 0.127303652497 Henry Cohn, 2026, needs more optimization.
17 78 0.135230868852 Henry Cohn, 2026, needs more optimization.
17 79 0.142557693199 Henry Cohn, 2026, needs more optimization.
17 80 0.147987559048 Henry Cohn, 2026, needs more optimization.
17 86 0.15 Henry Cohn, 2026.
20⁢x−3
17 87 0.151340636758 Henry Cohn, 2026, needs more optimization.
17 88 0.156652322692 Henry Cohn, 2026, needs more optimization.
17 89 0.158629733399 Henry Cohn, 2026, needs more optimization.
17 90 0.165410510828 Henry Cohn, 2026, needs more optimization.
17 91 0.167225196650 Henry Cohn, 2026, needs more optimization.
17 92 0.167349745040 Henry Cohn, 2026, needs more optimization.
17 93 0.167565564294 Henry Cohn, 2026, needs more optimization.
17 94 0.167892723246 Henry Cohn, 2026, needs more optimization.
17 95 0.168041891059 Henry Cohn, 2026, needs more optimization.
17 96 0.168354988168 Henry Cohn, 2026, needs more optimization.
17 97 0.168538299248 Henry Cohn, 2026, needs more optimization.
17 98 0.168603491172 Henry Cohn, 2026, needs more optimization.
17 99 0.168673100758 Henry Cohn, 2026, needs more optimization.
17 100 0.168675190337 Henry Cohn, 2026, needs more optimization.
17 101 0.168690039352 Henry Cohn, 2026, needs more optimization.
17 102 0.170743404074 Henry Cohn, 2026, needs more optimization.
17 104 0.170751369934 Henry Cohn, 2026, needs more optimization.
17 105 0.170751990216 Henry Cohn, 2026, needs more optimization.
17 106 0.170751990218 Henry Cohn, 2026, needs more optimization.
17 107 0.170761751944 Henry Cohn, 2026, needs more optimization.
17 108 0.175086042960 Henry Cohn, 2026, needs more optimization.
17 109 0.179937490226 Henry Cohn, 2026, needs more optimization.
17 110 0.180303341654 Henry Cohn, 2026, needs more optimization.
17 111 0.182496337254 Henry Cohn, 2026, needs more optimization.
17 115 0.184252183279 Henry Cohn, 2026, needs more optimization.
17 116 0.184847526060 Henry Cohn, 2026, needs more optimization.
17 117 0.186673771312 Henry Cohn, 2026, needs more optimization.
17 118 0.190910319598 Henry Cohn, 2026, needs more optimization.
17 119 0.191894554206 Henry Cohn, 2026, needs more optimization.
17 120 0.192193534430 Henry Cohn, 2026, needs more optimization.
17 121 0.192294195008 Henry Cohn, 2026, needs more optimization.
17 122 0.192377889101 Henry Cohn, 2026, needs more optimization.
17 123 0.192451522909 Henry Cohn, 2026, needs more optimization.
17 124 0.192974191327 Henry Cohn, 2026, needs more optimization.
17 125 0.195309576047 Henry Cohn, 2026, needs more optimization.
17 126 0.197435090100 Henry Cohn, 2026, needs more optimization.
17 127 0.197630497172 Henry Cohn, 2026, needs more optimization.
17 128 0.197714408997 Henry Cohn, 2026, needs more optimization.
17 129 0.198370062114 Henry Cohn, 2026, needs more optimization.
17 130 0.198652836813 Henry Cohn, 2026, needs more optimization.
17 131 0.199019953587 Henry Cohn, 2026, needs more optimization.
17 132 0.199042801579 Henry Cohn, 2026, needs more optimization.
17 133 0.199676840508 Henry Cohn, 2026, needs more optimization.
17 134 0.199819887906 Henry Cohn, 2026, needs more optimization.
17 135 0.199939723829 Henry Cohn, 2026, needs more optimization.
17 136 0.199980113924 Henry Cohn, 2026, needs more optimization.
17 137 0.200002125501 Henry Cohn, 2026, needs more optimization.
17 138 0.200129401103 Henry Cohn, 2026, needs more optimization.
17 139 0.200196373819 Henry Cohn, 2026, needs more optimization.
17 140 0.200347835143 Henry Cohn, 2026, needs more optimization.
17 141 0.202821778932 Henry Cohn, 2026, needs more optimization.
17 142 0.202853642986 Henry Cohn, 2026, needs more optimization.
17 143 0.202863811415 Henry Cohn, 2026, needs more optimization.
17 144 0.202885169604 Henry Cohn, 2026, needs more optimization.
17 148 0.202893418199 Henry Cohn, 2026, needs more optimization.
17 150 0.202896008575 Henry Cohn, 2026, needs more optimization.
17 151 0.202899805483 Henry Cohn, 2026, needs more optimization.
17 152 0.202913111858 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 0.202915764548 Henry Cohn, 2026, needs more optimization.
17 164 0.202921482872 Henry Cohn, 2026, needs more optimization.
17 165 0.203275495992 Henry Cohn, 2026, needs more optimization.
17 167 0.209702108524 Henry Cohn, 2026, needs more optimization.
17 168 0.209702108526 Henry Cohn, 2026, needs more optimization.
17 177 0.214580576913 Henry Cohn, 2026.
59⁢x2−8⁢x−1
17 178 0.215896344884 Henry Cohn, 2026, needs more optimization.
17 179 0.223840998025 Henry Cohn, 2026, needs more optimization.
17 180 0.224792206041 Henry Cohn, 2026, needs more optimization.
17 181 0.227669966811 Henry Cohn, 2026, needs more optimization.
17 188 0.228481712325 Henry Cohn, 2026, needs more optimization.
17 192 0.228757976713 Henry Cohn, 2026, needs more optimization.
17 193 0.233326399949 Henry Cohn, 2026, needs more optimization.
17 194 0.234633835742 Henry Cohn, 2026, needs more optimization.
17 195 0.236885684589 Henry Cohn, 2026, needs more optimization.
17 196 0.237321539329 Henry Cohn, 2026, needs more optimization.
17 197 0.238451337409 Henry Cohn, 2026, needs more optimization.
17 198 0.239226592963 Henry Cohn, 2026, needs more optimization.
17 199 0.240182161871 Henry Cohn, 2026, needs more optimization.
17 200 0.242010307825 Henry Cohn, 2026, needs more optimization.
17 201 0.242239275382 Henry Cohn, 2026, needs more optimization.
17 202 0.242888664641 Henry Cohn, 2026, needs more optimization.
17 203 0.243663561016 Henry Cohn, 2026, needs more optimization.
17 204 0.243840951693 Henry Cohn, 2026, needs more optimization.
17 205 0.244525508660 Henry Cohn, 2026, needs more optimization.
17 206 0.244543986332 Henry Cohn, 2026, needs more optimization.
17 207 0.244828742733 Henry Cohn, 2026, needs more optimization.
17 208 0.244963471087 Henry Cohn, 2026, needs more optimization.
17 209 0.245161899423 Henry Cohn, 2026, needs more optimization.
17 210 0.245838066197 Henry Cohn, 2026, needs more optimization.
17 211 0.246211369767 Henry Cohn, 2026, needs more optimization.
17 212 0.246496065299 Henry Cohn, 2026, needs more optimization.
17 213 0.246559865396 Henry Cohn, 2026, needs more optimization.
17 214 0.246948367915 Henry Cohn, 2026, needs more optimization.
17 215 0.247294665863 Henry Cohn, 2026, needs more optimization.
17 216 0.247412941739 Henry Cohn, 2026, needs more optimization.
17 217 0.247584589770 Henry Cohn, 2026, needs more optimization.
17 218 0.247865298023 Henry Cohn, 2026, needs more optimization.
17 219 0.248142826819 Henry Cohn, 2026, needs more optimization.
17 220 0.248256784302 Henry Cohn, 2026, needs more optimization.
17 221 0.248424529928 Henry Cohn, 2026, needs more optimization.
17 222 0.248532253300 Henry Cohn, 2026, needs more optimization.
17 223 0.248756057876 Henry Cohn, 2026, needs more optimization.
17 224 0.249060211765 Henry Cohn, 2026, needs more optimization.
17 225 0.249132652196 Henry Cohn, 2026, needs more optimization.
17 226 0.249296673345 Henry Cohn, 2026, needs more optimization.
17 227 0.249309570189 Henry Cohn, 2026, needs more optimization.
17 228 0.249324770936 Henry Cohn, 2026, needs more optimization.
17 229 0.249405427577 Henry Cohn, 2026, needs more optimization.
17 230 0.249479996450 Henry Cohn, 2026, needs more optimization.
17 231 0.249588299727 Henry Cohn, 2026, needs more optimization.
17 232 0.249606475967 Henry Cohn, 2026, needs more optimization.
17 233 0.249608509052 Henry Cohn, 2026, needs more optimization.
17 234 0.249654004766 Henry Cohn, 2026, needs more optimization.
17 235 0.249670528277 Henry Cohn, 2026, needs more optimization.
17 236 0.249673518578 Henry Cohn, 2026, needs more optimization.
17 237 0.249712933587 Henry Cohn, 2026, needs more optimization.
17 238 0.249742268899 Henry Cohn, 2026, needs more optimization.
17 239 0.249758969800 Henry Cohn, 2026, needs more optimization.
17 240 0.249772313572 Henry Cohn, 2026, needs more optimization.
17 241 0.249794739779 Henry Cohn, 2026, needs more optimization.
17 242 0.249812790373 Henry Cohn, 2026, needs more optimization.
17 243 0.249845449299 Henry Cohn, 2026, needs more optimization.
17 244 0.249853547579 Henry Cohn, 2026, needs more optimization.
17 245 0.249865440342 Henry Cohn, 2026, needs more optimization.
17 246 0.249886685906 Henry Cohn, 2026, needs more optimization.
17 247 0.249931585468 Henry Cohn, 2026, needs more optimization.
17 248 0.249932245511 Henry Cohn, 2026, needs more optimization.
17 249 0.249942644303 Henry Cohn, 2026, needs more optimization.
17 250 0.249946000212 Henry Cohn, 2026, needs more optimization.
17 251 0.249982768947 Henry Cohn, 2026, needs more optimization.
17 292 0.25 Henry Cohn, 2026.
4⁢x−1
17 293 0.250000384400 Henry Cohn, 2026, needs more optimization.
17 294 0.250000384866 Henry Cohn, 2026, needs more optimization.
17 295 0.250783847816 Henry Cohn, 2026, needs more optimization.
17 296 0.254276427158 Henry Cohn, 2026, needs more optimization.
17 297 0.256309483779 Henry Cohn, 2026, needs more optimization.
17 298 0.260011150424 Henry Cohn, 2026, needs more optimization.
17 299 0.261094026781 Henry Cohn, 2026, needs more optimization.
17 300 0.261094033474 Henry Cohn, 2026, needs more optimization.
17 301 0.261094046641 Henry Cohn, 2026, needs more optimization.
17 302 0.261094057601 Henry Cohn, 2026, needs more optimization.
17 303 0.261094066193 Henry Cohn, 2026, needs more optimization.
17 304 0.261094071374 Henry Cohn, 2026, needs more optimization.
17 305 0.261094076490 Henry Cohn, 2026, needs more optimization.
17 306 0.261094087906 Henry Cohn, 2026, needs more optimization.
17 307 0.261094093900 Henry Cohn, 2026, needs more optimization.
17 308 0.261094108312 Henry Cohn, 2026, needs more optimization.
17 309 0.261094118638 Henry Cohn, 2026, needs more optimization.
17 310 0.261094122089 Henry Cohn, 2026, needs more optimization.
17 311 0.261094125370 Henry Cohn, 2026, needs more optimization.
17 312 0.261094131104 Henry Cohn, 2026, needs more optimization.
17 313 0.261094132495 Henry Cohn, 2026, needs more optimization.
17 314 0.261094133860 Henry Cohn, 2026, needs more optimization.
17 315 0.261094136220 Henry Cohn, 2026, needs more optimization.
17 316 0.261094138755 Henry Cohn, 2026, needs more optimization.
17 317 0.261094141397 Henry Cohn, 2026, needs more optimization.
17 318 0.261094143319 Henry Cohn, 2026, needs more optimization.
17 319 0.261094145756 Henry Cohn, 2026, needs more optimization.
17 320 0.261094152773 Henry Cohn, 2026, needs more optimization.
17 321 0.281931510286 Henry Cohn, 2026, needs more optimization.
17 322 0.286746030797 Henry Cohn, 2026, needs more optimization.
17 323 0.289661402550 Henry Cohn, 2026, needs more optimization.
17 324 0.291747215212 Henry Cohn, 2026, needs more optimization.
17 325 0.293695253153 Henry Cohn, 2026, needs more optimization.
17 326 0.295129673220 Henry Cohn, 2026, needs more optimization.
17 327 0.296751493531 Henry Cohn, 2026, needs more optimization.
17 328 0.298824800817 Henry Cohn, 2026, needs more optimization.
17 329 0.300103587566 Henry Cohn, 2026, needs more optimization.
17 330 0.301277934112 Henry Cohn, 2026, needs more optimization.
17 331 0.302281162187 Henry Cohn, 2026, needs more optimization.
17 332 0.303391110338 Henry Cohn, 2026, needs more optimization.
17 333 0.303399430447 Henry Cohn, 2026, needs more optimization.
17 334 0.303404942486 Henry Cohn, 2026, needs more optimization.
17 335 0.303414545645 Henry Cohn, 2026, needs more optimization.
17 336 0.303436075867 Henry Cohn, 2026, needs more optimization.
17 337 0.303500728157 Henry Cohn, 2026, needs more optimization.
17 338 0.303577870167 Henry Cohn, 2026, needs more optimization.
17 339 0.303687778245 Henry Cohn, 2026, needs more optimization.
17 340 0.303845243455 Henry Cohn, 2026, needs more optimization.
17 341 0.303871724650 Henry Cohn, 2026, needs more optimization.
17 342 0.303874891650 Henry Cohn, 2026, needs more optimization.
17 343 0.305595597326 Henry Cohn, 2026, needs more optimization.
17 344 0.305595682956 Henry Cohn, 2026, needs more optimization.
17 345 0.306303069493 Henry Cohn, 2026, needs more optimization.
17 346 0.306303071450 Henry Cohn, 2026, needs more optimization.
17 347 0.306303073532 Henry Cohn, 2026, needs more optimization.
17 348 0.312616558512 Henry Cohn, 2026, needs more optimization.
17 349 0.314460433591 Henry Cohn, 2026, needs more optimization.
17 350 0.315723954841 Henry Cohn, 2026, needs more optimization.
17 351 0.316809040207 Henry Cohn, 2026, needs more optimization.
17 352 0.317472070099 Henry Cohn, 2026, needs more optimization.
17 353 0.318235681722 Henry Cohn, 2026, needs more optimization.
17 354 0.318993851938 Henry Cohn, 2026, needs more optimization.
17 355 0.319843034038 Henry Cohn, 2026, needs more optimization.
17 356 0.320388529238 Henry Cohn, 2026, needs more optimization.
17 357 0.321094565221 Henry Cohn, 2026, needs more optimization.
17 358 0.321674300231 Henry Cohn, 2026, needs more optimization.
17 359 0.321855570273 Henry Cohn, 2026, needs more optimization.
17 360 0.322379391811 Henry Cohn, 2026, needs more optimization.
17 361 0.326291117287 Henry Cohn, 2026, needs more optimization.
17 362 0.326416705972 Henry Cohn, 2026, needs more optimization.
17 363 0.327455626032 Henry Cohn, 2026, needs more optimization.
17 364 0.327561429557 Henry Cohn, 2026, needs more optimization.
17 365 0.327651951649 Henry Cohn, 2026, needs more optimization.
17 366 0.328509124763 Henry Cohn, 2026, needs more optimization.
17 367 0.329646236148 Henry Cohn, 2026, needs more optimization.
17 368 0.329922886827 Henry Cohn, 2026, needs more optimization.
17 369 0.330056604416 Henry Cohn, 2026, needs more optimization.
17 370 0.330761995777 Henry Cohn, 2026, needs more optimization.
17 371 0.331451114939 Henry Cohn, 2026, needs more optimization.
17 372 0.331528706361 Henry Cohn, 2026, needs more optimization.
17 373 0.332081573987 Henry Cohn, 2026, needs more optimization.
17 374 0.332714702592 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 0.353161218325 Henry Cohn, 2026, needs more optimization.
17 580 0.354578632854 Henry Cohn, 2026, needs more optimization.
17 581 0.358166019102 Henry Cohn, 2026, needs more optimization.
17 612 0.36 Henry Cohn, 2026.
25⁢x−9
17 617 0.363933680735 Henry Cohn, 2026, needs more optimization.
17 619 0.365090632953 Henry Cohn, 2026, needs more optimization.
17 622 0.365256334416 Henry Cohn, 2026, needs more optimization.
17 625 0.365318375863 Henry Cohn, 2026, needs more optimization.
17 626 0.366185314348 Henry Cohn, 2026, needs more optimization.
17 635 0.366284736193 Henry Cohn, 2026, needs more optimization.
17 643 0.367212730234 Henry Cohn, 2026, needs more optimization.
17 656 0.368035578672 Henry Cohn, 2026, needs more optimization.
17 663 0.368405440238 Henry Cohn, 2026, needs more optimization.
17 666 0.369224298381 Henry Cohn, 2026, needs more optimization.
17 668 0.369452621391 Henry Cohn, 2026, needs more optimization.
17 675 0.369601544512 Henry Cohn, 2026, needs more optimization.
17 677 0.369766154639 Henry Cohn, 2026, needs more optimization.
17 681 0.369973301540 Henry Cohn, 2026, needs more optimization.
17 682 0.370308265726 Henry Cohn, 2026, needs more optimization.
17 684 0.371766341239 Henry Cohn, 2026, needs more optimization.
17 685 0.371888704046 Henry Cohn, 2026, needs more optimization.
17 687 0.371981268563 Henry Cohn, 2026, needs more optimization.
17 688 0.372121419344 Henry Cohn, 2026, needs more optimization.
17 690 0.372141900351 Henry Cohn, 2026, needs more optimization.
17 692 0.372396412658 Henry Cohn, 2026, needs more optimization.
17 693 0.372415831902 Henry Cohn, 2026, needs more optimization.
17 696 0.372703205109 Henry Cohn, 2026, needs more optimization.
17 697 0.372805049215 Henry Cohn, 2026, needs more optimization.
17 700 0.372809109682 Henry Cohn, 2026, needs more optimization.
17 707 0.372839669884 Henry Cohn, 2026, needs more optimization.
17 709 0.373047782624 Henry Cohn, 2026, needs more optimization.
17 730 0.373089261092 Henry Cohn, 2026, needs more optimization.
17 733 0.378787379291 Henry Cohn, 2026, needs more optimization.
17 742 0.378900372340 Henry Cohn, 2026, needs more optimization.
17 746 0.379124620421 Henry Cohn, 2026, needs more optimization.
17 749 0.379129030143 Henry Cohn, 2026, needs more optimization.
17 768 0.379158562754 Henry Cohn, 2026, needs more optimization.
17 772 0.399996346965 Henry Cohn, 2026, needs more optimization.
17 1024 0.4 Henry Cohn, 2026, subcode of a code of size 1088.
5⁢x−2
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.
1392⁢x5+5600⁢x4−2304⁢x3+152⁢x2+12⁢x−1
18 69 0.101456854890 Henry Cohn, 2024.
176⁢x2−8⁢x−1
18 71 0.107360417201 Henry Cohn, 2026, needs more optimization.
18 72 0.109540130283 Henry Cohn, 2026, needs more optimization.
18 73 0.117134464846 Henry Cohn, 2026, needs more optimization.
18 74 0.120049808519 Henry Cohn, 2026, needs more optimization.
18 75 0.120367585573 Henry Cohn, 2026, needs more optimization.
18 76 0.122043871163 Henry Cohn, 2026, needs more optimization.
18 77 0.123493542007 Henry Cohn, 2026, needs more optimization.
18 78 0.125804804449 Henry Cohn, 2026, needs more optimization.
18 80 0.126224060072 Henry Cohn, 2026, needs more optimization.
18 81 0.126904281672 Henry Cohn, 2026, needs more optimization.
18 82 0.127626483898 Henry Cohn, 2026, needs more optimization.
18 83 0.129098755667 Henry Cohn, 2026, needs more optimization.
18 84 0.130579477836 Henry Cohn, 2026, needs more optimization.
18 85 0.132294284165 Henry Cohn, 2026, needs more optimization.
18 86 0.132700069009 Henry Cohn, 2026, needs more optimization.
18 87 0.133673762701 Henry Cohn, 2026, needs more optimization.
18 88 0.134264346430 Henry Cohn, 2025.
18 96 0.142857142858 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
7⁢x−1
18 97 0.152402949200 Henry Cohn, 2026.
16⁢x2−9⁢x+1
18 98 0.155249851767 Henry Cohn, 2026, needs more optimization.
18 99 0.164304351005 Henry Cohn, 2026, needs more optimization.
18 100 0.167503290084 Henry Cohn, 2026, needs more optimization.
18 101 0.167552867954 Henry Cohn, 2026, needs more optimization.
18 102 0.168066784104 Henry Cohn, 2026, needs more optimization.
18 103 0.168582533530 Henry Cohn, 2026, needs more optimization.
18 104 0.168996259570 Henry Cohn, 2026, needs more optimization.
18 105 0.168996259813 Henry Cohn, 2026, needs more optimization.
18 106 0.169219168427 Henry Cohn, 2026, needs more optimization.
18 107 0.169525749575 Henry Cohn, 2026, needs more optimization.
18 108 0.170156208820 Henry Cohn, 2026, needs more optimization.
18 109 0.170282176067 Henry Cohn, 2026, needs more optimization.
18 110 0.170589457559 Henry Cohn, 2026, needs more optimization.
18 111 0.170820540120 Henry Cohn, 2026, needs more optimization.
18 112 0.171227356448 Henry Cohn, 2026, needs more optimization.
18 113 0.172922506077 Henry Cohn, 2026, needs more optimization.
18 114 0.174636687826 Henry Cohn, 2026, needs more optimization.
18 115 0.177175825755 Henry Cohn, 2026, needs more optimization.
18 116 0.179458481184 Henry Cohn, 2026, needs more optimization.
18 117 0.181388784102 Henry Cohn, 2026, needs more optimization.
18 118 0.183022564827 Henry Cohn, 2026, needs more optimization.
18 119 0.184590358550 Henry Cohn, 2026, needs more optimization.
18 120 0.185137714617 Henry Cohn, 2026, needs more optimization.
18 121 0.185920335388 Henry Cohn, 2026, needs more optimization.
18 122 0.187309345015 Henry Cohn, 2026, needs more optimization.
18 123 0.188916057998 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 0.193070622507 Henry Cohn, 2026, needs more optimization.
18 134 0.193721012389 Henry Cohn, 2026, needs more optimization.
18 135 0.194298494257 Henry Cohn, 2026, needs more optimization.
18 136 0.194623021634 Henry Cohn, 2026, needs more optimization.
18 137 0.194954691186 Henry Cohn, 2026, needs more optimization.
18 138 0.195230146004 Henry Cohn, 2026, needs more optimization.
18 140 0.195281232517 Henry Cohn, 2026, needs more optimization.
18 141 0.197737209317 Henry Cohn, 2026, needs more optimization.
18 142 0.197853212291 Henry Cohn, 2026, needs more optimization.
18 143 0.198247270720 Henry Cohn, 2026, needs more optimization.
18 144 0.198446190441 Henry Cohn, 2026, needs more optimization.
18 145 0.198855088724 Henry Cohn, 2026, needs more optimization.
18 146 0.199219910274 Henry Cohn, 2026, needs more optimization.
18 147 0.199442341783 Henry Cohn, 2026, needs more optimization.
18 148 0.199460045186 Henry Cohn, 2026, needs more optimization.
18 149 0.199605612736 Henry Cohn, 2026, needs more optimization.
18 150 0.199807298212 Henry Cohn, 2026, needs more optimization.
18 151 0.199927662948 Henry Cohn, 2026, needs more optimization.
18 152 0.200591985819 Henry Cohn, 2026, needs more optimization.
18 153 0.200935578859 Henry Cohn, 2026, needs more optimization.
18 154 0.201346587538 Henry Cohn, 2026, needs more optimization.
18 155 0.201419970644 Henry Cohn, 2026, needs more optimization.
18 156 0.201493540404 Henry Cohn, 2026, needs more optimization.
18 157 0.201571967358 Henry Cohn, 2026, needs more optimization.
18 158 0.201593612280 Henry Cohn, 2026, needs more optimization.
18 159 0.201636335357 Henry Cohn, 2026, needs more optimization.
18 160 0.201667601115 Henry Cohn, 2026, needs more optimization.
18 161 0.202268702085 Henry Cohn, 2026, needs more optimization.
18 162 0.202319500870 Henry Cohn, 2026, needs more optimization.
18 163 0.202373950268 Henry Cohn, 2026, needs more optimization.
18 164 0.202469533773 Henry Cohn, 2026, needs more optimization.
18 165 0.202704578972 Henry Cohn, 2026, needs more optimization.
18 166 0.202859131199 Henry Cohn, 2026, needs more optimization.
18 167 0.202898266154 Henry Cohn, 2026, needs more optimization.
18 168 0.202918095644 Henry Cohn, 2026, needs more optimization.
18 169 0.202919922349 Henry Cohn, 2026, needs more optimization.
18 170 0.202919957833 Henry Cohn, 2026, needs more optimization.
18 171 0.203077457846 Henry Cohn, 2026, needs more optimization.
18 172 0.204258588628 Henry Cohn, 2026, needs more optimization.
18 173 0.206297694056 Henry Cohn, 2026, needs more optimization.
18 174 0.208717699363 Henry Cohn, 2026, needs more optimization.
18 175 0.212085431549 Henry Cohn, 2026, needs more optimization.
18 179 0.214580042766 Henry Cohn, 2026, needs more optimization.
18 180 0.214580042773 Henry Cohn, 2026, needs more optimization.
18 181 0.214580603161 Henry Cohn, 2026, needs more optimization.
18 184 0.214580882717 Henry Cohn, 2026, needs more optimization.
18 186 0.214580882720 Henry Cohn, 2026, needs more optimization.
18 187 0.214591633054 Henry Cohn, 2026, needs more optimization.
18 188 0.216515243503 Henry Cohn, 2026, needs more optimization.
18 189 0.217825582082 Henry Cohn, 2026, needs more optimization.
18 190 0.219958119572 Henry Cohn, 2026, needs more optimization.
18 191 0.221444638880 Henry Cohn, 2026, needs more optimization.
18 192 0.223220568761 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 0.227401792244 Henry Cohn, 2026, needs more optimization.
18 207 0.228476523906 Henry Cohn, 2026, needs more optimization.
18 208 0.229747213729 Henry Cohn, 2026, needs more optimization.
18 209 0.230552058424 Henry Cohn, 2026, needs more optimization.
18 210 0.230996740571 Henry Cohn, 2026, needs more optimization.
18 211 0.231265700956 Henry Cohn, 2026, needs more optimization.
18 212 0.232483249319 Henry Cohn, 2026, needs more optimization.
18 213 0.233085731721 Henry Cohn, 2026, needs more optimization.
18 214 0.233135834868 Henry Cohn, 2026, needs more optimization.
18 215 0.233985641681 Henry Cohn, 2026, needs more optimization.
18 216 0.235099459279 Henry Cohn, 2026, needs more optimization.
18 217 0.235825925446 Henry Cohn, 2026, needs more optimization.
18 218 0.237012293055 Henry Cohn, 2026, needs more optimization.
18 219 0.237605244907 Henry Cohn, 2026, needs more optimization.
18 220 0.238606567369 Henry Cohn, 2026, needs more optimization.
18 221 0.239743960942 Henry Cohn, 2026, needs more optimization.
18 222 0.240340151274 Henry Cohn, 2026, needs more optimization.
18 223 0.241205850542 Henry Cohn, 2026, needs more optimization.
18 224 0.241541391423 Henry Cohn, 2026, needs more optimization.
18 225 0.241648232184 Henry Cohn, 2026, needs more optimization.
18 226 0.241769187772 Henry Cohn, 2026, needs more optimization.
18 227 0.241906077006 Henry Cohn, 2026, needs more optimization.
18 228 0.242082865591 Henry Cohn, 2026, needs more optimization.
18 229 0.242323949627 Henry Cohn, 2026, needs more optimization.
18 230 0.242430679703 Henry Cohn, 2026, needs more optimization.
18 231 0.242554693360 Henry Cohn, 2026, needs more optimization.
18 232 0.242827910344 Henry Cohn, 2026, needs more optimization.
18 233 0.243062700838 Henry Cohn, 2026, needs more optimization.
18 234 0.243545060425 Henry Cohn, 2026, needs more optimization.
18 235 0.243863029048 Henry Cohn, 2026, needs more optimization.
18 236 0.244001550077 Henry Cohn, 2026, needs more optimization.
18 237 0.244152451192 Henry Cohn, 2026, needs more optimization.
18 238 0.244367160063 Henry Cohn, 2026, needs more optimization.
18 239 0.244872834185 Henry Cohn, 2026, needs more optimization.
18 240 0.244872837358 Henry Cohn, 2026, needs more optimization.
18 241 0.244884142148 Henry Cohn, 2026, needs more optimization.
18 242 0.245091189149 Henry Cohn, 2026, needs more optimization.
18 243 0.245153340881 Henry Cohn, 2026, needs more optimization.
18 244 0.245214453500 Henry Cohn, 2026, needs more optimization.
18 245 0.245289336590 Henry Cohn, 2026, needs more optimization.
18 246 0.245531751014 Henry Cohn, 2026, needs more optimization.
18 247 0.245678858494 Henry Cohn, 2026, needs more optimization.
18 248 0.245678885094 Henry Cohn, 2026, needs more optimization.
18 249 0.245914436448 Henry Cohn, 2026, needs more optimization.
18 250 0.246014709249 Henry Cohn, 2026, needs more optimization.
18 251 0.246014762740 Henry Cohn, 2026, needs more optimization.
18 252 0.246373320233 Henry Cohn, 2026, needs more optimization.
18 253 0.246435059472 Henry Cohn, 2026, needs more optimization.
18 256 0.246437043968 Henry Cohn, 2026, needs more optimization.
18 257 0.246750422810 Henry Cohn, 2026, needs more optimization.
18 258 0.247022465501 Henry Cohn, 2026, needs more optimization.
18 259 0.247040522556 Henry Cohn, 2026, needs more optimization.
18 260 0.247075617101 Henry Cohn, 2026, needs more optimization.
18 261 0.247108747278 Henry Cohn, 2026, needs more optimization.
18 262 0.247149816981 Henry Cohn, 2026, needs more optimization.
18 263 0.247180295469 Henry Cohn, 2026, needs more optimization.
18 264 0.247202560923 Henry Cohn, 2026, needs more optimization.
18 265 0.247271444079 Henry Cohn, 2026, needs more optimization.
18 266 0.247341828635 Henry Cohn, 2026, needs more optimization.
18 267 0.247376892717 Henry Cohn, 2026, needs more optimization.
18 268 0.247467619733 Henry Cohn, 2026, needs more optimization.
18 269 0.247474142751 Henry Cohn, 2026, needs more optimization.
18 270 0.247485365982 Henry Cohn, 2026, needs more optimization.
18 271 0.247527104009 Henry Cohn, 2026, needs more optimization.
18 272 0.247574180436 Henry Cohn, 2026, needs more optimization.
18 273 0.247582006648 Henry Cohn, 2026, needs more optimization.
18 274 0.247594186788 Henry Cohn, 2026, needs more optimization.
18 275 0.247626131441 Henry Cohn, 2026, needs more optimization.
18 276 0.247646419111 Henry Cohn, 2026, needs more optimization.
18 277 0.247700628484 Henry Cohn, 2026, needs more optimization.
18 278 0.247719852041 Henry Cohn, 2026, needs more optimization.
18 279 0.247739691570 Henry Cohn, 2026, needs more optimization.
18 280 0.247741668987 Henry Cohn, 2026, needs more optimization.
18 281 0.247790623265 Henry Cohn, 2026, needs more optimization.
18 282 0.247800395597 Henry Cohn, 2026, needs more optimization.
18 283 0.247855354547 Henry Cohn, 2026, needs more optimization.
18 284 0.247855356407 Henry Cohn, 2026, needs more optimization.
18 285 0.247856117220 Henry Cohn, 2026, needs more optimization.
18 286 0.247856125798 Henry Cohn, 2026, needs more optimization.
18 287 0.248234619311 Henry Cohn, 2026, needs more optimization.
18 288 0.248891328269 Henry Cohn, 2026, needs more optimization.
18 289 0.248937503346 Henry Cohn, 2026, needs more optimization.
18 290 0.249328977970 Henry Cohn, 2026, needs more optimization.
18 291 0.249401342871 Henry Cohn, 2026, needs more optimization.
18 292 0.249419599055 Henry Cohn, 2026, needs more optimization.
18 293 0.249674490863 Henry Cohn, 2026, needs more optimization.
18 294 0.249879944363 Henry Cohn, 2026, needs more optimization.
18 295 0.249879951217 Henry Cohn, 2026, needs more optimization.
18 296 0.249940681930 Henry Cohn, 2026, needs more optimization.
18 297 0.250014031084 Henry Cohn, 2026, needs more optimization.
18 298 0.250014106506 Henry Cohn, 2026, needs more optimization.
18 299 0.250015417613 Henry Cohn, 2026, needs more optimization.
18 300 0.250031608267 Henry Cohn, 2026, needs more optimization.
18 301 0.250044780398 Henry Cohn, 2026, needs more optimization.
18 302 0.250044813776 Henry Cohn, 2026, needs more optimization.
18 303 0.250068737460 Henry Cohn, 2026, needs more optimization.
18 304 0.250068755897 Henry Cohn, 2026, needs more optimization.
18 305 0.250275250546 Henry Cohn, 2026, needs more optimization.
18 306 0.250733189019 Henry Cohn, 2026, needs more optimization.
18 307 0.251253838542 Henry Cohn, 2026, needs more optimization.
18 308 0.252138230702 Henry Cohn, 2026, needs more optimization.
18 309 0.252689708239 Henry Cohn, 2026, needs more optimization.
18 310 0.253911866845 Henry Cohn, 2026, needs more optimization.
18 311 0.254930245696 Henry Cohn, 2026, needs more optimization.
18 312 0.256292833439 Henry Cohn, 2026, needs more optimization.
18 313 0.257059109063 Henry Cohn, 2026, needs more optimization.
18 314 0.258203324778 Henry Cohn, 2026, needs more optimization.
18 315 0.258956140289 Henry Cohn, 2026, needs more optimization.
18 316 0.258958031984 Henry Cohn, 2026, needs more optimization.
18 317 0.259002941364 Henry Cohn, 2026, needs more optimization.
18 318 0.259003287244 Henry Cohn, 2026, needs more optimization.
18 319 0.259099179060 Henry Cohn, 2026, needs more optimization.
18 320 0.259189851565 Henry Cohn, 2026, needs more optimization.
18 321 0.259199745929 Henry Cohn, 2026, needs more optimization.
18 322 0.259205442812 Henry Cohn, 2026, needs more optimization.
18 323 0.259338611088 Henry Cohn, 2026, needs more optimization.
18 324 0.259531965776 Henry Cohn, 2026, needs more optimization.
18 325 0.259879115714 Henry Cohn, 2026, needs more optimization.
18 326 0.259942570984 Henry Cohn, 2026, needs more optimization.
18 327 0.260123463980 Henry Cohn, 2026, needs more optimization.
18 328 0.260230609588 Henry Cohn, 2026, needs more optimization.
18 329 0.260458329194 Henry Cohn, 2026, needs more optimization.
18 330 0.260754026472 Henry Cohn, 2026, needs more optimization.
18 331 0.260754055896 Henry Cohn, 2026, needs more optimization.
18 332 0.260754090283 Henry Cohn, 2026, needs more optimization.
18 333 0.260754123290 Henry Cohn, 2026, needs more optimization.
18 334 0.260795620300 Henry Cohn, 2026, needs more optimization.
18 335 0.260798862450 Henry Cohn, 2026, needs more optimization.
18 336 0.260798890392 Henry Cohn, 2026, needs more optimization.
18 337 0.260845935805 Henry Cohn, 2026, needs more optimization.
18 338 0.260845947746 Henry Cohn, 2026, needs more optimization.
18 339 0.260871632752 Henry Cohn, 2026, needs more optimization.
18 340 0.260871644758 Henry Cohn, 2026, needs more optimization.
18 341 0.260885901878 Henry Cohn, 2026, needs more optimization.
18 342 0.260885912322 Henry Cohn, 2026, needs more optimization.
18 343 0.260898773545 Henry Cohn, 2026, needs more optimization.
18 344 0.260924764669 Henry Cohn, 2026, needs more optimization.
18 345 0.260943841470 Henry Cohn, 2026, needs more optimization.
18 346 0.260957147034 Henry Cohn, 2026, needs more optimization.
18 347 0.260957171913 Henry Cohn, 2026, needs more optimization.
18 348 0.260987573270 Henry Cohn, 2026, needs more optimization.
18 349 0.260987608306 Henry Cohn, 2026, needs more optimization.
18 350 0.261016769878 Henry Cohn, 2026, needs more optimization.
18 352 0.261203875260 Henry Cohn, 2026, needs more optimization.
18 353 0.262952286267 Henry Cohn, 2026, needs more optimization.
18 354 0.279698648063 Henry Cohn, 2026, needs more optimization.
18 355 0.284493576274 Henry Cohn, 2026, needs more optimization.
18 356 0.284744719206 Henry Cohn, 2026, needs more optimization.
18 357 0.288129558192 Henry Cohn, 2026, needs more optimization.
18 358 0.290501615253 Henry Cohn, 2026, needs more optimization.
18 359 0.291999324251 Henry Cohn, 2026, needs more optimization.
18 360 0.293228784216 Henry Cohn, 2026, needs more optimization.
18 368 0.294131745230 Henry Cohn, 2026, needs more optimization.
18 377 0.294133304863 Henry Cohn, 2026, needs more optimization.
18 379 0.294133937672 Henry Cohn, 2026, needs more optimization.
18 380 0.294135860610 Henry Cohn, 2026, needs more optimization.
18 382 0.294136970402 Henry Cohn, 2026, needs more optimization.
18 383 0.294137266417 Henry Cohn, 2026, needs more optimization.
18 385 0.294140297116 Henry Cohn, 2026, needs more optimization.
18 391 0.294142827036 Henry Cohn, 2026, needs more optimization.
18 396 0.294144334669 Henry Cohn, 2026, needs more optimization.
18 397 0.294147401603 Henry Cohn, 2026, needs more optimization.
18 398 0.294149687181 Henry Cohn, 2026, needs more optimization.
18 399 0.294160619577 Henry Cohn, 2026, needs more optimization.
18 400 0.294878841491 Henry Cohn, 2026, needs more optimization.
18 401 0.295075665372 Henry Cohn, 2026, needs more optimization.
18 405 0.295198793813 Henry Cohn, 2026, needs more optimization.
18 406 0.295203107295 Henry Cohn, 2026, needs more optimization.
18 407 0.295209176997 Henry Cohn, 2026, needs more optimization.
18 408 0.295473000873 Henry Cohn, 2026, needs more optimization.
18 409 0.295483717621 Henry Cohn, 2026, needs more optimization.
18 411 0.295487576150 Henry Cohn, 2026, needs more optimization.
18 414 0.295554837417 Henry Cohn, 2026, needs more optimization.
18 415 0.295557050766 Henry Cohn, 2026, needs more optimization.
18 416 0.295559561323 Henry Cohn, 2026, needs more optimization.
18 418 0.296041375072 Henry Cohn, 2026, needs more optimization.
18 419 0.296044582238 Henry Cohn, 2026, needs more optimization.
18 420 0.296233652176 Henry Cohn, 2026, needs more optimization.
18 480 0.296296296297 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
27⁢x−8
18 481 0.298382919725 Henry Cohn, 2026, needs more optimization.
18 482 0.300187180245 Henry Cohn, 2026, needs more optimization.
18 483 0.301461434788 Henry Cohn, 2026, needs more optimization.
18 484 0.302689723280 Henry Cohn, 2026, needs more optimization.
18 485 0.303488623580 Henry Cohn, 2026, needs more optimization.
18 486 0.305670068672 Henry Cohn, 2026, needs more optimization.
18 487 0.307369667820 Henry Cohn, 2026, needs more optimization.
18 488 0.309526899609 Henry Cohn, 2026, needs more optimization.
18 489 0.310112888442 Henry Cohn, 2026, needs more optimization.
18 490 0.310902484403 Henry Cohn, 2026, needs more optimization.
18 491 0.311795745655 Henry Cohn, 2026, needs more optimization.
18 492 0.312610168842 Henry Cohn, 2026, needs more optimization.
18 493 0.313258488264 Henry Cohn, 2026, needs more optimization.
18 494 0.313850878595 Henry Cohn, 2026, needs more optimization.
18 495 0.314057637604 Henry Cohn, 2026, needs more optimization.
18 496 0.314178945346 Henry Cohn, 2026, needs more optimization.
18 497 0.314457260822 Henry Cohn, 2026, needs more optimization.
18 498 0.314924405219 Henry Cohn, 2026, needs more optimization.
18 499 0.314989058124 Henry Cohn, 2026, needs more optimization.
18 500 0.315424309285 Henry Cohn, 2026, needs more optimization.
18 501 0.315968494486 Henry Cohn, 2026, needs more optimization.
18 502 0.316384763374 Henry Cohn, 2026, needs more optimization.
18 503 0.316639522753 Henry Cohn, 2026, needs more optimization.
18 504 0.316745631627 Henry Cohn, 2026, needs more optimization.
18 505 0.317119038026 Henry Cohn, 2026, needs more optimization.
18 506 0.317443095021 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 0.318757281393 Henry Cohn, 2026, needs more optimization.
18 510 0.318986256397 Henry Cohn, 2026, needs more optimization.
18 512 0.319282387643 Henry Cohn, 2026, needs more optimization.
18 513 0.319581287682 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 0.321228076250 Henry Cohn, 2026, needs more optimization.
18 518 0.322128900086 Henry Cohn, 2026, needs more optimization.
18 519 0.322493749121 Henry Cohn, 2026, needs more optimization.
18 520 0.323019247882 Henry Cohn, 2026, needs more optimization.
18 522 0.323090387833 Henry Cohn, 2026, needs more optimization.
18 523 0.323142457539 Henry Cohn, 2026, needs more optimization.
18 524 0.323194888113 Henry Cohn, 2026, needs more optimization.
18 525 0.323760897338 Henry Cohn, 2026, needs more optimization.
18 526 0.323970212432 Henry Cohn, 2026, needs more optimization.
18 527 0.324382990144 Henry Cohn, 2026, needs more optimization.
18 528 0.324682484519 Henry Cohn, 2026, needs more optimization.
18 529 0.324946782747 Henry Cohn, 2026, needs more optimization.
18 530 0.324958521260 Henry Cohn, 2026, needs more optimization.
18 531 0.325287555785 Henry Cohn, 2026, needs more optimization.
18 532 0.325703158941 Henry Cohn, 2026, needs more optimization.
18 533 0.326033598360 Henry Cohn, 2026, needs more optimization.
18 534 0.326345869617 Henry Cohn, 2026, needs more optimization.
18 535 0.326606574507 Henry Cohn, 2026, needs more optimization.
18 536 0.326887366802 Henry Cohn, 2026, needs more optimization.
18 537 0.327127767490 Henry Cohn, 2026, needs more optimization.
18 538 0.327736844213 Henry Cohn, 2026, needs more optimization.
18 539 0.327925978915 Henry Cohn, 2026, needs more optimization.
18 540 0.328341729179 Henry Cohn, 2026, needs more optimization.
18 541 0.328747057908 Henry Cohn, 2026, needs more optimization.
18 542 0.329012768415 Henry Cohn, 2026, needs more optimization.
18 543 0.329091129015 Henry Cohn, 2026, needs more optimization.
18 544 0.329530210378 Henry Cohn, 2026, needs more optimization.
18 545 0.329690168125 Henry Cohn, 2026, needs more optimization.
18 546 0.330058957098 Henry Cohn, 2026, needs more optimization.
18 547 0.330254207656 Henry Cohn, 2026, needs more optimization.
18 548 0.330528990192 Henry Cohn, 2026, needs more optimization.
18 549 0.330870565371 Henry Cohn, 2026, needs more optimization.
18 550 0.331312281827 Henry Cohn, 2026, needs more optimization.
18 551 0.331670098684 Henry Cohn, 2026, needs more optimization.
18 552 0.331969977970 Henry Cohn, 2026, needs more optimization.
18 553 0.332381372675 Henry Cohn, 2026, needs more optimization.
18 554 0.332456634515 Henry Cohn, 2026, needs more optimization.
18 555 0.332594211651 Henry Cohn, 2026, needs more optimization.
18 556 0.332866633211 Henry Cohn, 2026, needs more optimization.
18 557 0.332999060561 Henry Cohn, 2026, needs more optimization.
18 558 0.333214355934 Henry Cohn, 2026, needs more optimization.
18 672 0.333333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
3⁢x−1
18 704 0.333333333334 C. Ma, T. 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
18 705 0.342290519763 Henry Cohn, 2026, needs more optimization.
18 706 0.343345955846 Henry Cohn, 2026, needs more optimization.
18 707 0.344802055895 Henry Cohn, 2026, needs more optimization.
