High accuracy semidefinite programming bounds for kissing numbers
Abstract
The kissing number in ndimensional Euclidean space is the maximal number of nonoverlapping 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 16dimensional periodic point set with average theta series 1 + 7680q^3 + 4320q^4 + 276480q^5 + 61440q^6 + ...
 Publication:

arXiv eprints
 Pub Date:
 February 2009
 arXiv:
 arXiv:0902.1105
 Bibcode:
 2009arXiv0902.1105M
 Keywords:

 Mathematics  Optimization and Control;
 Mathematics  Metric Geometry;
 Mathematics  Number Theory;
 11F11;
 52C17;
 90C10
 EPrint:
 7 pages (v3) new numerical result in Section 4, to appear in Experiment. Math