High accuracy semidefinite programming bounds for kissing numbers

Details High accuracy semidefinite programming bounds for kissing numbers High accuracy semidefinite programming bounds for kissing numbers

2009-02-06

arxiv.org/abs/0902.1105v3

Experiment. Math. 19 (2010), 174-178

Mathematics

Optimization and Control

7 pages (v3) new numerical result in Section 4, to appear in Experiment. Math

Scientific paper

The kissing number in n-dimensional Euclidean space is the maximal number of non-overlapping unit spheres which simultaneously can touch a central unit sphere. Bachoc and Vallentin developed a method to find upper bounds for the kissing number based on semidefinite programming. This paper is a report on high accuracy calculations of these upper bounds for n <= 24. The bound for n = 16 implies a conjecture of Conway and Sloane: There is no 16-dimensional periodic point set with average theta series 1 + 7680q^3 + 4320q^4 + 276480q^5 + 61440q^6 + ...

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