18 708 0.345597222126 Henry Cohn, 2026, needs more optimization.
18 709 0.346198182869 Henry Cohn, 2026, needs more optimization.
18 710 0.346728272337 Henry Cohn, 2026, needs more optimization.
18 711 0.347238049631 Henry Cohn, 2026, needs more optimization.
18 712 0.347625051215 Henry Cohn, 2026, needs more optimization.
18 713 0.348097849654 Henry Cohn, 2026, needs more optimization.
18 714 0.348544782076 Henry Cohn, 2026, needs more optimization.
18 715 0.348858485897 Henry Cohn, 2026, needs more optimization.
18 716 0.348952639414 Henry Cohn, 2026, needs more optimization.
18 717 0.349238491658 Henry Cohn, 2026, needs more optimization.
18 718 0.349503364160 Henry Cohn, 2026, needs more optimization.
18 719 0.349836994894 Henry Cohn, 2026, needs more optimization.
18 720 0.350046860067 Henry Cohn, 2026, needs more optimization.
18 721 0.350318060845 Henry Cohn, 2026, needs more optimization.
18 722 0.350589738506 Henry Cohn, 2026, needs more optimization.
18 723 0.350639714302 Henry Cohn, 2026, needs more optimization.
18 724 0.350857607417 Henry Cohn, 2026, needs more optimization.
18 725 0.350980156479 Henry Cohn, 2026, needs more optimization.
18 726 0.351048996662 Henry Cohn, 2026, needs more optimization.
18 727 0.351258441645 Henry Cohn, 2026, needs more optimization.
18 728 0.351409487323 Henry Cohn, 2026, needs more optimization.
18 729 0.351545131311 Henry Cohn, 2026, needs more optimization.
18 730 0.351733627471 Henry Cohn, 2026, needs more optimization.
18 731 0.351802016429 Henry Cohn, 2026, needs more optimization.
18 732 0.351947644866 Henry Cohn, 2026, needs more optimization.
18 733 0.352103836940 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 0.373325362201 Henry Cohn, 2026, needs more optimization.
18 869 0.373337944343 Henry Cohn, 2026, needs more optimization.
18 870 0.376008166245 Henry Cohn, 2026, needs more optimization.
18 871 0.377703973166 Henry Cohn, 2026, needs more optimization.
18 872 0.379046608264 Henry Cohn, 2026, needs more optimization.
18 873 0.379976195107 Henry Cohn, 2026, needs more optimization.
18 874 0.379977366315 Henry Cohn, 2026, needs more optimization.
18 875 0.380040980392 Henry Cohn, 2026, needs more optimization.
18 876 0.380902504875 Henry Cohn, 2026, needs more optimization.
18 877 0.381755653885 Henry Cohn, 2026, needs more optimization.
18 878 0.382522849090 Henry Cohn, 2026, needs more optimization.
18 879 0.382608792359 Henry Cohn, 2026, needs more optimization.
18 880 0.383345851175 Henry Cohn, 2026, needs more optimization.
18 881 0.383485700238 Henry Cohn, 2026, needs more optimization.
18 882 0.383964557926 Henry Cohn, 2026, needs more optimization.
18 883 0.384095413329 Henry Cohn, 2026, needs more optimization.
18 1024 0.384615384616 Henry Cohn, 2026, subcode of a code of size 1152.
13⁢x−5
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 0.077599728978 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 0.083233613335 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 0.101319957446 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 0.101838513947 Henry Cohn, 2026, needs more optimization.
19 73 0.102201317334 Henry Cohn, 2026.
311⁢x2−22⁢x−1
19 74 0.104258069637 Henry Cohn, 2026, needs more optimization.
19 75 0.107816370262 Henry Cohn, 2026, needs more optimization.
19 76 0.111553284797 Henry Cohn, 2026, needs more optimization.
19 77 0.112839203138 Henry Cohn, 2026, needs more optimization.
19 89 0.112912613537 Henry Cohn, 2023.
167⁢x2−10⁢x−1
19 90 0.121308037796 Henry Cohn, 2024.
2809⁢x4−192⁢x3−86⁢x2+1
19 91 0.128902034018 Henry Cohn, 2026, needs more optimization.
19 92 0.134509811268 Henry Cohn, 2026, needs more optimization.
19 93 0.142640616401 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 0.149928121676 Henry Cohn, 2026, needs more optimization.
19 104 0.150748959749 Henry Cohn, 2026, needs more optimization.
19 105 0.152679567208 Henry Cohn, 2026, needs more optimization.
19 106 0.152679588795 Henry Cohn, 2026, needs more optimization.
19 107 0.155579732070 Henry Cohn, 2026, needs more optimization.
19 108 0.156351981287 Henry Cohn, 2026, needs more optimization.
19 132 0.157894736843 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
19⁢x−3
19 133 0.168802199651 Henry Cohn, 2026, needs more optimization.
19 134 0.174620105370 Henry Cohn, 2026, needs more optimization.
19 135 0.175029051634 Henry Cohn, 2026, needs more optimization.
19 136 0.175562701462 Henry Cohn, 2026, needs more optimization.
19 137 0.176564976450 Henry Cohn, 2026, needs more optimization.
19 138 0.177171129721 Henry Cohn, 2026, needs more optimization.
19 139 0.177638121637 Henry Cohn, 2026, needs more optimization.
19 140 0.178040731241 Henry Cohn, 2026, needs more optimization.
19 141 0.178330900311 Henry Cohn, 2026, needs more optimization.
19 142 0.178676198278 Henry Cohn, 2026, needs more optimization.
19 143 0.179211947607 Henry Cohn, 2026, needs more optimization.
19 144 0.179753654079 Henry Cohn, 2026, needs more optimization.
19 146 0.180721926193 Henry Cohn, 2026, needs more optimization.
19 147 0.182379011712 Henry Cohn, 2026, needs more optimization.
19 148 0.183303403825 Henry Cohn, 2026, needs more optimization.
19 149 0.183926698859 Henry Cohn, 2026, needs more optimization.
19 150 0.184646543855 Henry Cohn, 2026, needs more optimization.
19 151 0.186861702854 Henry Cohn, 2026, needs more optimization.
19 166 0.189189189190 Henry Cohn, 2026.
37⁢x−7
19 176 0.191919191920 Henry Cohn, 2025, by enlarging a code from T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
99⁢x−19
19 177 0.193637369254 Henry Cohn, 2026, needs more optimization.
19 178 0.194663251780 Henry Cohn, 2026, needs more optimization.
19 179 0.195475764516 Henry Cohn, 2026, needs more optimization.
19 180 0.195821119719 Henry Cohn, 2026, needs more optimization.
19 181 0.198082720083 Henry Cohn, 2026, needs more optimization.
19 182 0.198331860018 Henry Cohn, 2026, needs more optimization.
19 184 0.199288567282 Henry Cohn, 2026, needs more optimization.
19 185 0.199862574109 Henry Cohn, 2026, needs more optimization.
19 192 0.2 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
5⁢x−1
19 193 0.203357314598 Henry Cohn, 2026, needs more optimization.
19 194 0.205905415936 Henry Cohn, 2026, needs more optimization.
19 195 0.207110997819 Henry Cohn, 2026, needs more optimization.
19 196 0.208040896274 Henry Cohn, 2026, needs more optimization.
19 197 0.208693179574 Henry Cohn, 2026, needs more optimization.
19 198 0.209395690264 Henry Cohn, 2026, needs more optimization.
19 199 0.209808489087 Henry Cohn, 2026, needs more optimization.
19 200 0.210590897843 Henry Cohn, 2026, needs more optimization.
19 201 0.211119357125 Henry Cohn, 2026, needs more optimization.
19 202 0.211607234222 Henry Cohn, 2026, needs more optimization.
19 203 0.212023097497 Henry Cohn, 2026, needs more optimization.
19 204 0.212310394003 Henry Cohn, 2026, needs more optimization.
19 205 0.212685452332 Henry Cohn, 2026, needs more optimization.
19 206 0.212895489764 Henry Cohn, 2026, needs more optimization.
19 207 0.213597080950 Henry Cohn, 2026, needs more optimization.
19 208 0.214239462352 Henry Cohn, 2026, needs more optimization.
19 209 0.214710942008 Henry Cohn, 2026, needs more optimization.
19 210 0.215123194187 Henry Cohn, 2026, needs more optimization.
19 211 0.215406310349 Henry Cohn, 2026, needs more optimization.
19 212 0.215588826026 Henry Cohn, 2026, needs more optimization.
19 213 0.216096289150 Henry Cohn, 2026, needs more optimization.
19 214 0.216351820619 Henry Cohn, 2026, needs more optimization.
19 215 0.218058355290 Henry Cohn, 2026, needs more optimization.
19 216 0.219013596918 Henry Cohn, 2026, needs more optimization.
19 217 0.219774127079 Henry Cohn, 2026, needs more optimization.
19 218 0.220505256368 Henry Cohn, 2026, needs more optimization.
19 219 0.221099256029 Henry Cohn, 2026, needs more optimization.
19 220 0.221717716031 Henry Cohn, 2026, needs more optimization.
19 221 0.222111002808 Henry Cohn, 2026, needs more optimization.
19 222 0.222589737955 Henry Cohn, 2026, needs more optimization.
19 223 0.222957922284 Henry Cohn, 2026, needs more optimization.
19 224 0.223241218548 Henry Cohn, 2026, needs more optimization.
19 225 0.223444972964 Henry Cohn, 2026, needs more optimization.
19 226 0.223667459870 Henry Cohn, 2026, needs more optimization.
19 227 0.223958617778 Henry Cohn, 2026, needs more optimization.
19 228 0.224163593806 Henry Cohn, 2026, needs more optimization.
19 229 0.224246333348 Henry Cohn, 2026, needs more optimization.
19 230 0.224318648132 Henry Cohn, 2026, needs more optimization.
19 231 0.224476275393 Henry Cohn, 2026, needs more optimization.
19 232 0.224536829295 Henry Cohn, 2026, needs more optimization.
19 233 0.224695402728 Henry Cohn, 2026, needs more optimization.
19 234 0.224760800607 Henry Cohn, 2026, needs more optimization.
19 235 0.225429288881 Henry Cohn, 2026, needs more optimization.
19 236 0.225840054580 Henry Cohn, 2026, needs more optimization.
19 237 0.225953486735 Henry Cohn, 2026, needs more optimization.
19 238 0.225980562230 Henry Cohn, 2026, needs more optimization.
19 239 0.225988978726 Henry Cohn, 2026, needs more optimization.
19 240 0.226456452532 Henry Cohn, 2026, needs more optimization.
19 241 0.226638496354 Henry Cohn, 2026, needs more optimization.
19 242 0.226793897757 Henry Cohn, 2026, needs more optimization.
19 243 0.227021888020 Henry Cohn, 2026, needs more optimization.
19 244 0.228137646682 Henry Cohn, 2026, needs more optimization.
19 245 0.229078455086 Henry Cohn, 2026, needs more optimization.
19 246 0.229616952875 Henry Cohn, 2026, needs more optimization.
19 247 0.230104091894 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 0.235892414511 Henry Cohn, 2026, needs more optimization.
19 279 0.237144143878 Henry Cohn, 2026, needs more optimization.
19 280 0.238264863106 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 0.240889101959 Henry Cohn, 2026, needs more optimization.
19 293 0.244060224130 Henry Cohn, 2026, needs more optimization.
19 294 0.244062208570 Henry Cohn, 2026, needs more optimization.
19 295 0.244664981304 Henry Cohn, 2026, needs more optimization.
19 296 0.246058139657 Henry Cohn, 2026, needs more optimization.
19 297 0.246377987762 Henry Cohn, 2026, needs more optimization.
19 298 0.246530130331 Henry Cohn, 2026, needs more optimization.
19 299 0.246788777459 Henry Cohn, 2026, needs more optimization.
19 300 0.248038491486 Henry Cohn, 2026, needs more optimization.
19 301 0.248479726608 Henry Cohn, 2026, needs more optimization.
19 302 0.249588503764 Henry Cohn, 2026, needs more optimization.
19 303 0.249793771674 Henry Cohn, 2026, needs more optimization.
19 304 0.249909230239 Henry Cohn, 2026, needs more optimization.
19 306 0.249973855934 Henry Cohn, 2026, needs more optimization.
19 309 0.249974349203 Henry Cohn, 2026, needs more optimization.
19 310 0.249975043828 Henry Cohn, 2026, needs more optimization.
19 311 0.249978172303 Henry Cohn, 2026, needs more optimization.
19 312 0.249984012038 Henry Cohn, 2026, needs more optimization.
19 313 0.249988835414 Henry Cohn, 2026, needs more optimization.
19 314 0.249989242500 Henry Cohn, 2026, needs more optimization.
19 316 0.249990381288 Henry Cohn, 2026, needs more optimization.
19 318 0.249992724035 Henry Cohn, 2026, needs more optimization.
19 319 0.249996843418 Henry Cohn, 2026, needs more optimization.
19 321 0.250003743146 Henry Cohn, 2026, needs more optimization.
19 323 0.250012382958 Henry Cohn, 2026, needs more optimization.
19 324 0.250065274656 Henry Cohn, 2026, needs more optimization.
19 325 0.250105186498 Henry Cohn, 2026, needs more optimization.
19 326 0.250317760375 Henry Cohn, 2026, needs more optimization.
19 327 0.250905968060 Henry Cohn, 2026, needs more optimization.
19 328 0.251950370024 Henry Cohn, 2026, needs more optimization.
19 329 0.253111907747 Henry Cohn, 2026, needs more optimization.
19 330 0.253717141302 Henry Cohn, 2026, needs more optimization.
19 331 0.254462585366 Henry Cohn, 2026, needs more optimization.
19 332 0.255947460220 Henry Cohn, 2026, needs more optimization.
19 333 0.257073691565 Henry Cohn, 2026, needs more optimization.
19 334 0.258056599405 Henry Cohn, 2026, needs more optimization.
19 335 0.258079034394 Henry Cohn, 2026, needs more optimization.
19 336 0.258156350457 Henry Cohn, 2026, needs more optimization.
19 337 0.258272861301 Henry Cohn, 2026, needs more optimization.
19 338 0.258325021749 Henry Cohn, 2026, needs more optimization.
19 339 0.258440637655 Henry Cohn, 2026, needs more optimization.
19 340 0.258533561641 Henry Cohn, 2026, needs more optimization.
19 341 0.258610040579 Henry Cohn, 2026, needs more optimization.
19 342 0.258656451013 Henry Cohn, 2026, needs more optimization.
19 345 0.258872360088 Henry Cohn, 2026, needs more optimization.
19 346 0.258888558219 Henry Cohn, 2026, needs more optimization.
19 347 0.258912960132 Henry Cohn, 2026, needs more optimization.
19 348 0.258925056804 Henry Cohn, 2026, needs more optimization.
19 349 0.258987126977 Henry Cohn, 2026, needs more optimization.
19 350 0.259124006837 Henry Cohn, 2026, needs more optimization.
19 351 0.259318723241 Henry Cohn, 2026, needs more optimization.
19 352 0.259426971825 Henry Cohn, 2026, needs more optimization.
19 353 0.259506882585 Henry Cohn, 2026, needs more optimization.
19 354 0.259555509634 Henry Cohn, 2026, needs more optimization.
19 355 0.259672958475 Henry Cohn, 2026, needs more optimization.
19 356 0.259774332049 Henry Cohn, 2026, needs more optimization.
19 357 0.259828708409 Henry Cohn, 2026, needs more optimization.
19 358 0.260175836701 Henry Cohn, 2026, needs more optimization.
19 359 0.260276453930 Henry Cohn, 2026, needs more optimization.
19 360 0.260710156747 Henry Cohn, 2026, needs more optimization.
19 363 0.287391379370 Henry Cohn, 2026, needs more optimization.
19 364 0.287401975101 Henry Cohn, 2026, needs more optimization.
19 365 0.287403514022 Henry Cohn, 2026, needs more optimization.
19 367 0.287405560059 Henry Cohn, 2026, needs more optimization.
19 369 0.287407314030 Henry Cohn, 2026, needs more optimization.
19 371 0.287411130943 Henry Cohn, 2026, needs more optimization.
19 374 0.287412727586 Henry Cohn, 2026, needs more optimization.
19 379 0.287417039961 Henry Cohn, 2026, needs more optimization.
19 381 0.287422181826 Henry Cohn, 2026, needs more optimization.
19 388 0.287424311126 Henry Cohn, 2026, needs more optimization.
19 390 0.287434861261 Henry Cohn, 2026, needs more optimization.
19 392 0.287435915193 Henry Cohn, 2026, needs more optimization.
19 395 0.287437439540 Henry Cohn, 2026, needs more optimization.
19 397 0.287443619217 Henry Cohn, 2026, needs more optimization.
19 398 0.287638029157 Henry Cohn, 2026, needs more optimization.
19 399 0.287720241556 Henry Cohn, 2026, needs more optimization.
19 400 0.287765585153 Henry Cohn, 2026, needs more optimization.
19 401 0.287796866110 Henry Cohn, 2026, needs more optimization.
19 403 0.287805204011 Henry Cohn, 2026, needs more optimization.
19 404 0.287813661841 Henry Cohn, 2026, needs more optimization.
19 408 0.287816252619 Henry Cohn, 2026, needs more optimization.
19 412 0.287862920478 Henry Cohn, 2026, needs more optimization.
19 413 0.287884253286 Henry Cohn, 2026, needs more optimization.
19 414 0.287890844440 Henry Cohn, 2026, needs more optimization.
19 416 0.288243979439 Henry Cohn, 2026, needs more optimization.
19 418 0.288461146492 Henry Cohn, 2026, needs more optimization.
19 419 0.288780996201 Henry Cohn, 2026, needs more optimization.
19 432 0.289316873850 Henry Cohn, 2026, needs more optimization.
19 433 0.290138167179 Henry Cohn, 2026, needs more optimization.
19 434 0.290146139955 Henry Cohn, 2026, needs more optimization.
19 435 0.290157271998 Henry Cohn, 2026, needs more optimization.
19 436 0.290180094535 Henry Cohn, 2026, needs more optimization.
19 438 0.290183475909 Henry Cohn, 2026, needs more optimization.
19 439 0.290668324603 Henry Cohn, 2026, needs more optimization.
19 446 0.290708894433 Henry Cohn, 2026, needs more optimization.
19 447 0.290736359260 Henry Cohn, 2026, needs more optimization.
19 449 0.290799907130 Henry Cohn, 2026, needs more optimization.
19 451 0.290838561205 Henry Cohn, 2026, needs more optimization.
19 452 0.290913943030 Henry Cohn, 2026, needs more optimization.
19 453 0.290946996887 Henry Cohn, 2026, needs more optimization.
19 454 0.290981283971 Henry Cohn, 2026, needs more optimization.
19 455 0.291071594924 Henry Cohn, 2026, needs more optimization.
19 456 0.291091395962 Henry Cohn, 2026, needs more optimization.
19 457 0.291150907480 Henry Cohn, 2026, needs more optimization.
19 458 0.291192487052 Henry Cohn, 2026, needs more optimization.
19 459 0.291667987447 Henry Cohn, 2026, needs more optimization.
19 460 0.291788037345 Henry Cohn, 2026, needs more optimization.
19 461 0.292972094391 Henry Cohn, 2026, needs more optimization.
19 462 0.293958194502 Henry Cohn, 2026, needs more optimization.
19 463 0.294806158325 Henry Cohn, 2026, needs more optimization.
19 464 0.294970191122 Henry Cohn, 2026, needs more optimization.
19 465 0.295686497876 Henry Cohn, 2026, needs more optimization.
19 466 0.296021638770 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.
19 505 0.296314832931 Henry Cohn, 2026, needs more optimization.
19 510 0.296317819379 Henry Cohn, 2026, needs more optimization.
19 513 0.296321463709 Henry Cohn, 2026, needs more optimization.
19 516 0.296325844798 Henry Cohn, 2026, needs more optimization.
19 517 0.296331304863 Henry Cohn, 2026, needs more optimization.
19 518 0.296344622122 Henry Cohn, 2026, needs more optimization.
19 519 0.296393023033 Henry Cohn, 2026, needs more optimization.
19 520 0.296510805687 Henry Cohn, 2026, needs more optimization.
19 521 0.296614235238 Henry Cohn, 2026, needs more optimization.
19 522 0.296688082691 Henry Cohn, 2026, needs more optimization.
19 523 0.296793365869 Henry Cohn, 2026, needs more optimization.
19 524 0.296978526828 Henry Cohn, 2026, needs more optimization.
19 525 0.297108985080 Henry Cohn, 2026, needs more optimization.
19 526 0.297324498609 Henry Cohn, 2026, needs more optimization.
19 528 0.297646157264 Henry Cohn, 2026, needs more optimization.
19 529 0.297709717604 Henry Cohn, 2026, needs more optimization.
19 530 0.297843882118 Henry Cohn, 2026, needs more optimization.
19 531 0.297872293350 Henry Cohn, 2026, needs more optimization.
19 532 0.297893021021 Henry Cohn, 2026, needs more optimization.
19 533 0.297898036838 Henry Cohn, 2026, needs more optimization.
19 534 0.298137756994 Henry Cohn, 2026, needs more optimization.
19 535 0.298229283392 Henry Cohn, 2026, needs more optimization.
19 538 0.298282651528 Henry Cohn, 2026, needs more optimization.
19 539 0.298346924964 Henry Cohn, 2026, needs more optimization.
19 541 0.298520410494 Henry Cohn, 2026, needs more optimization.
19 542 0.298549459480 Henry Cohn, 2026, needs more optimization.
19 543 0.298563061120 Henry Cohn, 2026, needs more optimization.
19 544 0.298986424461 Henry Cohn, 2026, needs more optimization.
19 547 0.299029682220 Henry Cohn, 2026, needs more optimization.
19 548 0.299102396643 Henry Cohn, 2026, needs more optimization.
19 550 0.299346536514 Henry Cohn, 2026, needs more optimization.
19 551 0.299448653971 Henry Cohn, 2026, needs more optimization.
19 552 0.299464098729 Henry Cohn, 2026, needs more optimization.
19 553 0.299549757038 Henry Cohn, 2026, needs more optimization.
19 554 0.299732195295 Henry Cohn, 2026, needs more optimization.
19 555 0.299915611670 Henry Cohn, 2026, needs more optimization.
19 556 0.301120816052 Henry Cohn, 2026, needs more optimization.
19 557 0.301882477746 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 0.304506955025 Henry Cohn, 2026, needs more optimization.
19 578 0.304544966779 Henry Cohn, 2026, needs more optimization.
19 579 0.304597630574 Henry Cohn, 2026, needs more optimization.
19 580 0.304616094668 Henry Cohn, 2026, needs more optimization.
19 581 0.304624419441 Henry Cohn, 2026, needs more optimization.
19 582 0.304655240406 Henry Cohn, 2026, needs more optimization.
19 583 0.304677088093 Henry Cohn, 2026, needs more optimization.
19 584 0.304688572506 Henry Cohn, 2026, needs more optimization.
19 585 0.304701549079 Henry Cohn, 2026, needs more optimization.
19 586 0.304718530445 Henry Cohn, 2026, needs more optimization.
19 587 0.304747458560 Henry Cohn, 2026, needs more optimization.
19 588 0.304747554025 Henry Cohn, 2026, needs more optimization.
19 589 0.304758361947 Henry Cohn, 2026, needs more optimization.
19 590 0.304780871345 Henry Cohn, 2026, needs more optimization.
19 591 0.304798548670 Henry Cohn, 2026, needs more optimization.
19 592 0.304816887679 Henry Cohn, 2026, needs more optimization.
19 593 0.304849731463 Henry Cohn, 2026, needs more optimization.
19 594 0.304853512798 Henry Cohn, 2026, needs more optimization.
19 595 0.304882275894 Henry Cohn, 2026, needs more optimization.
19 596 0.304882572546 Henry Cohn, 2026, needs more optimization.
19 597 0.304902360440 Henry Cohn, 2026, needs more optimization.
19 598 0.304902665313 Henry Cohn, 2026, needs more optimization.
19 599 0.304924463917 Henry Cohn, 2026, needs more optimization.
19 600 0.304924768823 Henry Cohn, 2026, needs more optimization.
19 601 0.304950704526 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 0.305008597032 Henry Cohn, 2026, needs more optimization.
19 608 0.305013451984 Henry Cohn, 2026, needs more optimization.
19 610 0.305019653088 Henry Cohn, 2026, needs more optimization.
19 611 0.305031642029 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.
19 615 0.305049946907 Henry Cohn, 2026, needs more optimization.
19 616 0.305050192359 Henry Cohn, 2026, needs more optimization.
19 617 0.305068250118 Henry Cohn, 2026, needs more optimization.
19 618 0.305073545762 Henry Cohn, 2026, needs more optimization.
19 619 0.305081289395 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.
19 623 0.305097375164 Henry Cohn, 2026, needs more optimization.
19 624 0.305097417134 Henry Cohn, 2026, needs more optimization.
19 625 0.305107768878 Henry Cohn, 2026, needs more optimization.
19 626 0.305108073829 Henry Cohn, 2026, needs more optimization.
19 627 0.305119272625 Henry Cohn, 2026, needs more optimization.
19 628 0.305119407750 Henry Cohn, 2026, needs more optimization.
19 629 0.305130178745 Henry Cohn, 2026, needs more optimization.
19 630 0.305130483578 Henry Cohn, 2026, needs more optimization.
19 631 0.305145624414 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.
19 643 0.308325107943 Henry Cohn, 2026, needs more optimization.
19 644 0.309182666777 Henry Cohn, 2026, needs more optimization.
19 646 0.309834682035 Henry Cohn, 2026, needs more optimization.
19 647 0.310974890162 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.
19 653 0.312340169703 Henry Cohn, 2026, needs more optimization.
19 654 0.312821688736 Henry Cohn, 2026, needs more optimization.
19 655 0.313063307378 Henry Cohn, 2026, needs more optimization.
19 656 0.313222186607 Henry Cohn, 2026, needs more optimization.
19 657 0.313650390001 Henry Cohn, 2026, needs more optimization.
19 658 0.313880124979 Henry Cohn, 2026, needs more optimization.
19 659 0.314138244179 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.
19 663 0.314968501865 Henry Cohn, 2026, needs more optimization.
19 664 0.315048124686 Henry Cohn, 2026, needs more optimization.
19 665 0.315377874933 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 0.339564243399 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 0.349099897957 Henry Cohn, 2026, 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 0.351020534127 Henry Cohn, 2026, needs more optimization.
19 914 0.351427858586 Henry Cohn, 2026, 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 1024 0.354838709678 Henry Cohn, 2026, subcode of a code of size 1040.
31⁢x−11
20 41 0.038815055717 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
6480⁢x3−400⁢x2−20⁢x+1
20 42 0.045454545455 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
22⁢x−1
20 43 0.050117159654 Henry Cohn, 2024.
6493504⁢x6+4442432⁢x5−359919⁢x4−90844⁢x3+13006⁢x2−588⁢x+9
20 44 0.051781487230 Henry Cohn, 2023.
20 45 0.053400898990 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 46 0.053968966531 Henry Cohn, 2025.
20 47 0.053993355922 Henry Cohn, 2023.
120⁢x2−25⁢x+1
20 48 0.055838151510 Henry Cohn, 2023.
464⁢x2−8⁢x−1
20 49 0.060513303142 Henry Cohn, 2023.
Minimal polynomial listed in plain text data
20 50 0.063702950432 Henry Cohn, 2025.
20 56* 0.066666666667 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114; H. Cohn, D. de Laat, and N. Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024, arXiv:2403.16874.
15⁢x−1
20 60 0.076923076924 Kissing configuration of 77 points in 21 dimensions.
13⁢x−1
20 63 0.081967213115 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
61⁢x−5
20 64 0.087282748333 Henry Cohn, 2026.
20 65 0.087640553689 Henry Cohn, 2026, needs more optimization.
20 66 0.089602007875 Henry Cohn, 2026, needs more optimization.
20 67 0.090150903490 Henry Cohn, 2026.
2103⁢x4−1376⁢x3+230⁢x2−1
20 68 0.092979092406 Henry Cohn, 2026, needs more optimization.
20 69 0.098517496578 Henry Cohn, 2026, 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 83 0.112895349919 Henry Cohn, 2026, needs more optimization.
20 84 0.112895349921 Henry Cohn, 2026, needs more optimization.
20 85 0.112902505496 Henry Cohn, 2026, needs more optimization.
20 86 0.112908499193 Henry Cohn, 2026, needs more optimization.
20 87 0.112912074804 Henry Cohn, 2025, needs more optimization.
20 88 0.112912612812 Henry Cohn, 2025, needs more optimization.
20 89 0.112912613185 Henry Cohn, 2025, needs more optimization.
20 92 0.112912613537 Henry Cohn, 2025.
167⁢x2−10⁢x−1
20 93 0.118699001809 Henry Cohn, 2026, needs more optimization.
20 105 0.125 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
8⁢x−1
20 106 0.136915269061 Henry Cohn, 2026.
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
20 123 0.145853791080 Henry Cohn, 2026, needs more optimization.
20 124 0.145853791081 Henry Cohn, 2026, needs more optimization.
20 125 0.147670835572 Henry Cohn, 2026, needs more optimization.
20 126 0.149455666211 Henry Cohn, 2026, needs more optimization.
20 127 0.150087849973 Henry Cohn, 2026, needs more optimization.
20 128 0.150089331134 Henry Cohn, 2026, needs more optimization.
20 130 0.150481066847 Henry Cohn, 2026, needs more optimization.
20 131 0.150517754501 Henry Cohn, 2026, needs more optimization.
20 132 0.150546573424 Henry Cohn, 2026, needs more optimization.
20 133 0.151453018245 Henry Cohn, 2026, needs more optimization.
20 134 0.151500589041 Henry Cohn, 2026, needs more optimization.
20 135 0.151500614346 Henry Cohn, 2026, needs more optimization.
20 136 0.151500638559 Henry Cohn, 2026, needs more optimization.
20 137 0.153202651092 Henry Cohn, 2026, needs more optimization.
20 138 0.154396719006 Henry Cohn, 2026, needs more optimization.
20 139 0.155006059389 Henry Cohn, 2026, needs more optimization.
20 140 0.156027125137 Henry Cohn, 2026, needs more optimization.
20 141 0.157229456154 Henry Cohn, 2026, needs more optimization.
20 142 0.161809087523 Henry Cohn, 2026, needs more optimization.
20 170 0.166666666667 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
6⁢x−1
20 171 0.181540268746 Henry Cohn, 2026, needs more optimization.
20 172 0.187911735723 Henry Cohn, 2026, needs more optimization.
20 173 0.189191944103 Henry Cohn, 2026, needs more optimization.
20 174 0.189192012604 Henry Cohn, 2026, needs more optimization.
20 175 0.189192124061 Henry Cohn, 2026, needs more optimization.
20 176 0.189192195096 Henry Cohn, 2026, needs more optimization.
20 177 0.189192271208 Henry Cohn, 2026, needs more optimization.
20 178 0.189192368262 Henry Cohn, 2026, needs more optimization.
20 179 0.189192469190 Henry Cohn, 2026, needs more optimization.
20 180 0.189192485037 Henry Cohn, 2026, needs more optimization.
20 181 0.189192497762 Henry Cohn, 2026, needs more optimization.
20 182 0.189192612186 Henry Cohn, 2026, needs more optimization.
20 183 0.189192767429 Henry Cohn, 2026, needs more optimization.
20 184 0.189192857889 Henry Cohn, 2026, needs more optimization.
20 185 0.189192872203 Henry Cohn, 2026, needs more optimization.
20 186 0.189192980984 Henry Cohn, 2026, needs more optimization.
20 187 0.189192994143 Henry Cohn, 2026, needs more optimization.
20 188 0.189193019835 Henry Cohn, 2026, needs more optimization.
20 189 0.189194542214 Henry Cohn, 2026, needs more optimization.
20 190 0.189194550992 Henry Cohn, 2026, needs more optimization.
20 191 0.189889696439 Henry Cohn, 2026, needs more optimization.
20 201 0.191919593802 Henry Cohn, 2026, needs more optimization.
20 202 0.191921409459 Henry Cohn, 2026, needs more optimization.
20 203 0.192004796077 Henry Cohn, 2026, needs more optimization.
20 231 0.192307692308 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
20 256 0.2 T. Ericson and V. Zinoviev, Spherical codes generated by binary partitions of symmetric pointsets, IEEE Trans. Inform. Theory 41 (1995), 107–129, doi:10.1109/18.370114.
5⁢x−1
20 257 0.203357314598 Henry Cohn, 2026, needs more optimization.
20 258 0.205920911961 Henry Cohn, 2026, needs more optimization.
20 259 0.207516721309 Henry Cohn, 2026, needs more optimization.
20 262 0.208386799892 Henry Cohn, 2026, needs more optimization.
20 263 0.208834164016 Henry Cohn, 2026, needs more optimization.
20 264 0.208834164080 Henry Cohn, 2026, needs more optimization.
20 265 0.212174705319 Henry Cohn, 2026, needs more optimization.
20 266 0.212749730095 Henry Cohn, 2026, needs more optimization.
20 267 0.213297041964 Henry Cohn, 2026, needs more optimization.
20 268 0.213338636454 Henry Cohn, 2026, needs more optimization.
20 269 0.214424382134 Henry Cohn, 2026, needs more optimization.
20 270 0.214435554969 Henry Cohn, 2026, needs more optimization.
20 271 0.214440106736 Henry Cohn, 2026, needs more optimization.
20 272 0.215402251625 Henry Cohn, 2026, needs more optimization.
20 273 0.215516352242 Henry Cohn, 2026, needs more optimization.
20 274 0.215594802928 Henry Cohn, 2026, needs more optimization.
20 275 0.215832391430 Henry Cohn, 2026, needs more optimization.
20 276 0.215931921699 Henry Cohn, 2026, needs more optimization.
20 277 0.215984534158 Henry Cohn, 2026, needs more optimization.
20 278 0.216163017896 Henry Cohn, 2026, needs more optimization.
20 279 0.216315537238 Henry Cohn, 2026, needs more optimization.
20 280 0.216553448250 Henry Cohn, 2026, needs more optimization.
20 281 0.216765232408 Henry Cohn, 2026, needs more optimization.
20 282 0.217059842503 Henry Cohn, 2026, needs more optimization.
20 283 0.217450539838 Henry Cohn, 2026, needs more optimization.
20 284 0.217937600540 Henry Cohn, 2026, needs more optimization.
20 285 0.218274736928 Henry Cohn, 2026, needs more optimization.
20 286 0.218626303938 Henry Cohn, 2026, needs more optimization.
20 287 0.218962733841 Henry Cohn, 2026, needs more optimization.
20 288 0.219759759671 Henry Cohn, 2026, needs more optimization.
20 289 0.220229108564 Henry Cohn, 2026, needs more optimization.
20 290 0.220518689091 Henry Cohn, 2026, needs more optimization.
20 291 0.220669212257 Henry Cohn, 2026, needs more optimization.
20 293 0.220694466075 Henry Cohn, 2026, needs more optimization.
20 294 0.220694934042 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 0.244554820844 Henry Cohn, 2026, needs more optimization.
20 381 0.245519398599 Henry Cohn, 2026, needs more optimization.
20 382 0.246803518279 Henry Cohn, 2026, needs more optimization.
20 383 0.247231335732 Henry Cohn, 2026, needs more optimization.
20 384 0.248127412287 Henry Cohn, 2026, needs more optimization.
20 385 0.249167894975 Henry Cohn, 2026, needs more optimization.
20 386 0.249975327414 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 0.264995177952 Henry Cohn, 2026, needs more optimization.
20 473 0.266666666667 Henry Cohn, 2025.
15⁢x−4
20 474 0.269857967279 Henry Cohn, 2026, needs more optimization.
20 475 0.271268170563 Henry Cohn, 2026, needs more optimization.
20 476 0.272602361811 Henry Cohn, 2026, needs more optimization.
20 477 0.273427023276 Henry Cohn, 2026, needs more optimization.
20 478 0.274354647695 Henry Cohn, 2026, needs more optimization.
20 479 0.275156080454 Henry Cohn, 2026, needs more optimization.
20 480 0.275395006181 Henry Cohn, 2026, needs more optimization.
20 481 0.275400177323 Henry Cohn, 2026, needs more optimization.
20 482 0.275403243583 Henry Cohn, 2026, needs more optimization.
20 483 0.275416794805 Henry Cohn, 2026, needs more optimization.
20 484 0.275419898319 Henry Cohn, 2026, needs more optimization.
20 485 0.275436933318 Henry Cohn, 2026, needs more optimization.
20 486 0.275442921733 Henry Cohn, 2026, needs more optimization.
20 487 0.275450978142 Henry Cohn, 2026, needs more optimization.
20 489 0.275461985350 Henry Cohn, 2026, needs more optimization.
20 491 0.275464175061 Henry Cohn, 2026, needs more optimization.
20 492 0.275465408690 Henry Cohn, 2026, needs more optimization.
20 494 0.275468231728 Henry Cohn, 2026, needs more optimization.
20 497 0.275483290711 Henry Cohn, 2026, needs more optimization.
20 498 0.275494046848 Henry Cohn, 2026, needs more optimization.
20 499 0.281077845265 Henry Cohn, 2026, needs more optimization.
20 500 0.281183500891 Henry Cohn, 2026, needs more optimization.
20 501 0.281279955898 Henry Cohn, 2026, needs more optimization.
20 502 0.281281435772 Henry Cohn, 2026, needs more optimization.
20 503 0.281344175575 Henry Cohn, 2026, needs more optimization.
20 504 0.282698907691 Henry Cohn, 2026, needs more optimization.
20 511 0.283343212159 Henry Cohn, 2026, needs more optimization.
20 520 0.287891315628 Henry Cohn, 2026, needs more optimization.
20 521 0.289345521584 Henry Cohn, 2026, needs more optimization.
20 522 0.289726811056 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 0.289734759773 Henry Cohn, 2026, needs more optimization.
20 553 0.291238404411 Henry Cohn, 2026, needs more optimization.
20 554 0.292502856930 Henry Cohn, 2026, needs more optimization.
20 555 0.293219740864 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 0.300240990342 Henry Cohn, 2026, needs more optimization.
20 559 0.300429644160 Henry Cohn, 2026, needs more optimization.
20 562 0.300557700628 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 0.303208225214 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 0.304358208642 Henry Cohn, 2026, needs more optimization.
20 682 0.304366014514 Henry Cohn, 2026, needs more optimization.
20 685 0.304368291716 Henry Cohn, 2026, needs more optimization.
20 687 0.304369573720 Henry Cohn, 2026, needs more optimization.
20 688 0.304391063642 Henry Cohn, 2026, needs more optimization.
20 690 0.304503574811 Henry Cohn, 2026, needs more optimization.
20 691 0.304512466175 Henry Cohn, 2026, needs more optimization.
20 692 0.304552476334 Henry Cohn, 2026, needs more optimization.
20 694 0.304735982932 Henry Cohn, 2026, needs more optimization.
20 695 0.304787579237 Henry Cohn, 2026, needs more optimization.
20 696 0.304791456353 Henry Cohn, 2026, needs more optimization.
20 698 0.304988390998 Henry Cohn, 2026, needs more optimization.
20 699 0.304999999429 Henry Cohn, 2026, needs more optimization.
20 700 0.305021743306 Henry Cohn, 2026, needs more optimization.
20 701 0.305035535427 Henry Cohn, 2026, needs more optimization.
20 702 0.305631385727 Henry Cohn, 2026, needs more optimization.
20 703 0.305792580965 Henry Cohn, 2026, needs more optimization.
20 705 0.306381594726 Henry Cohn, 2026, needs more optimization.
20 717 0.306471253168 Henry Cohn, 2026, needs more optimization.
20 718 0.306721856961 Henry Cohn, 2026, needs more optimization.
20 730 0.307067020146 Henry Cohn, 2026, needs more optimization.
20 731 0.307273277195 Henry Cohn, 2026, needs more optimization.
20 732 0.307388988429 Henry Cohn, 2026, needs more optimization.
20 733 0.307507350776 Henry Cohn, 2026, needs more optimization.
20 737 0.307734103549 Henry Cohn, 2026, needs more optimization.
20 740 0.307842813109 Henry Cohn, 2026, needs more optimization.
20 742 0.308107444860 Henry Cohn, 2026, needs more optimization.
20 758 0.308301443706 Henry Cohn, 2026, needs more optimization.
20 759 0.308319258274 Henry Cohn, 2026, needs more optimization.
20 760 0.308342077973 Henry Cohn, 2026, needs more optimization.
20 761 0.308359469736 Henry Cohn, 2026, needs more optimization.
20 764 0.309195443197 Henry Cohn, 2026, needs more optimization.
20 765 0.309199050300 Henry Cohn, 2026, needs more optimization.
20 766 0.309202473115 Henry Cohn, 2026, needs more optimization.
20 773 0.309574163113 Henry Cohn, 2026, needs more optimization.
20 774 0.309647041795 Henry Cohn, 2026, needs more optimization.
20 775 0.309694523599 Henry Cohn, 2026, needs more optimization.
20 776 0.309766727223 Henry Cohn, 2026, needs more optimization.
20 777 0.309897694254 Henry Cohn, 2026, needs more optimization.
20 778 0.309922787539 Henry Cohn, 2026, needs more optimization.
20 779 0.310046299275 Henry Cohn, 2026, needs more optimization.
20 780 0.310213614885 Henry Cohn, 2026, needs more optimization.
20 781 0.310233878595 Henry Cohn, 2026, needs more optimization.
20 782 0.310523883726 Henry Cohn, 2026, needs more optimization.
20 783 0.310887392399 Henry Cohn, 2026, needs more optimization.
20 784 0.311245570947 Henry Cohn, 2026, needs more optimization.
20 785 0.311296849153 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 0.062635252426 Henry Cohn, 2026, needs more optimization.
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.
14481⁢x4−18000⁢x3+4848⁢x2−480⁢x+16
21 65 0.081966984768 Henry Cohn, 2026, 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 0.093247656078 Henry Cohn, 2026, needs more optimization.
21 82 0.093297851017 Henry Cohn, 2026.
144⁢x4−840⁢x3+192⁢x2−1
21 83 0.095523255230 Henry Cohn, 2026, needs more optimization.
21 84 0.096073235107 Henry Cohn, 2026, needs more optimization.
21 85 0.097702080330 Henry Cohn, 2026, needs more optimization.
21 86 0.104649382361 Henry Cohn, 2026, needs more optimization.
21 88 0.106199014100 Henry Cohn, 2026, needs more optimization.
21 89 0.108845760578 Henry Cohn, 2026, needs more optimization.
21 90 0.109639633905 Henry Cohn, 2026, needs more optimization.
21 92 0.109918568059 Henry Cohn, 2026, needs more optimization.
21 93 0.110695598499 Henry Cohn, 2026, needs more optimization.
21 112* 0.111111111112 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
9⁢x−1
21 113 0.127363959709 Henry Cohn, 2026, 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 0.139345069179 Henry Cohn, 2026, needs more optimization.
21 122 0.139345471216 Henry Cohn, 2026, needs more optimization.
21 123 0.139390045095 Henry Cohn, 2026, needs more optimization.
21 124 0.140535690962 Henry Cohn, 2026, needs more optimization.
21 162* 0.142857142858 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
7⁢x−1
21 163 0.153926281042 Henry Cohn, 2026, needs more optimization.
21 164 0.160022839714 Henry Cohn, 2026, needs more optimization.
21 165 0.160022886339 Henry Cohn, 2026, needs more optimization.
21 166 0.161615412621 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 0.172187000250 Henry Cohn, 2026, needs more optimization.
21 200 0.174798566499 Henry Cohn, 2026, needs more optimization.
21 201 0.174865046811 Henry Cohn, 2026, needs more optimization.
21 202 0.175166678532 Henry Cohn, 2026, needs more optimization.
21 203 0.175216416015 Henry Cohn, 2026, needs more optimization.
21 205 0.175533447351 Henry Cohn, 2026, needs more optimization.
21 206 0.175719357495 Henry Cohn, 2026, needs more optimization.
21 207 0.175850552632 Henry Cohn, 2026, needs more optimization.
21 208 0.176274057111 Henry Cohn, 2026, needs more optimization.
21 209 0.176275006302 Henry Cohn, 2026, needs more optimization.
21 210 0.176382034742 Henry Cohn, 2026, needs more optimization.
21 211 0.176514739216 Henry Cohn, 2026, needs more optimization.
21 212 0.176559125161 Henry Cohn, 2026, needs more optimization.
21 213 0.176677247355 Henry Cohn, 2026, needs more optimization.
21 214 0.176868120315 Henry Cohn, 2026, needs more optimization.
21 215 0.177016821407 Henry Cohn, 2026, needs more optimization.
21 216 0.177154865228 Henry Cohn, 2026, needs more optimization.
21 217 0.177234275664 Henry Cohn, 2026, needs more optimization.
21 218 0.177286556405 Henry Cohn, 2026, needs more optimization.
21 219 0.177401695423 Henry Cohn, 2026, needs more optimization.
21 220 0.177468399019 Henry Cohn, 2026, needs more optimization.
21 224 0.177492046263 Henry Cohn, 2026, needs more optimization.
21 225 0.178115188873 Henry Cohn, 2026, needs more optimization.
21 226 0.188774869265 Henry Cohn, 2026, needs more optimization.
21 233 0.192307692308 Code with 231 points in 20 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26⁢x−5
21 234 0.192307929309 Henry Cohn, 2026, needs more optimization.
