Spherical codes and Borsuk's conjecture
暂无分享，去创建一个
Abstract The approach of Kalai and Kahn towards counterexamples of Borsuk's conjecture is generalized to spherical codes. This allows the construction of a finite set in R 323 which cannot be partitioned into 561 sets of smaller diameter, thus improving upon the previous known examples. The construction is based on the subset of vectors of minimal length in the Leech lattice.
[1] A M Raigorodskii. On the dimension in Borsuk's problem , 1997 .
[2] J. Kahn,et al. A counterexample to Borsuk's conjecture , 1993, math/9307229.
[3] J. Seidel,et al. Spherical codes and designs , 1977 .
[4] Об одной оценке в проблеме Борсука@@@On a bound in Borsuk's problem , 1999 .
[5] N. J. A. Sloane,et al. Sphere Packings, Lattices and Groups , 1987, Grundlehren der mathematischen Wissenschaften.