Abstract
The kissing number in n-dimensional Euclidean space is themaximal number of nonoverlapping unit spheres that simultaneouslycan touch a central unit sphere. Bachoc and Vallentindeveloped a method to find upper bounds for the kissing numberbased on semidefinite programming. This paper is a reporton high-accuracy calculations of these upper bounds forn ≤ 24. The bound for n = 16 implies a conjecture of Conwayand Sloane: there is no 16-dimensional periodic sphere packingwith average theta series 1 + 7680q 3 + 4320q 4 + 276480q 5+ 61440q 6 + . .
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