21 235 0.192308006431 Henry Cohn, 2026, needs more optimization.
21 236 0.194983447850 Henry Cohn, 2026, needs more optimization.
21 237 0.195459638107 Henry Cohn, 2026, needs more optimization.
21 336 0.2 E. Bannai and N. J. A. Sloane, Uniqueness of certain spherical codes, Canadian J. Math. 33 (1981), 437–449, doi:10.4153/CJM-1981-038-7.
5⁢x−1
21 352 0.214285714286 Henry Cohn, 2026.
14⁢x−3
21 353 0.222395820677 Henry Cohn, 2026, needs more optimization.
21 354 0.230773929995 Henry Cohn, 2026, needs more optimization.
21 355 0.230774009305 Henry Cohn, 2026, needs more optimization.
21 356 0.230774642000 Henry Cohn, 2026, needs more optimization.
21 357 0.230774653449 Henry Cohn, 2026, needs more optimization.
21 358 0.230774754997 Henry Cohn, 2026, needs more optimization.
21 359 0.230774891512 Henry Cohn, 2026, needs more optimization.
21 360 0.230775019071 Henry Cohn, 2026, needs more optimization.
21 395 0.230775728466 Henry Cohn, 2026, needs more optimization.
21 396 0.233060960755 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 0.253544079776 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 0.277257037707 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 0.290306179867 Henry Cohn, 2026, needs more optimization.
21 852 0.291107216014 Henry Cohn, 2026, needs more optimization.
21 853 0.291735622773 Henry Cohn, 2026, needs more optimization.
21 854 0.292112205384 Henry Cohn, 2026, needs more optimization.
21 855 0.292435594190 Henry Cohn, 2026, needs more optimization.
21 856 0.292768184046 Henry Cohn, 2026, needs more optimization.
21 857 0.293060004621 Henry Cohn, 2026, needs more optimization.
21 858 0.293325013893 Henry Cohn, 2026, needs more optimization.
21 859 0.293640633169 Henry Cohn, 2026, needs more optimization.
21 860 0.294187435880 Henry Cohn, 2026, needs more optimization.
21 861 0.294648965761 Henry Cohn, 2026, needs more optimization.
21 862 0.294765632391 Henry Cohn, 2026, needs more optimization.
21 863 0.295040976764 Henry Cohn, 2026, needs more optimization.
21 864 0.295360800842 Henry Cohn, 2026, needs more optimization.
21 865 0.295533721580 Henry Cohn, 2026, needs more optimization.
21 866 0.295672229081 Henry Cohn, 2026, needs more optimization.
21 867 0.295902803628 Henry Cohn, 2026, needs more optimization.
21 868 0.296148590816 Henry Cohn, 2026, needs more optimization.
21 869 0.296401112803 Henry Cohn, 2026, needs more optimization.
21 870 0.296584275443 Henry Cohn, 2026, needs more optimization.
21 871 0.296708758756 Henry Cohn, 2026, needs more optimization.
21 872 0.296783482279 Henry Cohn, 2026, needs more optimization.
21 873 0.298085895064 Henry Cohn, 2026, needs more optimization.
21 874 0.298659015513 Henry Cohn, 2026, needs more optimization.
21 875 0.298875990997 Henry Cohn, 2026, needs more optimization.
21 876 0.299022598227 Henry Cohn, 2026, needs more optimization.
21 877 0.299186480921 Henry Cohn, 2026, needs more optimization.
21 878 0.299760484012 Henry Cohn, 2026, needs more optimization.
21 879 0.299904879461 Henry Cohn, 2026, needs more optimization.
21 880 0.300368490169 Henry Cohn, 2026, needs more optimization.
21 881 0.300454895686 Henry Cohn, 2026, needs more optimization.
21 882 0.300637402810 Henry Cohn, 2026, needs more optimization.
21 883 0.300904209748 Henry Cohn, 2026, needs more optimization.
21 884 0.301106078756 Henry Cohn, 2026, needs more optimization.
21 885 0.301399140183 Henry Cohn, 2026, needs more optimization.
21 886 0.301625032449 Henry Cohn, 2026, needs more optimization.
21 887 0.301759818931 Henry Cohn, 2026, needs more optimization.
21 888 0.301907359784 Henry Cohn, 2026, needs more optimization.
21 889 0.301964805886 Henry Cohn, 2026, needs more optimization.
21 890 0.302071350537 Henry Cohn, 2026, needs more optimization.
21 891 0.302184938725 Henry Cohn, 2026, needs more optimization.
21 892 0.302453129960 Henry Cohn, 2026, needs more optimization.
21 893 0.302640429251 Henry Cohn, 2026, needs more optimization.
21 894 0.302881235505 Henry Cohn, 2026, needs more optimization.
21 895 0.303005462006 Henry Cohn, 2026, needs more optimization.
21 896 0.303438838541 Henry Cohn, 2026, needs more optimization.
21 897 0.303741272867 Henry Cohn, 2026, needs more optimization.
21 898 0.303979079248 Henry Cohn, 2026, needs more optimization.
21 899 0.304211891783 Henry Cohn, 2026, needs more optimization.
21 900 0.304437332221 Henry Cohn, 2026, needs more optimization.
21 901 0.304567917234 Henry Cohn, 2026, needs more optimization.
21 902 0.304817798296 Henry Cohn, 2026, needs more optimization.
21 903 0.305067026171 Henry Cohn, 2026, needs more optimization.
21 904 0.305251994763 Henry Cohn, 2026, needs more optimization.
21 905 0.305351731433 Henry Cohn, 2026, needs more optimization.
21 906 0.305469602888 Henry Cohn, 2026, needs more optimization.
21 907 0.305564447959 Henry Cohn, 2026, needs more optimization.
21 908 0.305752151468 Henry Cohn, 2026, needs more optimization.
21 909 0.305864121062 Henry Cohn, 2026, needs more optimization.
21 910 0.306022546012 Henry Cohn, 2026, needs more optimization.
21 911 0.306112459253 Henry Cohn, 2026, needs more optimization.
21 912 0.306281848259 Henry Cohn, 2026, needs more optimization.
21 913 0.306380807250 Henry Cohn, 2026, needs more optimization.
21 914 0.306501894793 Henry Cohn, 2026, needs more optimization.
21 915 0.306607955156 Henry Cohn, 2026, needs more optimization.
21 916 0.306739544561 Henry Cohn, 2026, needs more optimization.
21 917 0.306905478734 Henry Cohn, 2026, needs more optimization.
21 918 0.306999316923 Henry Cohn, 2026, needs more optimization.
21 919 0.307084862460 Henry Cohn, 2026, needs more optimization.
21 920 0.307184705729 Henry Cohn, 2026, needs more optimization.
21 921 0.307299468774 Henry Cohn, 2026, needs more optimization.
21 922 0.307424640112 Henry Cohn, 2026, needs more optimization.
21 923 0.307520833737 Henry Cohn, 2026, needs more optimization.
21 924 0.307655007517 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.
736⁢x3+236⁢x2−34⁢x+1
22 48 0.047524915294 Henry Cohn, 2025, continuous family of codes without rattlers.
64⁢x2+18⁢x−1
22 49 0.047603596724 Henry Cohn, 2026.
22 50 0.047618606209 Henry Cohn, 2025, needs more optimization.
22 52 0.047619047316 Henry Cohn, 2025, needs more optimization.
22 53 0.057560345703 Henry Cohn, 2024.
22 54 0.060108874148 Henry Cohn, 2025.
22 55 0.064358164587 Henry Cohn, 2026, needs more optimization.
22 56 0.066532898150 Henry Cohn, 2026, needs more optimization.
22 57 0.066612218007 Henry Cohn, 2026, needs more optimization.
22 58 0.066639716879 Henry Cohn, 2026, needs more optimization.
22 59 0.066653900529 Henry Cohn, 2026, needs more optimization.
22 60 0.066662323881 Henry Cohn, 2026, needs more optimization.
22 61 0.069653549236 Henry Cohn, 2026, needs more optimization.
22 62 0.071702992549 Henry Cohn, 2026, needs more optimization.
22 63 0.076904418853 Henry Cohn, 2026, needs more optimization.
22 64 0.076919638871 Henry Cohn, 2026, needs more optimization.
22 65 0.076924075518 Henry Cohn, 2026, needs more optimization.
22 66 0.078243584884 Henry Cohn, 2026, needs more optimization.
22 67 0.079295785727 Henry Cohn, 2026, needs more optimization.
22 68 0.080927905652 Henry Cohn, 2026, needs more optimization.
22 69 0.083023887822 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 0.086876541302 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 0.109433688331 Henry Cohn, 2026.
6912⁢x4−560⁢x3−272⁢x2+3
22 114 0.111111111112 Code with 112 points in 21 dimensions, together with two antipodal points orthogonal to it; T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
9⁢x−1
22 115 0.112789665003 Henry Cohn, 2026.
68⁢x2−52⁢x+5
22 116 0.118359075808 Henry Cohn, 2026, needs more optimization.
22 117 0.122811162919 Henry Cohn, 2026, needs more optimization.
22 118 0.126503630021 Henry Cohn, 2026, needs more optimization.
22 119 0.126742538978 Henry Cohn, 2026, needs more optimization.
22 120 0.131231549766 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
22 127 0.131782945737 Henry Cohn, 2026.
129⁢x−17
22 136 0.135135135136 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
37⁢x−5
22 141 0.135135135136 Henry Cohn, 2026.
37⁢x−5
22 142 0.135523479798 Henry Cohn, 2026, needs more optimization.
22 143 0.138366666209 Henry Cohn, 2026, needs more optimization.
22 144 0.139626934393 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 0.147884248426 Henry Cohn, 2026, needs more optimization.
22 168 0.152246766646 Henry Cohn, 2026, needs more optimization.
22 169 0.153791128092 Henry Cohn, 2026, needs more optimization.
22 170 0.160003444403 Henry Cohn, 2026, needs more optimization.
22 171 0.160003448506 Henry Cohn, 2026, needs more optimization.
22 172 0.160015332294 Henry Cohn, 2026, needs more optimization.
22 173 0.160444280972 Henry Cohn, 2026, needs more optimization.
22 174 0.161555622155 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 0.161905113244 Henry Cohn, 2026, needs more optimization.
22 203 0.165621256192 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 0.178571428572 Henry Cohn, 2026.
28⁢x−5
22 277 0.185917436345 Henry Cohn, 2026, needs more optimization.
22 278 0.189307491623 Henry Cohn, 2026, needs more optimization.
22 279 0.191627492629 Henry Cohn, 2026, needs more optimization.
22 280 0.193250004424 Henry Cohn, 2026, needs more optimization.
22 281 0.194538024928 Henry Cohn, 2026, needs more optimization.
22 282 0.195736802127 Henry Cohn, 2026, needs more optimization.
22 283 0.196337950919 Henry Cohn, 2026, needs more optimization.
22 284 0.196354923109 Henry Cohn, 2026, needs more optimization.
22 286 0.196362023436 Henry Cohn, 2026, needs more optimization.
22 287 0.199281352015 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 0.201777989818 Henry Cohn, 2026, needs more optimization.
22 354 0.202842503838 Henry Cohn, 2026, needs more optimization.
22 355 0.203728567038 Henry Cohn, 2026, needs more optimization.
22 356 0.204034968218 Henry Cohn, 2026, needs more optimization.
22 357 0.204058374103 Henry Cohn, 2026, needs more optimization.
22 358 0.204059482324 Henry Cohn, 2026, needs more optimization.
22 359 0.204491312391 Henry Cohn, 2026, needs more optimization.
22 374 0.204624019941 Henry Cohn, 2026, needs more optimization.
22 375 0.205726260983 Henry Cohn, 2026, needs more optimization.
22 376 0.206395598603 Henry Cohn, 2026, needs more optimization.
22 377 0.206702468133 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.
22 388 0.207175951819 Henry Cohn, 2026, needs more optimization.
22 389 0.207175995211 Henry Cohn, 2026, needs more optimization.
22 390 0.207176019253 Henry Cohn, 2026, needs more optimization.
22 391 0.208469005766 Henry Cohn, 2026, needs more optimization.
22 392 0.208833201396 Henry Cohn, 2026, needs more optimization.
22 393 0.209057515935 Henry Cohn, 2026, needs more optimization.
22 394 0.209110265315 Henry Cohn, 2026, needs more optimization.
22 395 0.209433638600 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.
22 403 0.209622615370 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 0.209817069797 Henry Cohn, 2026, needs more optimization.
22 431 0.210993089892 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 0.212653226480 Henry Cohn, 2026, needs more optimization.
22 452 0.213200716356 Henry Cohn, 2026.
22⁢x2−1
22 485 0.229650347182 Henry Cohn, 2026, needs more optimization.
22 503 0.229926564594 Henry Cohn, 2026, needs more optimization.
22 504 0.229926564994 Henry Cohn, 2026, needs more optimization.
22 505 0.229926768274 Henry Cohn, 2026, needs more optimization.
22 506 0.231137104549 Henry Cohn, 2026, needs more optimization.
22 529 0.233333333334 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
30⁢x−7
22 556 0.238095238096 Orthogonal union of 554 points in 21 dimensions and 2 points in 1 dimension.
21⁢x−5
22 557 0.238101475164 Henry Cohn, 2026, needs more optimization.
22 558 0.238112444674 Henry Cohn, 2026, needs more optimization.
22 559 0.238729659962 Henry Cohn, 2026, needs more optimization.
22 560 0.239375035037 Henry Cohn, 2026, needs more optimization.
22 561 0.240992380706 Henry Cohn, 2026, needs more optimization.
22 562 0.244137952645 Henry Cohn, 2026, needs more optimization.
22 563 0.246188107893 Henry Cohn, 2026, needs more optimization.
22 564 0.248061756638 Henry Cohn, 2026, needs more optimization.
22 565 0.249942668114 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 0.047343032464 Henry Cohn, 2026, needs more optimization.
23 52 0.047477902076 Henry Cohn, 2026, needs more optimization.
23 53 0.047596642699 Henry Cohn, 2026, needs more optimization.
23 54 0.047609798559 Henry Cohn, 2024, needs more optimization.
23 55 0.055366146889 Henry Cohn, 2026, needs more optimization.
23 56 0.057275984127 Henry Cohn, 2025.
23 57 0.061654360911 Henry Cohn, 2026, needs more optimization.
23 58 0.064515997882 Henry Cohn, 2026, needs more optimization.
23 59 0.066320744412 Henry Cohn, 2026, needs more optimization.
23 61 0.066464177183 Henry Cohn, 2026, needs more optimization.
23 62 0.066599672692 Henry Cohn, 2026, needs more optimization.
23 63 0.067250815881 Henry Cohn, 2026, needs more optimization.
23 64 0.069716146261 Henry Cohn, 2026, needs more optimization.
23 65 0.073160707055 Henry Cohn, 2026, needs more optimization.
23 66 0.076375843612 Henry Cohn, 2026, needs more optimization.
23 67 0.076883023373 Henry Cohn, 2026, needs more optimization.
23 68 0.076898450808 Henry Cohn, 2026, needs more optimization.
23 69 0.077606449423 Henry Cohn, 2026, needs more optimization.
23 70 0.077985696567 Henry Cohn, 2026, needs more optimization.
23 71 0.079522620312 Henry Cohn, 2026, needs more optimization.
23 72 0.080064660880 Henry Cohn, 2026, needs more optimization.
23 73 0.081989242399 Henry Cohn, 2026, needs more optimization.
23 74 0.083306336565 Henry Cohn, 2026, needs more optimization.
23 76 0.083320662985 Henry Cohn, 2026, needs more optimization.
23 77 0.083331616679 Henry Cohn, 2026, needs more optimization.
23 79 0.083333145503 Henry Cohn, 2026, needs more optimization.
23 81 0.083333222004 Henry Cohn, 2025, needs more optimization.
23 82 0.083396419021 Henry Cohn, 2026, needs more optimization.
23 83 0.087272831288 Henry Cohn, 2026, needs more optimization.
23 84 0.089256525763 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 0.102490106780 Henry Cohn, 2026, needs more optimization.
23 106 0.109392443214 Henry Cohn, 2026.
2175⁢x2+210⁢x−49
23 107 0.111111109507 Henry Cohn, 2026, needs more optimization.
23 108 0.111111109516 Henry Cohn, 2026, needs more optimization.
23 109 0.111111109529 Henry Cohn, 2026, needs more optimization.
23 110 0.111111109658 Henry Cohn, 2026, needs more optimization.
23 113 0.111111109682 Henry Cohn, 2026, needs more optimization.
23 115 0.111111109683 Henry Cohn, 2026, needs more optimization.
23 116 0.111111109684 Henry Cohn, 2026, needs more optimization.
23 117 0.111112090255 Henry Cohn, 2026, needs more optimization.
23 118 0.111112859878 Henry Cohn, 2026, needs more optimization.
23 119 0.115967905820 Henry Cohn, 2026, needs more optimization.
23 120 0.121010042034 Henry Cohn, 2026, needs more optimization.
23 121 0.124525092913 Henry Cohn, 2026, needs more optimization.
23 122 0.126158021701 Henry Cohn, 2026, needs more optimization.
23 123 0.131779371379 Henry Cohn, 2025, needs more optimization.
23 129 0.131782945737 Orthogonal union of 127 points in 22 dimensions and 2 points in 1 dimension.
129⁢x−17
23 130 0.131807428500 Henry Cohn, 2026, needs more optimization.
23 131 0.132302114733 Henry Cohn, 2026, needs more optimization.
23 132 0.134363121495 Henry Cohn, 2026, needs more optimization.
23 133 0.134854439458 Henry Cohn, 2026, needs more optimization.
23 134 0.135065335336 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 0.135957012344 Henry Cohn, 2026, needs more optimization.
23 150 0.136651127323 Henry Cohn, 2026, needs more optimization.
23 151 0.137560947018 Henry Cohn, 2026, needs more optimization.
23 152 0.139001582470 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
23 169 0.142857630115 Henry Cohn, 2026, needs more optimization.
23 170 0.142857630117 Henry Cohn, 2026, needs more optimization.
23 171 0.145112601824 Henry Cohn, 2026, needs more optimization.
23 172 0.146954876375 Henry Cohn, 2026, needs more optimization.
23 173 0.147176365070 Henry Cohn, 2026, needs more optimization.
23 174 0.153135947269 Henry Cohn, 2026, needs more optimization.
23 175 0.153452348726 Henry Cohn, 2026, needs more optimization.
23 176 0.155738720767 Henry Cohn, 2026, needs more optimization.
23 177 0.156428326689 Henry Cohn, 2026, needs more optimization.
23 178 0.157406039754 Henry Cohn, 2026, needs more optimization.
23 179 0.159171793376 Henry Cohn, 2026, needs more optimization.
23 180 0.159731592859 Henry Cohn, 2026, needs more optimization.
23 181 0.160297150719 Henry Cohn, 2026, needs more optimization.
23 182 0.161211872482 Henry Cohn, 2026, needs more optimization.
23 183 0.161674572101 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 0.161904891178 Henry Cohn, 2026, needs more optimization.
23 205 0.161904895839 Henry Cohn, 2026, needs more optimization.
23 206 0.161907076292 Henry Cohn, 2026, needs more optimization.
23 207 0.161918513785 Henry Cohn, 2026, needs more optimization.
23 208 0.161983171785 Henry Cohn, 2026, needs more optimization.
23 209 0.164066346824 Henry Cohn, 2026, needs more optimization.
23 210 0.165089958698 Henry Cohn, 2026, needs more optimization.
23 211 0.165544296123 Henry Cohn, 2026, needs more optimization.
23 212 0.166161680908 Henry Cohn, 2026, needs more optimization.
23 213 0.166496194617 Henry Cohn, 2026, needs more optimization.
23 214 0.166612269397 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 0.168170313999 Henry Cohn, 2026, needs more optimization.
23 280 0.174251763047 Henry Cohn, 2026, needs more optimization.
23 281 0.178781002297 Henry Cohn, 2026, needs more optimization.
23 282 0.181998777322 Henry Cohn, 2026, needs more optimization.
23 283 0.183346566557 Henry Cohn, 2026, needs more optimization.
23 284 0.185752191682 Henry Cohn, 2026, needs more optimization.
23 285 0.186070195929 Henry Cohn, 2026, needs more optimization.
23 286 0.187611047821 Henry Cohn, 2026, needs more optimization.
23 287 0.188088289047 Henry Cohn, 2026, needs more optimization.
23 288 0.188368553482 Henry Cohn, 2026, needs more optimization.
23 289 0.189243626085 Henry Cohn, 2026, needs more optimization.
23 290 0.189397082690 Henry Cohn, 2026, needs more optimization.
23 291 0.189520800554 Henry Cohn, 2026, needs more optimization.
23 292 0.189597957975 Henry Cohn, 2026, needs more optimization.
23 293 0.189645727874 Henry Cohn, 2026, needs more optimization.
23 294 0.189662794105 Henry Cohn, 2026, needs more optimization.
23 295 0.189662879157 Henry Cohn, 2026, needs more optimization.
23 296 0.189663473988 Henry Cohn, 2026, needs more optimization.
23 297 0.189664904675 Henry Cohn, 2026, needs more optimization.
23 298 0.189665087048 Henry Cohn, 2026, needs more optimization.
23 299 0.189665226652 Henry Cohn, 2026, needs more optimization.
23 300 0.189665231150 Henry Cohn, 2026, needs more optimization.
23 301 0.190667965673 Henry Cohn, 2026, needs more optimization.
23 302 0.193085454420 Henry Cohn, 2026, needs more optimization.
23 303 0.194195758554 Henry Cohn, 2026, needs more optimization.
23 304 0.196079153823 Henry Cohn, 2026, needs more optimization.
23 305 0.196888769510 Henry Cohn, 2026, needs more optimization.
23 306 0.197761366734 Henry Cohn, 2026, needs more optimization.
23 307 0.198657692694 Henry Cohn, 2026, needs more optimization.
23 308 0.199133005867 Henry Cohn, 2026, needs more optimization.
23 309 0.199285096240 Henry Cohn, 2026, needs more optimization.
23 552* 0.2 P. Delsarte, J. M. Goethals, and J. J. Seidel, Spherical codes and designs, Geometriae Dedicata 6 (1977), 363–388, doi:10.1007/bf03187604; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421.
5⁢x−1
23 553 0.232851959963 Henry Cohn, 2026, needs more optimization.
23 554 0.235339459922 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 0.238112444674 Orthogonal union of 558 points in 22 dimensions and 2 points in 1 dimension.
23 562 0.238348613777 Henry Cohn, 2026, needs more optimization.
23 563 0.238386184838 Henry Cohn, 2026, needs more optimization.
23 566 0.239408123987 Henry Cohn, 2026, needs more optimization.
23 572 0.239576682166 Henry Cohn, 2026, needs more optimization.
23 573 0.239955607731 Henry Cohn, 2026, needs more optimization.
23 574 0.240237424792 Henry Cohn, 2026, needs more optimization.
23 575 0.241465824705 Henry Cohn, 2026, needs more optimization.
23 577 0.242398923811 Henry Cohn, 2026, needs more optimization.
23 578 0.243386756754 Henry Cohn, 2026, needs more optimization.
23 579 0.244065103387 Henry Cohn, 2026, needs more optimization.
23 581 0.244427256810 Henry Cohn, 2026, needs more optimization.
23 582 0.245122938757 Henry Cohn, 2026, needs more optimization.
23 583 0.245382720090 Henry Cohn, 2026, needs more optimization.
23 584 0.245723054210 Henry Cohn, 2026, needs more optimization.
23 588 0.246217617047 Henry Cohn, 2026, needs more optimization.
23 589 0.246326002450 Henry Cohn, 2026, needs more optimization.
23 590 0.246356425736 Henry Cohn, 2026, needs more optimization.
23 592 0.246656691266 Henry Cohn, 2026, needs more optimization.
23 593 0.247275427854 Henry Cohn, 2026, needs more optimization.
23 594 0.247298348283 Henry Cohn, 2026, needs more optimization.
23 595 0.247630112221 Henry Cohn, 2026, needs more optimization.
23 596 0.247831038018 Henry Cohn, 2026, needs more optimization.
23 597 0.248039640898 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 0.249024295181 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 0.249927304977 Henry Cohn, 2026, needs more optimization.
23 894 0.25 Henry Cohn, 2026.
4⁢x−1
23 895 0.251368084213 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 0.047563041303 Henry Cohn, 2026, needs more optimization.
24 57 0.053295300087 Henry Cohn, 2026, needs more optimization.
24 58 0.054367446903 Henry Cohn, 2026, needs more optimization.
24 59 0.057903810057 Henry Cohn, 2026.
24 60 0.061561862472 Henry Cohn, 2026, needs more optimization.
24 61 0.064594321339 Henry Cohn, 2026, needs more optimization.
24 62 0.065400650416 Henry Cohn, 2026, needs more optimization.
24 63 0.065859029129 Henry Cohn, 2026, needs more optimization.
24 64 0.065897906912 Henry Cohn, 2026, needs more optimization.
24 65 0.066587690949 Henry Cohn, 2026, needs more optimization.
24 66 0.068180518550 Henry Cohn, 2026, needs more optimization.
24 67 0.070763242116 Henry Cohn, 2026, needs more optimization.
24 68 0.072116568734 Henry Cohn, 2026, needs more optimization.
24 69 0.073247208238 Henry Cohn, 2026, needs more optimization.
24 70 0.076553864650 Henry Cohn, 2026, needs more optimization.
24 71 0.076921819102 Henry Cohn, 2026, needs more optimization.
24 72 0.077412163760 Henry Cohn, 2026, needs more optimization.
24 73 0.077740721430 Henry Cohn, 2026, needs more optimization.
24 74 0.077908661685 Henry Cohn, 2026, needs more optimization.
24 75 0.078509915326 Henry Cohn, 2026, needs more optimization.
24 76 0.078850061999 Henry Cohn, 2026, needs more optimization.
24 77 0.081784626344 Henry Cohn, 2026, needs more optimization.
24 78 0.082774174913 Henry Cohn, 2026, needs more optimization.
24 79 0.083242091361 Henry Cohn, 2026, needs more optimization.
24 80 0.083247406439 Henry Cohn, 2026, needs more optimization.
24 81 0.083292973669 Henry Cohn, 2026, needs more optimization.
24 83 0.083316966042 Henry Cohn, 2026, needs more optimization.
24 84 0.083328318494 Henry Cohn, 2026, needs more optimization.
24 85 0.083328479334 Henry Cohn, 2026, needs more optimization.
24 86 0.086249099522 Henry Cohn, 2026, needs more optimization.
24 87 0.088155666895 Henry Cohn, 2026, needs more optimization.
24 88 0.089790539195 Henry Cohn, 2026, needs more optimization.
24 89 0.090234714713 Henry Cohn, 2026, needs more optimization.
24 90 0.090581638338 Henry Cohn, 2026, needs more optimization.
24 91 0.090735899874 Henry Cohn, 2026, needs more optimization.
24 92 0.090834706154 Henry Cohn, 2026, needs more optimization.
24 93 0.090893763530 Henry Cohn, 2026, needs more optimization.
24 97 0.090909090540 Henry Cohn, 2026, needs more optimization.
24 98 0.090909090562 Henry Cohn, 2026, needs more optimization.
24 104 0.090909090572 Henry Cohn, 2026, needs more optimization.
24 105 0.091498626709 Henry Cohn, 2026, needs more optimization.
24 106 0.095233377765 Henry Cohn, 2026, needs more optimization.
24 107 0.100984753572 Henry Cohn, 2026, needs more optimization.
24 108 0.105659350879 Henry Cohn, 2026, needs more optimization.
24 109 0.111057104209 Henry Cohn, 2026, needs more optimization.
24 110 0.111071980173 Henry Cohn, 2026, needs more optimization.
24 111 0.111089896145 Henry Cohn, 2026, needs more optimization.
24 118 0.111099565428 Henry Cohn, 2025, needs more optimization.
24 120 0.111111404425 Henry Cohn, 2026, needs more optimization.
24 121 0.111111857060 Henry Cohn, 2026, needs more optimization.
24 122 0.112368301532 Henry Cohn, 2026, needs more optimization.
24 123 0.116166524744 Henry Cohn, 2026, needs more optimization.
24 124 0.117892571871 Henry Cohn, 2026, needs more optimization.
24 125 0.122807017544 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
57⁢x−7
24 126 0.131755624893 Henry Cohn, 2026, needs more optimization.
24 128 0.131763931510 Henry Cohn, 2026, needs more optimization.
24 129 0.131770782935 Henry Cohn, 2026, needs more optimization.
24 130 0.131772891330 Henry Cohn, 2026, needs more optimization.
24 131 0.131776134525 Henry Cohn, 2026, needs more optimization.
24 132 0.131778295980 Henry Cohn, 2026, needs more optimization.
24 133 0.131787571401 Henry Cohn, 2026, needs more optimization.
24 134 0.131788299896 Henry Cohn, 2026, needs more optimization.
24 135 0.131963226856 Henry Cohn, 2026, needs more optimization.
24 136 0.132226459959 Henry Cohn, 2026, needs more optimization.
24 137 0.132941114869 Henry Cohn, 2026, needs more optimization.
24 138 0.133282124409 Henry Cohn, 2026, needs more optimization.
24 139 0.134287650695 Henry Cohn, 2026, needs more optimization.
24 140 0.134484360339 Henry Cohn, 2026, needs more optimization.
24 141 0.134899501162 Henry Cohn, 2026, needs more optimization.
24 142 0.135004142861 Henry Cohn, 2026, needs more optimization.
24 143 0.135119483064 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 0.135136896745 Henry Cohn, 2026, needs more optimization.
24 151 0.135174335576 Henry Cohn, 2026, needs more optimization.
24 152 0.135430750874 Henry Cohn, 2026, needs more optimization.
24 153 0.136301751656 Henry Cohn, 2026, needs more optimization.
24 154 0.137492458317 Henry Cohn, 2026, needs more optimization.
24 155 0.137719553575 Henry Cohn, 2026, needs more optimization.
24 157 0.142857107090 Henry Cohn, 2026, needs more optimization.
24 158 0.142857107582 Henry Cohn, 2026, needs more optimization.
24 160 0.142857111030 Henry Cohn, 2026, needs more optimization.
24 161 0.142857112577 Henry Cohn, 2026, needs more optimization.
24 162 0.142857116323 Henry Cohn, 2026, needs more optimization.
24 163 0.142857116337 Henry Cohn, 2026, needs more optimization.
24 164 0.142857116418 Henry Cohn, 2026, needs more optimization.
24 166 0.142857121940 Henry Cohn, 2026, needs more optimization.
24 167 0.142857122812 Henry Cohn, 2026, needs more optimization.
24 168 0.142857138924 Henry Cohn, 2026, needs more optimization.
24 169 0.142857139013 Henry Cohn, 2026, needs more optimization.
24 172 0.142857140416 Henry Cohn, 2026, needs more optimization.
24 173 0.142857171601 Henry Cohn, 2026, needs more optimization.
24 174 0.142857172713 Henry Cohn, 2026, needs more optimization.
24 175 0.143487677049 Henry Cohn, 2026, needs more optimization.
24 176 0.146010723797 Henry Cohn, 2026, needs more optimization.
24 177 0.146025328521 Henry Cohn, 2026, needs more optimization.
24 178 0.146068837176 Henry Cohn, 2026, needs more optimization.
24 179 0.146648909400 Henry Cohn, 2026, needs more optimization.
24 180 0.149030383692 Henry Cohn, 2026, needs more optimization.
24 181 0.151587906469 Henry Cohn, 2026, needs more optimization.
24 182 0.152665326678 Henry Cohn, 2026, needs more optimization.
24 183 0.153482570694 Henry Cohn, 2026, needs more optimization.
24 184 0.154898548903 Henry Cohn, 2026, needs more optimization.
24 185 0.155544254661 Henry Cohn, 2026, needs more optimization.
24 186 0.156465213766 Henry Cohn, 2026, needs more optimization.
24 187 0.157763896447 Henry Cohn, 2026, needs more optimization.
24 188 0.158909419708 Henry Cohn, 2026, needs more optimization.
24 189 0.159707269316 Henry Cohn, 2026, needs more optimization.
24 190 0.160152346221 Henry Cohn, 2026, needs more optimization.
24 191 0.160891788539 Henry Cohn, 2026, needs more optimization.
24 192 0.161222580762 Henry Cohn, 2026, needs more optimization.
24 193 0.161832291993 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
24 206 0.161904779055 Henry Cohn, 2026, needs more optimization.
24 207 0.161904779270 Henry Cohn, 2026, needs more optimization.
24 208 0.161904789474 Henry Cohn, 2026, needs more optimization.
24 209 0.161904789522 Henry Cohn, 2026, needs more optimization.
24 210 0.161904789666 Henry Cohn, 2026, needs more optimization.
24 212 0.161904799606 Henry Cohn, 2026, needs more optimization.
24 213 0.161905360980 Henry Cohn, 2026, needs more optimization.
24 214 0.162019999282 Henry Cohn, 2026, needs more optimization.
24 215 0.162171552532 Henry Cohn, 2026, needs more optimization.
24 216 0.163090002458 Henry Cohn, 2026, needs more optimization.
24 217 0.163195047007 Henry Cohn, 2026, needs more optimization.
24 218 0.164193523326 Henry Cohn, 2026, needs more optimization.
24 219 0.164935001029 Henry Cohn, 2026, needs more optimization.
24 220 0.165068299357 Henry Cohn, 2026, needs more optimization.
24 221 0.165683545161 Henry Cohn, 2026, needs more optimization.
24 222 0.165904998408 Henry Cohn, 2026, needs more optimization.
24 223 0.166301059314 Henry Cohn, 2026, needs more optimization.
24 224 0.166487438988 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 0.166666872447 Henry Cohn, 2026, needs more optimization.
24 283 0.166666872448 Henry Cohn, 2026, needs more optimization.
24 284 0.168072917935 Henry Cohn, 2026, needs more optimization.
24 285 0.170028130302 Henry Cohn, 2026, needs more optimization.
24 286 0.171815894222 Henry Cohn, 2026, needs more optimization.
24 287 0.174972659276 Henry Cohn, 2026, needs more optimization.
24 288 0.177034908162 Henry Cohn, 2026, needs more optimization.
24 289 0.179253538548 Henry Cohn, 2026, needs more optimization.
24 290 0.181710552910 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 0.183144990435 Henry Cohn, 2026, needs more optimization.
24 315 0.187003579352 Henry Cohn, 2026, needs more optimization.
24 316 0.190933881995 Henry Cohn, 2026, needs more optimization.
24 317 0.191622833484 Henry Cohn, 2026, needs more optimization.
24 318 0.192065153925 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 0.200456528216 Henry Cohn, 2026.
39⁢x2+72⁢x−16
24 556 0.201245500080 Henry Cohn, 2026, needs more optimization.
24 557 0.206715145855 Henry Cohn, 2026, needs more optimization.
24 558 0.213707298177 Henry Cohn, 2026, needs more optimization.
24 559 0.219381709126 Henry Cohn, 2026, needs more optimization.
24 560 0.220707832127 Henry Cohn, 2026, needs more optimization.
24 561 0.222463863141 Henry Cohn, 2026, needs more optimization.
24 562 0.222828512031 Henry Cohn, 2026, needs more optimization.
24 563 0.224231247807 Henry Cohn, 2026, needs more optimization.
24 564 0.225406721847 Henry Cohn, 2026, needs more optimization.
24 565 0.226608110055 Henry Cohn, 2026, needs more optimization.
24 566 0.228284591565 Henry Cohn, 2026, needs more optimization.
24 567 0.229324276349 Henry Cohn, 2026, needs more optimization.
24 568 0.230560316408 Henry Cohn, 2026, needs more optimization.
24 569 0.231747959857 Henry Cohn, 2026, needs more optimization.
24 570 0.233353109924 Henry Cohn, 2026, needs more optimization.
24 571 0.234121767211 Henry Cohn, 2026, needs more optimization.
24 572 0.234868068236 Henry Cohn, 2026, needs more optimization.
24 577 0.234996896379 Henry Cohn, 2026, needs more optimization.
24 579 0.235336452412 Henry Cohn, 2026, needs more optimization.
24 580 0.236927305760 Henry Cohn, 2026, needs more optimization.
24 584 0.237297233095 Henry Cohn, 2026, needs more optimization.
24 585 0.237988702371 Henry Cohn, 2026, needs more optimization.
24 586 0.238472704601 Henry Cohn, 2026, needs more optimization.
24 587 0.239033519400 Henry Cohn, 2026, needs more optimization.
24 591 0.240049942347 Henry Cohn, 2026, needs more optimization.
24 593 0.240096235956 Henry Cohn, 2026, needs more optimization.
24 594 0.241504327560 Henry Cohn, 2026, needs more optimization.
24 595 0.241561717253 Henry Cohn, 2026, needs more optimization.
24 596 0.241664552145 Henry Cohn, 2026, needs more optimization.
24 598 0.241843421557 Henry Cohn, 2026, needs more optimization.
24 599 0.242151175489 Henry Cohn, 2026, needs more optimization.
24 605 0.243511996169 Henry Cohn, 2026, needs more optimization.
24 607 0.245122215658 Henry Cohn, 2026, needs more optimization.
24 610 0.245122363890 Henry Cohn, 2026, needs more optimization.
24 612 0.245360690580 Henry Cohn, 2026, needs more optimization.
24 613 0.245643639818 Henry Cohn, 2026, needs more optimization.
24 614 0.246067944057 Henry Cohn, 2026, needs more optimization.
24 615 0.246292031874 Henry Cohn, 2026, needs more optimization.
24 616 0.246481473685 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 0.247767786463 Henry Cohn, 2026, needs more optimization.
24 620 0.247913306838 Henry Cohn, 2026, needs more optimization.
24 621 0.248252160001 Henry Cohn, 2026, needs more optimization.
24 622 0.248438137982 Henry Cohn, 2026, needs more optimization.
24 623 0.248635670255 Henry Cohn, 2026, needs more optimization.
24 624 0.249080033754 Henry Cohn, 2026, needs more optimization.
24 625 0.249363000813 Henry Cohn, 2026, needs more optimization.
24 626 0.249646168474 Henry Cohn, 2026, needs more optimization.
24 628 0.249815974879 Henry Cohn, 2026, needs more optimization.
24 629 0.249987117285 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 0.251368084213 Orthogonal union of 895 points in 23 dimensions and 2 points in 1 dimension.
24 910 0.252512722583 Henry Cohn, 2026, needs more optimization.
24 917 0.261217665124 Henry Cohn, 2026, needs more optimization.
24 924 0.261217665129 Henry Cohn, 2026, needs more optimization.
24 925 0.261363854340 Henry Cohn, 2026, needs more optimization.
24 926 0.262130915543 Henry Cohn, 2026, needs more optimization.
24 928 0.263132256238 Henry Cohn, 2026, needs more optimization.
24 929 0.263919868299 Henry Cohn, 2026, needs more optimization.
24 930 0.265028913117 Henry Cohn, 2026, needs more optimization.
24 933 0.265642477021 Henry Cohn, 2026, needs more optimization.
24 934 0.266687976774 Henry Cohn, 2026, needs more optimization.
24 935 0.267189238314 Henry Cohn, 2026, needs more optimization.
24 936 0.267842298155 Henry Cohn, 2026, needs more optimization.
24 937 0.268216432142 Henry Cohn, 2026, needs more optimization.
24 938 0.268497175455 Henry Cohn, 2026, needs more optimization.
24 939 0.269340570473 Henry Cohn, 2026, needs more optimization.
24 940 0.269681534261 Henry Cohn, 2026, needs more optimization.
24 941 0.269935983660 Henry Cohn, 2026, needs more optimization.
24 942 0.270553515101 Henry Cohn, 2026, needs more optimization.
24 943 0.270972931442 Henry Cohn, 2026, needs more optimization.
24 944 0.271416308517 Henry Cohn, 2026, needs more optimization.
24 945 0.272249995975 Henry Cohn, 2026, needs more optimization.
24 946 0.272448652271 Henry Cohn, 2026, needs more optimization.
24 1024 0.272727272728 Code with 1024 points in 22 dimensions.
11⁢x−3
24 196560* 0.5 J. Leech, Notes on sphere packings, Canadian J. Math. 19 (1967), 251–267, doi:10.4153/CJM-1967-017-0; V. I. Levenšteĭn, On bounds for packings in n-dimensional Euclidean space (Russian), Dokl. Akad. Nauk SSSR 245 (1979), 1299–1303, English translation in Soviet Math. Dokl. 20 (1979), 417–421; A. M. Odlyzko and N. J. A. Sloane, New bounds on the number of unit spheres that can touch a unit sphere in n dimensions, J. Combin. Theory Ser. A 26 (1979), 210–214, doi:10.1016/0097-3165(79)90074-8.
2⁢x−1
25 51 0.031729360276 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
13225⁢x3−625⁢x2−25⁢x+1
25 52 0.037068271283 Henry Cohn, 2025.
25 55 0.04 Henry Cohn, 2026.
25⁢x−1
25 56 0.046433703861 Henry Cohn, 2025, needs more optimization.
25 57 0.046863894921 Henry Cohn, 2025.
25 58 0.046863920964 Henry Cohn, 2025.
25 59 0.051394584232 Henry Cohn, 2024.
25 60 0.052966771692 Henry Cohn, 2026, needs more optimization.
25 61 0.056074458805 Henry Cohn, 2026, needs more optimization.
25 62 0.060614046765 Henry Cohn, 2026, needs more optimization.
25 63 0.062393204113 Henry Cohn, 2026, needs more optimization.
25 64 0.064224592903 Henry Cohn, 2026, needs more optimization.
25 65 0.065052412053 Henry Cohn, 2026, needs more optimization.
25 66 0.065052412054 Henry Cohn, 2026, needs more optimization.
25 67 0.066213050219 Henry Cohn, 2026, needs more optimization.
25 68 0.066469737585 Henry Cohn, 2026, needs more optimization.
25 69 0.068628304595 Henry Cohn, 2026, needs more optimization.
25 70 0.071056156195 Henry Cohn, 2026, needs more optimization.
25 71 0.071832239550 Henry Cohn, 2026, needs more optimization.
25 72 0.073357367259 Henry Cohn, 2026, needs more optimization.
25 73 0.076172581623 Henry Cohn, 2026, needs more optimization.
25 74 0.076833417592 Henry Cohn, 2026, needs more optimization.
25 76 0.076923161283 Henry Cohn, 2026, needs more optimization.
25 77 0.077470279337 Henry Cohn, 2026, needs more optimization.
25 78 0.077920644306 Henry Cohn, 2026, needs more optimization.
25 79 0.078551974254 Henry Cohn, 2026, needs more optimization.
25 80 0.080840286627 Henry Cohn, 2026, needs more optimization.
25 81 0.082232650014 Henry Cohn, 2026, needs more optimization.
25 82 0.082621203638 Henry Cohn, 2026, needs more optimization.
25 83 0.082980524786 Henry Cohn, 2026, needs more optimization.
25 85 0.083095965811 Henry Cohn, 2026, needs more optimization.
25 86 0.083271833347 Henry Cohn, 2026, needs more optimization.
25 87 0.083304914428 Henry Cohn, 2026, needs more optimization.
25 88 0.083317142846 Henry Cohn, 2026, needs more optimization.
25 89 0.085175114088 Henry Cohn, 2026, needs more optimization.
25 90 0.087169375561 Henry Cohn, 2026, needs more optimization.
25 91 0.087278836679 Henry Cohn, 2026, needs more optimization.
25 92 0.088771795091 Henry Cohn, 2026, needs more optimization.
25 93 0.089638353276 Henry Cohn, 2026, needs more optimization.
25 94 0.089925041041 Henry Cohn, 2026, needs more optimization.
25 95 0.090474803165 Henry Cohn, 2026, needs more optimization.
25 96 0.090646506699 Henry Cohn, 2026, needs more optimization.
25 97 0.090830860718 Henry Cohn, 2026, needs more optimization.
25 98 0.090837311876 Henry Cohn, 2026, needs more optimization.
25 99 0.090896960218 Henry Cohn, 2026, needs more optimization.
25 100 0.090907038701 Henry Cohn, 2026, needs more optimization.
25 101 0.090908872557 Henry Cohn, 2026, needs more optimization.
25 104 0.090909090571 Henry Cohn, 2026, needs more optimization.
25 106 0.090909090572 Orthogonal union of 104 points in 24 dimensions and 2 points in 1 dimension.
25 107 0.090909472483 Henry Cohn, 2026, needs more optimization.
25 108 0.090911537399 Henry Cohn, 2026, needs more optimization.
25 109 0.095542644965 Henry Cohn, 2026, needs more optimization.
25 110 0.099775964507 Henry Cohn, 2026, needs more optimization.
25 111 0.102647688133 Henry Cohn, 2026, needs more optimization.
25 117 0.105319726475 Henry Cohn, 2026.
375⁢x2−30⁢x−1
25 118 0.107225148391 Henry Cohn, 2026, needs more optimization.
25 119 0.108659079180 Henry Cohn, 2026, needs more optimization.
25 120 0.108684698063 Henry Cohn, 2026, needs more optimization.
25 121 0.109313067329 Henry Cohn, 2026, needs more optimization.
25 122 0.109589580066 Henry Cohn, 2026, needs more optimization.
25 123 0.111103656837 Henry Cohn, 2026, needs more optimization.
25 124 0.111106076289 Henry Cohn, 2026, needs more optimization.
25 125 0.111109898207 Henry Cohn, 2026, needs more optimization.
