High accuracy semidefinite programming bounds for kissing numbers

Hans D. Mittelmann (mittelmannasu.edu)
Frank Vallentin (f.vallentincwi.nl)

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 + ...

Keywords: kissing number, semidefinite programming, average theta series, extremal modular form

Category 1: Applications -- Science and Engineering

Category 2: Linear, Cone and Semidefinite Programming

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

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Entry Submitted: 02/09/2009
Entry Accepted: 02/09/2009
Entry Last Modified: 05/04/2009

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