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Original Article

High-Accuracy Semidefinite Programming Bounds for Kissing Numbers

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Pages 175-179 | Published online: 30 Jan 2011
 

Abstract

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 + . . . .

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