25 126 0.111126206430 Henry Cohn, 2026, needs more optimization.
25 127 0.111143895763 Henry Cohn, 2026, needs more optimization.
25 128 0.111341725336 Henry Cohn, 2026, needs more optimization.
25 129 0.117080391727 Henry Cohn, 2026, needs more optimization.
25 130 0.120012444105 Henry Cohn, 2026, needs more optimization.
25 131 0.121764571067 Henry Cohn, 2026, needs more optimization.
25 132 0.123583659410 Henry Cohn, 2026, needs more optimization.
25 133 0.124985789969 Henry Cohn, 2026, needs more optimization.
25 134 0.126246752801 Henry Cohn, 2026, needs more optimization.
25 135 0.128192665800 Henry Cohn, 2026, needs more optimization.
25 136 0.129733344697 Henry Cohn, 2026, needs more optimization.
25 137 0.131718875164 Henry Cohn, 2026, needs more optimization.
25 138 0.131763224153 Henry Cohn, 2026, needs more optimization.
25 139 0.131778131298 Henry Cohn, 2026, needs more optimization.
25 140 0.131785392225 Henry Cohn, 2026, needs more optimization.
25 141 0.131870385323 Henry Cohn, 2026, needs more optimization.
25 142 0.132313713455 Henry Cohn, 2026, needs more optimization.
25 143 0.132968029606 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 0.135174273044 Henry Cohn, 2026, needs more optimization.
25 158 0.137173808345 Henry Cohn, 2026, needs more optimization.
25 159 0.138178885256 Henry Cohn, 2026, needs more optimization.
25 160 0.140562527716 Henry Cohn, 2026, needs more optimization.
25 161 0.141385145507 Henry Cohn, 2026, needs more optimization.
25 162 0.142857111030 Orthogonal union of 160 points in 24 dimensions and 2 points in 1 dimension.
25 163 0.142857111964 Henry Cohn, 2026, needs more optimization.
25 166 0.142857116300 Henry Cohn, 2026, needs more optimization.
25 168 0.142857121940 Orthogonal union of 166 points in 24 dimensions and 2 points in 1 dimension.
25 169 0.142857122415 Henry Cohn, 2026, needs more optimization.
25 170 0.142857138919 Henry Cohn, 2026, needs more optimization.
25 171 0.142857139012 Henry Cohn, 2026, needs more optimization.
25 174 0.142857140416 Orthogonal union of 172 points in 24 dimensions and 2 points in 1 dimension.
25 175 0.142857171601 Orthogonal union of 173 points in 24 dimensions and 2 points in 1 dimension.
25 176 0.142857172713 Orthogonal union of 174 points in 24 dimensions and 2 points in 1 dimension.
25 177 0.142861253435 Henry Cohn, 2026, needs more optimization.
25 178 0.142890511016 Henry Cohn, 2026, needs more optimization.
25 179 0.142939517490 Henry Cohn, 2026, needs more optimization.
25 180 0.143255116467 Henry Cohn, 2026, needs more optimization.
25 181 0.144736712194 Henry Cohn, 2026, needs more optimization.
25 182 0.144744271264 Henry Cohn, 2026, needs more optimization.
25 183 0.145949224073 Henry Cohn, 2026, needs more optimization.
25 184 0.147691671806 Henry Cohn, 2026, needs more optimization.
25 185 0.148688724530 Henry Cohn, 2026, needs more optimization.
25 186 0.148817861641 Henry Cohn, 2026, needs more optimization.
25 187 0.149333826929 Henry Cohn, 2026, needs more optimization.
25 188 0.150972175226 Henry Cohn, 2026, needs more optimization.
25 189 0.151833545819 Henry Cohn, 2026, needs more optimization.
25 190 0.152874036711 Henry Cohn, 2026, needs more optimization.
25 191 0.153285676269 Henry Cohn, 2026, needs more optimization.
25 192 0.153471146612 Henry Cohn, 2026, needs more optimization.
25 193 0.153619847503 Henry Cohn, 2026, needs more optimization.
25 194 0.154412238373 Henry Cohn, 2026, needs more optimization.
25 195 0.156268962778 Henry Cohn, 2026, needs more optimization.
25 196 0.156990514522 Henry Cohn, 2026, needs more optimization.
25 197 0.157155196114 Henry Cohn, 2026, needs more optimization.
25 198 0.158027703233 Henry Cohn, 2026, needs more optimization.
25 199 0.158997250260 Henry Cohn, 2026, needs more optimization.
25 200 0.159767802234 Henry Cohn, 2026, needs more optimization.
25 201 0.160346417334 Henry Cohn, 2026, needs more optimization.
25 202 0.161134465416 Henry Cohn, 2026, needs more optimization.
25 203 0.161696845710 Henry Cohn, 2026, needs more optimization.
25 204 0.161838661841 Henry Cohn, 2026, needs more optimization.
25 205 0.161876321830 Henry Cohn, 2026, needs more optimization.
25 206 0.161883413318 Henry Cohn, 2026, needs more optimization.
25 207 0.161891104824 Henry Cohn, 2026, needs more optimization.
25 208 0.161891107389 Henry Cohn, 2026, needs more optimization.
25 209 0.161897260397 Henry Cohn, 2026, needs more optimization.
25 210 0.161900216148 Henry Cohn, 2026, needs more optimization.
25 211 0.161901321455 Henry Cohn, 2026, needs more optimization.
25 212 0.161903900730 Henry Cohn, 2026, needs more optimization.
25 214 0.161904799606 Orthogonal union of 212 points in 24 dimensions and 2 points in 1 dimension.
25 215 0.161905360980 Orthogonal union of 213 points in 24 dimensions and 2 points in 1 dimension.
25 216 0.161908024317 Henry Cohn, 2026, needs more optimization.
25 217 0.161914413347 Henry Cohn, 2026, needs more optimization.
25 218 0.161917195112 Henry Cohn, 2026, needs more optimization.
25 219 0.161927442210 Henry Cohn, 2026, needs more optimization.
25 220 0.161927444588 Henry Cohn, 2026, needs more optimization.
25 221 0.161932081258 Henry Cohn, 2026, needs more optimization.
25 222 0.161950279655 Henry Cohn, 2026, needs more optimization.
25 223 0.162278421556 Henry Cohn, 2026, needs more optimization.
25 224 0.162666500878 Henry Cohn, 2026, needs more optimization.
25 225 0.162919249089 Henry Cohn, 2026, needs more optimization.
25 226 0.163628452053 Henry Cohn, 2026, needs more optimization.
25 227 0.164362396406 Henry Cohn, 2026, needs more optimization.
25 228 0.164708885217 Henry Cohn, 2026, needs more optimization.
25 229 0.165196062256 Henry Cohn, 2026, needs more optimization.
25 230 0.165483602801 Henry Cohn, 2026, needs more optimization.
25 231 0.165907314484 Henry Cohn, 2026, needs more optimization.
25 232 0.166060773901 Henry Cohn, 2026, needs more optimization.
25 233 0.166317087723 Henry Cohn, 2026, needs more optimization.
25 234 0.166434704957 Henry Cohn, 2026, needs more optimization.
25 235 0.166531468921 Henry Cohn, 2026, needs more optimization.
25 236 0.166586338986 Henry Cohn, 2026, needs more optimization.
25 237 0.166626155932 Henry Cohn, 2026, needs more optimization.
25 282 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 4 points in 2 dimensions.
6⁢x−1
25 285 0.166666872445 Henry Cohn, 2026, needs more optimization.
25 286 0.166677862039 Henry Cohn, 2026, needs more optimization.
25 287 0.166678377381 Henry Cohn, 2026, needs more optimization.
25 288 0.166679117388 Henry Cohn, 2026, needs more optimization.
25 289 0.166687310500 Henry Cohn, 2026, needs more optimization.
25 290 0.166787952155 Henry Cohn, 2026, needs more optimization.
25 291 0.169166863576 Henry Cohn, 2026, needs more optimization.
25 292 0.169498696948 Henry Cohn, 2026, needs more optimization.
25 293 0.170021857269 Henry Cohn, 2026, needs more optimization.
25 294 0.172096470058 Henry Cohn, 2026, needs more optimization.
25 295 0.173797855168 Henry Cohn, 2026, needs more optimization.
25 296 0.175980124829 Henry Cohn, 2026, needs more optimization.
25 297 0.177359572729 Henry Cohn, 2026, needs more optimization.
25 298 0.178958657825 Henry Cohn, 2026, needs more optimization.
25 299 0.180535568651 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 0.181821589191 Henry Cohn, 2026, needs more optimization.
25 317 0.181824176483 Henry Cohn, 2026, needs more optimization.
25 318 0.181825523564 Henry Cohn, 2026, needs more optimization.
25 319 0.181832168515 Henry Cohn, 2026, needs more optimization.
25 320 0.181834552272 Henry Cohn, 2026, needs more optimization.
25 321 0.182787779544 Henry Cohn, 2026, needs more optimization.
25 322 0.184639459982 Henry Cohn, 2026, needs more optimization.
25 323 0.185637241294 Henry Cohn, 2026, needs more optimization.
25 324 0.186502611117 Henry Cohn, 2026, needs more optimization.
25 325 0.187404986290 Henry Cohn, 2026, needs more optimization.
25 326 0.188494903896 Henry Cohn, 2026, needs more optimization.
25 327 0.190329502835 Henry Cohn, 2026, needs more optimization.
25 328 0.191407721159 Henry Cohn, 2026, needs more optimization.
25 329 0.192558786029 Henry Cohn, 2026, needs more optimization.
25 332 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 2 points in 1 dimension.
31⁢x−6
25 333 0.193558304535 Henry Cohn, 2026, needs more optimization.
25 334 0.193558515467 Henry Cohn, 2026, needs more optimization.
25 335 0.193913174741 Henry Cohn, 2026, needs more optimization.
25 336 0.194409107343 Henry Cohn, 2026, needs more optimization.
25 337 0.195913570209 Henry Cohn, 2026, needs more optimization.
25 338 0.197357470976 Henry Cohn, 2026, needs more optimization.
25 339 0.198279270261 Henry Cohn, 2026, needs more optimization.
25 340 0.198981574399 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.
25 562 0.200360932197 Henry Cohn, 2026, needs more optimization.
25 563 0.200682527169 Henry Cohn, 2026, needs more optimization.
25 564 0.201503264503 Henry Cohn, 2026, needs more optimization.
25 565 0.203941843367 Henry Cohn, 2026, needs more optimization.
25 566 0.207273992508 Henry Cohn, 2026, needs more optimization.
25 567 0.210103866214 Henry Cohn, 2026, needs more optimization.
25 568 0.212130131864 Henry Cohn, 2026, needs more optimization.
25 569 0.214581788784 Henry Cohn, 2026, needs more optimization.
25 570 0.216720833110 Henry Cohn, 2026, needs more optimization.
25 571 0.218232230827 Henry Cohn, 2026, needs more optimization.
25 572 0.219804327688 Henry Cohn, 2026, needs more optimization.
25 573 0.221601749599 Henry Cohn, 2026, needs more optimization.
25 574 0.222663462008 Henry Cohn, 2026, needs more optimization.
25 575 0.224156996905 Henry Cohn, 2026, needs more optimization.
25 576 0.225072231650 Henry Cohn, 2026, needs more optimization.
25 577 0.226703519329 Henry Cohn, 2026, needs more optimization.
25 578 0.227109598382 Henry Cohn, 2026, needs more optimization.
25 579 0.228066547407 Henry Cohn, 2026, needs more optimization.
25 580 0.228606600234 Henry Cohn, 2026, needs more optimization.
25 582 0.229796238320 Henry Cohn, 2026, needs more optimization.
25 583 0.231249070986 Henry Cohn, 2026, needs more optimization.
25 584 0.231972541096 Henry Cohn, 2026, needs more optimization.
25 585 0.232281215846 Henry Cohn, 2026, needs more optimization.
25 586 0.233414506364 Henry Cohn, 2026, needs more optimization.
25 587 0.233721904710 Henry Cohn, 2026, needs more optimization.
25 588 0.234416186521 Henry Cohn, 2026, needs more optimization.
25 589 0.235298272371 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 0.238047650539 Henry Cohn, 2026, needs more optimization.
25 599 0.238510615216 Henry Cohn, 2026, needs more optimization.
25 601 0.238575338270 Henry Cohn, 2026, needs more optimization.
25 606 0.238649157341 Henry Cohn, 2026, needs more optimization.
25 612 0.239388994568 Henry Cohn, 2026, needs more optimization.
25 613 0.240092289842 Henry Cohn, 2026, needs more optimization.
25 616 0.240115267820 Henry Cohn, 2026, needs more optimization.
25 619 0.240526475248 Henry Cohn, 2026, needs more optimization.
25 622 0.241539929322 Henry Cohn, 2026, needs more optimization.
25 623 0.242411285062 Henry Cohn, 2026, needs more optimization.
25 626 0.243102293950 Henry Cohn, 2026, needs more optimization.
25 627 0.248418650146 Henry Cohn, 2026, needs more optimization.
25 630 0.248897931800 Henry Cohn, 2026, needs more optimization.
25 631 0.248975963274 Henry Cohn, 2026, needs more optimization.
25 636 0.249032769364 Henry Cohn, 2026, needs more optimization.
25 637 0.249152174380 Henry Cohn, 2026, needs more optimization.
25 641 0.249307826773 Henry Cohn, 2026, needs more optimization.
25 642 0.249312488919 Henry Cohn, 2026, needs more optimization.
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 0.250037345487 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 0.035747894970 Henry Cohn, 2026, needs more optimization.
26 57 0.04 Orthogonal union of 55 points in 25 dimensions and 2 points in 1 dimension.
25⁢x−1
26 58 0.045550434603 Henry Cohn, 2024.
26 59 0.046163974402 Henry Cohn, 2025.
26 60 0.046456376975 Henry Cohn, 2026, needs more optimization.
26 61 0.049243792037 Henry Cohn, 2026, needs more optimization.
26 62 0.051910677048 Henry Cohn, 2026, needs more optimization.
26 63 0.054428665253 Henry Cohn, 2026, needs more optimization.
26 64 0.056899291427 Henry Cohn, 2026, needs more optimization.
26 65 0.060274304039 Henry Cohn, 2026, needs more optimization.
26 66 0.062099840477 Henry Cohn, 2026, needs more optimization.
26 67 0.063559235386 Henry Cohn, 2026, needs more optimization.
26 68 0.063600411317 Henry Cohn, 2026, needs more optimization.
26 69 0.064916628444 Henry Cohn, 2026, needs more optimization.
26 70 0.065400202062 Henry Cohn, 2026, needs more optimization.
26 71 0.067315893905 Henry Cohn, 2026, needs more optimization.
26 72 0.068297564144 Henry Cohn, 2026, needs more optimization.
26 73 0.070930211069 Henry Cohn, 2026, needs more optimization.
26 74 0.073191111903 Henry Cohn, 2026, needs more optimization.
26 75 0.074028141344 Henry Cohn, 2026, needs more optimization.
26 76 0.075372326349 Henry Cohn, 2026, needs more optimization.
26 77 0.076354800296 Henry Cohn, 2026, needs more optimization.
26 78 0.076864989269 Henry Cohn, 2026, needs more optimization.
26 79 0.076920089044 Henry Cohn, 2026, needs more optimization.
26 80 0.076967637465 Henry Cohn, 2026, needs more optimization.
26 81 0.077577284859 Henry Cohn, 2026, needs more optimization.
26 82 0.077924828163 Henry Cohn, 2026, needs more optimization.
26 83 0.078212605456 Henry Cohn, 2026, needs more optimization.
26 84 0.079371400118 Henry Cohn, 2026, needs more optimization.
26 85 0.081229455540 Henry Cohn, 2026, needs more optimization.
26 86 0.082351600474 Henry Cohn, 2026, needs more optimization.
26 87 0.082763061879 Henry Cohn, 2026, needs more optimization.
26 88 0.082947476349 Henry Cohn, 2026, needs more optimization.
26 89 0.083148916254 Henry Cohn, 2026, needs more optimization.
26 90 0.083216662904 Henry Cohn, 2026, needs more optimization.
26 91 0.083295950601 Henry Cohn, 2026, needs more optimization.
26 92 0.084262077393 Henry Cohn, 2026, needs more optimization.
26 93 0.085534564121 Henry Cohn, 2026, needs more optimization.
26 94 0.086904412986 Henry Cohn, 2026, needs more optimization.
26 95 0.088207119358 Henry Cohn, 2026, needs more optimization.
26 96 0.088414219476 Henry Cohn, 2026, needs more optimization.
26 97 0.089313042237 Henry Cohn, 2026, needs more optimization.
26 98 0.089793227596 Henry Cohn, 2026, needs more optimization.
26 99 0.090058550732 Henry Cohn, 2026, needs more optimization.
26 100 0.090364074883 Henry Cohn, 2026, needs more optimization.
26 101 0.090572450429 Henry Cohn, 2026, needs more optimization.
26 102 0.090686733783 Henry Cohn, 2026, needs more optimization.
26 103 0.090772374883 Henry Cohn, 2026, needs more optimization.
26 104 0.090847260148 Henry Cohn, 2026, needs more optimization.
26 105 0.090867443639 Henry Cohn, 2026, needs more optimization.
26 106 0.090898073286 Henry Cohn, 2026, needs more optimization.
26 108 0.090899908501 Henry Cohn, 2026, needs more optimization.
26 109 0.090904435391 Henry Cohn, 2026, needs more optimization.
26 110 0.090909315688 Henry Cohn, 2026, needs more optimization.
26 111 0.091919143144 Henry Cohn, 2026, needs more optimization.
26 112 0.094492508573 Henry Cohn, 2026, needs more optimization.
26 113 0.097432439227 Henry Cohn, 2026, needs more optimization.
26 114 0.100692911134 Henry Cohn, 2026, needs more optimization.
26 120 0.103125332235 Henry Cohn, 2026.
191⁢x2−10⁢x−1
26 121 0.103746590293 Henry Cohn, 2026, needs more optimization.
26 122 0.105414644930 Henry Cohn, 2026, needs more optimization.
26 123 0.106265323074 Henry Cohn, 2026, needs more optimization.
26 124 0.107120793359 Henry Cohn, 2026, needs more optimization.
26 125 0.107687912388 Henry Cohn, 2026, needs more optimization.
26 126 0.108579416894 Henry Cohn, 2026, needs more optimization.
26 127 0.109103950369 Henry Cohn, 2026, needs more optimization.
26 128 0.111064854283 Henry Cohn, 2026, needs more optimization.
26 129 0.111074194437 Henry Cohn, 2026, needs more optimization.
26 130 0.111088611292 Henry Cohn, 2026, needs more optimization.
26 131 0.111106517793 Henry Cohn, 2026, needs more optimization.
26 132 0.112890660420 Henry Cohn, 2026, needs more optimization.
26 133 0.114695232652 Henry Cohn, 2026, needs more optimization.
26 134 0.116047379700 Henry Cohn, 2026, needs more optimization.
26 135 0.116309937036 Henry Cohn, 2026, needs more optimization.
26 136 0.116455215942 Henry Cohn, 2026, needs more optimization.
26 137 0.117200980474 Henry Cohn, 2026, needs more optimization.
26 138 0.118744757563 Henry Cohn, 2026, needs more optimization.
26 139 0.122355946133 Henry Cohn, 2026, needs more optimization.
26 140 0.125422364350 Henry Cohn, 2026, needs more optimization.
26 141 0.128359041276 Henry Cohn, 2026, needs more optimization.
26 142 0.130267791632 Henry Cohn, 2026, needs more optimization.
26 143 0.131473134529 Henry Cohn, 2026, needs more optimization.
26 144 0.131692062923 Henry Cohn, 2026, needs more optimization.
26 145 0.131732744992 Henry Cohn, 2026, needs more optimization.
26 146 0.131788608491 Henry Cohn, 2026, needs more optimization.
26 147 0.131911831418 Henry Cohn, 2026, needs more optimization.
26 148 0.132110546945 Henry Cohn, 2026, needs more optimization.
26 149 0.132445018080 Henry Cohn, 2026, needs more optimization.
26 150 0.133025923503 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 0.133338374473 Henry Cohn, 2026, needs more optimization.
26 160 0.134598514469 Henry Cohn, 2026, needs more optimization.
26 161 0.135140900081 Henry Cohn, 2026, needs more optimization.
26 162 0.135384609258 Henry Cohn, 2026, needs more optimization.
26 163 0.136053494191 Henry Cohn, 2026, needs more optimization.
26 164 0.136787993641 Henry Cohn, 2026, needs more optimization.
26 165 0.138337750976 Henry Cohn, 2026, needs more optimization.
26 166 0.138941425001 Henry Cohn, 2026, needs more optimization.
26 167 0.140080194233 Henry Cohn, 2026, needs more optimization.
26 168 0.141037807838 Henry Cohn, 2026, needs more optimization.
26 169 0.142717078946 Henry Cohn, 2026, needs more optimization.
26 170 0.142752958832 Henry Cohn, 2026, needs more optimization.
26 171 0.142761491970 Henry Cohn, 2026, needs more optimization.
26 172 0.142769118996 Henry Cohn, 2026, needs more optimization.
26 173 0.142786123270 Henry Cohn, 2026, needs more optimization.
26 174 0.142803823595 Henry Cohn, 2026, needs more optimization.
26 175 0.142812739319 Henry Cohn, 2026, needs more optimization.
26 176 0.142822314937 Henry Cohn, 2026, needs more optimization.
26 177 0.142823022665 Henry Cohn, 2026, needs more optimization.
26 178 0.142828219289 Henry Cohn, 2026, needs more optimization.
26 179 0.142829608974 Henry Cohn, 2026, needs more optimization.
26 180 0.142829840256 Henry Cohn, 2026, needs more optimization.
26 181 0.142839205356 Henry Cohn, 2026, needs more optimization.
26 182 0.142851597616 Henry Cohn, 2026, needs more optimization.
26 183 0.142856621072 Henry Cohn, 2026, needs more optimization.
26 184 0.142861712361 Henry Cohn, 2026, needs more optimization.
26 185 0.142903415909 Henry Cohn, 2026, needs more optimization.
26 186 0.143134830766 Henry Cohn, 2026, needs more optimization.
26 187 0.143817566258 Henry Cohn, 2026, needs more optimization.
26 188 0.145302495964 Henry Cohn, 2026, needs more optimization.
26 189 0.146581659416 Henry Cohn, 2026, needs more optimization.
26 190 0.147507722995 Henry Cohn, 2026, needs more optimization.
26 191 0.147521402493 Henry Cohn, 2026, needs more optimization.
26 192 0.147606579953 Henry Cohn, 2026, needs more optimization.
26 193 0.148353952329 Henry Cohn, 2026, needs more optimization.
26 194 0.148683621320 Henry Cohn, 2026, needs more optimization.
26 195 0.150076750546 Henry Cohn, 2026, needs more optimization.
26 196 0.150169804485 Henry Cohn, 2026, needs more optimization.
26 197 0.150608173374 Henry Cohn, 2026, needs more optimization.
26 198 0.150998251626 Henry Cohn, 2026, needs more optimization.
26 199 0.151321140975 Henry Cohn, 2026, needs more optimization.
26 200 0.152756041754 Henry Cohn, 2026, needs more optimization.
26 201 0.153075211013 Henry Cohn, 2026, needs more optimization.
26 202 0.153740973214 Henry Cohn, 2026, needs more optimization.
26 203 0.154315269418 Henry Cohn, 2026, needs more optimization.
26 204 0.155099011765 Henry Cohn, 2026, needs more optimization.
26 205 0.155221911226 Henry Cohn, 2026, needs more optimization.
26 206 0.155835956097 Henry Cohn, 2026, needs more optimization.
26 207 0.156023165863 Henry Cohn, 2026, needs more optimization.
26 208 0.156660623749 Henry Cohn, 2026, needs more optimization.
26 209 0.157434116569 Henry Cohn, 2026, needs more optimization.
26 210 0.157826197638 Henry Cohn, 2026, needs more optimization.
26 211 0.158744355994 Henry Cohn, 2026, needs more optimization.
26 212 0.159280233924 Henry Cohn, 2026, needs more optimization.
26 213 0.160263030839 Henry Cohn, 2026, needs more optimization.
26 214 0.160761280075 Henry Cohn, 2026, needs more optimization.
26 215 0.161067903759 Henry Cohn, 2026, needs more optimization.
26 216 0.161829871926 Henry Cohn, 2026, needs more optimization.
26 217 0.161831091720 Henry Cohn, 2026, needs more optimization.
26 218 0.161846546235 Henry Cohn, 2026, needs more optimization.
26 219 0.161848047328 Henry Cohn, 2026, needs more optimization.
26 220 0.161864564200 Henry Cohn, 2026, needs more optimization.
26 221 0.161873354315 Henry Cohn, 2026, needs more optimization.
26 222 0.161877334076 Henry Cohn, 2026, needs more optimization.
26 223 0.161893578086 Henry Cohn, 2026, needs more optimization.
26 224 0.161893580403 Henry Cohn, 2026, needs more optimization.
26 225 0.161902953208 Henry Cohn, 2026, needs more optimization.
26 226 0.161905469032 Henry Cohn, 2026, needs more optimization.
26 227 0.161907666265 Henry Cohn, 2026, needs more optimization.
26 228 0.161910106574 Henry Cohn, 2026, needs more optimization.
26 229 0.161910926933 Henry Cohn, 2026, needs more optimization.
26 230 0.161914726501 Henry Cohn, 2026, needs more optimization.
26 231 0.161942940703 Henry Cohn, 2026, needs more optimization.
26 232 0.161976552256 Henry Cohn, 2026, needs more optimization.
26 233 0.162068506664 Henry Cohn, 2026, needs more optimization.
26 234 0.162639491272 Henry Cohn, 2026, needs more optimization.
26 235 0.163457160280 Henry Cohn, 2026, needs more optimization.
26 236 0.163994923544 Henry Cohn, 2026, needs more optimization.
26 237 0.164269767527 Henry Cohn, 2026, needs more optimization.
26 238 0.164612056638 Henry Cohn, 2026, needs more optimization.
26 239 0.164867307882 Henry Cohn, 2026, needs more optimization.
26 240 0.165205282847 Henry Cohn, 2026, needs more optimization.
26 241 0.165408988159 Henry Cohn, 2026, needs more optimization.
26 242 0.165653753354 Henry Cohn, 2026, needs more optimization.
26 243 0.165734093215 Henry Cohn, 2026, needs more optimization.
26 244 0.166077450995 Henry Cohn, 2026, needs more optimization.
26 245 0.166227549240 Henry Cohn, 2026, needs more optimization.
26 246 0.166271699148 Henry Cohn, 2026, needs more optimization.
26 247 0.166430952015 Henry Cohn, 2026, needs more optimization.
26 248 0.166457491592 Henry Cohn, 2026, needs more optimization.
26 249 0.166457673580 Henry Cohn, 2026, needs more optimization.
26 250 0.166564462071 Henry Cohn, 2026, needs more optimization.
26 251 0.166649831254 Henry Cohn, 2026, needs more optimization.
26 285 0.166666666667 Orthogonal union of 275 points in 22 dimensions and 10 points in 4 dimensions.
6⁢x−1
26 287 0.166666872444 Henry Cohn, 2026, needs more optimization.
26 288 0.166672479782 Henry Cohn, 2026, needs more optimization.
26 289 0.166672486058 Henry Cohn, 2026, needs more optimization.
26 290 0.166674207283 Henry Cohn, 2026, needs more optimization.
26 291 0.166675755089 Henry Cohn, 2026, needs more optimization.
26 292 0.166677150171 Henry Cohn, 2026, needs more optimization.
26 293 0.166678088999 Henry Cohn, 2026, needs more optimization.
26 294 0.166682122890 Henry Cohn, 2026, needs more optimization.
26 295 0.166697169805 Henry Cohn, 2026, needs more optimization.
26 296 0.166725580929 Henry Cohn, 2026, needs more optimization.
26 297 0.166917093460 Henry Cohn, 2026, needs more optimization.
26 298 0.167392491373 Henry Cohn, 2026, needs more optimization.
26 299 0.168507873875 Henry Cohn, 2026, needs more optimization.
26 300 0.170234605564 Henry Cohn, 2026, needs more optimization.
26 301 0.170997227580 Henry Cohn, 2026, needs more optimization.
26 302 0.172578074879 Henry Cohn, 2026, needs more optimization.
26 303 0.174248066437 Henry Cohn, 2026, needs more optimization.
26 304 0.175775990573 Henry Cohn, 2026, needs more optimization.
26 305 0.176948577968 Henry Cohn, 2026, needs more optimization.
26 306 0.178752130052 Henry Cohn, 2026, needs more optimization.
26 307 0.180437553810 Henry Cohn, 2026, needs more optimization.
26 308 0.181193756157 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 0.181821516768 Henry Cohn, 2026, needs more optimization.
26 319 0.181824176483 Orthogonal union of 317 points in 25 dimensions and 2 points in 1 dimension.
26 320 0.181825523564 Orthogonal union of 318 points in 25 dimensions and 2 points in 1 dimension.
26 321 0.181832168515 Orthogonal union of 319 points in 25 dimensions and 2 points in 1 dimension.
26 322 0.181834552272 Orthogonal union of 320 points in 25 dimensions and 2 points in 1 dimension.
26 323 0.182787779544 Orthogonal union of 321 points in 25 dimensions and 2 points in 1 dimension.
26 324 0.184639459982 Orthogonal union of 322 points in 25 dimensions and 2 points in 1 dimension.
26 325 0.185637241294 Orthogonal union of 323 points in 25 dimensions and 2 points in 1 dimension.
26 326 0.186502611117 Orthogonal union of 324 points in 25 dimensions and 2 points in 1 dimension.
26 327 0.187404986290 Orthogonal union of 325 points in 25 dimensions and 2 points in 1 dimension.
26 328 0.188494903896 Orthogonal union of 326 points in 25 dimensions and 2 points in 1 dimension.
26 329 0.190329502835 Orthogonal union of 327 points in 25 dimensions and 2 points in 1 dimension.
26 330 0.191407721159 Orthogonal union of 328 points in 25 dimensions and 2 points in 1 dimension.
26 331 0.192558786029 Orthogonal union of 329 points in 25 dimensions and 2 points in 1 dimension.
26 334 0.193548387097 Orthogonal union of 330 points in 24 dimensions and 4 points in 2 dimensions.
31⁢x−6
26 335 0.193557120184 Henry Cohn, 2026, needs more optimization.
26 336 0.193557140572 Henry Cohn, 2026, needs more optimization.
26 337 0.193557152876 Henry Cohn, 2026, needs more optimization.
26 338 0.193560225097 Henry Cohn, 2026, needs more optimization.
26 339 0.193560235079 Henry Cohn, 2026, needs more optimization.
26 340 0.193568836694 Henry Cohn, 2026, needs more optimization.
26 341 0.193580406740 Henry Cohn, 2026, needs more optimization.
26 342 0.193608017022 Henry Cohn, 2026, needs more optimization.
26 343 0.196084570153 Henry Cohn, 2026, needs more optimization.
26 345 0.196145364572 Henry Cohn, 2026, needs more optimization.
26 346 0.196342422422 Henry Cohn, 2026, needs more optimization.
26 347 0.196679971552 Henry Cohn, 2026, needs more optimization.
26 348 0.196751421066 Henry Cohn, 2026, needs more optimization.
26 349 0.196859821074 Henry Cohn, 2026, needs more optimization.
26 350 0.197010865950 Henry Cohn, 2026, needs more optimization.
26 351 0.197106772296 Henry Cohn, 2026, needs more optimization.
26 352 0.197251913076 Henry Cohn, 2026, needs more optimization.
26 353 0.197380944685 Henry Cohn, 2026, needs more optimization.
26 354 0.197452506353 Henry Cohn, 2026, needs more optimization.
26 355 0.197506757907 Henry Cohn, 2026, needs more optimization.
26 356 0.197801678997 Henry Cohn, 2026, needs more optimization.
26 357 0.197967020495 Henry Cohn, 2026, needs more optimization.
26 358 0.198126217359 Henry Cohn, 2026, needs more optimization.
26 359 0.198173467083 Henry Cohn, 2026, needs more optimization.
26 360 0.198311007512 Henry Cohn, 2026, needs more optimization.
26 361 0.198455573259 Henry Cohn, 2026, needs more optimization.
26 362 0.198491915969 Henry Cohn, 2026, needs more optimization.
26 363 0.198547375399 Henry Cohn, 2026, needs more optimization.
26 364 0.198712434746 Henry Cohn, 2026, needs more optimization.
26 365 0.198880903691 Henry Cohn, 2026, needs more optimization.
26 366 0.198982536416 Henry Cohn, 2026, needs more optimization.
26 367 0.198991046825 Henry Cohn, 2026, needs more optimization.
26 370 0.199014163219 Henry Cohn, 2026, needs more optimization.
26 371 0.199130923578 Henry Cohn, 2026, needs more optimization.
26 372 0.199153116058 Henry Cohn, 2026, needs more optimization.
26 373 0.199257214906 Henry Cohn, 2026, needs more optimization.
26 374 0.199381229100 Henry Cohn, 2026, needs more optimization.
26 375 0.199408085859 Henry Cohn, 2026, needs more optimization.
26 376 0.199408085860 Henry Cohn, 2026, needs more optimization.
26 377 0.199434342692 Henry Cohn, 2026, needs more optimization.
26 378 0.199507146278 Henry Cohn, 2026, needs more optimization.
26 380 0.199573774857 Henry Cohn, 2026, needs more optimization.
26 381 0.199648313110 Henry Cohn, 2026, needs more optimization.
26 382 0.199724394599 Henry Cohn, 2026, needs more optimization.
26 384 0.199749333628 Henry Cohn, 2026, needs more optimization.
26 386 0.199787515799 Henry Cohn, 2026, needs more optimization.
26 388 0.199819140559 Henry Cohn, 2026, needs more optimization.
26 389 0.199903742104 Henry Cohn, 2026, needs more optimization.
26 390 0.199910956603 Henry Cohn, 2026, needs more optimization.
26 394 0.199930405165 Henry Cohn, 2026, needs more optimization.
26 400 0.199985742154 Henry Cohn, 2026, needs more optimization.
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 0.200085756133 Henry Cohn, 2026, needs more optimization.
26 563 0.200101499640 Henry Cohn, 2026, needs more optimization.
26 566 0.200279396443 Henry Cohn, 2026, needs more optimization.
26 568 0.200305136848 Henry Cohn, 2026, needs more optimization.
26 569 0.200732358527 Henry Cohn, 2026, needs more optimization.
26 570 0.200852538277 Henry Cohn, 2026, needs more optimization.
26 572 0.201614695043 Henry Cohn, 2026, needs more optimization.
26 573 0.202897586222 Henry Cohn, 2026, needs more optimization.
26 574 0.203145803645 Henry Cohn, 2026, needs more optimization.
26 575 0.205677961643 Henry Cohn, 2026, needs more optimization.
26 576 0.206768170923 Henry Cohn, 2026, needs more optimization.
26 577 0.209206422331 Henry Cohn, 2026, needs more optimization.
26 578 0.211160594470 Henry Cohn, 2026, needs more optimization.
26 579 0.212800830577 Henry Cohn, 2026, needs more optimization.
26 580 0.213919807448 Henry Cohn, 2026, needs more optimization.
26 581 0.215622823173 Henry Cohn, 2026, needs more optimization.
26 582 0.217268244315 Henry Cohn, 2026, needs more optimization.
26 584 0.217939658104 Henry Cohn, 2026, needs more optimization.
26 585 0.219294640276 Henry Cohn, 2026, needs more optimization.
26 586 0.221142775896 Henry Cohn, 2026, needs more optimization.
26 587 0.221573512398 Henry Cohn, 2026, needs more optimization.
26 588 0.222199050582 Henry Cohn, 2026, needs more optimization.
26 589 0.222856005585 Henry Cohn, 2026, needs more optimization.
26 590 0.223689609778 Henry Cohn, 2026, needs more optimization.
26 591 0.224464871312 Henry Cohn, 2026, needs more optimization.
26 592 0.225181931085 Henry Cohn, 2026, needs more optimization.
26 593 0.225561570976 Henry Cohn, 2026, needs more optimization.
26 594 0.226719621100 Henry Cohn, 2026, needs more optimization.
26 595 0.227342766717 Henry Cohn, 2026, needs more optimization.
26 596 0.227774316995 Henry Cohn, 2026, needs more optimization.
26 602 0.238385714845 Henry Cohn, 2026, needs more optimization.
26 603 0.238575338270 Orthogonal union of 601 points in 25 dimensions and 2 points in 1 dimension.
26 610 0.238583462947 Henry Cohn, 2026, needs more optimization.
26 612 0.238583520649 Henry Cohn, 2026, needs more optimization.
26 613 0.238653362259 Henry Cohn, 2026, needs more optimization.
26 614 0.238879267660 Henry Cohn, 2026, needs more optimization.
26 615 0.238969003752 Henry Cohn, 2026, needs more optimization.
26 618 0.239095822987 Henry Cohn, 2026, needs more optimization.
26 625 0.239203838996 Henry Cohn, 2026, needs more optimization.
26 628 0.239280073804 Henry Cohn, 2026, needs more optimization.
26 630 0.244441458801 Henry Cohn, 2026, needs more optimization.
26 632 0.246375919095 Henry Cohn, 2026, needs more optimization.
26 633 0.246399599876 Henry Cohn, 2026, needs more optimization.
26 644 0.247222979983 Henry Cohn, 2026, needs more optimization.
26 652 0.248143825551 Henry Cohn, 2026, needs more optimization.
26 653 0.248503195406 Henry Cohn, 2026, needs more optimization.
26 664 0.248610752172 Henry Cohn, 2026, needs more optimization.
26 665 0.248792968284 Henry Cohn, 2026, needs more optimization.
26 671 0.248793993988 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 0.039953014084 Henry Cohn, 2026, needs more optimization.
27 59 0.039968383367 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 0.047652492898 Henry Cohn, 2026, needs more optimization.
27 64 0.050067815256 Henry Cohn, 2026, needs more optimization.
27 65 0.054260336916 Henry Cohn, 2026, needs more optimization.
27 66 0.056203243141 Henry Cohn, 2026, needs more optimization.
27 67 0.058358240886 Henry Cohn, 2026, needs more optimization.
27 68 0.060150593990 Henry Cohn, 2026, needs more optimization.
27 69 0.061646770087 Henry Cohn, 2026, needs more optimization.
27 70 0.062922671881 Henry Cohn, 2026, needs more optimization.
27 71 0.064107549661 Henry Cohn, 2026, needs more optimization.
27 72 0.064938703542 Henry Cohn, 2026, needs more optimization.
27 73 0.065805542685 Henry Cohn, 2026, needs more optimization.
27 74 0.066308366331 Henry Cohn, 2026, needs more optimization.
27 75 0.068047317688 Henry Cohn, 2026, needs more optimization.
27 76 0.069937587917 Henry Cohn, 2026, needs more optimization.
27 77 0.072325860054 Henry Cohn, 2026, needs more optimization.
27 78 0.074624795263 Henry Cohn, 2026, needs more optimization.
27 79 0.075331327086 Henry Cohn, 2026, needs more optimization.
27 80 0.076122276896 Henry Cohn, 2026, needs more optimization.
27 81 0.076640303470 Henry Cohn, 2026, needs more optimization.
27 82 0.076894452738 Henry Cohn, 2026, needs more optimization.
27 83 0.076908998860 Henry Cohn, 2026, needs more optimization.
27 84 0.077005220886 Henry Cohn, 2026, needs more optimization.
27 85 0.077375337738 Henry Cohn, 2026, needs more optimization.
27 86 0.077605690790 Henry Cohn, 2026, needs more optimization.
27 87 0.078411573509 Henry Cohn, 2026, needs more optimization.
27 88 0.078632181564 Henry Cohn, 2026, needs more optimization.
27 89 0.079086756261 Henry Cohn, 2026, needs more optimization.
27 90 0.079979736508 Henry Cohn, 2026, needs more optimization.
27 91 0.080270744374 Henry Cohn, 2026, needs more optimization.
27 92 0.080397348706 Henry Cohn, 2026, needs more optimization.
27 93 0.080671661896 Henry Cohn, 2026, needs more optimization.
27 94 0.080682780934 Henry Cohn, 2026, needs more optimization.
27 95 0.080684833766 Henry Cohn, 2026, needs more optimization.
27 96 0.080685565583 Henry Cohn, 2026, needs more optimization.
27 97 0.080685567004 Henry Cohn, 2026, needs more optimization.
27 98 0.080685608415 Henry Cohn, 2026, needs more optimization.
27 99 0.084158666674 Henry Cohn, 2026, needs more optimization.
27 100 0.086593018699 Henry Cohn, 2026, needs more optimization.
27 101 0.088590539850 Henry Cohn, 2026, needs more optimization.
27 102 0.089495200163 Henry Cohn, 2026, needs more optimization.
27 103 0.089776459760 Henry Cohn, 2026, needs more optimization.
27 104 0.089999203474 Henry Cohn, 2026, needs more optimization.
27 105 0.090247516948 Henry Cohn, 2026, needs more optimization.
27 106 0.090283952777 Henry Cohn, 2026, needs more optimization.
27 107 0.090522581532 Henry Cohn, 2026, needs more optimization.
27 108 0.090586419301 Henry Cohn, 2026, needs more optimization.
27 110 0.090642434465 Henry Cohn, 2026, needs more optimization.
27 111 0.090819812517 Henry Cohn, 2026, needs more optimization.
27 112 0.090862857273 Henry Cohn, 2026, needs more optimization.
27 113 0.090892295771 Henry Cohn, 2026, needs more optimization.
27 114 0.091267483441 Henry Cohn, 2026, needs more optimization.
27 115 0.092925161070 Henry Cohn, 2026, needs more optimization.
27 116 0.095589786752 Henry Cohn, 2026, needs more optimization.
27 117 0.098608853019 Henry Cohn, 2026, needs more optimization.
27 118 0.101376691762 Henry Cohn, 2026, needs more optimization.
27 119 0.102972750465 Henry Cohn, 2026, needs more optimization.
27 120 0.103038125871 Henry Cohn, 2026, needs more optimization.
27 121 0.103104869434 Henry Cohn, 2026, needs more optimization.
27 122 0.103124108082 Henry Cohn, 2026, needs more optimization.
27 125 0.103125332576 Henry Cohn, 2026, needs more optimization.
27 126 0.104333762706 Henry Cohn, 2026, needs more optimization.
27 127 0.105170975896 Henry Cohn, 2026, needs more optimization.
27 128 0.106540758365 Henry Cohn, 2026, needs more optimization.
27 129 0.107240832617 Henry Cohn, 2026, needs more optimization.
27 130 0.107692440425 Henry Cohn, 2026, needs more optimization.
27 131 0.108500531090 Henry Cohn, 2026, needs more optimization.
27 132 0.109607869386 Henry Cohn, 2026, needs more optimization.
27 133 0.110569212799 Henry Cohn, 2026, needs more optimization.
27 134 0.111032480239 Henry Cohn, 2026, needs more optimization.
27 135 0.111034837033 Henry Cohn, 2026, needs more optimization.
27 136 0.111511174279 Henry Cohn, 2026, needs more optimization.
27 137 0.113429904827 Henry Cohn, 2026, needs more optimization.
27 138 0.114536636754 Henry Cohn, 2026, needs more optimization.
27 139 0.114844731119 Henry Cohn, 2026, needs more optimization.
27 140 0.115322556532 Henry Cohn, 2026, needs more optimization.
27 141 0.116318047836 Henry Cohn, 2026, needs more optimization.
27 142 0.117570361854 Henry Cohn, 2026, needs more optimization.
27 143 0.119266731252 Henry Cohn, 2026, needs more optimization.
27 144 0.121001772343 Henry Cohn, 2026, needs more optimization.
27 145 0.123136128144 Henry Cohn, 2026, needs more optimization.
27 146 0.125388443986 Henry Cohn, 2026, needs more optimization.
27 147 0.127237443095 Henry Cohn, 2026, needs more optimization.
27 148 0.128605193997 Henry Cohn, 2026, needs more optimization.
27 149 0.130142526553 Henry Cohn, 2026, needs more optimization.
27 150 0.131308256896 Henry Cohn, 2026, needs more optimization.
27 151 0.131434238600 Henry Cohn, 2026, needs more optimization.
27 152 0.131654886468 Henry Cohn, 2026, needs more optimization.
27 153 0.131796065659 Henry Cohn, 2026, needs more optimization.
27 154 0.132044884779 Henry Cohn, 2026, needs more optimization.
27 155 0.132284785691 Henry Cohn, 2026, needs more optimization.
27 156 0.132624015998 Henry Cohn, 2026, needs more optimization.
27 157 0.132757433596 Henry Cohn, 2026, needs more optimization.
27 158 0.132903526457 Henry Cohn, 2026, needs more optimization.
27 159 0.133281642330 Henry Cohn, 2026, needs more optimization.
27 160 0.133281645713 Henry Cohn, 2026, needs more optimization.
27 161 0.133306799873 Henry Cohn, 2026, needs more optimization.
27 162 0.133328342251 Henry Cohn, 2026, needs more optimization.
27 163 0.133332016211 Henry Cohn, 2026, needs more optimization.
27 164 0.133500761749 Henry Cohn, 2026, needs more optimization.
27 165 0.135091588737 Henry Cohn, 2026, needs more optimization.
27 166 0.135091591897 Henry Cohn, 2026, needs more optimization.
27 167 0.135116293760 Henry Cohn, 2026, needs more optimization.
