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arXiv · 0902.1105

High accuracy semidefinite programming bounds for kissing numbers

Hans D. Mittelmann·Frank Vallentin
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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 + ...

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Hans D. Mittelmann, Frank Vallentin. 2009-06-26. High accuracy semidefinite programming bounds for kissing numbers. https://doi.org/10.1080/10586458.2010.10129070

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