High accuracy semidefinite programming bounds for kissing numbers
Optimization and Control
2019-11-07 v3 Metric Geometry
Number Theory
Abstract
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 + ...
Cite
@article{arxiv.0902.1105,
title = {High accuracy semidefinite programming bounds for kissing numbers},
author = {Hans D. Mittelmann and Frank Vallentin},
journal= {arXiv preprint arXiv:0902.1105},
year = {2019}
}
Comments
7 pages (v3) new numerical result in Section 4, to appear in Experiment. Math