27 168 0.135132302157 Henry Cohn, 2026, needs more optimization.
27 169 0.135297589081 Henry Cohn, 2026, needs more optimization.
27 170 0.135944002626 Henry Cohn, 2026, needs more optimization.
27 171 0.136384005455 Henry Cohn, 2026, needs more optimization.
27 172 0.137281177794 Henry Cohn, 2026, needs more optimization.
27 173 0.138904481187 Henry Cohn, 2026, needs more optimization.
27 174 0.139555738541 Henry Cohn, 2026, needs more optimization.
27 175 0.140952152383 Henry Cohn, 2026, needs more optimization.
27 176 0.142310276142 Henry Cohn, 2026, needs more optimization.
27 177 0.142310278301 Henry Cohn, 2026, needs more optimization.
27 178 0.142477449261 Henry Cohn, 2026, needs more optimization.
27 179 0.142477458794 Henry Cohn, 2026, needs more optimization.
27 180 0.142533321527 Henry Cohn, 2026, needs more optimization.
27 181 0.142570874648 Henry Cohn, 2026, needs more optimization.
27 182 0.142588284279 Henry Cohn, 2026, needs more optimization.
27 183 0.142588296380 Henry Cohn, 2026, needs more optimization.
27 184 0.142715427339 Henry Cohn, 2026, needs more optimization.
27 185 0.142731389455 Henry Cohn, 2026, needs more optimization.
27 186 0.142770864149 Henry Cohn, 2026, needs more optimization.
27 187 0.142770898990 Henry Cohn, 2026, needs more optimization.
27 188 0.142801034779 Henry Cohn, 2026, needs more optimization.
27 189 0.142801311529 Henry Cohn, 2026, needs more optimization.
27 190 0.142801314098 Henry Cohn, 2026, needs more optimization.
27 191 0.142841959273 Henry Cohn, 2026, needs more optimization.
27 192 0.142974739288 Henry Cohn, 2026, needs more optimization.
27 193 0.142979721026 Henry Cohn, 2026, needs more optimization.
27 194 0.143908234799 Henry Cohn, 2026, needs more optimization.
27 195 0.144426448550 Henry Cohn, 2026, needs more optimization.
27 196 0.146036588993 Henry Cohn, 2026, needs more optimization.
27 197 0.146650328930 Henry Cohn, 2026, needs more optimization.
27 198 0.147562525494 Henry Cohn, 2026, needs more optimization.
27 199 0.148384082020 Henry Cohn, 2026, needs more optimization.
27 200 0.148964106503 Henry Cohn, 2026, needs more optimization.
27 201 0.149750034624 Henry Cohn, 2026, needs more optimization.
27 202 0.150177897947 Henry Cohn, 2026, needs more optimization.
27 203 0.150196657093 Henry Cohn, 2026, needs more optimization.
27 204 0.150709980019 Henry Cohn, 2026, needs more optimization.
27 205 0.151181567085 Henry Cohn, 2026, needs more optimization.
27 206 0.151769165479 Henry Cohn, 2026, needs more optimization.
27 207 0.152486483437 Henry Cohn, 2026, needs more optimization.
27 208 0.152887661855 Henry Cohn, 2026, needs more optimization.
27 209 0.153752634433 Henry Cohn, 2026, needs more optimization.
27 210 0.153815279000 Henry Cohn, 2026, needs more optimization.
27 211 0.154377232614 Henry Cohn, 2026, needs more optimization.
27 212 0.154743278834 Henry Cohn, 2026, needs more optimization.
27 213 0.155149414380 Henry Cohn, 2026, needs more optimization.
27 214 0.155572215063 Henry Cohn, 2026, needs more optimization.
27 215 0.156079019652 Henry Cohn, 2026, needs more optimization.
27 216 0.156833631730 Henry Cohn, 2026, needs more optimization.
27 217 0.157616255282 Henry Cohn, 2026, needs more optimization.
27 218 0.158268315110 Henry Cohn, 2026, needs more optimization.
27 219 0.158848365811 Henry Cohn, 2026, needs more optimization.
27 220 0.159287800355 Henry Cohn, 2026, needs more optimization.
27 221 0.159753148956 Henry Cohn, 2026, needs more optimization.
27 222 0.160323378697 Henry Cohn, 2026, needs more optimization.
27 223 0.160600283113 Henry Cohn, 2026, needs more optimization.
27 224 0.160986207049 Henry Cohn, 2026, needs more optimization.
27 225 0.161608771971 Henry Cohn, 2026, needs more optimization.
27 226 0.161610965334 Henry Cohn, 2026, needs more optimization.
27 227 0.161610972452 Henry Cohn, 2026, needs more optimization.
27 228 0.161657360648 Henry Cohn, 2026, needs more optimization.
27 229 0.161669396516 Henry Cohn, 2026, needs more optimization.
27 230 0.161669437326 Henry Cohn, 2026, needs more optimization.
27 231 0.161757625655 Henry Cohn, 2026, needs more optimization.
27 232 0.161788350905 Henry Cohn, 2026, needs more optimization.
27 233 0.161827512935 Henry Cohn, 2026, needs more optimization.
27 234 0.161827772102 Henry Cohn, 2026, needs more optimization.
27 235 0.161842182779 Henry Cohn, 2026, needs more optimization.
27 236 0.161898297768 Henry Cohn, 2026, needs more optimization.
27 237 0.161916546246 Henry Cohn, 2026, needs more optimization.
27 238 0.161919132827 Henry Cohn, 2026, needs more optimization.
27 239 0.161924075884 Henry Cohn, 2026, needs more optimization.
27 240 0.161924713889 Henry Cohn, 2026, needs more optimization.
27 241 0.161924785871 Henry Cohn, 2026, needs more optimization.
27 242 0.161948378677 Henry Cohn, 2026, needs more optimization.
27 243 0.161979333703 Henry Cohn, 2026, needs more optimization.
27 244 0.162278813261 Henry Cohn, 2026, needs more optimization.
27 245 0.162340715905 Henry Cohn, 2026, needs more optimization.
27 246 0.162563980330 Henry Cohn, 2026, needs more optimization.
27 247 0.162693338703 Henry Cohn, 2026, needs more optimization.
27 248 0.162750970781 Henry Cohn, 2026, needs more optimization.
27 249 0.162915304952 Henry Cohn, 2026, needs more optimization.
27 250 0.163025750502 Henry Cohn, 2026, needs more optimization.
27 251 0.163661921328 Henry Cohn, 2026, needs more optimization.
27 252 0.163925809010 Henry Cohn, 2026, needs more optimization.
27 253 0.164157347792 Henry Cohn, 2026, needs more optimization.
27 254 0.164227161650 Henry Cohn, 2026, needs more optimization.
27 255 0.164518421569 Henry Cohn, 2026, needs more optimization.
27 256 0.164658059432 Henry Cohn, 2026, needs more optimization.
27 257 0.164873277428 Henry Cohn, 2026, needs more optimization.
27 258 0.165054446814 Henry Cohn, 2026, needs more optimization.
27 259 0.165185847044 Henry Cohn, 2026, needs more optimization.
27 260 0.165391762840 Henry Cohn, 2026, needs more optimization.
27 261 0.165491027964 Henry Cohn, 2026, needs more optimization.
27 262 0.165586922750 Henry Cohn, 2026, needs more optimization.
27 263 0.165659078943 Henry Cohn, 2026, needs more optimization.
27 264 0.165853722618 Henry Cohn, 2026, needs more optimization.
27 265 0.165882270223 Henry Cohn, 2026, needs more optimization.
27 266 0.165920640770 Henry Cohn, 2026, needs more optimization.
27 267 0.166011863794 Henry Cohn, 2026, needs more optimization.
27 268 0.166040003254 Henry Cohn, 2026, needs more optimization.
27 269 0.166183741332 Henry Cohn, 2026, needs more optimization.
27 270 0.166228268372 Henry Cohn, 2026, needs more optimization.
27 271 0.166340525150 Henry Cohn, 2026, needs more optimization.
27 272 0.166408470378 Henry Cohn, 2026, needs more optimization.
27 273 0.166473252010 Henry Cohn, 2026, needs more optimization.
27 274 0.166508242117 Henry Cohn, 2026, needs more optimization.
27 275 0.166538484133 Henry Cohn, 2026, needs more optimization.
27 276 0.166600032535 Henry Cohn, 2026, needs more optimization.
27 277 0.166605676704 Henry Cohn, 2026, needs more optimization.
27 278 0.166617018393 Henry Cohn, 2026, needs more optimization.
27 279 0.166645068892 Henry Cohn, 2026, needs more optimization.
27 280 0.166652112816 Henry Cohn, 2026, needs more optimization.
27 281 0.166652831856 Henry Cohn, 2026, needs more optimization.
27 288 0.166666666667 Orthogonal union of 278 points in 23 dimensions and 10 points in 4 dimensions.
6⁢x−1
27 289 0.166666872444 Orthogonal union of 287 points in 26 dimensions and 2 points in 1 dimension.
27 290 0.166671912385 Henry Cohn, 2026, needs more optimization.
27 291 0.166671915029 Henry Cohn, 2026, needs more optimization.
27 292 0.166671918138 Henry Cohn, 2026, needs more optimization.
27 293 0.166673164429 Henry Cohn, 2026, needs more optimization.
27 294 0.166673167049 Henry Cohn, 2026, needs more optimization.
27 295 0.166674368012 Henry Cohn, 2026, needs more optimization.
27 296 0.166674371849 Henry Cohn, 2026, needs more optimization.
27 297 0.166675359512 Henry Cohn, 2026, needs more optimization.
27 298 0.166675363158 Henry Cohn, 2026, needs more optimization.
27 299 0.166678969073 Henry Cohn, 2026, needs more optimization.
27 300 0.166678975745 Henry Cohn, 2026, needs more optimization.
27 301 0.166678985330 Henry Cohn, 2026, needs more optimization.
27 302 0.166678993560 Henry Cohn, 2026, needs more optimization.
27 303 0.166687186322 Henry Cohn, 2026, needs more optimization.
27 304 0.172578074879 Orthogonal union of 302 points in 26 dimensions and 2 points in 1 dimension.
27 305 0.174248066437 Orthogonal union of 303 points in 26 dimensions and 2 points in 1 dimension.
27 306 0.175775990573 Orthogonal union of 304 points in 26 dimensions and 2 points in 1 dimension.
27 307 0.176948577968 Orthogonal union of 305 points in 26 dimensions and 2 points in 1 dimension.
27 308 0.178752130052 Orthogonal union of 306 points in 26 dimensions and 2 points in 1 dimension.
27 310 0.179512071062 Henry Cohn, 2026, needs more optimization.
27 311 0.179556193146 Henry Cohn, 2026, needs more optimization.
27 312 0.179680502611 Henry Cohn, 2026, needs more optimization.
27 314 0.179863251458 Henry Cohn, 2026, needs more optimization.
27 315 0.180051754696 Henry Cohn, 2026, needs more optimization.
27 316 0.180135728042 Henry Cohn, 2026, needs more optimization.
27 317 0.180329494601 Henry Cohn, 2026, needs more optimization.
27 318 0.180520154616 Henry Cohn, 2026, needs more optimization.
27 319 0.180830737268 Henry Cohn, 2026, needs more optimization.
27 320 0.181112560655 Henry Cohn, 2026, needs more optimization.
27 321 0.181165553739 Henry Cohn, 2026, needs more optimization.
27 322 0.181303810911 Henry Cohn, 2026, needs more optimization.
27 323 0.181372548227 Henry Cohn, 2026, needs more optimization.
27 324 0.181374578268 Henry Cohn, 2026, needs more optimization.
27 325 0.181502075000 Henry Cohn, 2026, needs more optimization.
27 326 0.181610001586 Henry Cohn, 2026, needs more optimization.
27 328 0.181646411616 Henry Cohn, 2026, needs more optimization.
27 329 0.181766387537 Henry Cohn, 2026, needs more optimization.
27 330 0.181786175435 Henry Cohn, 2026, needs more optimization.
27 331 0.181787125803 Henry Cohn, 2026, needs more optimization.
27 332 0.181816764825 Henry Cohn, 2026, needs more optimization.
27 333 0.181833670937 Henry Cohn, 2026, needs more optimization.
27 334 0.181849018125 Henry Cohn, 2026, needs more optimization.
27 335 0.181853241416 Henry Cohn, 2026, needs more optimization.
27 337 0.181882000985 Henry Cohn, 2026, needs more optimization.
27 338 0.181991830560 Henry Cohn, 2026, needs more optimization.
27 339 0.182172332103 Henry Cohn, 2026, needs more optimization.
27 340 0.182663876477 Henry Cohn, 2026, needs more optimization.
27 341 0.183223949966 Henry Cohn, 2026, needs more optimization.
27 342 0.184110057828 Henry Cohn, 2026, needs more optimization.
27 343 0.184353464542 Henry Cohn, 2026, needs more optimization.
27 344 0.185220528443 Henry Cohn, 2026, needs more optimization.
27 345 0.185746207913 Henry Cohn, 2026, needs more optimization.
27 346 0.186599047694 Henry Cohn, 2026, needs more optimization.
27 347 0.187404938731 Henry Cohn, 2026, needs more optimization.
27 348 0.188067189806 Henry Cohn, 2026, needs more optimization.
27 349 0.188775049776 Henry Cohn, 2026, needs more optimization.
27 350 0.189485871439 Henry Cohn, 2026, needs more optimization.
27 351 0.190452656361 Henry Cohn, 2026, needs more optimization.
27 352 0.191131331532 Henry Cohn, 2026, needs more optimization.
27 353 0.191941599790 Henry Cohn, 2026, needs more optimization.
27 354 0.193093051328 Henry Cohn, 2026, needs more optimization.
27 355 0.193625877820 Henry Cohn, 2026, needs more optimization.
27 356 0.193873197936 Henry Cohn, 2026, needs more optimization.
27 357 0.193940013803 Henry Cohn, 2026, needs more optimization.
27 358 0.194022490122 Henry Cohn, 2026, needs more optimization.
27 359 0.194311214692 Henry Cohn, 2026, needs more optimization.
27 360 0.194641954466 Henry Cohn, 2026, needs more optimization.
27 361 0.196338257006 Henry Cohn, 2026, needs more optimization.
27 362 0.196778040663 Henry Cohn, 2026, needs more optimization.
27 363 0.197299159675 Henry Cohn, 2026, needs more optimization.
27 376 0.197649477641 Henry Cohn, 2026, needs more optimization.
27 377 0.197774571903 Henry Cohn, 2026, needs more optimization.
27 378 0.197819004233 Henry Cohn, 2026, needs more optimization.
27 379 0.197956221814 Henry Cohn, 2026, needs more optimization.
27 381 0.198019468860 Henry Cohn, 2026, needs more optimization.
27 382 0.198088951730 Henry Cohn, 2026, needs more optimization.
27 383 0.198188582128 Henry Cohn, 2026, needs more optimization.
27 384 0.198247952866 Henry Cohn, 2026, needs more optimization.
27 385 0.198373639689 Henry Cohn, 2026, needs more optimization.
27 386 0.198453831011 Henry Cohn, 2026, needs more optimization.
27 388 0.198658270488 Henry Cohn, 2026, needs more optimization.
27 389 0.198794340465 Henry Cohn, 2026, needs more optimization.
27 390 0.198886514152 Henry Cohn, 2026, needs more optimization.
27 391 0.198919032382 Henry Cohn, 2026, needs more optimization.
27 392 0.199117268299 Henry Cohn, 2026, needs more optimization.
27 394 0.199251359946 Henry Cohn, 2026, needs more optimization.
27 396 0.199260118134 Henry Cohn, 2026, needs more optimization.
27 397 0.199280935457 Henry Cohn, 2026, needs more optimization.
27 398 0.199292211765 Henry Cohn, 2026, needs more optimization.
27 400 0.199450227192 Henry Cohn, 2026, needs more optimization.
27 401 0.199487173350 Henry Cohn, 2026, needs more optimization.
27 402 0.199569955585 Henry Cohn, 2026, needs more optimization.
27 403 0.199570076985 Henry Cohn, 2026, needs more optimization.
27 405 0.199574652271 Henry Cohn, 2026, needs more optimization.
27 406 0.199619822963 Henry Cohn, 2026, needs more optimization.
27 407 0.199732863872 Henry Cohn, 2026, needs more optimization.
27 409 0.199832911687 Henry Cohn, 2026, needs more optimization.
27 410 0.199866679505 Henry Cohn, 2026, needs more optimization.
27 411 0.199875571530 Henry Cohn, 2026, needs more optimization.
27 413 0.199879705936 Henry Cohn, 2026, needs more optimization.
27 414 0.199921790959 Henry Cohn, 2026, needs more optimization.
27 417 0.199930259058 Henry Cohn, 2026, needs more optimization.
27 418 0.199957575082 Henry Cohn, 2026, needs more optimization.
27 420 0.199973868119 Henry Cohn, 2026, needs more optimization.
27 423 0.199977121868 Henry Cohn, 2026, needs more optimization.
27 424 0.199992353685 Henry Cohn, 2026, needs more optimization.
27 425 0.199997296928 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 0.200066701491 Henry Cohn, 2026, needs more optimization.
27 566 0.200071148254 Henry Cohn, 2026, needs more optimization.
27 567 0.200134990681 Henry Cohn, 2026, needs more optimization.
27 568 0.200135057860 Henry Cohn, 2026, needs more optimization.
27 570 0.200305136848 Orthogonal union of 568 points in 26 dimensions and 2 points in 1 dimension.
27 572 0.200439308189 Henry Cohn, 2026, needs more optimization.
27 574 0.200495292066 Henry Cohn, 2026, needs more optimization.
27 575 0.200573470028 Henry Cohn, 2026, needs more optimization.
27 578 0.200719105833 Henry Cohn, 2026, needs more optimization.
27 579 0.201293858473 Henry Cohn, 2026, needs more optimization.
27 580 0.201560576837 Henry Cohn, 2026, needs more optimization.
27 581 0.201570539272 Henry Cohn, 2026, needs more optimization.
27 582 0.202261692470 Henry Cohn, 2026, needs more optimization.
27 583 0.202524840022 Henry Cohn, 2026, needs more optimization.
27 584 0.203071347273 Henry Cohn, 2026, needs more optimization.
27 585 0.204946944161 Henry Cohn, 2026, needs more optimization.
27 586 0.205904136043 Henry Cohn, 2026, needs more optimization.
27 587 0.206859620820 Henry Cohn, 2026, needs more optimization.
27 588 0.208005656136 Henry Cohn, 2026, needs more optimization.
27 589 0.208559168494 Henry Cohn, 2026, needs more optimization.
27 590 0.210397519897 Henry Cohn, 2026, needs more optimization.
27 591 0.211247912132 Henry Cohn, 2026, needs more optimization.
27 592 0.211937872709 Henry Cohn, 2026, needs more optimization.
27 593 0.212635025856 Henry Cohn, 2026, needs more optimization.
27 594 0.213211281010 Henry Cohn, 2026, needs more optimization.
27 595 0.213843654701 Henry Cohn, 2026, needs more optimization.
27 596 0.214462921830 Henry Cohn, 2026, needs more optimization.
27 597 0.214868238010 Henry Cohn, 2026, needs more optimization.
27 598 0.215490002698 Henry Cohn, 2026, needs more optimization.
27 602 0.238151490905 Henry Cohn, 2026, needs more optimization.
27 606 0.238174171959 Henry Cohn, 2026, needs more optimization.
27 607 0.238220675291 Henry Cohn, 2026, needs more optimization.
27 608 0.238220790081 Henry Cohn, 2026, needs more optimization.
27 610 0.238220864253 Henry Cohn, 2026, needs more optimization.
27 611 0.238329663085 Henry Cohn, 2026, needs more optimization.
27 614 0.238329663155 Henry Cohn, 2026, needs more optimization.
27 617 0.238368696869 Henry Cohn, 2026, needs more optimization.
27 618 0.238484787597 Henry Cohn, 2026, needs more optimization.
27 628 0.238646797174 Henry Cohn, 2026, needs more optimization.
27 630 0.238731930346 Henry Cohn, 2026, needs more optimization.
27 631 0.239456692161 Henry Cohn, 2026, needs more optimization.
27 634 0.240120572643 Henry Cohn, 2026, needs more optimization.
27 636 0.240431248672 Henry Cohn, 2026, needs more optimization.
27 637 0.240955563996 Henry Cohn, 2026, needs more optimization.
27 638 0.241640099674 Henry Cohn, 2026, needs more optimization.
27 639 0.242375133970 Henry Cohn, 2026, needs more optimization.
27 643 0.242450851170 Henry Cohn, 2026, needs more optimization.
27 662 0.244005195609 Henry Cohn, 2026, needs more optimization.
27 670 0.245274670443 Henry Cohn, 2026, needs more optimization.
27 673 0.245606548231 Henry Cohn, 2026, needs more optimization.
27 674 0.245758653261 Henry Cohn, 2026, needs more optimization.
27 680 0.245862184491 Henry Cohn, 2026, needs more optimization.
27 681 0.246225273147 Henry Cohn, 2026, needs more optimization.
27 682 0.246228681511 Henry Cohn, 2026, needs more optimization.
27 684 0.246259842023 Henry Cohn, 2026, needs more optimization.
27 686 0.246261081545 Henry Cohn, 2026, needs more optimization.
27 687 0.246305015457 Henry Cohn, 2026, needs more optimization.
27 688 0.246684498329 Henry Cohn, 2026, needs more optimization.
27 689 0.246684498455 Henry Cohn, 2026, needs more optimization.
27 691 0.246684510266 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
27 908 0.250004158573 Henry Cohn, 2026, needs more optimization.
27 909 0.250009240338 Henry Cohn, 2026, needs more optimization.
27 911 0.250013201690 Henry Cohn, 2026, needs more optimization.
27 912 0.250020478108 Henry Cohn, 2026, needs more optimization.
27 913 0.250026574894 Henry Cohn, 2026, needs more optimization.
27 915 0.250032126124 Henry Cohn, 2026, needs more optimization.
27 918 0.250032588316 Henry Cohn, 2026, needs more optimization.
27 919 0.250041259520 Henry Cohn, 2026, needs more optimization.
27 920 0.250043204872 Henry Cohn, 2026, needs more optimization.
27 922 0.250044481441 Henry Cohn, 2026, needs more optimization.
27 925 0.250047149148 Henry Cohn, 2026, needs more optimization.
27 926 0.250049058519 Henry Cohn, 2026, needs more optimization.
27 927 0.250055521079 Henry Cohn, 2026, needs more optimization.
27 928 0.250057106872 Henry Cohn, 2026, needs more optimization.
27 930 0.250058730360 Henry Cohn, 2026, needs more optimization.
27 933 0.250062275514 Henry Cohn, 2026, needs more optimization.
27 935 0.250062986328 Henry Cohn, 2026, needs more optimization.
27 936 0.250068354014 Henry Cohn, 2026, needs more optimization.
27 944 0.250206005760 Henry Cohn, 2026, needs more optimization.
27 960 0.251389086497 Henry Cohn, 2026, needs more optimization.
27 983 0.256642378157 Henry Cohn, 2026, needs more optimization.
27 1000 0.265268447670 Henry Cohn, 2026, needs more optimization.
27 1008 0.265268606542 Henry Cohn, 2026, needs more optimization.
27 1013 0.265271701921 Henry Cohn, 2026, needs more optimization.
27 1014 0.265519460030 Henry Cohn, 2026, needs more optimization.
27 1015 0.265753045300 Henry Cohn, 2026, needs more optimization.
27 1016 0.265978352389 Henry Cohn, 2026, needs more optimization.
27 1017 0.266270915128 Henry Cohn, 2026, needs more optimization.
27 1018 0.266502986644 Henry Cohn, 2026, needs more optimization.
27 1019 0.266723414053 Henry Cohn, 2026, needs more optimization.
27 1020 0.267032584120 Henry Cohn, 2026, needs more optimization.
27 1021 0.267233463605 Henry Cohn, 2026, needs more optimization.
27 1022 0.267456828974 Henry Cohn, 2026, needs more optimization.
27 1023 0.267748088526 Henry Cohn, 2026, needs more optimization.
27 1024 0.267991471031 Henry Cohn, 2026, needs more optimization.
28 57 0.028627089329 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
18928⁢x3−784⁢x2−28⁢x+1
28 58 0.033333333334 Henry Cohn, 2025.
30⁢x−1
28 59 0.039700386339 Henry Cohn, 2026, needs more optimization.
28 60 0.039795696625 Henry Cohn, 2026, needs more optimization.
28 61 0.039862976521 Henry Cohn, 2026, 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 0.046144682615 Henry Cohn, 2026, needs more optimization.
28 66 0.047459655816 Henry Cohn, 2026, needs more optimization.
28 67 0.052250985308 Henry Cohn, 2026, needs more optimization.
28 68 0.054257777956 Henry Cohn, 2026, needs more optimization.
28 69 0.055901502440 Henry Cohn, 2026, needs more optimization.
28 70 0.058160876254 Henry Cohn, 2026, needs more optimization.
28 71 0.059587018519 Henry Cohn, 2026, needs more optimization.
28 72 0.061336366335 Henry Cohn, 2026, needs more optimization.
28 73 0.063218203873 Henry Cohn, 2026, needs more optimization.
28 74 0.063894406204 Henry Cohn, 2026, needs more optimization.
28 75 0.064460441492 Henry Cohn, 2026, needs more optimization.
28 76 0.064717246563 Henry Cohn, 2026, needs more optimization.
28 77 0.065929172613 Henry Cohn, 2026, needs more optimization.
28 78 0.067448950547 Henry Cohn, 2026, needs more optimization.
28 79 0.069484886893 Henry Cohn, 2026, needs more optimization.
28 80 0.070912616827 Henry Cohn, 2026, needs more optimization.
28 81 0.072768932746 Henry Cohn, 2026, needs more optimization.
28 82 0.074536648258 Henry Cohn, 2026, needs more optimization.
28 83 0.074910321301 Henry Cohn, 2026, needs more optimization.
28 84 0.075994545567 Henry Cohn, 2026, needs more optimization.
28 85 0.076728633607 Henry Cohn, 2026, needs more optimization.
28 86 0.076884537542 Henry Cohn, 2026, needs more optimization.
28 87 0.076915256965 Henry Cohn, 2026, needs more optimization.
28 88 0.076926979972 Henry Cohn, 2026, needs more optimization.
28 89 0.077241411225 Henry Cohn, 2026, needs more optimization.
28 90 0.077491331789 Henry Cohn, 2026, needs more optimization.
28 91 0.078294912860 Henry Cohn, 2026, needs more optimization.
28 92 0.078682988548 Henry Cohn, 2026, needs more optimization.
28 93 0.079255323811 Henry Cohn, 2026, needs more optimization.
28 94 0.079399739590 Henry Cohn, 2026, needs more optimization.
28 95 0.079800755375 Henry Cohn, 2026, needs more optimization.
28 96 0.080120914814 Henry Cohn, 2026, needs more optimization.
28 97 0.080284244842 Henry Cohn, 2026, needs more optimization.
28 98 0.080499447629 Henry Cohn, 2026, needs more optimization.
28 99 0.080634601073 Henry Cohn, 2026, needs more optimization.
28 100 0.080685071015 Henry Cohn, 2026, needs more optimization.
28 101 0.080685483983 Henry Cohn, 2026, needs more optimization.
28 102 0.080917519837 Henry Cohn, 2026, needs more optimization.
28 103 0.083873260276 Henry Cohn, 2026, needs more optimization.
28 104 0.086415033790 Henry Cohn, 2026, needs more optimization.
28 105 0.086937107911 Henry Cohn, 2026, needs more optimization.
28 106 0.088325312621 Henry Cohn, 2026, needs more optimization.
28 107 0.088694019055 Henry Cohn, 2026, needs more optimization.
28 108 0.089298535377 Henry Cohn, 2026, needs more optimization.
28 109 0.089568787549 Henry Cohn, 2026, needs more optimization.
28 110 0.090120538528 Henry Cohn, 2026, needs more optimization.
28 111 0.090270046523 Henry Cohn, 2026, needs more optimization.
28 112 0.090270049029 Henry Cohn, 2026, needs more optimization.
28 113 0.090270049248 Henry Cohn, 2026, needs more optimization.
28 114 0.090596460445 Henry Cohn, 2026, needs more optimization.
28 115 0.090767280681 Henry Cohn, 2026, needs more optimization.
28 116 0.090842218595 Henry Cohn, 2026, needs more optimization.
28 117 0.090877261769 Henry Cohn, 2026, needs more optimization.
28 118 0.091675659471 Henry Cohn, 2026, needs more optimization.
28 119 0.094289635950 Henry Cohn, 2026, needs more optimization.
28 120 0.096167003383 Henry Cohn, 2026, needs more optimization.
28 121 0.098113599758 Henry Cohn, 2026, needs more optimization.
28 122 0.099654963974 Henry Cohn, 2026, needs more optimization.
28 123 0.101610959661 Henry Cohn, 2026, needs more optimization.
28 124 0.102878763367 Henry Cohn, 2026, needs more optimization.
28 126 0.102923495257 Henry Cohn, 2026, needs more optimization.
28 128 0.103110996862 Henry Cohn, 2026, needs more optimization.
28 129 0.103114200556 Henry Cohn, 2026, needs more optimization.
28 130 0.103125334023 Henry Cohn, 2026, needs more optimization.
28 131 0.104367494186 Henry Cohn, 2026, needs more optimization.
28 132 0.105443884569 Henry Cohn, 2026, needs more optimization.
28 133 0.106279457420 Henry Cohn, 2026, needs more optimization.
28 134 0.108059382593 Henry Cohn, 2026, needs more optimization.
28 135 0.108634808245 Henry Cohn, 2026, needs more optimization.
28 136 0.109571351187 Henry Cohn, 2026, needs more optimization.
28 137 0.109869844862 Henry Cohn, 2026, needs more optimization.
28 138 0.110916124123 Henry Cohn, 2026, needs more optimization.
28 139 0.110935530250 Henry Cohn, 2026, needs more optimization.
28 140 0.111089570549 Henry Cohn, 2026, needs more optimization.
28 150 0.111112389333 Henry Cohn, 2026, needs more optimization.
28 151 0.111780599380 Henry Cohn, 2026, needs more optimization.
28 152 0.118371316423 Henry Cohn, 2026, needs more optimization.
28 153 0.120325049604 Henry Cohn, 2026, needs more optimization.
28 154 0.123353297274 Henry Cohn, 2026, needs more optimization.
28 155 0.125281652732 Henry Cohn, 2026, needs more optimization.
28 156 0.126334484103 Henry Cohn, 2026, needs more optimization.
28 157 0.127125591129 Henry Cohn, 2026, needs more optimization.
28 158 0.127806692866 Henry Cohn, 2026, needs more optimization.
28 182 0.128238684469 Henry Cohn, 2026.
92⁢x2−4⁢x−1
28 183 0.130665724291 Henry Cohn, 2026, needs more optimization.
28 184 0.141664716807 Henry Cohn, 2026, needs more optimization.
28 185 0.142185843953 Henry Cohn, 2026, needs more optimization.
28 186 0.142206483273 Henry Cohn, 2026, needs more optimization.
28 187 0.142215630061 Henry Cohn, 2026, needs more optimization.
28 188 0.142226856537 Henry Cohn, 2026, needs more optimization.
28 189 0.142278813806 Henry Cohn, 2026, needs more optimization.
28 190 0.142278819881 Henry Cohn, 2026, needs more optimization.
28 191 0.142278876726 Henry Cohn, 2026, needs more optimization.
28 192 0.142476217047 Henry Cohn, 2026, needs more optimization.
28 193 0.142524096609 Henry Cohn, 2026, needs more optimization.
28 194 0.142565014391 Henry Cohn, 2026, needs more optimization.
28 195 0.142635250345 Henry Cohn, 2026, needs more optimization.
28 196 0.142728309465 Henry Cohn, 2026, needs more optimization.
28 197 0.142775214194 Henry Cohn, 2026, needs more optimization.
28 198 0.142803496837 Henry Cohn, 2026, needs more optimization.
28 199 0.142881414159 Henry Cohn, 2026, needs more optimization.
28 200 0.143371737286 Henry Cohn, 2026, needs more optimization.
28 201 0.143698799415 Henry Cohn, 2026, needs more optimization.
28 202 0.144188611855 Henry Cohn, 2026, needs more optimization.
28 203 0.145069379356 Henry Cohn, 2026, needs more optimization.
28 204 0.145915089770 Henry Cohn, 2026, needs more optimization.
28 205 0.146229579139 Henry Cohn, 2026, needs more optimization.
28 206 0.146980963062 Henry Cohn, 2026, needs more optimization.
28 208 0.147011287858 Henry Cohn, 2026, needs more optimization.
28 210 0.147012930848 Henry Cohn, 2026, needs more optimization.
28 211 0.147055533113 Henry Cohn, 2026, needs more optimization.
28 212 0.147081490759 Henry Cohn, 2026, needs more optimization.
28 213 0.147107386915 Henry Cohn, 2026, needs more optimization.
28 214 0.147166894972 Henry Cohn, 2026, needs more optimization.
28 215 0.147203837077 Henry Cohn, 2026, needs more optimization.
28 216 0.147655094874 Henry Cohn, 2026, needs more optimization.
28 217 0.147668466428 Henry Cohn, 2026, needs more optimization.
28 218 0.147678412379 Henry Cohn, 2026, needs more optimization.
28 219 0.147983557747 Henry Cohn, 2026, needs more optimization.
28 220 0.148204210015 Henry Cohn, 2026, needs more optimization.
28 222 0.148566688861 Henry Cohn, 2026, needs more optimization.
28 223 0.148696728213 Henry Cohn, 2026, needs more optimization.
28 224 0.148726038305 Henry Cohn, 2026, needs more optimization.
28 225 0.148851163358 Henry Cohn, 2026, needs more optimization.
28 226 0.148960707929 Henry Cohn, 2026, needs more optimization.
28 227 0.148999949099 Henry Cohn, 2026, needs more optimization.
28 228 0.149044632605 Henry Cohn, 2026, needs more optimization.
28 229 0.149218555091 Henry Cohn, 2026, needs more optimization.
28 230 0.149220284210 Henry Cohn, 2026, needs more optimization.
28 231 0.149282465082 Henry Cohn, 2026, needs more optimization.
28 232 0.149288896507 Henry Cohn, 2026, needs more optimization.
28 233 0.149324437626 Henry Cohn, 2026, needs more optimization.
28 234 0.149324921357 Henry Cohn, 2026, needs more optimization.
28 235 0.149326349208 Henry Cohn, 2026, needs more optimization.
28 236 0.149336339563 Henry Cohn, 2026, needs more optimization.
28 237 0.149336371360 Henry Cohn, 2026, needs more optimization.
28 238 0.149624753606 Henry Cohn, 2026, needs more optimization.
28 239 0.149626524762 Henry Cohn, 2026, needs more optimization.
28 240 0.150237459918 Henry Cohn, 2026, needs more optimization.
28 241 0.151243503975 Henry Cohn, 2026, needs more optimization.
28 242 0.152035081157 Henry Cohn, 2026, needs more optimization.
28 243 0.153499196630 Henry Cohn, 2026, needs more optimization.
28 244 0.154489402264 Henry Cohn, 2026, needs more optimization.
28 245 0.155461033491 Henry Cohn, 2026, needs more optimization.
28 246 0.157102308169 Henry Cohn, 2026, needs more optimization.
28 247 0.158396822643 Henry Cohn, 2026, needs more optimization.
28 248 0.159271956576 Henry Cohn, 2026, needs more optimization.
28 249 0.159589966235 Henry Cohn, 2026, needs more optimization.
28 250 0.160322711365 Henry Cohn, 2026, needs more optimization.
28 251 0.161874491306 Henry Cohn, 2026, needs more optimization.
28 252 0.162039629104 Henry Cohn, 2026, needs more optimization.
28 253 0.162058281916 Henry Cohn, 2026, needs more optimization.
28 254 0.162129149890 Henry Cohn, 2026, needs more optimization.
28 255 0.162162307430 Henry Cohn, 2026, needs more optimization.
28 256 0.162449010558 Henry Cohn, 2026, needs more optimization.
28 257 0.162665553308 Henry Cohn, 2026, needs more optimization.
28 258 0.162871904872 Henry Cohn, 2026, needs more optimization.
28 259 0.163037246843 Henry Cohn, 2026, needs more optimization.
28 260 0.163404738224 Henry Cohn, 2026, needs more optimization.
28 261 0.163587790256 Henry Cohn, 2026, needs more optimization.
28 262 0.163845681555 Henry Cohn, 2026, needs more optimization.
28 263 0.163944650165 Henry Cohn, 2026, needs more optimization.
28 264 0.164167674866 Henry Cohn, 2026, needs more optimization.
28 265 0.164369303912 Henry Cohn, 2026, needs more optimization.
28 266 0.164673244644 Henry Cohn, 2026, needs more optimization.
28 267 0.164750155608 Henry Cohn, 2026, needs more optimization.
28 268 0.164862651755 Henry Cohn, 2026, needs more optimization.
28 269 0.164968779717 Henry Cohn, 2026, needs more optimization.
28 270 0.165098211968 Henry Cohn, 2026, needs more optimization.
28 271 0.165237582705 Henry Cohn, 2026, needs more optimization.
28 272 0.165357085615 Henry Cohn, 2026, needs more optimization.
28 273 0.165389003068 Henry Cohn, 2026, needs more optimization.
28 274 0.165401721725 Henry Cohn, 2026, needs more optimization.
28 275 0.165487469623 Henry Cohn, 2026, needs more optimization.
28 276 0.165505526194 Henry Cohn, 2026, needs more optimization.
28 277 0.165526766003 Henry Cohn, 2026, needs more optimization.
28 278 0.165666112293 Henry Cohn, 2026, needs more optimization.
28 279 0.165688301344 Henry Cohn, 2026, needs more optimization.
28 280 0.165729819673 Henry Cohn, 2026, needs more optimization.
28 281 0.165747023350 Henry Cohn, 2026, needs more optimization.
28 282 0.166086064761 Henry Cohn, 2026, needs more optimization.
28 283 0.166133732969 Henry Cohn, 2026, needs more optimization.
28 284 0.166373395798 Henry Cohn, 2026, needs more optimization.
28 285 0.166400948078 Henry Cohn, 2026, needs more optimization.
28 286 0.166437754172 Henry Cohn, 2026, needs more optimization.
28 287 0.166494940512 Henry Cohn, 2026, needs more optimization.
28 288 0.166514174159 Henry Cohn, 2026, needs more optimization.
28 289 0.166579334031 Henry Cohn, 2026, needs more optimization.
28 290 0.166603210092 Henry Cohn, 2026, needs more optimization.
28 291 0.166629471733 Henry Cohn, 2026, needs more optimization.
28 292 0.166637147189 Henry Cohn, 2026, needs more optimization.
28 293 0.166644821013 Henry Cohn, 2026, needs more optimization.
28 294 0.166653434067 Henry Cohn, 2026, needs more optimization.
28 295 0.166656857757 Henry Cohn, 2026, needs more optimization.
28 296 0.166657865125 Henry Cohn, 2026, needs more optimization.
28 297 0.166664586519 Henry Cohn, 2026, needs more optimization.
28 298 0.166667544631 Henry Cohn, 2026, needs more optimization.
28 299 0.166671232342 Henry Cohn, 2026, needs more optimization.
28 300 0.166671235958 Henry Cohn, 2026, needs more optimization.
28 301 0.166671347225 Henry Cohn, 2026, needs more optimization.
28 302 0.166675966664 Henry Cohn, 2026, needs more optimization.
28 303 0.166676419856 Henry Cohn, 2026, needs more optimization.
28 304 0.166676706928 Henry Cohn, 2026, needs more optimization.
28 305 0.166678441956 Henry Cohn, 2026, needs more optimization.
28 306 0.172578074879 Orthogonal union of 302 points in 26 dimensions and 4 points in 2 dimensions.
28 307 0.174248066437 Orthogonal union of 303 points in 26 dimensions and 4 points in 2 dimensions.
28 308 0.175775990573 Orthogonal union of 304 points in 26 dimensions and 4 points in 2 dimensions.
28 309 0.176948577968 Orthogonal union of 305 points in 26 dimensions and 4 points in 2 dimensions.
28 311 0.178580682542 Henry Cohn, 2026, needs more optimization.
28 314 0.178581228334 Henry Cohn, 2026, needs more optimization.
28 320 0.178582132899 Henry Cohn, 2026, needs more optimization.
28 324 0.178586145226 Henry Cohn, 2026, needs more optimization.
28 325 0.178589673361 Henry Cohn, 2026, needs more optimization.
28 326 0.178601949626 Henry Cohn, 2026, needs more optimization.
28 327 0.178607028108 Henry Cohn, 2026, needs more optimization.
28 329 0.178609113711 Henry Cohn, 2026, needs more optimization.
28 330 0.178612606775 Henry Cohn, 2026, needs more optimization.
28 331 0.178905097986 Henry Cohn, 2026, needs more optimization.
28 333 0.178918951529 Henry Cohn, 2026, needs more optimization.
28 334 0.178930808861 Henry Cohn, 2026, needs more optimization.
28 335 0.180176661879 Henry Cohn, 2026, needs more optimization.
28 336 0.180197778151 Henry Cohn, 2026, needs more optimization.
28 337 0.180233366833 Henry Cohn, 2026, needs more optimization.
28 338 0.180567282618 Henry Cohn, 2026, needs more optimization.
28 339 0.181882000985 Orthogonal union of 337 points in 27 dimensions and 2 points in 1 dimension.
28 340 0.181991830560 Orthogonal union of 338 points in 27 dimensions and 2 points in 1 dimension.
28 341 0.182172332103 Orthogonal union of 339 points in 27 dimensions and 2 points in 1 dimension.
28 342 0.182663876477 Orthogonal union of 340 points in 27 dimensions and 2 points in 1 dimension.
28 343 0.182834754256 Henry Cohn, 2026, needs more optimization.
28 344 0.183755876003 Henry Cohn, 2026, needs more optimization.
28 345 0.183921615565 Henry Cohn, 2026, needs more optimization.
28 346 0.185046095191 Henry Cohn, 2026, needs more optimization.
28 347 0.185746207913 Orthogonal union of 345 points in 27 dimensions and 2 points in 1 dimension.
28 348 0.186599047694 Orthogonal union of 346 points in 27 dimensions and 2 points in 1 dimension.
28 349 0.187404938731 Orthogonal union of 347 points in 27 dimensions and 2 points in 1 dimension.
28 350 0.187660154409 Henry Cohn, 2026, needs more optimization.
28 351 0.187684446429 Henry Cohn, 2026, needs more optimization.
28 352 0.187868028334 Henry Cohn, 2026, needs more optimization.
28 353 0.187878000698 Henry Cohn, 2026, needs more optimization.
28 354 0.187934840191 Henry Cohn, 2026, needs more optimization.
28 355 0.189013786516 Henry Cohn, 2026, needs more optimization.
28 357 0.189226023507 Henry Cohn, 2026, needs more optimization.
28 358 0.189408390158 Henry Cohn, 2026, needs more optimization.
28 359 0.189449010037 Henry Cohn, 2026, needs more optimization.
28 360 0.190275421573 Henry Cohn, 2026, needs more optimization.
28 361 0.192229000144 Henry Cohn, 2026, needs more optimization.
28 362 0.192562880306 Henry Cohn, 2026, needs more optimization.
28 363 0.192777470921 Henry Cohn, 2026, needs more optimization.
28 364 0.193104924518 Henry Cohn, 2026, needs more optimization.
28 365 0.193151920776 Henry Cohn, 2026, needs more optimization.
28 366 0.193266825461 Henry Cohn, 2026, needs more optimization.
28 367 0.193549835038 Henry Cohn, 2026, needs more optimization.
28 368 0.193935947397 Henry Cohn, 2026, needs more optimization.
28 369 0.194067272048 Henry Cohn, 2026, needs more optimization.
28 370 0.194316968463 Henry Cohn, 2026, needs more optimization.
28 371 0.194545710456 Henry Cohn, 2026, needs more optimization.
28 372 0.194824396989 Henry Cohn, 2026, needs more optimization.
28 373 0.195074885010 Henry Cohn, 2026, needs more optimization.
28 374 0.195272993703 Henry Cohn, 2026, needs more optimization.
28 375 0.195531121940 Henry Cohn, 2026, needs more optimization.
28 376 0.195637298111 Henry Cohn, 2026, needs more optimization.
28 377 0.195669949670 Henry Cohn, 2026, needs more optimization.
28 378 0.195916731513 Henry Cohn, 2026, needs more optimization.
28 380 0.196138206509 Henry Cohn, 2026, needs more optimization.
28 381 0.196305185685 Henry Cohn, 2026, needs more optimization.
28 382 0.196526995837 Henry Cohn, 2026, needs more optimization.
28 383 0.196963823838 Henry Cohn, 2026, needs more optimization.
28 384 0.197085990477 Henry Cohn, 2026, needs more optimization.
28 387 0.197323514189 Henry Cohn, 2026, needs more optimization.
28 388 0.197368103933 Henry Cohn, 2026, needs more optimization.
28 389 0.197552442243 Henry Cohn, 2026, needs more optimization.
28 390 0.197764976336 Henry Cohn, 2026, needs more optimization.
28 392 0.197856627530 Henry Cohn, 2026, needs more optimization.
28 393 0.197949892668 Henry Cohn, 2026, needs more optimization.
28 394 0.198135859985 Henry Cohn, 2026, needs more optimization.
