ABSTRACT
The kissing number of is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. Mittelmann and Vallentin [CitationMittelmann and Vallentin 10], based on the semidefinite programming bound of Bachoc and Vallentin [CitationBachoc and Vallentin 08], computed the best known upper bounds for the kissing number for several values of n ⩽ 23. In this article, we exploit the symmetry present in the semidefinite programming bound to provide improved upper bounds for n = 9, …, 23.
Funding
The first author was supported by the São Paulo State Research Foundation (FAPESP) under grants 2015/05648-4 and 2014/16058-0. The second author was partially supported by FAPESP grant 2013/03447-6.