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2010 High-Accuracy Semidefinite Programming Bounds for Kissing Numbers
Hans D. Mittelmann, Frank Vallentin
Experiment. Math. 19(2): 174-178 (2010).

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 $n \leq 24$. The bound for $n = 16$ implies a conjecture of Conway and Sloane: there is no $16$-dimensional periodic sphere packing with average theta series $1 + 7680q^3 + 4320q^4 + 276480q^5 + 61440q^6 + \cdots.$

Citation

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Hans D. Mittelmann. Frank Vallentin. "High-Accuracy Semidefinite Programming Bounds for Kissing Numbers." Experiment. Math. 19 (2) 174 - 178, 2010.

Information

Published: 2010
First available in Project Euclid: 17 June 2010

zbMATH: 1279.11070
MathSciNet: MR2676746

Subjects:
Primary: 11F11, 52C17, 90C10

Rights: Copyright © 2010 A K Peters, Ltd.

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Vol.19 • No. 2 • 2010
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