28 395 0.198280691218 Henry Cohn, 2026, needs more optimization.
28 396 0.198354970496 Henry Cohn, 2026, needs more optimization.
28 398 0.198389832321 Henry Cohn, 2026, needs more optimization.
28 399 0.198434485932 Henry Cohn, 2026, needs more optimization.
28 400 0.198569807320 Henry Cohn, 2026, needs more optimization.
28 401 0.198682779325 Henry Cohn, 2026, needs more optimization.
28 404 0.198714110483 Henry Cohn, 2026, needs more optimization.
28 405 0.198799396519 Henry Cohn, 2026, needs more optimization.
28 407 0.198898723880 Henry Cohn, 2026, needs more optimization.
28 408 0.198978321947 Henry Cohn, 2026, needs more optimization.
28 409 0.199006861647 Henry Cohn, 2026, needs more optimization.
28 410 0.199113655627 Henry Cohn, 2026, needs more optimization.
28 412 0.199199389291 Henry Cohn, 2026, needs more optimization.
28 413 0.199213513699 Henry Cohn, 2026, needs more optimization.
28 414 0.199324971339 Henry Cohn, 2026, needs more optimization.
28 416 0.199332885938 Henry Cohn, 2026, needs more optimization.
28 417 0.199398565535 Henry Cohn, 2026, needs more optimization.
28 418 0.199404096004 Henry Cohn, 2026, needs more optimization.
28 419 0.199505269366 Henry Cohn, 2026, needs more optimization.
28 420 0.199507146105 Henry Cohn, 2026, needs more optimization.
28 421 0.199534031853 Henry Cohn, 2026, needs more optimization.
28 422 0.199537797325 Henry Cohn, 2026, needs more optimization.
28 423 0.199567023965 Henry Cohn, 2026, needs more optimization.
28 424 0.199573287248 Henry Cohn, 2026, needs more optimization.
28 431 0.199600608407 Henry Cohn, 2026, needs more optimization.
28 433 0.199613415549 Henry Cohn, 2026, needs more optimization.
28 434 0.199637803699 Henry Cohn, 2026, needs more optimization.
28 435 0.199648653258 Henry Cohn, 2026, needs more optimization.
28 436 0.199658350741 Henry Cohn, 2026, needs more optimization.
28 438 0.199719096986 Henry Cohn, 2026, needs more optimization.
28 439 0.199726409077 Henry Cohn, 2026, needs more optimization.
28 440 0.199756079493 Henry Cohn, 2026, needs more optimization.
28 441 0.199770157905 Henry Cohn, 2026, needs more optimization.
28 442 0.199787627767 Henry Cohn, 2026, needs more optimization.
28 443 0.199787792489 Henry Cohn, 2026, needs more optimization.
28 445 0.199810285549 Henry Cohn, 2026, needs more optimization.
28 446 0.199854474802 Henry Cohn, 2026, needs more optimization.
28 447 0.199875701565 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.
28 451 0.199914641024 Henry Cohn, 2026, needs more optimization.
28 452 0.199921532351 Henry Cohn, 2026, needs more optimization.
28 453 0.199928246100 Henry Cohn, 2026, needs more optimization.
28 455 0.199963902508 Henry Cohn, 2026, needs more optimization.
28 459 0.199972736148 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
28 569 0.200113680374 Henry Cohn, 2026, needs more optimization.
28 570 0.200113699705 Henry Cohn, 2026, needs more optimization.
28 571 0.200237259974 Henry Cohn, 2026, needs more optimization.
28 572 0.200274494357 Henry Cohn, 2026, needs more optimization.
28 577 0.200286669385 Henry Cohn, 2026, needs more optimization.
28 581 0.200370396719 Henry Cohn, 2026, needs more optimization.
28 583 0.200537601232 Henry Cohn, 2026, needs more optimization.
28 586 0.200635904115 Henry Cohn, 2026, needs more optimization.
28 587 0.200811882539 Henry Cohn, 2026, needs more optimization.
28 588 0.201225169044 Henry Cohn, 2026, needs more optimization.
28 589 0.201253079623 Henry Cohn, 2026, needs more optimization.
28 590 0.201432830586 Henry Cohn, 2026, needs more optimization.
28 592 0.201767903636 Henry Cohn, 2026, needs more optimization.
28 594 0.202509090744 Henry Cohn, 2026, needs more optimization.
28 595 0.202806345581 Henry Cohn, 2026, needs more optimization.
28 596 0.203304964017 Henry Cohn, 2026, needs more optimization.
28 597 0.203951251933 Henry Cohn, 2026, needs more optimization.
28 598 0.204403213900 Henry Cohn, 2026, needs more optimization.
28 599 0.204837762363 Henry Cohn, 2026, needs more optimization.
28 600 0.205540213988 Henry Cohn, 2026, needs more optimization.
28 604 0.238031278755 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.
28 620 0.238200670778 Henry Cohn, 2026, needs more optimization.
28 621 0.238200678941 Henry Cohn, 2026, needs more optimization.
28 622 0.238200729711 Henry Cohn, 2026, needs more optimization.
28 626 0.238310332742 Henry Cohn, 2026, needs more optimization.
28 627 0.238318363955 Henry Cohn, 2026, needs more optimization.
28 631 0.238355762765 Henry Cohn, 2026, needs more optimization.
28 633 0.238383171871 Henry Cohn, 2026, needs more optimization.
28 634 0.238667344495 Henry Cohn, 2026, needs more optimization.
28 639 0.238676577895 Henry Cohn, 2026, needs more optimization.
28 640 0.238997089727 Henry Cohn, 2026, needs more optimization.
28 651 0.239075539203 Henry Cohn, 2026, needs more optimization.
28 658 0.239364615860 Henry Cohn, 2026, needs more optimization.
28 662 0.240074039007 Henry Cohn, 2026, needs more optimization.
28 676 0.240148496034 Henry Cohn, 2026, needs more optimization.
28 680 0.241144265153 Henry Cohn, 2026, needs more optimization.
28 681 0.243101333884 Henry Cohn, 2026, needs more optimization.
28 694 0.243105277549 Henry Cohn, 2026, needs more optimization.
28 699 0.244096812452 Henry Cohn, 2026, needs more optimization.
28 704 0.245149483066 Henry Cohn, 2026, needs more optimization.
28 706 0.245327361287 Henry Cohn, 2026, needs more optimization.
28 713 0.245427589598 Henry Cohn, 2026, needs more optimization.
28 714 0.246521027446 Henry Cohn, 2026, needs more optimization.
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 0.250024209405 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 0.038083347705 Henry Cohn, 2026, needs more optimization.
29 62 0.039262684438 Henry Cohn, 2026, needs more optimization.
29 63 0.039606569084 Henry Cohn, 2026, needs more optimization.
29 64 0.044358602714 Henry Cohn, 2026, needs more optimization.
29 65 0.044606014596 Henry Cohn, 2026, needs more optimization.
29 66 0.044624560378 Henry Cohn, 2026, needs more optimization.
29 67 0.044634959638 Henry Cohn, 2026, needs more optimization.
29 68 0.046023755275 Henry Cohn, 2026, needs more optimization.
29 69 0.050838211850 Henry Cohn, 2026, needs more optimization.
29 70 0.052553724181 Henry Cohn, 2026, needs more optimization.
29 71 0.054294848299 Henry Cohn, 2026, needs more optimization.
29 72 0.056102523445 Henry Cohn, 2026, needs more optimization.
29 73 0.057724695253 Henry Cohn, 2026, needs more optimization.
29 74 0.059424887877 Henry Cohn, 2026, needs more optimization.
29 75 0.060942469775 Henry Cohn, 2026, needs more optimization.
29 76 0.062593921311 Henry Cohn, 2026, needs more optimization.
29 77 0.063118772153 Henry Cohn, 2026, needs more optimization.
29 78 0.063579419232 Henry Cohn, 2026, needs more optimization.
29 79 0.064149508725 Henry Cohn, 2026, needs more optimization.
29 80 0.065731223905 Henry Cohn, 2026, needs more optimization.
29 81 0.066916771097 Henry Cohn, 2026, needs more optimization.
29 82 0.068551140992 Henry Cohn, 2026, needs more optimization.
29 83 0.070359470510 Henry Cohn, 2026, needs more optimization.
29 84 0.072177323531 Henry Cohn, 2026, needs more optimization.
29 85 0.073571723199 Henry Cohn, 2026, needs more optimization.
29 86 0.074839660480 Henry Cohn, 2026, needs more optimization.
29 87 0.075744746089 Henry Cohn, 2026, needs more optimization.
29 88 0.075920843902 Henry Cohn, 2026, needs more optimization.
29 89 0.076456234973 Henry Cohn, 2026, needs more optimization.
29 90 0.076802873164 Henry Cohn, 2026, needs more optimization.
29 91 0.076986011909 Henry Cohn, 2026, needs more optimization.
29 92 0.077171103398 Henry Cohn, 2026, needs more optimization.
29 93 0.077370861783 Henry Cohn, 2026, needs more optimization.
29 94 0.077819999579 Henry Cohn, 2026, needs more optimization.
29 95 0.078080044551 Henry Cohn, 2026, needs more optimization.
29 96 0.078171353101 Henry Cohn, 2026, needs more optimization.
29 97 0.078819540020 Henry Cohn, 2026, needs more optimization.
29 98 0.078879345670 Henry Cohn, 2026, needs more optimization.
29 99 0.079122369282 Henry Cohn, 2026, needs more optimization.
29 100 0.079421807827 Henry Cohn, 2026, needs more optimization.
29 101 0.080120970703 Henry Cohn, 2026, needs more optimization.
29 102 0.080261661364 Henry Cohn, 2026, needs more optimization.
29 103 0.080658815687 Henry Cohn, 2026, needs more optimization.
29 104 0.080673075187 Henry Cohn, 2026, needs more optimization.
29 105 0.080717042485 Henry Cohn, 2026, needs more optimization.
29 106 0.082053148437 Henry Cohn, 2026, needs more optimization.
29 107 0.083055104647 Henry Cohn, 2026, needs more optimization.
29 108 0.084789498759 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 0.089548687633 Henry Cohn, 2026, needs more optimization.
29 114 0.089843801757 Henry Cohn, 2026, needs more optimization.
29 115 0.089940094460 Henry Cohn, 2026, needs more optimization.
29 116 0.090013372974 Henry Cohn, 2026, needs more optimization.
29 117 0.090304373822 Henry Cohn, 2026, needs more optimization.
29 118 0.090583599238 Henry Cohn, 2026, needs more optimization.
29 119 0.090701484137 Henry Cohn, 2026, needs more optimization.
29 120 0.090751274265 Henry Cohn, 2026, needs more optimization.
29 121 0.091123624162 Henry Cohn, 2026, needs more optimization.
29 122 0.091845015676 Henry Cohn, 2026, needs more optimization.
29 123 0.093254360064 Henry Cohn, 2026, needs more optimization.
29 124 0.094254725390 Henry Cohn, 2026, needs more optimization.
29 125 0.096614678439 Henry Cohn, 2026, needs more optimization.
29 126 0.098256839001 Henry Cohn, 2026, needs more optimization.
29 127 0.100033346593 Henry Cohn, 2026, needs more optimization.
29 128 0.101514436638 Henry Cohn, 2026, needs more optimization.
29 129 0.102427503855 Henry Cohn, 2026, needs more optimization.
29 130 0.102457215282 Henry Cohn, 2026, needs more optimization.
29 131 0.102540925709 Henry Cohn, 2026, needs more optimization.
29 132 0.102579884357 Henry Cohn, 2026, needs more optimization.
29 133 0.102601074720 Henry Cohn, 2026, needs more optimization.
29 134 0.102731718092 Henry Cohn, 2026, needs more optimization.
29 135 0.103129981697 Henry Cohn, 2026, needs more optimization.
29 136 0.103853517527 Henry Cohn, 2026, needs more optimization.
29 137 0.105306990633 Henry Cohn, 2026, needs more optimization.
29 138 0.106385463525 Henry Cohn, 2026, needs more optimization.
29 139 0.107478191292 Henry Cohn, 2026, needs more optimization.
29 140 0.108487734178 Henry Cohn, 2026, needs more optimization.
29 141 0.108745094421 Henry Cohn, 2026, needs more optimization.
29 142 0.109632640157 Henry Cohn, 2026, needs more optimization.
29 143 0.110516657907 Henry Cohn, 2026, needs more optimization.
29 144 0.110745676934 Henry Cohn, 2026, needs more optimization.
29 145 0.110906903518 Henry Cohn, 2026, needs more optimization.
29 150 0.111111895633 Henry Cohn, 2026, needs more optimization.
29 152 0.111112389333 Orthogonal union of 150 points in 28 dimensions and 2 points in 1 dimension.
29 153 0.111780599380 Orthogonal union of 151 points in 28 dimensions and 2 points in 1 dimension.
29 154 0.117383167379 Henry Cohn, 2026, needs more optimization.
29 155 0.118312403129 Henry Cohn, 2026, needs more optimization.
29 156 0.119780105874 Henry Cohn, 2026, needs more optimization.
29 157 0.121414532866 Henry Cohn, 2026, needs more optimization.
29 158 0.123124288763 Henry Cohn, 2026, needs more optimization.
29 159 0.124379562430 Henry Cohn, 2026, needs more optimization.
29 160 0.125449501229 Henry Cohn, 2026, needs more optimization.
29 161 0.126539347563 Henry Cohn, 2026, needs more optimization.
29 163 0.127297587557 Henry Cohn, 2026, needs more optimization.
29 164 0.128083991317 Henry Cohn, 2026, needs more optimization.
29 165 0.128100520123 Henry Cohn, 2026, needs more optimization.
29 184 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 2 points in 1 dimension.
92⁢x2−4⁢x−1
29 185 0.128250599002 Henry Cohn, 2026, needs more optimization.
29 186 0.136346491585 Henry Cohn, 2026, needs more optimization.
29 187 0.137216070237 Henry Cohn, 2026, needs more optimization.
29 188 0.137966039982 Henry Cohn, 2026, needs more optimization.
29 189 0.138336938537 Henry Cohn, 2026, needs more optimization.
29 190 0.138986581470 Henry Cohn, 2026, needs more optimization.
29 191 0.139947916613 Henry Cohn, 2026, needs more optimization.
29 192 0.140859553993 Henry Cohn, 2026, needs more optimization.
29 193 0.141751388311 Henry Cohn, 2026, needs more optimization.
29 194 0.141868050770 Henry Cohn, 2026, needs more optimization.
29 195 0.141873898361 Henry Cohn, 2026, needs more optimization.
29 196 0.142057892938 Henry Cohn, 2026, needs more optimization.
29 197 0.142095652590 Henry Cohn, 2026, needs more optimization.
29 198 0.142170558725 Henry Cohn, 2026, needs more optimization.
29 199 0.142205576416 Henry Cohn, 2026, needs more optimization.
29 200 0.142286569800 Henry Cohn, 2026, needs more optimization.
29 201 0.142348967207 Henry Cohn, 2026, needs more optimization.
29 202 0.142400306465 Henry Cohn, 2026, needs more optimization.
29 203 0.142422959551 Henry Cohn, 2026, needs more optimization.
29 204 0.142451066101 Henry Cohn, 2026, needs more optimization.
29 205 0.142558045283 Henry Cohn, 2026, needs more optimization.
29 206 0.142703152642 Henry Cohn, 2026, needs more optimization.
29 207 0.142865553344 Henry Cohn, 2026, needs more optimization.
29 208 0.142994666733 Henry Cohn, 2026, needs more optimization.
29 209 0.143548836595 Henry Cohn, 2026, needs more optimization.
29 210 0.143761526148 Henry Cohn, 2026, needs more optimization.
29 211 0.144242298137 Henry Cohn, 2026, needs more optimization.
29 212 0.144978931600 Henry Cohn, 2026, needs more optimization.
29 213 0.145546804335 Henry Cohn, 2026, needs more optimization.
29 214 0.145856275004 Henry Cohn, 2026, needs more optimization.
29 215 0.145880057184 Henry Cohn, 2026, needs more optimization.
29 217 0.145880090481 Henry Cohn, 2026, needs more optimization.
29 218 0.146072663394 Henry Cohn, 2026, needs more optimization.
29 219 0.146217902110 Henry Cohn, 2026, needs more optimization.
29 220 0.146490977011 Henry Cohn, 2026, needs more optimization.
29 221 0.146551619035 Henry Cohn, 2026, needs more optimization.
29 222 0.146671785537 Henry Cohn, 2026, needs more optimization.
29 223 0.146780915738 Henry Cohn, 2026, needs more optimization.
29 224 0.146957787643 Henry Cohn, 2026, needs more optimization.
29 225 0.147081984880 Henry Cohn, 2026, needs more optimization.
29 235 0.147102976680 Henry Cohn, 2026.
87⁢x2−6⁢x−1
29 236 0.147900562342 Henry Cohn, 2026, needs more optimization.
29 237 0.147931207917 Henry Cohn, 2026, needs more optimization.
29 238 0.147942688509 Henry Cohn, 2026, needs more optimization.
29 239 0.148004983252 Henry Cohn, 2026, needs more optimization.
29 240 0.148020405224 Henry Cohn, 2026, needs more optimization.
29 241 0.148381406284 Henry Cohn, 2026, needs more optimization.
29 242 0.148441709754 Henry Cohn, 2026, needs more optimization.
29 243 0.148873301948 Henry Cohn, 2026, needs more optimization.
29 244 0.148962613820 Henry Cohn, 2026, needs more optimization.
29 245 0.149661791039 Henry Cohn, 2026, needs more optimization.
29 246 0.149996674505 Henry Cohn, 2026, needs more optimization.
29 247 0.150271923158 Henry Cohn, 2026, needs more optimization.
29 248 0.150805649817 Henry Cohn, 2026, needs more optimization.
29 249 0.151106771674 Henry Cohn, 2026, needs more optimization.
29 250 0.152418951812 Henry Cohn, 2026, needs more optimization.
29 251 0.153298055353 Henry Cohn, 2026, needs more optimization.
29 252 0.154040120935 Henry Cohn, 2026, needs more optimization.
29 253 0.154588562497 Henry Cohn, 2026, needs more optimization.
29 254 0.155263727542 Henry Cohn, 2026, needs more optimization.
29 255 0.156078836254 Henry Cohn, 2026, needs more optimization.
29 256 0.157035377059 Henry Cohn, 2026, needs more optimization.
29 257 0.157801201318 Henry Cohn, 2026, needs more optimization.
29 258 0.159169161134 Henry Cohn, 2026, needs more optimization.
29 259 0.159312161208 Henry Cohn, 2026, needs more optimization.
29 260 0.160851162807 Henry Cohn, 2026, needs more optimization.
29 261 0.161397669904 Henry Cohn, 2026, needs more optimization.
29 262 0.161907759590 Henry Cohn, 2026, needs more optimization.
29 263 0.162276708391 Henry Cohn, 2026, needs more optimization.
29 264 0.162330363491 Henry Cohn, 2026, needs more optimization.
29 265 0.162353672775 Henry Cohn, 2026, needs more optimization.
29 266 0.162366893561 Henry Cohn, 2026, needs more optimization.
29 267 0.162366923526 Henry Cohn, 2026, needs more optimization.
29 268 0.162436932183 Henry Cohn, 2026, needs more optimization.
29 269 0.162826795135 Henry Cohn, 2026, needs more optimization.
29 270 0.162863899942 Henry Cohn, 2026, needs more optimization.
29 271 0.162924159877 Henry Cohn, 2026, needs more optimization.
29 272 0.163181208252 Henry Cohn, 2026, needs more optimization.
29 273 0.163378113491 Henry Cohn, 2026, needs more optimization.
29 274 0.163440175444 Henry Cohn, 2026, needs more optimization.
29 275 0.163521349949 Henry Cohn, 2026, needs more optimization.
29 276 0.163583763433 Henry Cohn, 2026, needs more optimization.
29 277 0.163665938784 Henry Cohn, 2026, needs more optimization.
29 278 0.163816135491 Henry Cohn, 2026, needs more optimization.
29 279 0.163890031745 Henry Cohn, 2026, needs more optimization.
29 280 0.163968312003 Henry Cohn, 2026, needs more optimization.
29 281 0.164186510370 Henry Cohn, 2026, needs more optimization.
29 282 0.164312398073 Henry Cohn, 2026, needs more optimization.
29 283 0.164462025605 Henry Cohn, 2026, needs more optimization.
29 284 0.164572133281 Henry Cohn, 2026, needs more optimization.
29 285 0.164699160396 Henry Cohn, 2026, needs more optimization.
29 286 0.164742208005 Henry Cohn, 2026, needs more optimization.
29 287 0.164849275196 Henry Cohn, 2026, needs more optimization.
29 288 0.164985454925 Henry Cohn, 2026, needs more optimization.
29 289 0.165071302230 Henry Cohn, 2026, needs more optimization.
29 290 0.165161107494 Henry Cohn, 2026, needs more optimization.
29 292 0.165196763508 Henry Cohn, 2026, needs more optimization.
29 293 0.165216910358 Henry Cohn, 2026, needs more optimization.
29 294 0.165293758046 Henry Cohn, 2026, needs more optimization.
29 295 0.165295698421 Henry Cohn, 2026, needs more optimization.
29 296 0.165317868958 Henry Cohn, 2026, needs more optimization.
29 297 0.165365010133 Henry Cohn, 2026, needs more optimization.
29 298 0.165425006833 Henry Cohn, 2026, needs more optimization.
29 299 0.165538654678 Henry Cohn, 2026, needs more optimization.
29 300 0.165578459040 Henry Cohn, 2026, needs more optimization.
29 301 0.165637765885 Henry Cohn, 2026, needs more optimization.
29 302 0.166669106994 Henry Cohn, 2026, needs more optimization.
29 303 0.166671343196 Henry Cohn, 2026, needs more optimization.
29 304 0.166674408621 Henry Cohn, 2026, needs more optimization.
29 305 0.166674414071 Henry Cohn, 2026, needs more optimization.
29 306 0.166674419072 Henry Cohn, 2026, needs more optimization.
29 307 0.166675692499 Henry Cohn, 2026, needs more optimization.
29 308 0.172578074879 Orthogonal union of 302 points in 26 dimensions and 6 points in 3 dimensions.
29 309 0.174248066437 Orthogonal union of 303 points in 26 dimensions and 6 points in 3 dimensions.
29 310 0.175775990573 Orthogonal union of 304 points in 26 dimensions and 6 points in 3 dimensions.
29 311 0.176948577968 Orthogonal union of 305 points in 26 dimensions and 6 points in 3 dimensions.
29 312 0.178289243338 Henry Cohn, 2026, needs more optimization.
29 314 0.178305695420 Henry Cohn, 2026, needs more optimization.
29 315 0.178308400425 Henry Cohn, 2026, needs more optimization.
29 316 0.178339040728 Henry Cohn, 2026, needs more optimization.
29 317 0.178339291980 Henry Cohn, 2026, needs more optimization.
29 318 0.178345034910 Henry Cohn, 2026, needs more optimization.
29 320 0.178372247701 Henry Cohn, 2026, needs more optimization.
29 322 0.178524343678 Henry Cohn, 2026, needs more optimization.
29 323 0.178541036631 Henry Cohn, 2026, needs more optimization.
29 324 0.178541366817 Henry Cohn, 2026, needs more optimization.
29 325 0.178541709961 Henry Cohn, 2026, needs more optimization.
29 326 0.178541952339 Henry Cohn, 2026, needs more optimization.
29 328 0.178541991575 Henry Cohn, 2026, needs more optimization.
29 330 0.178548498923 Henry Cohn, 2026, needs more optimization.
29 332 0.178548990399 Henry Cohn, 2026, needs more optimization.
29 333 0.178557654419 Henry Cohn, 2026, needs more optimization.
29 334 0.178563852807 Henry Cohn, 2026, needs more optimization.
29 335 0.178564844746 Henry Cohn, 2026, needs more optimization.
29 337 0.178574760369 Henry Cohn, 2026, needs more optimization.
29 338 0.178605114677 Henry Cohn, 2026, needs more optimization.
29 339 0.178607388032 Henry Cohn, 2026, needs more optimization.
29 340 0.178614605001 Henry Cohn, 2026, needs more optimization.
29 341 0.178617197389 Henry Cohn, 2026, needs more optimization.
29 342 0.178627344547 Henry Cohn, 2026, needs more optimization.
29 343 0.178629568501 Henry Cohn, 2026, needs more optimization.
29 344 0.178658948428 Henry Cohn, 2026, needs more optimization.
29 345 0.178690763665 Henry Cohn, 2026, needs more optimization.
29 346 0.180473484460 Henry Cohn, 2026, needs more optimization.
29 347 0.180500928215 Henry Cohn, 2026, needs more optimization.
29 348 0.180537667254 Henry Cohn, 2026, needs more optimization.
29 349 0.181806305259 Henry Cohn, 2026, needs more optimization.
29 350 0.182396911441 Henry Cohn, 2026, needs more optimization.
29 351 0.182491815983 Henry Cohn, 2026, needs more optimization.
29 352 0.182611403430 Henry Cohn, 2026, needs more optimization.
29 354 0.182626535799 Henry Cohn, 2026, needs more optimization.
29 355 0.183380426679 Henry Cohn, 2026, needs more optimization.
29 357 0.183566656909 Henry Cohn, 2026, needs more optimization.
29 358 0.183614164959 Henry Cohn, 2026, needs more optimization.
29 359 0.183646554623 Henry Cohn, 2026, needs more optimization.
29 360 0.183663502854 Henry Cohn, 2026, needs more optimization.
29 361 0.185113459633 Henry Cohn, 2026, needs more optimization.
29 362 0.185730723291 Henry Cohn, 2026, needs more optimization.
29 363 0.186092791518 Henry Cohn, 2026, needs more optimization.
29 364 0.186267764045 Henry Cohn, 2026, needs more optimization.
29 365 0.186330643034 Henry Cohn, 2026, needs more optimization.
29 366 0.186815845909 Henry Cohn, 2026, needs more optimization.
29 367 0.187168752710 Henry Cohn, 2026, needs more optimization.
29 368 0.188024489630 Henry Cohn, 2026, needs more optimization.
29 369 0.188249748982 Henry Cohn, 2026, needs more optimization.
29 370 0.188594960737 Henry Cohn, 2026, needs more optimization.
29 371 0.188700870572 Henry Cohn, 2026, needs more optimization.
29 372 0.188786507535 Henry Cohn, 2026, needs more optimization.
29 373 0.189118010311 Henry Cohn, 2026, needs more optimization.
29 374 0.189559578374 Henry Cohn, 2026, needs more optimization.
29 375 0.189713108965 Henry Cohn, 2026, needs more optimization.
29 376 0.190337911750 Henry Cohn, 2026, needs more optimization.
29 377 0.190500240928 Henry Cohn, 2026, needs more optimization.
29 378 0.190678039801 Henry Cohn, 2026, needs more optimization.
29 379 0.190825317144 Henry Cohn, 2026, needs more optimization.
29 380 0.190993949791 Henry Cohn, 2026, needs more optimization.
29 381 0.191195028532 Henry Cohn, 2026, needs more optimization.
29 382 0.191293729804 Henry Cohn, 2026, needs more optimization.
29 383 0.191626584910 Henry Cohn, 2026, needs more optimization.
29 384 0.191735891023 Henry Cohn, 2026, needs more optimization.
29 385 0.191892834128 Henry Cohn, 2026, needs more optimization.
29 386 0.192051748660 Henry Cohn, 2026, needs more optimization.
29 387 0.192227781327 Henry Cohn, 2026, needs more optimization.
29 388 0.192391626451 Henry Cohn, 2026, needs more optimization.
29 389 0.193028488758 Henry Cohn, 2026, needs more optimization.
29 390 0.193086351866 Henry Cohn, 2026, needs more optimization.
29 391 0.193386927384 Henry Cohn, 2026, needs more optimization.
29 392 0.193705012828 Henry Cohn, 2026, needs more optimization.
29 393 0.194018198082 Henry Cohn, 2026, needs more optimization.
29 394 0.194110963188 Henry Cohn, 2026, needs more optimization.
29 395 0.194378062557 Henry Cohn, 2026, needs more optimization.
29 396 0.194605906787 Henry Cohn, 2026, needs more optimization.
29 451 0.194630872484 Henry Cohn, 2026, needs more optimization.
149⁢x−29
29 452 0.196848794833 Henry Cohn, 2026, needs more optimization.
29 453 0.199420023879 Henry Cohn, 2026, needs more optimization.
29 454 0.199438434019 Henry Cohn, 2026, needs more optimization.
29 456 0.199456243600 Henry Cohn, 2026, needs more optimization.
29 459 0.199487282311 Henry Cohn, 2026, needs more optimization.
29 460 0.199552879083 Henry Cohn, 2026, needs more optimization.
29 461 0.199563993671 Henry Cohn, 2026, needs more optimization.
29 462 0.199615431080 Henry Cohn, 2026, needs more optimization.
29 463 0.199675971837 Henry Cohn, 2026, needs more optimization.
29 464 0.199681133967 Henry Cohn, 2026, needs more optimization.
29 469 0.199696006041 Henry Cohn, 2026, needs more optimization.
29 470 0.199698908936 Henry Cohn, 2026, needs more optimization.
29 471 0.199733843674 Henry Cohn, 2026, needs more optimization.
29 472 0.199748418709 Henry Cohn, 2026, needs more optimization.
29 474 0.199751561085 Henry Cohn, 2026, needs more optimization.
29 475 0.199779471040 Henry Cohn, 2026, needs more optimization.
29 476 0.199789732707 Henry Cohn, 2026, needs more optimization.
29 477 0.199800848732 Henry Cohn, 2026, needs more optimization.
29 479 0.199820166734 Henry Cohn, 2026, needs more optimization.
29 480 0.199827484413 Henry Cohn, 2026, needs more optimization.
29 481 0.199832082424 Henry Cohn, 2026, needs more optimization.
29 482 0.199834253646 Henry Cohn, 2026, needs more optimization.
29 483 0.199835704011 Henry Cohn, 2026, needs more optimization.
29 484 0.199850270116 Henry Cohn, 2026, needs more optimization.
29 485 0.199871259571 Henry Cohn, 2026, needs more optimization.
29 486 0.199873817750 Henry Cohn, 2026, needs more optimization.
29 487 0.199913495443 Henry Cohn, 2026, needs more optimization.
29 488 0.199924367649 Henry Cohn, 2026, needs more optimization.
29 490 0.199932108085 Henry Cohn, 2026, needs more optimization.
29 491 0.199945064238 Henry Cohn, 2026, needs more optimization.
29 495 0.199962130881 Henry Cohn, 2026, needs more optimization.
29 496 0.199985100134 Henry Cohn, 2026, needs more optimization.
29 576 0.2 Henry Cohn, 2026.
5⁢x−1
29 585 0.200046648867 Henry Cohn, 2026, needs more optimization.
29 602 0.200199339107 Henry Cohn, 2026, needs more optimization.
29 603 0.205964306346 Henry Cohn, 2026, needs more optimization.
29 604 0.236755244569 Henry Cohn, 2026, needs more optimization.
29 605 0.236786138587 Henry Cohn, 2026, needs more optimization.
29 606 0.236866667916 Henry Cohn, 2026, needs more optimization.
29 607 0.237568763383 Henry Cohn, 2026, needs more optimization.
29 608 0.237579102548 Henry Cohn, 2026, needs more optimization.
29 610 0.237667717656 Henry Cohn, 2026, needs more optimization.
29 611 0.237813136538 Henry Cohn, 2026, needs more optimization.
29 614 0.237821281448 Henry Cohn, 2026, needs more optimization.
29 618 0.237864772658 Henry Cohn, 2026, needs more optimization.
29 619 0.237911164625 Henry Cohn, 2026, needs more optimization.
29 622 0.237969504979 Henry Cohn, 2026, needs more optimization.
29 623 0.238015446024 Henry Cohn, 2026, needs more optimization.
29 626 0.238027035787 Henry Cohn, 2026, needs more optimization.
29 628 0.238073610791 Henry Cohn, 2026, needs more optimization.
29 630 0.238073782076 Henry Cohn, 2026, needs more optimization.
29 634 0.238109438615 Henry Cohn, 2026, needs more optimization.
29 639 0.238127969980 Henry Cohn, 2026, needs more optimization.
29 643 0.238474375482 Henry Cohn, 2026, needs more optimization.
29 653 0.238521203115 Henry Cohn, 2026, needs more optimization.
29 660 0.238549507809 Henry Cohn, 2026, needs more optimization.
29 662 0.238617109768 Henry Cohn, 2026, needs more optimization.
29 663 0.238975391560 Henry Cohn, 2026, needs more optimization.
29 681 0.239016460087 Henry Cohn, 2026, needs more optimization.
29 682 0.240331685542 Henry Cohn, 2026, needs more optimization.
29 684 0.242427140583 Henry Cohn, 2026, needs more optimization.
29 686 0.242483733183 Henry Cohn, 2026, needs more optimization.
29 690 0.242564515191 Henry Cohn, 2026, needs more optimization.
29 693 0.242615980984 Henry Cohn, 2026, needs more optimization.
29 694 0.242689239887 Henry Cohn, 2026, needs more optimization.
29 695 0.242795560856 Henry Cohn, 2026, needs more optimization.
29 696 0.242795561922 Henry Cohn, 2026, needs more optimization.
29 697 0.242818965852 Henry Cohn, 2026, needs more optimization.
29 698 0.242967225801 Henry Cohn, 2026, needs more optimization.
29 699 0.242967987667 Henry Cohn, 2026, needs more optimization.
29 701 0.242986920816 Henry Cohn, 2026, needs more optimization.
29 704 0.243216511620 Henry Cohn, 2026, needs more optimization.
29 708 0.243224530244 Henry Cohn, 2026, needs more optimization.
29 710 0.243403572527 Henry Cohn, 2026, needs more optimization.
29 711 0.243424885804 Henry Cohn, 2026, needs more optimization.
29 713 0.243705051317 Henry Cohn, 2026, needs more optimization.
29 725 0.243718348025 Henry Cohn, 2026, needs more optimization.
29 726 0.243734019361 Henry Cohn, 2026, needs more optimization.
29 727 0.243742073257 Henry Cohn, 2026, needs more optimization.
29 729 0.243820012464 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 0.250024209405 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 0.250805775254 Henry Cohn, 2026, needs more optimization.
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 0.037939283120 Henry Cohn, 2026, needs more optimization.
30 64 0.038350090034 Henry Cohn, 2026, needs more optimization.
30 65 0.038479664976 Henry Cohn, 2026, needs more optimization.
30 66 0.044301112845 Henry Cohn, 2026, needs more optimization.
30 67 0.044456014514 Henry Cohn, 2026, needs more optimization.
30 68 0.044556632069 Henry Cohn, 2026, needs more optimization.
30 69 0.044563860713 Henry Cohn, 2026, needs more optimization.
30 70 0.044757477296 Henry Cohn, 2026, needs more optimization.
30 71 0.049847237720 Henry Cohn, 2026, needs more optimization.
30 72 0.051259526089 Henry Cohn, 2026, needs more optimization.
30 73 0.052421740293 Henry Cohn, 2026, needs more optimization.
30 74 0.054131831062 Henry Cohn, 2026, needs more optimization.
30 75 0.056243923398 Henry Cohn, 2026, needs more optimization.
30 76 0.057552662592 Henry Cohn, 2026, needs more optimization.
30 77 0.059053189763 Henry Cohn, 2026, needs more optimization.
30 78 0.060498966176 Henry Cohn, 2026, needs more optimization.
30 79 0.062140014437 Henry Cohn, 2026, needs more optimization.
30 80 0.062598281088 Henry Cohn, 2026, needs more optimization.
30 81 0.062840662714 Henry Cohn, 2026, needs more optimization.
30 82 0.064290492948 Henry Cohn, 2026, needs more optimization.
30 83 0.065112988237 Henry Cohn, 2026, needs more optimization.
30 84 0.066460260059 Henry Cohn, 2026, needs more optimization.
30 85 0.068030731665 Henry Cohn, 2026, needs more optimization.
30 86 0.069489198711 Henry Cohn, 2026, needs more optimization.
30 87 0.070938522143 Henry Cohn, 2026, needs more optimization.
30 88 0.072505464092 Henry Cohn, 2026, needs more optimization.
30 89 0.073901964498 Henry Cohn, 2026, needs more optimization.
30 90 0.074431580844 Henry Cohn, 2026, needs more optimization.
30 91 0.075429099944 Henry Cohn, 2026, needs more optimization.
30 92 0.076276608709 Henry Cohn, 2026, needs more optimization.
30 93 0.076899897327 Henry Cohn, 2026, needs more optimization.
30 94 0.076905066488 Henry Cohn, 2026, needs more optimization.
30 95 0.076937703910 Henry Cohn, 2026, needs more optimization.
30 96 0.077028877611 Henry Cohn, 2026, needs more optimization.
30 97 0.077180874406 Henry Cohn, 2026, needs more optimization.
30 98 0.077277068549 Henry Cohn, 2026, needs more optimization.
30 99 0.077386848379 Henry Cohn, 2026, needs more optimization.
30 100 0.077770052790 Henry Cohn, 2026, needs more optimization.
30 101 0.077944330281 Henry Cohn, 2026, needs more optimization.
30 102 0.078190137598 Henry Cohn, 2026, needs more optimization.
30 103 0.078825214426 Henry Cohn, 2026, needs more optimization.
30 104 0.079148121366 Henry Cohn, 2026, needs more optimization.
30 105 0.079631984215 Henry Cohn, 2026, needs more optimization.
30 106 0.080491310066 Henry Cohn, 2026, needs more optimization.
30 107 0.080667019097 Henry Cohn, 2026, needs more optimization.
30 108 0.080814373233 Henry Cohn, 2026, needs more optimization.
30 109 0.081524428652 Henry Cohn, 2026, needs more optimization.
30 110 0.082137984074 Henry Cohn, 2026, needs more optimization.
30 111 0.082309250507 Henry Cohn, 2026, needs more optimization.
30 112 0.083254192355 Henry Cohn, 2026, needs more optimization.
30 113 0.085914923911 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 0.088092135650 Henry Cohn, 2026, needs more optimization.
30 116 0.088188851441 Henry Cohn, 2026, needs more optimization.
30 117 0.088552613743 Henry Cohn, 2026, needs more optimization.
30 118 0.089022485384 Henry Cohn, 2026, needs more optimization.
30 119 0.089392923339 Henry Cohn, 2026, needs more optimization.
30 120 0.089821344667 Henry Cohn, 2026, needs more optimization.
30 121 0.090076155813 Henry Cohn, 2026, needs more optimization.
30 122 0.090368148616 Henry Cohn, 2026, needs more optimization.
30 123 0.090523748851 Henry Cohn, 2026, needs more optimization.
30 124 0.090790939581 Henry Cohn, 2026, needs more optimization.
30 125 0.091076674415 Henry Cohn, 2026, needs more optimization.
30 126 0.091624817005 Henry Cohn, 2026, needs more optimization.
30 127 0.092702729313 Henry Cohn, 2026, needs more optimization.
30 128 0.094034337955 Henry Cohn, 2026, needs more optimization.
30 129 0.095273918185 Henry Cohn, 2026, needs more optimization.
30 130 0.097302108081 Henry Cohn, 2026, needs more optimization.
30 131 0.098512387987 Henry Cohn, 2026, needs more optimization.
30 132 0.099549074965 Henry Cohn, 2026, needs more optimization.
30 133 0.100627373644 Henry Cohn, 2026, needs more optimization.
30 134 0.102005780605 Henry Cohn, 2026, needs more optimization.
30 135 0.102542681986 Henry Cohn, 2026, needs more optimization.
30 136 0.102554222719 Henry Cohn, 2026, needs more optimization.
30 137 0.102576170200 Henry Cohn, 2026, needs more optimization.
30 138 0.102582654799 Henry Cohn, 2026, needs more optimization.
30 139 0.102619157638 Henry Cohn, 2026, needs more optimization.
30 140 0.102663226391 Henry Cohn, 2026, needs more optimization.
30 141 0.102770104367 Henry Cohn, 2026, needs more optimization.
30 142 0.104129008184 Henry Cohn, 2026, needs more optimization.
30 143 0.105327318639 Henry Cohn, 2026, needs more optimization.
30 144 0.106168230383 Henry Cohn, 2026, needs more optimization.
30 145 0.107203617009 Henry Cohn, 2026, needs more optimization.
30 146 0.108228518318 Henry Cohn, 2026, needs more optimization.
30 147 0.108928257728 Henry Cohn, 2026, needs more optimization.
30 148 0.109291334792 Henry Cohn, 2026, needs more optimization.
30 149 0.109890878850 Henry Cohn, 2026, needs more optimization.
30 150 0.110412128461 Henry Cohn, 2026, needs more optimization.
30 151 0.110744160769 Henry Cohn, 2026, needs more optimization.
30 152 0.111111895633 Orthogonal union of 150 points in 29 dimensions and 2 points in 1 dimension.
30 154 0.111112389333 Orthogonal union of 150 points in 28 dimensions and 4 points in 2 dimensions.
30 155 0.111128016277 Henry Cohn, 2026, needs more optimization.
30 156 0.114001613698 Henry Cohn, 2026, needs more optimization.
30 157 0.115172511122 Henry Cohn, 2026, needs more optimization.
30 158 0.116171210634 Henry Cohn, 2026, needs more optimization.
30 159 0.117143959868 Henry Cohn, 2026, needs more optimization.
30 160 0.118118645397 Henry Cohn, 2026, needs more optimization.
30 161 0.118698421162 Henry Cohn, 2026, needs more optimization.
30 162 0.119883308291 Henry Cohn, 2026, needs more optimization.
30 163 0.120528256433 Henry Cohn, 2026, needs more optimization.
30 164 0.121560008630 Henry Cohn, 2026, needs more optimization.
30 165 0.122518921133 Henry Cohn, 2026, needs more optimization.
30 166 0.123252063659 Henry Cohn, 2026, needs more optimization.
30 167 0.124276530338 Henry Cohn, 2026, needs more optimization.
30 168 0.125310611640 Henry Cohn, 2026, needs more optimization.
30 169 0.126468094247 Henry Cohn, 2026, needs more optimization.
30 170 0.127109069999 Henry Cohn, 2026, needs more optimization.
30 171 0.127785020266 Henry Cohn, 2026, needs more optimization.
30 186 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 4 points in 2 dimensions.
92⁢x2−4⁢x−1
30 187 0.128249759466 Henry Cohn, 2026, needs more optimization.
30 188 0.134366787094 Henry Cohn, 2026, needs more optimization.
30 189 0.134549378147 Henry Cohn, 2026, needs more optimization.
30 190 0.134739801229 Henry Cohn, 2026, needs more optimization.
30 191 0.134967378025 Henry Cohn, 2026, needs more optimization.
30 192 0.135182951889 Henry Cohn, 2026, needs more optimization.
30 193 0.135698685076 Henry Cohn, 2026, needs more optimization.
30 194 0.136212268673 Henry Cohn, 2026, needs more optimization.
30 195 0.136991613126 Henry Cohn, 2026, needs more optimization.
30 196 0.137592707374 Henry Cohn, 2026, needs more optimization.
30 197 0.137965894920 Henry Cohn, 2026, needs more optimization.
30 198 0.138517739496 Henry Cohn, 2026, needs more optimization.
30 199 0.139406147392 Henry Cohn, 2026, needs more optimization.
30 200 0.140310314368 Henry Cohn, 2026, needs more optimization.
30 201 0.141158133266 Henry Cohn, 2026, needs more optimization.
30 202 0.141185162809 Henry Cohn, 2026, needs more optimization.
30 203 0.141280717205 Henry Cohn, 2026, needs more optimization.
30 204 0.141306235724 Henry Cohn, 2026, needs more optimization.
30 205 0.141407419325 Henry Cohn, 2026, needs more optimization.
30 206 0.141523592771 Henry Cohn, 2026, needs more optimization.
30 207 0.141571883573 Henry Cohn, 2026, needs more optimization.
30 208 0.141645556606 Henry Cohn, 2026, needs more optimization.
30 209 0.141837661680 Henry Cohn, 2026, needs more optimization.
30 210 0.141994337136 Henry Cohn, 2026, needs more optimization.
30 211 0.142244545399 Henry Cohn, 2026, needs more optimization.
30 212 0.142298901058 Henry Cohn, 2026, needs more optimization.
30 213 0.142299933392 Henry Cohn, 2026, needs more optimization.
30 214 0.142370711739 Henry Cohn, 2026, needs more optimization.
30 215 0.142512668843 Henry Cohn, 2026, needs more optimization.
30 216 0.142827784831 Henry Cohn, 2026, needs more optimization.
30 217 0.142871444937 Henry Cohn, 2026, needs more optimization.
30 218 0.143128476635 Henry Cohn, 2026, needs more optimization.
30 219 0.143711246788 Henry Cohn, 2026, needs more optimization.
30 220 0.143960995079 Henry Cohn, 2026, needs more optimization.
30 221 0.144389951345 Henry Cohn, 2026, needs more optimization.
30 222 0.144505717468 Henry Cohn, 2026, needs more optimization.
30 223 0.144863504163 Henry Cohn, 2026, needs more optimization.
30 224 0.144985253688 Henry Cohn, 2026, needs more optimization.
30 225 0.145290144375 Henry Cohn, 2026, needs more optimization.
30 226 0.145428372730 Henry Cohn, 2026, needs more optimization.
30 227 0.145579774556 Henry Cohn, 2026, needs more optimization.
