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High accuracy semidefinite programming bounds for kissing numbers

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arxiv 0902.1105 v3 pith:EP5SCLVA submitted 2009-02-06 math.OC math.MGmath.NT

Hans D. Mittelmann , Frank Vallentin This is my paper · ORCID
classification math.OCmath.MGmath.NT
keywords boundskissingnumberaccuracyhighprogrammingsemidefiniteunit
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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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  1. Variations on five-dimensional sphere packings

    math.MG 2024-12 accept novelty 7.0 of 10

    New non-isometric kissing configurations are constructed in dimensions 5 and 9, and the uniform 5D packings containing the known kissing configurations are classified.

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