High-Accuracy Semidefinite Programming Bounds for Kissing Numbers

摘要

The kissing number in n-dimensional Euclidean space is the maximal number of nonoverlapping unit spheres that 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 sphere packing with average theta series 1 + 7680q(3) + 4320q(4) + 276480q(5) + 61440q(6) + ... .