30 228 0.146116086843 Henry Cohn, 2026, needs more optimization.
30 229 0.146445186717 Henry Cohn, 2026, needs more optimization.
30 230 0.146502602106 Henry Cohn, 2026, needs more optimization.
30 231 0.146664782534 Henry Cohn, 2026, needs more optimization.
30 232 0.146768339651 Henry Cohn, 2026, needs more optimization.
30 233 0.146934298719 Henry Cohn, 2026, needs more optimization.
30 234 0.147085806540 Henry Cohn, 2026, needs more optimization.
30 235 0.147096908280 Henry Cohn, 2026, needs more optimization.
30 237 0.147102976680 Orthogonal union of 235 points in 29 dimensions and 2 points in 1 dimension.
87⁢x2−6⁢x−1
30 238 0.147211919371 Henry Cohn, 2026, needs more optimization.
30 239 0.147349396440 Henry Cohn, 2026, needs more optimization.
30 240 0.147405485692 Henry Cohn, 2026, needs more optimization.
30 241 0.147627634210 Henry Cohn, 2026, needs more optimization.
30 242 0.147846462054 Henry Cohn, 2026, needs more optimization.
30 243 0.147846678756 Henry Cohn, 2026, needs more optimization.
30 244 0.147883428721 Henry Cohn, 2026, needs more optimization.
30 245 0.147883547537 Henry Cohn, 2026, needs more optimization.
30 246 0.147963888861 Henry Cohn, 2026, needs more optimization.
30 247 0.147963889299 Henry Cohn, 2026, needs more optimization.
30 248 0.147992684340 Henry Cohn, 2026, needs more optimization.
30 249 0.147996293996 Henry Cohn, 2026, needs more optimization.
30 250 0.148285325949 Henry Cohn, 2026, needs more optimization.
30 251 0.148466978980 Henry Cohn, 2026, needs more optimization.
30 252 0.148818942399 Henry Cohn, 2026, needs more optimization.
30 253 0.149009093266 Henry Cohn, 2026, needs more optimization.
30 254 0.149607435160 Henry Cohn, 2026, needs more optimization.
30 255 0.150039036697 Henry Cohn, 2026, needs more optimization.
30 256 0.150735586801 Henry Cohn, 2026, needs more optimization.
30 257 0.151098050444 Henry Cohn, 2026, needs more optimization.
30 258 0.151149524351 Henry Cohn, 2026, needs more optimization.
30 259 0.151564083598 Henry Cohn, 2026, needs more optimization.
30 260 0.152833556590 Henry Cohn, 2026, needs more optimization.
30 261 0.153148166703 Henry Cohn, 2026, needs more optimization.
30 262 0.153850560118 Henry Cohn, 2026, needs more optimization.
30 263 0.154950921442 Henry Cohn, 2026, needs more optimization.
30 264 0.155045641816 Henry Cohn, 2026, needs more optimization.
30 265 0.155907924836 Henry Cohn, 2026, needs more optimization.
30 266 0.157384730318 Henry Cohn, 2026, needs more optimization.
30 267 0.158015483641 Henry Cohn, 2026, needs more optimization.
30 268 0.158654202197 Henry Cohn, 2026, needs more optimization.
30 269 0.159230624864 Henry Cohn, 2026, needs more optimization.
30 270 0.160233796245 Henry Cohn, 2026, needs more optimization.
30 271 0.160868988609 Henry Cohn, 2026, needs more optimization.
30 272 0.161452591478 Henry Cohn, 2026, needs more optimization.
30 273 0.161795337663 Henry Cohn, 2026, needs more optimization.
30 274 0.161795461422 Henry Cohn, 2026, needs more optimization.
30 275 0.161798396253 Henry Cohn, 2026, needs more optimization.
30 276 0.161841930984 Henry Cohn, 2026, needs more optimization.
30 277 0.161855021689 Henry Cohn, 2026, needs more optimization.
30 278 0.161894760862 Henry Cohn, 2026, needs more optimization.
30 279 0.161901461353 Henry Cohn, 2026, needs more optimization.
30 280 0.161917194910 Henry Cohn, 2026, needs more optimization.
30 281 0.161985159186 Henry Cohn, 2026, needs more optimization.
30 282 0.162021574548 Henry Cohn, 2026, needs more optimization.
30 283 0.162125276379 Henry Cohn, 2026, needs more optimization.
30 284 0.162331211986 Henry Cohn, 2026, needs more optimization.
30 285 0.162391884341 Henry Cohn, 2026, needs more optimization.
30 286 0.162531986093 Henry Cohn, 2026, needs more optimization.
30 287 0.162788068941 Henry Cohn, 2026, needs more optimization.
30 288 0.162895207913 Henry Cohn, 2026, needs more optimization.
30 289 0.163012696287 Henry Cohn, 2026, needs more optimization.
30 290 0.163071982460 Henry Cohn, 2026, needs more optimization.
30 291 0.163201019190 Henry Cohn, 2026, needs more optimization.
30 292 0.163381662507 Henry Cohn, 2026, needs more optimization.
30 293 0.163382928773 Henry Cohn, 2026, needs more optimization.
30 294 0.163475144339 Henry Cohn, 2026, needs more optimization.
30 295 0.163597411813 Henry Cohn, 2026, needs more optimization.
30 297 0.163753287460 Henry Cohn, 2026, needs more optimization.
30 298 0.163786783907 Henry Cohn, 2026, needs more optimization.
30 299 0.163897906311 Henry Cohn, 2026, needs more optimization.
30 300 0.163966322119 Henry Cohn, 2026, needs more optimization.
30 301 0.164076580222 Henry Cohn, 2026, needs more optimization.
30 302 0.164312822720 Henry Cohn, 2026, needs more optimization.
30 303 0.164447720065 Henry Cohn, 2026, needs more optimization.
30 307 0.166555188748 Henry Cohn, 2026, needs more optimization.
30 308 0.166560425465 Henry Cohn, 2026, needs more optimization.
30 309 0.166573926000 Henry Cohn, 2026, needs more optimization.
30 311 0.166602659297 Henry Cohn, 2026, needs more optimization.
30 312 0.175775990573 Orthogonal union of 304 points in 26 dimensions and 8 points in 4 dimensions.
30 313 0.176281220522 Henry Cohn, 2026, needs more optimization.
30 314 0.176317796826 Henry Cohn, 2026, needs more optimization.
30 315 0.177024344904 Henry Cohn, 2026, needs more optimization.
30 317 0.177027868396 Henry Cohn, 2026, needs more optimization.
30 318 0.177362209165 Henry Cohn, 2026, needs more optimization.
30 319 0.177501774610 Henry Cohn, 2026, needs more optimization.
30 320 0.177913253225 Henry Cohn, 2026, needs more optimization.
30 321 0.177931576081 Henry Cohn, 2026, needs more optimization.
30 322 0.177942743972 Henry Cohn, 2026, needs more optimization.
30 323 0.177982638381 Henry Cohn, 2026, needs more optimization.
30 324 0.178007779871 Henry Cohn, 2026, needs more optimization.
30 325 0.178034189069 Henry Cohn, 2026, needs more optimization.
30 326 0.178047369374 Henry Cohn, 2026, needs more optimization.
30 327 0.178095280027 Henry Cohn, 2026, needs more optimization.
30 328 0.178111003975 Henry Cohn, 2026, needs more optimization.
30 329 0.178120086872 Henry Cohn, 2026, needs more optimization.
30 331 0.178127656430 Henry Cohn, 2026, needs more optimization.
30 332 0.178146739485 Henry Cohn, 2026, needs more optimization.
30 333 0.178158427599 Henry Cohn, 2026, needs more optimization.
30 335 0.178170193694 Henry Cohn, 2026, needs more optimization.
30 336 0.178230387738 Henry Cohn, 2026, needs more optimization.
30 337 0.178403026849 Henry Cohn, 2026, needs more optimization.
30 338 0.178425444265 Henry Cohn, 2026, needs more optimization.
30 341 0.178427879599 Henry Cohn, 2026, needs more optimization.
30 342 0.178454403076 Henry Cohn, 2026, needs more optimization.
30 346 0.178472049599 Henry Cohn, 2026, needs more optimization.
30 347 0.178490049651 Henry Cohn, 2026, needs more optimization.
30 349 0.178744387005 Henry Cohn, 2026, needs more optimization.
30 350 0.178749812839 Henry Cohn, 2026, needs more optimization.
30 351 0.178783324386 Henry Cohn, 2026, needs more optimization.
30 352 0.179113121631 Henry Cohn, 2026, needs more optimization.
30 353 0.179286389549 Henry Cohn, 2026, needs more optimization.
30 354 0.179291580213 Henry Cohn, 2026, needs more optimization.
30 355 0.179301823351 Henry Cohn, 2026, needs more optimization.
30 356 0.180268521965 Henry Cohn, 2026, needs more optimization.
30 357 0.180281036718 Henry Cohn, 2026, needs more optimization.
30 358 0.180445475310 Henry Cohn, 2026, needs more optimization.
30 359 0.180505081130 Henry Cohn, 2026, needs more optimization.
30 360 0.180521953595 Henry Cohn, 2026, needs more optimization.
30 361 0.180779811395 Henry Cohn, 2026, needs more optimization.
30 362 0.181215025487 Henry Cohn, 2026, needs more optimization.
30 363 0.181545872580 Henry Cohn, 2026, needs more optimization.
30 364 0.182608464402 Henry Cohn, 2026, needs more optimization.
30 365 0.182678111289 Henry Cohn, 2026, needs more optimization.
30 366 0.182977308514 Henry Cohn, 2026, needs more optimization.
30 367 0.183080269698 Henry Cohn, 2026, needs more optimization.
30 368 0.183333365413 Henry Cohn, 2026, needs more optimization.
30 369 0.183522517923 Henry Cohn, 2026, needs more optimization.
30 371 0.185253874359 Henry Cohn, 2026, needs more optimization.
30 372 0.185616349731 Henry Cohn, 2026, needs more optimization.
30 373 0.185909538693 Henry Cohn, 2026, needs more optimization.
30 374 0.186700623973 Henry Cohn, 2026, needs more optimization.
30 375 0.186866978888 Henry Cohn, 2026, needs more optimization.
30 376 0.186986484166 Henry Cohn, 2026, needs more optimization.
30 377 0.187130364141 Henry Cohn, 2026, needs more optimization.
30 378 0.187169417283 Henry Cohn, 2026, needs more optimization.
30 379 0.187307975094 Henry Cohn, 2026, needs more optimization.
30 380 0.187364250548 Henry Cohn, 2026, needs more optimization.
30 381 0.187375095138 Henry Cohn, 2026, needs more optimization.
30 382 0.187390724373 Henry Cohn, 2026, needs more optimization.
30 383 0.187564086927 Henry Cohn, 2026, needs more optimization.
30 384 0.187905077593 Henry Cohn, 2026, needs more optimization.
30 385 0.188063967209 Henry Cohn, 2026, needs more optimization.
30 386 0.188068144746 Henry Cohn, 2026, needs more optimization.
30 387 0.188074263113 Henry Cohn, 2026, needs more optimization.
30 388 0.188698080934 Henry Cohn, 2026, needs more optimization.
30 389 0.188758300884 Henry Cohn, 2026, needs more optimization.
30 390 0.188828953173 Henry Cohn, 2026, needs more optimization.
30 391 0.189108843361 Henry Cohn, 2026, needs more optimization.
30 392 0.189179634983 Henry Cohn, 2026, needs more optimization.
30 393 0.189562311105 Henry Cohn, 2026, needs more optimization.
30 394 0.189681604508 Henry Cohn, 2026, needs more optimization.
30 395 0.189983788953 Henry Cohn, 2026, needs more optimization.
30 396 0.190081443006 Henry Cohn, 2026, needs more optimization.
30 397 0.190452582988 Henry Cohn, 2026, needs more optimization.
30 398 0.190833612044 Henry Cohn, 2026, needs more optimization.
30 399 0.190920894609 Henry Cohn, 2026, needs more optimization.
30 400 0.191313567620 Henry Cohn, 2026, needs more optimization.
30 401 0.191592880737 Henry Cohn, 2026, needs more optimization.
30 402 0.191709544015 Henry Cohn, 2026, needs more optimization.
30 403 0.192249018241 Henry Cohn, 2026, needs more optimization.
30 404 0.192423719648 Henry Cohn, 2026, needs more optimization.
30 405 0.192623640430 Henry Cohn, 2026, needs more optimization.
30 406 0.192915163349 Henry Cohn, 2026, needs more optimization.
30 407 0.193184153010 Henry Cohn, 2026, needs more optimization.
30 408 0.193247584954 Henry Cohn, 2026, needs more optimization.
30 409 0.193611780935 Henry Cohn, 2026, needs more optimization.
30 410 0.193908885863 Henry Cohn, 2026, needs more optimization.
30 411 0.194247011250 Henry Cohn, 2026, needs more optimization.
30 412 0.194530622139 Henry Cohn, 2026, needs more optimization.
30 453 0.194630872484 Orthogonal union of 451 points in 29 dimensions and 2 points in 1 dimension.
149⁢x−29
30 454 0.194658336866 Henry Cohn, 2026, needs more optimization.
30 455 0.198037817394 Henry Cohn, 2026, needs more optimization.
30 456 0.198060884405 Henry Cohn, 2026, needs more optimization.
30 457 0.198123882682 Henry Cohn, 2026, needs more optimization.
30 458 0.198145987530 Henry Cohn, 2026, needs more optimization.
30 459 0.198167742690 Henry Cohn, 2026, needs more optimization.
30 460 0.198232032100 Henry Cohn, 2026, needs more optimization.
30 461 0.198248477696 Henry Cohn, 2026, needs more optimization.
30 462 0.198393603155 Henry Cohn, 2026, needs more optimization.
30 463 0.198500002641 Henry Cohn, 2026, needs more optimization.
30 464 0.198536250113 Henry Cohn, 2026, needs more optimization.
30 465 0.198574804596 Henry Cohn, 2026, needs more optimization.
30 466 0.198596886881 Henry Cohn, 2026, needs more optimization.
30 467 0.198649427795 Henry Cohn, 2026, needs more optimization.
30 468 0.198665837670 Henry Cohn, 2026, needs more optimization.
30 469 0.198714633983 Henry Cohn, 2026, needs more optimization.
30 470 0.198800944917 Henry Cohn, 2026, needs more optimization.
30 471 0.198827136887 Henry Cohn, 2026, needs more optimization.
30 472 0.198932648793 Henry Cohn, 2026, needs more optimization.
30 473 0.198950693898 Henry Cohn, 2026, needs more optimization.
30 474 0.199021305922 Henry Cohn, 2026, needs more optimization.
30 475 0.199083966327 Henry Cohn, 2026, needs more optimization.
30 476 0.199104992204 Henry Cohn, 2026, needs more optimization.
30 477 0.199178384672 Henry Cohn, 2026, needs more optimization.
30 478 0.199184397570 Henry Cohn, 2026, needs more optimization.
30 479 0.199218076059 Henry Cohn, 2026, needs more optimization.
30 480 0.199281195480 Henry Cohn, 2026, needs more optimization.
30 482 0.199301935075 Henry Cohn, 2026, needs more optimization.
30 483 0.199336319561 Henry Cohn, 2026, needs more optimization.
30 484 0.199364934343 Henry Cohn, 2026, needs more optimization.
30 485 0.199381168878 Henry Cohn, 2026, needs more optimization.
30 487 0.199388617137 Henry Cohn, 2026, needs more optimization.
30 488 0.199437225647 Henry Cohn, 2026, needs more optimization.
30 489 0.199475285637 Henry Cohn, 2026, needs more optimization.
30 490 0.199502402853 Henry Cohn, 2026, needs more optimization.
30 491 0.199511334455 Henry Cohn, 2026, needs more optimization.
30 492 0.199551357964 Henry Cohn, 2026, needs more optimization.
30 501 0.199559146397 Henry Cohn, 2026, needs more optimization.
30 502 0.199641432561 Henry Cohn, 2026, needs more optimization.
30 505 0.199644277438 Henry Cohn, 2026, needs more optimization.
30 506 0.199669205601 Henry Cohn, 2026, needs more optimization.
30 507 0.199676602486 Henry Cohn, 2026, needs more optimization.
30 508 0.199691358811 Henry Cohn, 2026, needs more optimization.
30 509 0.199724674908 Henry Cohn, 2026, needs more optimization.
30 510 0.199730387386 Henry Cohn, 2026, needs more optimization.
30 511 0.199737938155 Henry Cohn, 2026, needs more optimization.
30 512 0.199795913476 Henry Cohn, 2026, needs more optimization.
30 513 0.199806096227 Henry Cohn, 2026, needs more optimization.
30 514 0.199849224728 Henry Cohn, 2026, needs more optimization.
30 515 0.199851340485 Henry Cohn, 2026, needs more optimization.
30 517 0.199858118045 Henry Cohn, 2026, needs more optimization.
30 519 0.199867254494 Henry Cohn, 2026, needs more optimization.
30 520 0.199867895375 Henry Cohn, 2026, needs more optimization.
30 521 0.199884214385 Henry Cohn, 2026, needs more optimization.
30 522 0.199893525002 Henry Cohn, 2026, needs more optimization.
30 523 0.199898304315 Henry Cohn, 2026, needs more optimization.
30 524 0.199910663741 Henry Cohn, 2026, needs more optimization.
30 525 0.199915359834 Henry Cohn, 2026, needs more optimization.
30 527 0.199941029291 Henry Cohn, 2026, needs more optimization.
30 528 0.199944965502 Henry Cohn, 2026, needs more optimization.
30 529 0.199945229559 Henry Cohn, 2026, needs more optimization.
30 532 0.199964962671 Henry Cohn, 2026, needs more optimization.
30 534 0.199975962979 Henry Cohn, 2026, needs more optimization.
30 537 0.199981527559 Henry Cohn, 2026, needs more optimization.
30 538 0.199985616364 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.
30 656 0.2 Henry Cohn, 2026.
5⁢x−1
30 657 0.203357314626 Henry Cohn, 2026, needs more optimization.
30 663 0.238294826155 Henry Cohn, 2026, needs more optimization.
30 673 0.238553683006 Henry Cohn, 2026, needs more optimization.
30 675 0.238666044718 Henry Cohn, 2026, needs more optimization.
30 677 0.238926508361 Henry Cohn, 2026, needs more optimization.
30 683 0.238977655473 Henry Cohn, 2026, needs more optimization.
30 692 0.239738524068 Henry Cohn, 2026, needs more optimization.
30 695 0.240405531897 Henry Cohn, 2026, needs more optimization.
30 697 0.240491612347 Henry Cohn, 2026, needs more optimization.
30 698 0.240525864273 Henry Cohn, 2026, needs more optimization.
30 705 0.240575958333 Henry Cohn, 2026, needs more optimization.
30 706 0.240596369236 Henry Cohn, 2026, needs more optimization.
30 709 0.240597885390 Henry Cohn, 2026, needs more optimization.
30 710 0.240615762431 Henry Cohn, 2026, needs more optimization.
30 711 0.240655409506 Henry Cohn, 2026, needs more optimization.
30 714 0.240670921606 Henry Cohn, 2026, needs more optimization.
30 715 0.240682652389 Henry Cohn, 2026, needs more optimization.
30 716 0.240687696011 Henry Cohn, 2026, needs more optimization.
30 719 0.240702840048 Henry Cohn, 2026, needs more optimization.
30 724 0.240713402979 Henry Cohn, 2026, needs more optimization.
30 731 0.240805366205 Henry Cohn, 2026, needs more optimization.
30 732 0.240942214723 Henry Cohn, 2026, needs more optimization.
30 733 0.240946025242 Henry Cohn, 2026, needs more optimization.
30 734 0.240969592012 Henry Cohn, 2026, needs more optimization.
30 735 0.240980607171 Henry Cohn, 2026, needs more optimization.
30 737 0.241118003965 Henry Cohn, 2026, needs more optimization.
30 738 0.241182747082 Henry Cohn, 2026, needs more optimization.
30 740 0.241426986090 Henry Cohn, 2026, needs more optimization.
30 744 0.241451366095 Henry Cohn, 2026, needs more optimization.
30 747 0.241497654970 Henry Cohn, 2026, needs more optimization.
30 748 0.241516965260 Henry Cohn, 2026, needs more optimization.
30 749 0.241560150922 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 1024 0.249939028962 Henry Cohn, 2026, needs more optimization.
31 63 0.026092422671 T. Ericson and V. Zinoviev, Codes on Euclidean spheres, North-Holland Mathematical Library 63, North-Holland Publishing Co., Amsterdam, 2001.
26071⁢x3−961⁢x2−31⁢x+1
31 64 0.030325216616 Henry Cohn, 2026, needs more optimization.
31 65 0.037332538423 Henry Cohn, 2026, needs more optimization.
31 66 0.037771121676 Henry Cohn, 2026, needs more optimization.
31 67 0.038152750954 Henry Cohn, 2026, needs more optimization.
31 68 0.043324044242 Henry Cohn, 2026, needs more optimization.
31 69 0.043538634448 Henry Cohn, 2026, needs more optimization.
31 70 0.043787493765 Henry Cohn, 2026, needs more optimization.
31 71 0.044034234378 Henry Cohn, 2026, needs more optimization.
31 72 0.044583881514 Henry Cohn, 2026, needs more optimization.
31 73 0.048631532114 Henry Cohn, 2026, needs more optimization.
31 74 0.050068906633 Henry Cohn, 2026, needs more optimization.
31 75 0.051024214945 Henry Cohn, 2026, needs more optimization.
31 76 0.052578474476 Henry Cohn, 2026, needs more optimization.
31 77 0.054427328702 Henry Cohn, 2026, needs more optimization.
31 78 0.055755031760 Henry Cohn, 2026, needs more optimization.
31 79 0.057284635753 Henry Cohn, 2026, needs more optimization.
31 80 0.058637544433 Henry Cohn, 2026, needs more optimization.
31 81 0.060011313372 Henry Cohn, 2026, needs more optimization.
31 82 0.061360497540 Henry Cohn, 2026, needs more optimization.
31 83 0.061682454668 Henry Cohn, 2026, needs more optimization.
31 84 0.062332555905 Henry Cohn, 2026, needs more optimization.
31 85 0.063452446643 Henry Cohn, 2026, needs more optimization.
31 86 0.064362380190 Henry Cohn, 2026, needs more optimization.
31 87 0.065619149576 Henry Cohn, 2026, needs more optimization.
31 88 0.067040280402 Henry Cohn, 2026, needs more optimization.
31 89 0.068535259195 Henry Cohn, 2026, needs more optimization.
31 90 0.071124886411 Henry Cohn, 2026, needs more optimization.
31 91 0.072101908742 Henry Cohn, 2026, needs more optimization.
31 92 0.073155110844 Henry Cohn, 2026, needs more optimization.
31 93 0.074056359375 Henry Cohn, 2026, needs more optimization.
31 94 0.074944641928 Henry Cohn, 2026, needs more optimization.
31 95 0.075316375078 Henry Cohn, 2026, needs more optimization.
31 96 0.075939747325 Henry Cohn, 2026, needs more optimization.
31 97 0.076307020585 Henry Cohn, 2026, needs more optimization.
31 98 0.076842148130 Henry Cohn, 2026, needs more optimization.
31 99 0.076884238015 Henry Cohn, 2026, needs more optimization.
31 100 0.076928944328 Henry Cohn, 2026, needs more optimization.
31 101 0.076991736784 Henry Cohn, 2026, needs more optimization.
31 102 0.077155218229 Henry Cohn, 2026, needs more optimization.
31 103 0.077296130985 Henry Cohn, 2026, needs more optimization.
31 104 0.077401069874 Henry Cohn, 2026, needs more optimization.
31 105 0.077815145498 Henry Cohn, 2026, needs more optimization.
31 106 0.078227953716 Henry Cohn, 2026, needs more optimization.
31 107 0.078676677442 Henry Cohn, 2026, needs more optimization.
31 108 0.079523994166 Henry Cohn, 2026, needs more optimization.
31 109 0.079853120315 Henry Cohn, 2026, needs more optimization.
31 110 0.080318497739 Henry Cohn, 2026, needs more optimization.
31 111 0.080631466005 Henry Cohn, 2026, needs more optimization.
31 112 0.080739352359 Henry Cohn, 2026, needs more optimization.
31 113 0.081339754371 Henry Cohn, 2026, needs more optimization.
31 114 0.081694453685 Henry Cohn, 2026, needs more optimization.
31 115 0.082456612902 Henry Cohn, 2026, needs more optimization.
31 116 0.083371330803 Henry Cohn, 2026, needs more optimization.
31 117 0.084483653652 Henry Cohn, 2026, needs more optimization.
31 118 0.085723716760 Henry Cohn, 2026, needs more optimization.
31 119 0.086800330222 Henry Cohn, 2026, needs more optimization.
31 120 0.087844519791 Henry Cohn, 2026, needs more optimization.
31 121 0.088325092336 Henry Cohn, 2026, needs more optimization.
31 122 0.088727575967 Henry Cohn, 2026, needs more optimization.
31 123 0.088884899395 Henry Cohn, 2026, needs more optimization.
31 124 0.089206296500 Henry Cohn, 2026, needs more optimization.
31 125 0.089609398562 Henry Cohn, 2026, needs more optimization.
31 126 0.089920694234 Henry Cohn, 2026, needs more optimization.
31 127 0.090331294117 Henry Cohn, 2026, needs more optimization.
31 128 0.090531122934 Henry Cohn, 2026, needs more optimization.
31 129 0.090757885950 Henry Cohn, 2026, needs more optimization.
31 130 0.091274921879 Henry Cohn, 2026, needs more optimization.
31 131 0.092244415319 Henry Cohn, 2026, needs more optimization.
31 132 0.093190738514 Henry Cohn, 2026, needs more optimization.
31 133 0.094606477357 Henry Cohn, 2026, needs more optimization.
31 134 0.095448357669 Henry Cohn, 2026, needs more optimization.
31 135 0.096348341664 Henry Cohn, 2026, needs more optimization.
31 136 0.097760271672 Henry Cohn, 2026, needs more optimization.
31 137 0.098801227519 Henry Cohn, 2026, needs more optimization.
31 138 0.099762218836 Henry Cohn, 2026, needs more optimization.
31 139 0.100459784718 Henry Cohn, 2026, needs more optimization.
31 140 0.101796233133 Henry Cohn, 2026, needs more optimization.
31 141 0.102478840426 Henry Cohn, 2026, needs more optimization.
31 142 0.102494583546 Henry Cohn, 2026, needs more optimization.
31 143 0.102507701639 Henry Cohn, 2026, needs more optimization.
31 144 0.102565680534 Henry Cohn, 2026, needs more optimization.
31 145 0.102677611737 Henry Cohn, 2026, needs more optimization.
31 146 0.102851682026 Henry Cohn, 2026, needs more optimization.
31 147 0.103822486747 Henry Cohn, 2026, needs more optimization.
31 148 0.104757380090 Henry Cohn, 2026, needs more optimization.
31 149 0.105241075816 Henry Cohn, 2026, needs more optimization.
31 150 0.106275090349 Henry Cohn, 2026, needs more optimization.
31 151 0.107100845523 Henry Cohn, 2026, needs more optimization.
31 152 0.107984512456 Henry Cohn, 2026, needs more optimization.
31 153 0.108645666325 Henry Cohn, 2026, needs more optimization.
31 154 0.109383694228 Henry Cohn, 2026, needs more optimization.
31 155 0.109986284352 Henry Cohn, 2026, needs more optimization.
31 156 0.110202673601 Henry Cohn, 2026, needs more optimization.
31 157 0.110367715115 Henry Cohn, 2026, needs more optimization.
31 158 0.110466553363 Henry Cohn, 2026, needs more optimization.
31 159 0.110683803273 Henry Cohn, 2026, needs more optimization.
31 160 0.111063834251 Henry Cohn, 2026, needs more optimization.
31 161 0.111539507559 Henry Cohn, 2026, needs more optimization.
31 162 0.111973404685 Henry Cohn, 2026, needs more optimization.
31 163 0.113078481516 Henry Cohn, 2026, needs more optimization.
31 164 0.113823417172 Henry Cohn, 2026, needs more optimization.
31 165 0.114415827797 Henry Cohn, 2026, needs more optimization.
31 166 0.115495178752 Henry Cohn, 2026, needs more optimization.
31 167 0.116398095959 Henry Cohn, 2026, needs more optimization.
31 168 0.117357578141 Henry Cohn, 2026, needs more optimization.
31 169 0.118638424580 Henry Cohn, 2026, needs more optimization.
31 170 0.119353672776 Henry Cohn, 2026, needs more optimization.
31 171 0.120236563716 Henry Cohn, 2026, needs more optimization.
31 172 0.122052749994 Henry Cohn, 2026, needs more optimization.
31 173 0.123043185394 Henry Cohn, 2026, needs more optimization.
31 174 0.123654081020 Henry Cohn, 2026, needs more optimization.
31 175 0.124763897966 Henry Cohn, 2026, needs more optimization.
31 176 0.125771223720 Henry Cohn, 2026, needs more optimization.
31 177 0.126364877108 Henry Cohn, 2026, needs more optimization.
31 178 0.127056451651 Henry Cohn, 2026, needs more optimization.
31 179 0.127668293745 Henry Cohn, 2026, needs more optimization.
31 188 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 6 points in 3 dimensions.
92⁢x2−4⁢x−1
31 189 0.128249747777 Henry Cohn, 2026, needs more optimization.
31 190 0.131771807484 Henry Cohn, 2026, needs more optimization.
31 191 0.132157022018 Henry Cohn, 2026, needs more optimization.
31 192 0.132425385343 Henry Cohn, 2026, needs more optimization.
31 193 0.132910517178 Henry Cohn, 2026, needs more optimization.
31 194 0.133413213326 Henry Cohn, 2026, needs more optimization.
31 195 0.133760569165 Henry Cohn, 2026, needs more optimization.
31 196 0.133940027764 Henry Cohn, 2026, needs more optimization.
31 197 0.134012083304 Henry Cohn, 2026, needs more optimization.
31 198 0.134336713507 Henry Cohn, 2026, needs more optimization.
31 199 0.134613289327 Henry Cohn, 2026, needs more optimization.
31 200 0.134735987411 Henry Cohn, 2026, needs more optimization.
31 201 0.135039657114 Henry Cohn, 2026, needs more optimization.
31 202 0.135900340420 Henry Cohn, 2026, needs more optimization.
31 203 0.136750801304 Henry Cohn, 2026, needs more optimization.
31 204 0.137364167601 Henry Cohn, 2026, needs more optimization.
31 205 0.137534137818 Henry Cohn, 2026, needs more optimization.
31 206 0.138237068994 Henry Cohn, 2026, needs more optimization.
31 207 0.138689633306 Henry Cohn, 2026, needs more optimization.
31 208 0.138984498381 Henry Cohn, 2026, needs more optimization.
31 209 0.139756251619 Henry Cohn, 2026, needs more optimization.
31 210 0.140531075501 Henry Cohn, 2026, needs more optimization.
31 211 0.140544388742 Henry Cohn, 2026, needs more optimization.
31 212 0.140689929609 Henry Cohn, 2026, needs more optimization.
31 213 0.140779207106 Henry Cohn, 2026, needs more optimization.
31 214 0.140917386355 Henry Cohn, 2026, needs more optimization.
31 215 0.141026126696 Henry Cohn, 2026, needs more optimization.
31 216 0.141127010933 Henry Cohn, 2026, needs more optimization.
31 217 0.141225567184 Henry Cohn, 2026, needs more optimization.
31 218 0.141309938568 Henry Cohn, 2026, needs more optimization.
31 219 0.141544151010 Henry Cohn, 2026, needs more optimization.
31 220 0.141918946049 Henry Cohn, 2026, needs more optimization.
31 221 0.141979638668 Henry Cohn, 2026, needs more optimization.
31 222 0.142057837981 Henry Cohn, 2026, needs more optimization.
31 223 0.142108907305 Henry Cohn, 2026, needs more optimization.
31 224 0.142165234659 Henry Cohn, 2026, needs more optimization.
31 225 0.142451774415 Henry Cohn, 2026, needs more optimization.
31 226 0.142820242868 Henry Cohn, 2026, needs more optimization.
31 227 0.142972400095 Henry Cohn, 2026, needs more optimization.
31 228 0.143198539609 Henry Cohn, 2026, needs more optimization.
31 229 0.143790628677 Henry Cohn, 2026, needs more optimization.
31 230 0.144364147698 Henry Cohn, 2026, needs more optimization.
31 231 0.144763465014 Henry Cohn, 2026, needs more optimization.
31 232 0.144900582618 Henry Cohn, 2026, needs more optimization.
31 233 0.145151202354 Henry Cohn, 2026, needs more optimization.
31 234 0.145346772519 Henry Cohn, 2026, needs more optimization.
31 235 0.145415595875 Henry Cohn, 2026, needs more optimization.
31 236 0.145518131964 Henry Cohn, 2026, needs more optimization.
31 237 0.145639988438 Henry Cohn, 2026, needs more optimization.
31 238 0.145808938103 Henry Cohn, 2026, needs more optimization.
31 239 0.145936440423 Henry Cohn, 2026, needs more optimization.
31 240 0.146048091409 Henry Cohn, 2026, needs more optimization.
31 241 0.146088602138 Henry Cohn, 2026, needs more optimization.
31 242 0.146220486624 Henry Cohn, 2026, needs more optimization.
31 243 0.146421832231 Henry Cohn, 2026, needs more optimization.
31 244 0.146544904532 Henry Cohn, 2026, needs more optimization.
31 245 0.146696778785 Henry Cohn, 2026, needs more optimization.
31 246 0.146761069246 Henry Cohn, 2026, needs more optimization.
31 247 0.147020859230 Henry Cohn, 2026, needs more optimization.
31 248 0.147085893321 Henry Cohn, 2026, needs more optimization.
31 249 0.147165084247 Henry Cohn, 2026, needs more optimization.
31 250 0.147257765533 Henry Cohn, 2026, needs more optimization.
31 251 0.147341963626 Henry Cohn, 2026, needs more optimization.
31 252 0.147392295108 Henry Cohn, 2026, needs more optimization.
31 253 0.147540150583 Henry Cohn, 2026, needs more optimization.
31 254 0.147665125749 Henry Cohn, 2026, needs more optimization.
31 255 0.147822884472 Henry Cohn, 2026, needs more optimization.
31 256 0.147899938663 Henry Cohn, 2026, needs more optimization.
31 257 0.148026591766 Henry Cohn, 2026, needs more optimization.
31 258 0.148290235911 Henry Cohn, 2026, needs more optimization.
31 259 0.148601540303 Henry Cohn, 2026, needs more optimization.
31 260 0.148702165468 Henry Cohn, 2026, needs more optimization.
31 261 0.148724932682 Henry Cohn, 2026, needs more optimization.
31 262 0.149195818181 Henry Cohn, 2026, needs more optimization.
31 263 0.149343586393 Henry Cohn, 2026, needs more optimization.
31 264 0.149751794695 Henry Cohn, 2026, needs more optimization.
31 265 0.150360920146 Henry Cohn, 2026, needs more optimization.
31 266 0.150618574821 Henry Cohn, 2026, needs more optimization.
31 267 0.151169513321 Henry Cohn, 2026, needs more optimization.
31 268 0.151684477252 Henry Cohn, 2026, needs more optimization.
31 269 0.152373142032 Henry Cohn, 2026, needs more optimization.
31 270 0.152683488587 Henry Cohn, 2026, needs more optimization.
31 271 0.153408960787 Henry Cohn, 2026, needs more optimization.
31 272 0.153829597449 Henry Cohn, 2026, needs more optimization.
31 273 0.154377691415 Henry Cohn, 2026, needs more optimization.
31 274 0.154698957121 Henry Cohn, 2026, needs more optimization.
31 275 0.155093703196 Henry Cohn, 2026, needs more optimization.
31 276 0.155517960921 Henry Cohn, 2026, needs more optimization.
31 277 0.156159047071 Henry Cohn, 2026, needs more optimization.
31 278 0.156870664181 Henry Cohn, 2026, needs more optimization.
31 279 0.157041590572 Henry Cohn, 2026, needs more optimization.
31 280 0.157812953973 Henry Cohn, 2026, needs more optimization.
31 281 0.158337972384 Henry Cohn, 2026, needs more optimization.
31 282 0.158931198310 Henry Cohn, 2026, needs more optimization.
31 283 0.159253199949 Henry Cohn, 2026, needs more optimization.
31 284 0.159966285941 Henry Cohn, 2026, needs more optimization.
31 285 0.160422635750 Henry Cohn, 2026, needs more optimization.
31 286 0.160882992178 Henry Cohn, 2026, needs more optimization.
31 287 0.161587137509 Henry Cohn, 2026, needs more optimization.
31 288 0.161684551696 Henry Cohn, 2026, needs more optimization.
31 289 0.161711184284 Henry Cohn, 2026, needs more optimization.
31 290 0.161749060427 Henry Cohn, 2026, needs more optimization.
31 291 0.161751781902 Henry Cohn, 2026, needs more optimization.
31 292 0.161811919704 Henry Cohn, 2026, needs more optimization.
31 293 0.161822338499 Henry Cohn, 2026, needs more optimization.
31 294 0.161826867440 Henry Cohn, 2026, needs more optimization.
31 295 0.161849981160 Henry Cohn, 2026, needs more optimization.
31 296 0.161871237026 Henry Cohn, 2026, needs more optimization.
31 297 0.161916347411 Henry Cohn, 2026, needs more optimization.
31 298 0.161953161156 Henry Cohn, 2026, needs more optimization.
31 299 0.162075043993 Henry Cohn, 2026, needs more optimization.
31 300 0.162208224634 Henry Cohn, 2026, needs more optimization.
31 301 0.162225721372 Henry Cohn, 2026, needs more optimization.
31 302 0.162473855690 Henry Cohn, 2026, needs more optimization.
31 303 0.162522402029 Henry Cohn, 2026, needs more optimization.
31 304 0.162543284748 Henry Cohn, 2026, needs more optimization.
31 305 0.163198661880 Henry Cohn, 2026, needs more optimization.
31 306 0.165489063031 Henry Cohn, 2026, needs more optimization.
31 307 0.165806167681 Henry Cohn, 2026, needs more optimization.
31 308 0.165844900179 Henry Cohn, 2026, needs more optimization.
31 310 0.165859978870 Henry Cohn, 2026, needs more optimization.
31 311 0.166333597960 Henry Cohn, 2026, needs more optimization.
31 313 0.166366344140 Henry Cohn, 2026, needs more optimization.
31 315 0.166368597686 Henry Cohn, 2026, needs more optimization.
31 316 0.166418187526 Henry Cohn, 2026, needs more optimization.
31 317 0.166441901453 Henry Cohn, 2026, needs more optimization.
31 318 0.166442390726 Henry Cohn, 2026, needs more optimization.
31 319 0.166463873238 Henry Cohn, 2026, needs more optimization.
31 320 0.166478082926 Henry Cohn, 2026, needs more optimization.
31 321 0.166484130371 Henry Cohn, 2026, needs more optimization.
31 322 0.166510334310 Henry Cohn, 2026, needs more optimization.
31 323 0.166515891120 Henry Cohn, 2026, needs more optimization.
31 325 0.166521831493 Henry Cohn, 2026, needs more optimization.
31 326 0.166536971336 Henry Cohn, 2026, needs more optimization.
31 327 0.166541592396 Henry Cohn, 2026, needs more optimization.
31 329 0.166543744322 Henry Cohn, 2026, needs more optimization.
31 331 0.166556481301 Henry Cohn, 2026, needs more optimization.
31 332 0.176893595492 Henry Cohn, 2026, needs more optimization.
31 333 0.176948785649 Henry Cohn, 2026, needs more optimization.
31 334 0.176986594256 Henry Cohn, 2026, needs more optimization.
31 335 0.176992794420 Henry Cohn, 2026, needs more optimization.
31 336 0.177031615727 Henry Cohn, 2026, needs more optimization.
31 337 0.177081629601 Henry Cohn, 2026, needs more optimization.
31 338 0.177135375685 Henry Cohn, 2026, needs more optimization.
31 339 0.177146621572 Henry Cohn, 2026, needs more optimization.
31 340 0.177209952644 Henry Cohn, 2026, needs more optimization.
31 342 0.177283993137 Henry Cohn, 2026, needs more optimization.
31 343 0.177453488794 Henry Cohn, 2026, needs more optimization.
31 344 0.177456408621 Henry Cohn, 2026, needs more optimization.
31 345 0.177482657042 Henry Cohn, 2026, needs more optimization.
31 346 0.177738183021 Henry Cohn, 2026, needs more optimization.
31 347 0.177740162702 Henry Cohn, 2026, needs more optimization.
31 348 0.177751719210 Henry Cohn, 2026, needs more optimization.
31 349 0.177776271557 Henry Cohn, 2026, needs more optimization.
31 350 0.177801354961 Henry Cohn, 2026, needs more optimization.
31 351 0.177802211707 Henry Cohn, 2026, needs more optimization.
31 352 0.177847386608 Henry Cohn, 2026, needs more optimization.
31 353 0.178128801406 Henry Cohn, 2026, needs more optimization.
31 355 0.178130313783 Henry Cohn, 2026, needs more optimization.
31 356 0.178169685182 Henry Cohn, 2026, needs more optimization.
31 357 0.178177269213 Henry Cohn, 2026, needs more optimization.
31 358 0.178202558128 Henry Cohn, 2026, needs more optimization.
31 359 0.178227577692 Henry Cohn, 2026, needs more optimization.
31 360 0.178254829193 Henry Cohn, 2026, needs more optimization.
31 361 0.178438133292 Henry Cohn, 2026, needs more optimization.
31 362 0.178450921755 Henry Cohn, 2026, needs more optimization.
31 363 0.178478760246 Henry Cohn, 2026, needs more optimization.
31 364 0.178485240345 Henry Cohn, 2026, needs more optimization.
31 365 0.178510005456 Henry Cohn, 2026, needs more optimization.
31 366 0.178654716864 Henry Cohn, 2026, needs more optimization.
31 367 0.178667783927 Henry Cohn, 2026, needs more optimization.
31 368 0.178693219092 Henry Cohn, 2026, needs more optimization.
31 369 0.178768734281 Henry Cohn, 2026, needs more optimization.
31 370 0.178955589856 Henry Cohn, 2026, needs more optimization.
31 371 0.179084053497 Henry Cohn, 2026, needs more optimization.
31 372 0.179610436773 Henry Cohn, 2026, needs more optimization.
31 373 0.179706522413 Henry Cohn, 2026, needs more optimization.
31 374 0.180242384861 Henry Cohn, 2026, needs more optimization.
31 375 0.180446333116 Henry Cohn, 2026, needs more optimization.
31 376 0.180616572504 Henry Cohn, 2026, needs more optimization.
31 377 0.181112815458 Henry Cohn, 2026, needs more optimization.
31 378 0.181742856274 Henry Cohn, 2026, needs more optimization.
31 379 0.181990900759 Henry Cohn, 2026, needs more optimization.
31 380 0.182042807649 Henry Cohn, 2026, needs more optimization.
31 381 0.182080793472 Henry Cohn, 2026, needs more optimization.
31 382 0.182139544276 Henry Cohn, 2026, needs more optimization.
31 383 0.182219232073 Henry Cohn, 2026, needs more optimization.
31 384 0.182236122303 Henry Cohn, 2026, needs more optimization.
31 385 0.182481510732 Henry Cohn, 2026, needs more optimization.
31 386 0.182489166636 Henry Cohn, 2026, needs more optimization.
31 387 0.182495508900 Henry Cohn, 2026, needs more optimization.
31 388 0.182642725099 Henry Cohn, 2026, needs more optimization.
31 389 0.182753814549 Henry Cohn, 2026, needs more optimization.
31 390 0.183020739924 Henry Cohn, 2026, needs more optimization.
31 391 0.183185738644 Henry Cohn, 2026, needs more optimization.
31 392 0.183673014177 Henry Cohn, 2026, needs more optimization.
31 395 0.184232966137 Henry Cohn, 2026, needs more optimization.
31 396 0.184753846574 Henry Cohn, 2026, needs more optimization.
31 397 0.184952146691 Henry Cohn, 2026, needs more optimization.
31 398 0.185352717494 Henry Cohn, 2026, needs more optimization.
31 399 0.185892323574 Henry Cohn, 2026, needs more optimization.
31 400 0.186016760521 Henry Cohn, 2026, needs more optimization.
31 401 0.186085173200 Henry Cohn, 2026, needs more optimization.
31 402 0.186149040467 Henry Cohn, 2026, needs more optimization.
31 403 0.186390639120 Henry Cohn, 2026, needs more optimization.
31 404 0.186654758030 Henry Cohn, 2026, needs more optimization.
31 405 0.187150057189 Henry Cohn, 2026, needs more optimization.
31 406 0.187238615145 Henry Cohn, 2026, needs more optimization.
31 407 0.187444730524 Henry Cohn, 2026, needs more optimization.
31 408 0.187782411790 Henry Cohn, 2026, needs more optimization.
31 409 0.187832248780 Henry Cohn, 2026, needs more optimization.
31 410 0.187937135601 Henry Cohn, 2026, needs more optimization.
31 411 0.188213983865 Henry Cohn, 2026, needs more optimization.
31 412 0.188659331148 Henry Cohn, 2026, needs more optimization.
31 413 0.188978880031 Henry Cohn, 2026, needs more optimization.
31 414 0.189112812761 Henry Cohn, 2026, needs more optimization.
31 415 0.189297081135 Henry Cohn, 2026, needs more optimization.
31 416 0.189355056241 Henry Cohn, 2026, needs more optimization.
31 417 0.189693859243 Henry Cohn, 2026, needs more optimization.
31 418 0.189845785828 Henry Cohn, 2026, needs more optimization.
31 419 0.190108692546 Henry Cohn, 2026, needs more optimization.
31 420 0.190315738048 Henry Cohn, 2026, needs more optimization.
31 421 0.190443805155 Henry Cohn, 2026, needs more optimization.
31 422 0.190707082553 Henry Cohn, 2026, needs more optimization.
31 423 0.190882116176 Henry Cohn, 2026, needs more optimization.
31 424 0.191189738885 Henry Cohn, 2026, needs more optimization.
31 425 0.191500617129 Henry Cohn, 2026, needs more optimization.
31 426 0.191647004338 Henry Cohn, 2026, needs more optimization.
31 427 0.191824595518 Henry Cohn, 2026, needs more optimization.
31 428 0.191941140439 Henry Cohn, 2026, needs more optimization.
31 429 0.192063208286 Henry Cohn, 2026, needs more optimization.
31 430 0.192158062364 Henry Cohn, 2026, needs more optimization.
31 431 0.192588063905 Henry Cohn, 2026, needs more optimization.
31 432 0.192684135182 Henry Cohn, 2026, needs more optimization.
31 433 0.192977622333 Henry Cohn, 2026, needs more optimization.
31 434 0.193194503358 Henry Cohn, 2026, needs more optimization.
31 435 0.193634074886 Henry Cohn, 2026, needs more optimization.
31 436 0.193832081368 Henry Cohn, 2026, needs more optimization.
31 438 0.194162198171 Henry Cohn, 2026, needs more optimization.
31 439 0.194236004143 Henry Cohn, 2026, needs more optimization.
31 455 0.194630872484 Orthogonal union of 451 points in 29 dimensions and 4 points in 2 dimensions.
149⁢x−29
31 456 0.194658336866 Orthogonal union of 454 points in 30 dimensions and 2 points in 1 dimension.
31 457 0.195876219297 Henry Cohn, 2026, needs more optimization.
31 458 0.195969034924 Henry Cohn, 2026, needs more optimization.
31 459 0.196033244156 Henry Cohn, 2026, needs more optimization.
31 460 0.196260340188 Henry Cohn, 2026, needs more optimization.
31 461 0.196485284005 Henry Cohn, 2026, needs more optimization.
31 462 0.196547918616 Henry Cohn, 2026, needs more optimization.
31 463 0.196701378498 Henry Cohn, 2026, needs more optimization.
31 464 0.196818265662 Henry Cohn, 2026, needs more optimization.
31 465 0.196956713356 Henry Cohn, 2026, needs more optimization.
31 466 0.197028214168 Henry Cohn, 2026, needs more optimization.
31 467 0.197191974654 Henry Cohn, 2026, needs more optimization.
31 468 0.197380140862 Henry Cohn, 2026, needs more optimization.
31 469 0.197418871616 Henry Cohn, 2026, needs more optimization.
31 470 0.197483434170 Henry Cohn, 2026, needs more optimization.
31 471 0.197577322039 Henry Cohn, 2026, needs more optimization.
31 472 0.197630812022 Henry Cohn, 2026, needs more optimization.
31 473 0.197674996052 Henry Cohn, 2026, needs more optimization.
31 474 0.197698388718 Henry Cohn, 2026, needs more optimization.
31 475 0.197804527101 Henry Cohn, 2026, needs more optimization.
31 476 0.197871995513 Henry Cohn, 2026, needs more optimization.
31 477 0.197946523378 Henry Cohn, 2026, needs more optimization.
31 478 0.197961905715 Henry Cohn, 2026, needs more optimization.
31 479 0.198106895627 Henry Cohn, 2026, needs more optimization.
31 480 0.198138987736 Henry Cohn, 2026, needs more optimization.
31 481 0.198227097691 Henry Cohn, 2026, needs more optimization.
31 482 0.198299777073 Henry Cohn, 2026, needs more optimization.
31 483 0.198355231406 Henry Cohn, 2026, needs more optimization.
31 484 0.198405675725 Henry Cohn, 2026, needs more optimization.
31 485 0.198429802183 Henry Cohn, 2026, needs more optimization.
31 487 0.198465995389 Henry Cohn, 2026, needs more optimization.
31 488 0.198563973314 Henry Cohn, 2026, needs more optimization.
31 489 0.198595331757 Henry Cohn, 2026, needs more optimization.
31 490 0.198646668422 Henry Cohn, 2026, needs more optimization.
31 492 0.198674836532 Henry Cohn, 2026, needs more optimization.
31 493 0.198737781060 Henry Cohn, 2026, needs more optimization.
31 494 0.198771783530 Henry Cohn, 2026, needs more optimization.
31 495 0.198834242100 Henry Cohn, 2026, needs more optimization.
31 496 0.198895412761 Henry Cohn, 2026, needs more optimization.
31 497 0.198940896631 Henry Cohn, 2026, needs more optimization.
31 498 0.198974585373 Henry Cohn, 2026, needs more optimization.
31 502 0.199037232397 Henry Cohn, 2026, needs more optimization.
31 503 0.199075797496 Henry Cohn, 2026, needs more optimization.
31 504 0.199090976891 Henry Cohn, 2026, needs more optimization.
31 505 0.199092748836 Henry Cohn, 2026, needs more optimization.
31 506 0.199145287112 Henry Cohn, 2026, needs more optimization.
31 508 0.199203913036 Henry Cohn, 2026, needs more optimization.
31 509 0.199226442141 Henry Cohn, 2026, needs more optimization.
31 510 0.199257269341 Henry Cohn, 2026, needs more optimization.
31 513 0.199266043143 Henry Cohn, 2026, needs more optimization.
31 514 0.199290384373 Henry Cohn, 2026, needs more optimization.
31 515 0.199386359454 Henry Cohn, 2026, needs more optimization.
31 518 0.199431324350 Henry Cohn, 2026, needs more optimization.
31 519 0.199450433826 Henry Cohn, 2026, needs more optimization.
31 520 0.199467094158 Henry Cohn, 2026, needs more optimization.
31 521 0.199484423621 Henry Cohn, 2026, needs more optimization.
31 522 0.199516908487 Henry Cohn, 2026, needs more optimization.
31 523 0.199518645747 Henry Cohn, 2026, needs more optimization.
31 524 0.199539830344 Henry Cohn, 2026, needs more optimization.
31 525 0.199548586576 Henry Cohn, 2026, needs more optimization.
31 526 0.199560767785 Henry Cohn, 2026, needs more optimization.
31 527 0.199581827151 Henry Cohn, 2026, needs more optimization.
31 528 0.199582152082 Henry Cohn, 2026, needs more optimization.
31 529 0.199601559982 Henry Cohn, 2026, needs more optimization.
31 530 0.199639453199 Henry Cohn, 2026, needs more optimization.
31 533 0.199652689780 Henry Cohn, 2026, needs more optimization.
31 534 0.199662980760 Henry Cohn, 2026, needs more optimization.
31 535 0.199666973890 Henry Cohn, 2026, needs more optimization.
31 536 0.199698541954 Henry Cohn, 2026, needs more optimization.
31 537 0.199703586132 Henry Cohn, 2026, needs more optimization.
31 538 0.199724993288 Henry Cohn, 2026, needs more optimization.
31 539 0.199726182070 Henry Cohn, 2026, needs more optimization.
31 542 0.199732970270 Henry Cohn, 2026, needs more optimization.
31 546 0.199737858140 Henry Cohn, 2026, needs more optimization.
31 548 0.199766849123 Henry Cohn, 2026, needs more optimization.
31 550 0.199802364269 Henry Cohn, 2026, needs more optimization.
31 554 0.199817463810 Henry Cohn, 2026, needs more optimization.
31 555 0.199840963646 Henry Cohn, 2026, needs more optimization.
31 556 0.199846745191 Henry Cohn, 2026, needs more optimization.
31 557 0.199858861555 Henry Cohn, 2026, needs more optimization.
31 558 0.199881990850 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.
31 688 0.2 Henry Cohn, 2026.
5⁢x−1
31 689 0.206397208140 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 0.036593565615 Henry Cohn, 2026, needs more optimization.
32 68 0.036921898561 Henry Cohn, 2026, needs more optimization.
32 69 0.037652347087 Henry Cohn, 2026, needs more optimization.
32 70 0.042762186484 Henry Cohn, 2026, needs more optimization.
32 71 0.043042345588 Henry Cohn, 2026, needs more optimization.
32 72 0.043340506635 Henry Cohn, 2026, needs more optimization.
32 73 0.043649527601 Henry Cohn, 2026, needs more optimization.
32 74 0.044346293969 Henry Cohn, 2026, needs more optimization.
32 75 0.046983087351 Henry Cohn, 2026, needs more optimization.
32 76 0.048916158897 Henry Cohn, 2026, needs more optimization.
32 77 0.049882260350 Henry Cohn, 2026, needs more optimization.
32 78 0.051414444810 Henry Cohn, 2026, needs more optimization.
32 79 0.053166694893 Henry Cohn, 2026, needs more optimization.
32 80 0.054716199899 Henry Cohn, 2026, needs more optimization.
32 81 0.055651596272 Henry Cohn, 2026, needs more optimization.
32 82 0.056964486782 Henry Cohn, 2026, needs more optimization.
32 83 0.058225444672 Henry Cohn, 2026, needs more optimization.
32 84 0.059657784392 Henry Cohn, 2026, needs more optimization.
32 85 0.060925480895 Henry Cohn, 2026, needs more optimization.
32 86 0.061924997346 Henry Cohn, 2026, needs more optimization.
32 87 0.063171707740 Henry Cohn, 2026, needs more optimization.
32 88 0.064359806694 Henry Cohn, 2026, needs more optimization.
32 89 0.065582105025 Henry Cohn, 2026, needs more optimization.
32 90 0.066403448391 Henry Cohn, 2026, needs more optimization.
32 91 0.067775431578 Henry Cohn, 2026, needs more optimization.
32 92 0.068708894786 Henry Cohn, 2026, needs more optimization.
32 93 0.069830639940 Henry Cohn, 2026, needs more optimization.
32 94 0.070634408682 Henry Cohn, 2026, needs more optimization.
32 95 0.071715164404 Henry Cohn, 2026, needs more optimization.
32 96 0.072860781694 Henry Cohn, 2026, needs more optimization.
32 97 0.073898376460 Henry Cohn, 2026, needs more optimization.
32 98 0.074158289674 Henry Cohn, 2026, needs more optimization.
32 99 0.074680739147 Henry Cohn, 2026, needs more optimization.
32 100 0.075274765242 Henry Cohn, 2026, needs more optimization.
32 101 0.075940927831 Henry Cohn, 2026, needs more optimization.
32 102 0.076146477049 Henry Cohn, 2026, needs more optimization.
32 103 0.076810152181 Henry Cohn, 2026, needs more optimization.
32 104 0.076963640703 Henry Cohn, 2026, needs more optimization.
32 105 0.077085289970 Henry Cohn, 2026, needs more optimization.
32 106 0.077298508112 Henry Cohn, 2026, needs more optimization.
32 107 0.077429838350 Henry Cohn, 2026, needs more optimization.
32 108 0.077645636259 Henry Cohn, 2026, needs more optimization.
32 109 0.077735185877 Henry Cohn, 2026, needs more optimization.
32 110 0.078037359868 Henry Cohn, 2026, needs more optimization.
32 111 0.078890320065 Henry Cohn, 2026, needs more optimization.
32 112 0.079498099797 Henry Cohn, 2026, needs more optimization.
32 113 0.079894749350 Henry Cohn, 2026, needs more optimization.
32 114 0.080474568091 Henry Cohn, 2026, needs more optimization.
32 115 0.080617065836 Henry Cohn, 2026, needs more optimization.
32 116 0.080914992027 Henry Cohn, 2026, needs more optimization.
32 117 0.080994875491 Henry Cohn, 2026, needs more optimization.
32 118 0.081659658551 Henry Cohn, 2026, needs more optimization.
32 119 0.082502674851 Henry Cohn, 2026, needs more optimization.
32 120 0.083465319900 Henry Cohn, 2026, needs more optimization.
32 121 0.084548770090 Henry Cohn, 2026, needs more optimization.
32 122 0.085353236109 Henry Cohn, 2026, needs more optimization.
32 123 0.086443364914 Henry Cohn, 2026, needs more optimization.
32 124 0.086625363929 Henry Cohn, 2026, needs more optimization.
32 125 0.088023907730 Henry Cohn, 2026, needs more optimization.
32 126 0.088202668688 Henry Cohn, 2026, needs more optimization.
32 127 0.088536803026 Henry Cohn, 2026, needs more optimization.
32 128 0.088920195618 Henry Cohn, 2026, needs more optimization.
32 129 0.089228067938 Henry Cohn, 2026, needs more optimization.
32 130 0.089599647768 Henry Cohn, 2026, needs more optimization.
32 131 0.089746267258 Henry Cohn, 2026, needs more optimization.
32 132 0.089804388665 Henry Cohn, 2026, needs more optimization.
32 133 0.090010895764 Henry Cohn, 2026, needs more optimization.
32 134 0.090101255884 Henry Cohn, 2026, needs more optimization.
32 135 0.090204304524 Henry Cohn, 2026, needs more optimization.
32 136 0.090818066959 Henry Cohn, 2026, needs more optimization.
32 137 0.091992515452 Henry Cohn, 2026, needs more optimization.
32 138 0.093029041667 Henry Cohn, 2026, needs more optimization.
32 139 0.094049590086 Henry Cohn, 2026, needs more optimization.
32 140 0.094546656748 Henry Cohn, 2026, needs more optimization.
32 141 0.095710943375 Henry Cohn, 2026, needs more optimization.
32 142 0.096831784865 Henry Cohn, 2026, needs more optimization.
32 143 0.097584738682 Henry Cohn, 2026, needs more optimization.
32 144 0.099166987652 Henry Cohn, 2026, needs more optimization.
32 145 0.100740921556 Henry Cohn, 2026, needs more optimization.
32 146 0.101444062535 Henry Cohn, 2026, needs more optimization.
32 147 0.102323306102 Henry Cohn, 2026, needs more optimization.
32 148 0.102455353440 Henry Cohn, 2026, needs more optimization.
32 149 0.102456813314 Henry Cohn, 2026, needs more optimization.
32 150 0.102501515650 Henry Cohn, 2026, needs more optimization.
32 151 0.102501518444 Henry Cohn, 2026, needs more optimization.
32 152 0.102632693401 Henry Cohn, 2026, needs more optimization.
32 153 0.103194763947 Henry Cohn, 2026, needs more optimization.
32 154 0.104024106360 Henry Cohn, 2026, needs more optimization.
32 155 0.105154672872 Henry Cohn, 2026, needs more optimization.
32 156 0.105926665918 Henry Cohn, 2026, needs more optimization.
32 157 0.106533005168 Henry Cohn, 2026, needs more optimization.
32 158 0.107102606706 Henry Cohn, 2026, needs more optimization.
32 159 0.107330372174 Henry Cohn, 2026, needs more optimization.
32 160 0.107702642827 Henry Cohn, 2026, needs more optimization.
32 161 0.107950191167 Henry Cohn, 2026, needs more optimization.
32 162 0.108598905441 Henry Cohn, 2026, needs more optimization.
32 163 0.109016620888 Henry Cohn, 2026, needs more optimization.
32 164 0.109560375447 Henry Cohn, 2026, needs more optimization.
32 165 0.110157341997 Henry Cohn, 2026, needs more optimization.
32 166 0.110631224937 Henry Cohn, 2026, needs more optimization.
32 167 0.111509042505 Henry Cohn, 2026, needs more optimization.
32 168 0.112375842527 Henry Cohn, 2026, needs more optimization.
32 169 0.112846264975 Henry Cohn, 2026, needs more optimization.
32 170 0.113548769124 Henry Cohn, 2026, needs more optimization.
32 171 0.115022966250 Henry Cohn, 2026, needs more optimization.
32 172 0.115840284719 Henry Cohn, 2026, needs more optimization.
32 173 0.116658212406 Henry Cohn, 2026, needs more optimization.
32 174 0.117549582248 Henry Cohn, 2026, needs more optimization.
32 175 0.118177394537 Henry Cohn, 2026, needs more optimization.
32 176 0.119025618260 Henry Cohn, 2026, needs more optimization.
32 177 0.119592725479 Henry Cohn, 2026, needs more optimization.
32 178 0.120418872556 Henry Cohn, 2026, needs more optimization.
32 179 0.121444615748 Henry Cohn, 2026, needs more optimization.
32 180 0.121966363186 Henry Cohn, 2026, needs more optimization.
32 181 0.122754483680 Henry Cohn, 2026, needs more optimization.
32 182 0.123469211836 Henry Cohn, 2026, needs more optimization.
32 183 0.124137146124 Henry Cohn, 2026, needs more optimization.
32 184 0.125019992123 Henry Cohn, 2026, needs more optimization.
32 185 0.125751758172 Henry Cohn, 2026, needs more optimization.
32 186 0.126202970908 Henry Cohn, 2026, needs more optimization.
32 187 0.126981387371 Henry Cohn, 2026, needs more optimization.
32 188 0.127638593883 Henry Cohn, 2026, needs more optimization.
32 190 0.128238684469 Orthogonal union of 182 points in 28 dimensions and 8 points in 4 dimensions.
92⁢x2−4⁢x−1
32 191 0.128249741507 Henry Cohn, 2026, needs more optimization.
32 192 0.130940593104 Henry Cohn, 2026, needs more optimization.
32 193 0.131067861511 Henry Cohn, 2026, needs more optimization.
32 194 0.131238712356 Henry Cohn, 2026, needs more optimization.
32 195 0.131433574714 Henry Cohn, 2026, needs more optimization.
32 196 0.131886143103 Henry Cohn, 2026, needs more optimization.
32 197 0.132083459893 Henry Cohn, 2026, needs more optimization.
32 198 0.132189041332 Henry Cohn, 2026, needs more optimization.
32 199 0.132453328920 Henry Cohn, 2026, needs more optimization.
32 200 0.132668968543 Henry Cohn, 2026, needs more optimization.
32 201 0.132748232031 Henry Cohn, 2026, needs more optimization.
32 202 0.132937851295 Henry Cohn, 2026, needs more optimization.
32 203 0.133265582341 Henry Cohn, 2026, needs more optimization.
32 204 0.133493731666 Henry Cohn, 2026, needs more optimization.
32 205 0.133762121671 Henry Cohn, 2026, needs more optimization.
32 206 0.133925435180 Henry Cohn, 2026, needs more optimization.
32 207 0.134235174056 Henry Cohn, 2026, needs more optimization.
32 208 0.134420452531 Henry Cohn, 2026, needs more optimization.
32 209 0.134560054280 Henry Cohn, 2026, needs more optimization.
32 210 0.134993085245 Henry Cohn, 2026, needs more optimization.
32 211 0.135574181636 Henry Cohn, 2026, needs more optimization.
32 212 0.135902304507 Henry Cohn, 2026, needs more optimization.
32 213 0.136448417876 Henry Cohn, 2026, needs more optimization.
32 214 0.136795692533 Henry Cohn, 2026, needs more optimization.
32 215 0.137422336857 Henry Cohn, 2026, needs more optimization.
32 216 0.137930063425 Henry Cohn, 2026, needs more optimization.
32 217 0.138575394683 Henry Cohn, 2026, needs more optimization.
32 218 0.138901268838 Henry Cohn, 2026, needs more optimization.
32 219 0.139994527316 Henry Cohn, 2026, needs more optimization.
32 220 0.140166374403 Henry Cohn, 2026, needs more optimization.
32 221 0.140299807093 Henry Cohn, 2026, needs more optimization.
32 222 0.140460061377 Henry Cohn, 2026, needs more optimization.
32 223 0.140540829574 Henry Cohn, 2026, needs more optimization.
32 224 0.140706945468 Henry Cohn, 2026, needs more optimization.
32 225 0.140757070443 Henry Cohn, 2026, needs more optimization.
32 226 0.140896421262 Henry Cohn, 2026, needs more optimization.
32 227 0.141159495322 Henry Cohn, 2026, needs more optimization.
32 228 0.141248086992 Henry Cohn, 2026, needs more optimization.
32 229 0.141420943880 Henry Cohn, 2026, needs more optimization.
32 230 0.141503636857 Henry Cohn, 2026, needs more optimization.
32 231 0.141750662442 Henry Cohn, 2026, needs more optimization.
32 232 0.141909408552 Henry Cohn, 2026, needs more optimization.
32 233 0.142036374864 Henry Cohn, 2026, needs more optimization.
32 234 0.142131439463 Henry Cohn, 2026, needs more optimization.
32 235 0.142513621650 Henry Cohn, 2026, needs more optimization.
32 236 0.142699837797 Henry Cohn, 2026, needs more optimization.
32 237 0.142777469639 Henry Cohn, 2026, needs more optimization.
32 238 0.142903038419 Henry Cohn, 2026, needs more optimization.
32 239 0.143079482003 Henry Cohn, 2026, needs more optimization.
32 240 0.143627436472 Henry Cohn, 2026, needs more optimization.
32 241 0.143698079386 Henry Cohn, 2026, needs more optimization.
32 242 0.143937980150 Henry Cohn, 2026, needs more optimization.
32 243 0.144306680488 Henry Cohn, 2026, needs more optimization.
32 244 0.144649090662 Henry Cohn, 2026, needs more optimization.
32 245 0.144878852232 Henry Cohn, 2026, needs more optimization.
32 246 0.144958595141 Henry Cohn, 2026, needs more optimization.
32 247 0.145092846593 Henry Cohn, 2026, needs more optimization.
32 248 0.145394724311 Henry Cohn, 2026, needs more optimization.
32 249 0.145609227119 Henry Cohn, 2026, needs more optimization.
32 250 0.145794269575 Henry Cohn, 2026, needs more optimization.
32 251 0.146021733599 Henry Cohn, 2026, needs more optimization.
32 252 0.146061600407 Henry Cohn, 2026, needs more optimization.
32 253 0.146263884028 Henry Cohn, 2026, needs more optimization.
32 254 0.146396196054 Henry Cohn, 2026, needs more optimization.
32 255 0.146486267216 Henry Cohn, 2026, needs more optimization.
32 256 0.146626054582 Henry Cohn, 2026, needs more optimization.
32 257 0.146628394738 Henry Cohn, 2026, needs more optimization.
32 258 0.146746553609 Henry Cohn, 2026, needs more optimization.
32 259 0.146917881084 Henry Cohn, 2026, needs more optimization.
32 260 0.147355032894 Henry Cohn, 2026, needs more optimization.
32 261 0.147652208725 Henry Cohn, 2026, needs more optimization.
32 262 0.147924717813 Henry Cohn, 2026, needs more optimization.
32 263 0.147943904504 Henry Cohn, 2026, needs more optimization.
32 264 0.148070055406 Henry Cohn, 2026, needs more optimization.
32 265 0.148211440852 Henry Cohn, 2026, needs more optimization.
32 266 0.148416583580 Henry Cohn, 2026, needs more optimization.
32 267 0.148633679679 Henry Cohn, 2026, needs more optimization.
32 268 0.148792390818 Henry Cohn, 2026, needs more optimization.
32 269 0.149040692977 Henry Cohn, 2026, needs more optimization.
32 270 0.149163717018 Henry Cohn, 2026, needs more optimization.
32 271 0.149385919066 Henry Cohn, 2026, needs more optimization.
32 272 0.150067643087 Henry Cohn, 2026, needs more optimization.
32 273 0.150479570358 Henry Cohn, 2026, needs more optimization.
32 274 0.151066601407 Henry Cohn, 2026, needs more optimization.
32 275 0.151488292800 Henry Cohn, 2026, needs more optimization.
32 276 0.151960987526 Henry Cohn, 2026, needs more optimization.
32 277 0.152608100254 Henry Cohn, 2026, needs more optimization.
32 278 0.152878987594 Henry Cohn, 2026, needs more optimization.
32 279 0.153165091903 Henry Cohn, 2026, needs more optimization.
32 280 0.153421440636 Henry Cohn, 2026, needs more optimization.
32 281 0.153854625253 Henry Cohn, 2026, needs more optimization.
32 282 0.154402211609 Henry Cohn, 2026, needs more optimization.
32 283 0.154742558217 Henry Cohn, 2026, needs more optimization.
32 284 0.155303078837 Henry Cohn, 2026, needs more optimization.
32 285 0.155770698185 Henry Cohn, 2026, needs more optimization.
32 286 0.156539820246 Henry Cohn, 2026, needs more optimization.
32 287 0.156936526249 Henry Cohn, 2026, needs more optimization.
32 288 0.157374155445 Henry Cohn, 2026, needs more optimization.
32 289 0.157775330452 Henry Cohn, 2026, needs more optimization.
32 290 0.158535714295 Henry Cohn, 2026, needs more optimization.
32 291 0.158827380535 Henry Cohn, 2026, needs more optimization.
32 292 0.159296764850 Henry Cohn, 2026, needs more optimization.
32 293 0.159618856124 Henry Cohn, 2026, needs more optimization.
32 294 0.160049711016 Henry Cohn, 2026, needs more optimization.
32 295 0.160373434129 Henry Cohn, 2026, needs more optimization.
32 296 0.160848212449 Henry Cohn, 2026, needs more optimization.
32 297 0.160962814008 Henry Cohn, 2026, needs more optimization.
32 298 0.161000140937 Henry Cohn, 2026, needs more optimization.
32 299 0.161028458100 Henry Cohn, 2026, needs more optimization.
32 300 0.161042090991 Henry Cohn, 2026, needs more optimization.
32 301 0.161086247257 Henry Cohn, 2026, needs more optimization.
32 302 0.161283880036 Henry Cohn, 2026, needs more optimization.
32 303 0.161523247181 Henry Cohn, 2026, needs more optimization.
32 304 0.161552833589 Henry Cohn, 2026, needs more optimization.
32 305 0.161571622320 Henry Cohn, 2026, needs more optimization.
32 306 0.161578907192 Henry Cohn, 2026, needs more optimization.
32 307 0.162152910149 Henry Cohn, 2026, needs more optimization.
32 308 0.163870702645 Henry Cohn, 2026, needs more optimization.
32 309 0.163920653173 Henry Cohn, 2026, needs more optimization.
32 310 0.163989973952 Henry Cohn, 2026, needs more optimization.
32 311 0.163994931066 Henry Cohn, 2026, needs more optimization.
32 312 0.164019658918 Henry Cohn, 2026, needs more optimization.
32 313 0.164067273511 Henry Cohn, 2026, needs more optimization.
32 314 0.164070343434 Henry Cohn, 2026, needs more optimization.
32 315 0.164092104321 Henry Cohn, 2026, needs more optimization.
32 316 0.164114712520 Henry Cohn, 2026, needs more optimization.
32 317 0.164134491243 Henry Cohn, 2026, needs more optimization.
32 318 0.166156052625 Henry Cohn, 2026, needs more optimization.
32 319 0.166163740704 Henry Cohn, 2026, needs more optimization.
32 320 0.166179399024 Henry Cohn, 2026, needs more optimization.
32 321 0.166202875876 Henry Cohn, 2026, needs more optimization.
32 323 0.166212884654 Henry Cohn, 2026, needs more optimization.
32 324 0.166242747158 Henry Cohn, 2026, needs more optimization.
32 326 0.166259707732 Henry Cohn, 2026, needs more optimization.
32 327 0.166306223721 Henry Cohn, 2026, needs more optimization.
32 328 0.166338252899 Henry Cohn, 2026, needs more optimization.
32 329 0.166384439133 Henry Cohn, 2026, needs more optimization.
32 331 0.166385721061 Henry Cohn, 2026, needs more optimization.
32 332 0.166407721312 Henry Cohn, 2026, needs more optimization.
32 333 0.166442549916 Henry Cohn, 2026, needs more optimization.
32 335 0.166450490747 Henry Cohn, 2026, needs more optimization.
32 338 0.166461613814 Henry Cohn, 2026, needs more optimization.
32 339 0.166485195789 Henry Cohn, 2026, needs more optimization.
32 340 0.166508699556 Henry Cohn, 2026, needs more optimization.
32 341 0.166531499516 Henry Cohn, 2026, needs more optimization.
32 342 0.166562264361 Henry Cohn, 2026, needs more optimization.
32 343 0.166580258255 Henry Cohn, 2026, needs more optimization.
32 344 0.166581872982 Henry Cohn, 2026, needs more optimization.
32 345 0.166596738092 Henry Cohn, 2026, needs more optimization.
32 346 0.166613601384 Henry Cohn, 2026, needs more optimization.
32 347 0.166635106855 Henry Cohn, 2026, needs more optimization.
32 348 0.166640258337 Henry Cohn, 2026, needs more optimization.
32 349 0.166642282302 Henry Cohn, 2026, needs more optimization.
32 350 0.166645527936 Henry Cohn, 2026, needs more optimization.
32 351 0.166661417952 Henry Cohn, 2026, needs more optimization.
32 353 0.166683629348 Henry Cohn, 2026, needs more optimization.
32 354 0.166707784191 Henry Cohn, 2026, needs more optimization.
32 355 0.166726752866 Henry Cohn, 2026, needs more optimization.
32 356 0.166728935526 Henry Cohn, 2026, needs more optimization.
32 357 0.166734894984 Henry Cohn, 2026, needs more optimization.
32 358 0.177127164794 Henry Cohn, 2026, needs more optimization.
32 359 0.177192058502 Henry Cohn, 2026, needs more optimization.
32 360 0.177227394608 Henry Cohn, 2026, needs more optimization.
32 361 0.177242388668 Henry Cohn, 2026, needs more optimization.
32 362 0.177293432698 Henry Cohn, 2026, needs more optimization.
32 363 0.177322086194 Henry Cohn, 2026, needs more optimization.
32 364 0.177343819162 Henry Cohn, 2026, needs more optimization.
32 365 0.177355748200 Henry Cohn, 2026, needs more optimization.
32 366 0.177381774891 Henry Cohn, 2026, needs more optimization.
32 367 0.177406377710 Henry Cohn, 2026, needs more optimization.
32 368 0.177906744336 Henry Cohn, 2026, needs more optimization.
32 370 0.177949297611 Henry Cohn, 2026, needs more optimization.
32 371 0.177972987201 Henry Cohn, 2026, needs more optimization.
32 372 0.178008973437 Henry Cohn, 2026, needs more optimization.
32 373 0.178216100018 Henry Cohn, 2026, needs more optimization.
32 374 0.178217530858 Henry Cohn, 2026, needs more optimization.
32 376 0.178255851482 Henry Cohn, 2026, needs more optimization.
32 378 0.178313229545 Henry Cohn, 2026, needs more optimization.
32 379 0.178368548631 Henry Cohn, 2026, needs more optimization.
32 381 0.178578421446 Henry Cohn, 2026, needs more optimization.
32 382 0.178584053610 Henry Cohn, 2026, needs more optimization.
32 384 0.178608368680 Henry Cohn, 2026, needs more optimization.
32 385 0.178610083225 Henry Cohn, 2026, needs more optimization.
32 386 0.178626750285 Henry Cohn, 2026, needs more optimization.
32 387 0.178640808738 Henry Cohn, 2026, needs more optimization.
32 388 0.178669534078 Henry Cohn, 2026, needs more optimization.
32 389 0.178714203450 Henry Cohn, 2026, needs more optimization.
32 390 0.178730418023 Henry Cohn, 2026, needs more optimization.
32 391 0.178741647892 Henry Cohn, 2026, needs more optimization.
32 392 0.178784168375 Henry Cohn, 2026, needs more optimization.
32 393 0.178852298879 Henry Cohn, 2026, needs more optimization.
32 394 0.178870067208 Henry Cohn, 2026, needs more optimization.
32 395 0.178889949735 Henry Cohn, 2026, needs more optimization.
32 396 0.178964032426 Henry Cohn, 2026, needs more optimization.
32 397 0.179085512493 Henry Cohn, 2026, needs more optimization.
32 398 0.179533664751 Henry Cohn, 2026, needs more optimization.
32 399 0.179875902653 Henry Cohn, 2026, needs more optimization.
32 400 0.180097742033 Henry Cohn, 2026, needs more optimization.
32 401 0.180223016182 Henry Cohn, 2026, needs more optimization.
32 402 0.180467028107 Henry Cohn, 2026, needs more optimization.
32 403 0.180971084845 Henry Cohn, 2026, needs more optimization.
32 404 0.181064955629 Henry Cohn, 2026, needs more optimization.
32 405 0.181496075346 Henry Cohn, 2026, needs more optimization.
32 406 0.181636508811 Henry Cohn, 2026, needs more optimization.
32 407 0.181722444739 Henry Cohn, 2026, needs more optimization.
32 408 0.182348336214 Henry Cohn, 2026, needs more optimization.
32 409 0.182430197050 Henry Cohn, 2026, needs more optimization.
32 410 0.182632614126 Henry Cohn, 2026, needs more optimization.
32 411 0.182932427206 Henry Cohn, 2026, needs more optimization.
32 412 0.183067822622 Henry Cohn, 2026, needs more optimization.
32 413 0.183213310871 Henry Cohn, 2026, needs more optimization.
32 414 0.183332708449 Henry Cohn, 2026, needs more optimization.
32 415 0.183604996431 Henry Cohn, 2026, needs more optimization.
32 416 0.184156780043 Henry Cohn, 2026, needs more optimization.
32 417 0.184552051669 Henry Cohn, 2026, needs more optimization.
32 418 0.184796954638 Henry Cohn, 2026, needs more optimization.
32 419 0.185362082770 Henry Cohn, 2026, needs more optimization.
32 420 0.185438458594 Henry Cohn, 2026, needs more optimization.
32 421 0.185710485044 Henry Cohn, 2026, needs more optimization.
32 422 0.185957306579 Henry Cohn, 2026, needs more optimization.
32 423 0.186187857920 Henry Cohn, 2026, needs more optimization.
32 424 0.186420775702 Henry Cohn, 2026, needs more optimization.
32 425 0.186617136680 Henry Cohn, 2026, needs more optimization.
32 426 0.186728540335 Henry Cohn, 2026, needs more optimization.
32 427 0.187208000420 Henry Cohn, 2026, needs more optimization.
32 428 0.187338106089 Henry Cohn, 2026, needs more optimization.
32 429 0.187523489229 Henry Cohn, 2026, needs more optimization.
32 430 0.187619255632 Henry Cohn, 2026, needs more optimization.
32 431 0.187771875643 Henry Cohn, 2026, needs more optimization.
32 432 0.188399333510 Henry Cohn, 2026, needs more optimization.
32 433 0.188592035209 Henry Cohn, 2026, needs more optimization.
32 434 0.188778634767 Henry Cohn, 2026, needs more optimization.
32 435 0.188797844862 Henry Cohn, 2026, needs more optimization.
32 436 0.189001362215 Henry Cohn, 2026, needs more optimization.
32 437 0.189052730102 Henry Cohn, 2026, needs more optimization.
32 438 0.189132846875 Henry Cohn, 2026, needs more optimization.
32 439 0.189393055650 Henry Cohn, 2026, needs more optimization.
32 440 0.189631224107 Henry Cohn, 2026, needs more optimization.
32 441 0.189706205821 Henry Cohn, 2026, needs more optimization.
32 442 0.189910546668 Henry Cohn, 2026, needs more optimization.
32 443 0.190002488527 Henry Cohn, 2026, needs more optimization.
32 444 0.190235646853 Henry Cohn, 2026, needs more optimization.
32 445 0.190313410180 Henry Cohn, 2026, needs more optimization.
32 446 0.190577610403 Henry Cohn, 2026, needs more optimization.
32 447 0.190881742501 Henry Cohn, 2026, needs more optimization.
32 448 0.191018894048 Henry Cohn, 2026, needs more optimization.
32 449 0.191405754140 Henry Cohn, 2026, needs more optimization.
32 450 0.191475383857 Henry Cohn, 2026, needs more optimization.
32 451 0.191527601352 Henry Cohn, 2026, needs more optimization.
32 452 0.191601541901 Henry Cohn, 2026, needs more optimization.
32 453 0.191663345495 Henry Cohn, 2026, needs more optimization.
32 454 0.191707359832 Henry Cohn, 2026, needs more optimization.
32 455 0.191876099246 Henry Cohn, 2026, needs more optimization.
32 456 0.192095681100 Henry Cohn, 2026, needs more optimization.
32 457 0.192183079790 Henry Cohn, 2026, needs more optimization.
32 458 0.192217285327 Henry Cohn, 2026, needs more optimization.
32 459 0.192493157063 Henry Cohn, 2026, needs more optimization.
32 460 0.192632142858 Henry Cohn, 2026, needs more optimization.
32 461 0.192701408834 Henry Cohn, 2026, needs more optimization.
32 462 0.192930181404 Henry Cohn, 2026, needs more optimization.
32 463 0.193038737349 Henry Cohn, 2026, needs more optimization.
32 464 0.193225115964 Henry Cohn, 2026, needs more optimization.
32 465 0.193280227481 Henry Cohn, 2026, needs more optimization.
32 466 0.193537739643 Henry Cohn, 2026, needs more optimization.
32 467 0.193692090491 Henry Cohn, 2026, needs more optimization.
32 468 0.193782461962 Henry Cohn, 2026, needs more optimization.
32 469 0.194062194830 Henry Cohn, 2026, needs more optimization.
32 470 0.194124356079 Henry Cohn, 2026, needs more optimization.
32 471 0.194173544683 Henry Cohn, 2026, needs more optimization.
32 472 0.194197317895 Henry Cohn, 2026, needs more optimization.
32 473 0.194399918862 Henry Cohn, 2026, needs more optimization.
32 474 0.194467287633 Henry Cohn, 2026, needs more optimization.
32 475 0.194510625805 Henry Cohn, 2026, needs more optimization.
32 476 0.194560708764 Henry Cohn, 2026, needs more optimization.
32 477 0.194744839767 Henry Cohn, 2026, needs more optimization.
32 478 0.194841724955 Henry Cohn, 2026, needs more optimization.
32 528 0.195121951220 Henry Cohn, 2026.
41⁢x−8
32 530 0.199443254205 Henry Cohn, 2026, needs more optimization.
32 534 0.199461067451 Henry Cohn, 2026, needs more optimization.
32 536 0.199464104306 Henry Cohn, 2026, needs more optimization.
32 538 0.199488712147 Henry Cohn, 2026, needs more optimization.
32 541 0.199525615353 Henry Cohn, 2026, needs more optimization.
32 543 0.199628760251 Henry Cohn, 2026, needs more optimization.
32 547 0.199665901945 Henry Cohn, 2026, needs more optimization.
32 548 0.199679347360 Henry Cohn, 2026, needs more optimization.
32 551 0.199692763531 Henry Cohn, 2026, needs more optimization.
32 554 0.199703010506 Henry Cohn, 2026, needs more optimization.
32 556 0.199714508438 Henry Cohn, 2026, needs more optimization.
32 557 0.199734287665 Henry Cohn, 2026, needs more optimization.
32 558 0.199743484296 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 0.199960619875 Henry Cohn, 2026, needs more optimization.
32 596 0.199971184268 Henry Cohn, 2026, needs more optimization.
32 604 0.199982913915 Henry Cohn, 2026, needs more optimization.
32 606 0.199984920928 Henry Cohn, 2026, needs more optimization.
32 607 0.199986035956 Henry Cohn, 2026, needs more optimization.
32 608 0.199986232750 Henry Cohn, 2026, needs more optimization.
32 609 0.199988689299 Henry Cohn, 2026, needs more optimization.
32 610 0.199988776418 Henry Cohn, 2026, needs more optimization.
32 611 0.199989163274 Henry Cohn, 2026, needs more optimization.
32 612 0.199990356673 Henry Cohn, 2026, needs more optimization.
32 615 0.199992556595 Henry Cohn, 2026, needs more optimization.
32 616 0.199993842672 Henry Cohn, 2026, needs more optimization.
32 617 0.199996838150 Henry Cohn, 2026, needs more optimization.
32 704 0.2 Henry Cohn, 2026.
5⁢x−1
32 705 0.209693852100 Henry Cohn, 2026, needs more optimization.
32 706 0.212872707781 Henry Cohn, 2026, needs more optimization.
32 707 0.212916574261 Henry Cohn, 2026, needs more optimization.
32 708 0.213268859415 Henry Cohn, 2026, needs more optimization.
32 709 0.213303627502 Henry Cohn, 2026, needs more optimization.
32 710 0.214510390357 Henry Cohn, 2026, needs more optimization.
32 711 0.214702279664 Henry Cohn, 2026, needs more optimization.
32 712 0.214762443027 Henry Cohn, 2026, needs more optimization.
32 713 0.214897348514 Henry Cohn, 2026, needs more optimization.
32 714 0.215009729264 Henry Cohn, 2026, needs more optimization.
32 715 0.215038770350 Henry Cohn, 2026, needs more optimization.
32 716 0.215284668717 Henry Cohn, 2026, needs more optimization.
32 717 0.215382217321 Henry Cohn, 2026, needs more optimization.
32 718 0.216580011059 Henry Cohn, 2026, needs more optimization.
32 719 0.216649445112 Henry Cohn, 2026, needs more optimization.
32 720 0.216826994211 Henry Cohn, 2026, needs more optimization.
32 721 0.216871981889 Henry Cohn, 2026, needs more optimization.
32 722 0.217231686991 Henry Cohn, 2026, needs more optimization.
32 723 0.217307413842 Henry Cohn, 2026, needs more optimization.
32 725 0.217874611449 Henry Cohn, 2026, needs more optimization.
32 726 0.218182173100 Henry Cohn, 2026, needs more optimization.
32 727 0.218224908472 Henry Cohn, 2026, needs more optimization.
32 728 0.218261601723 Henry Cohn, 2026, needs more optimization.
32 729 0.218311610327 Henry Cohn, 2026, needs more optimization.
32 730 0.218383143037 Henry Cohn, 2026, needs more optimization.
32 731 0.219254664104 Henry Cohn, 2026, needs more optimization.
32 732 0.219475661403 Henry Cohn, 2026, needs more optimization.
32 733 0.219515823981 Henry Cohn, 2026, needs more optimization.
32 734 0.219796359529 Henry Cohn, 2026, needs more optimization.
32 735 0.219811114823 Henry Cohn, 2026, needs more optimization.
32 736 0.220234158812 Henry Cohn, 2026, needs more optimization.
32 737 0.220303059401 Henry Cohn, 2026, needs more optimization.
32 738 0.220599424320 Henry Cohn, 2026, needs more optimization.
32 739 0.220707859133 Henry Cohn, 2026, needs more optimization.
32 740 0.220733810986 Henry Cohn, 2026, needs more optimization.
32 741 0.221651005838 Henry Cohn, 2026, needs more optimization.
32 742 0.221677098014 Henry Cohn, 2026, needs more optimization.
32 743 0.221806046090 Henry Cohn, 2026, needs more optimization.
32 744 0.221844167435 Henry Cohn, 2026, needs more optimization.
32 745 0.221992693637 Henry Cohn, 2026, needs more optimization.
32 746 0.222053228501 Henry Cohn, 2026, needs more optimization.
32 747 0.222277306518 Henry Cohn, 2026, needs more optimization.
32 748 0.222293316571 Henry Cohn, 2026, needs more optimization.
32 749 0.222308075520 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 0.223634612451 Henry Cohn, 2026, needs more optimization.
32 753 0.223770468388 Henry Cohn, 2026, needs more optimization.
32 754 0.223804787115 Henry Cohn, 2026, needs more optimization.
32 755 0.224020914822 Henry Cohn, 2026, needs more optimization.
32 756 0.224035915832 Henry Cohn, 2026, needs more optimization.
32 757 0.224198873960 Henry Cohn, 2026, needs more optimization.
32 758 0.224488909132 Henry Cohn, 2026, needs more optimization.
32 759 0.225246257784 Henry Cohn, 2026, needs more optimization.
32 760 0.225327171947 Henry Cohn, 2026, needs more optimization.
32 762 0.225486850904 Henry Cohn, 2026, needs more optimization.
32 763 0.225690425243 Henry Cohn, 2026, needs more optimization.
32 764 0.225716256814 Henry Cohn, 2026, needs more optimization.
32 765 0.225744803471 Henry Cohn, 2026, needs more optimization.
32 766 0.226387794030 Henry Cohn, 2026, needs more optimization.
32 767 0.226529410839 Henry Cohn, 2026, needs more optimization.
32 768 0.226563540544 Henry Cohn, 2026, needs more optimization.
32 769 0.226774314347 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 0.227996457826 Henry Cohn, 2026, needs more optimization.
32 775 0.228005438332 Henry Cohn, 2026, needs more optimization.
32 776 0.228194971862 Henry Cohn, 2026, needs more optimization.
32 778 0.228425057444 Henry Cohn, 2026, needs more optimization.
32 779 0.228697315446 Henry Cohn, 2026, needs more optimization.
32 780 0.228827288386 Henry Cohn, 2026, needs more optimization.
32 781 0.228903499702 Henry Cohn, 2026, needs more optimization.
32 782 0.228975657698 Henry Cohn, 2026, needs more optimization.
32 783 0.229009847115 Henry Cohn, 2026, needs more optimization.
32 784 0.229110875812 Henry Cohn, 2026, needs more optimization.
32 785 0.229271461081 Henry Cohn, 2026, needs more optimization.
32 786 0.237599980857 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