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Mathematics > Optimization and Control

arXiv:0902.1105 (math)
[Submitted on 6 Feb 2009 (v1), last revised 26 Jun 2009 (this version, v3)]

Title:High accuracy semidefinite programming bounds for kissing numbers

Authors: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 + ...
Comments: 7 pages (v3) new numerical result in Section 4, to appear in Experiment. Math
Subjects: Optimization and Control (math.OC); Metric Geometry (math.MG); Number Theory (math.NT)
MSC classes: 11F11, 52C17, 90C10
Cite as: arXiv:0902.1105 [math.OC]
  (or arXiv:0902.1105v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.0902.1105
Journal reference: Experiment. Math. 19 (2010), 174-178
Related DOI: https://doi.org/10.1080/10586458.2010.10129070

Submission history

From: Frank Vallentin [view email]
[v1] Fri, 6 Feb 2009 17:15:35 UTC (7 KB)
[v2] Mon, 4 May 2009 06:11:49 UTC (8 KB)
[v3] Fri, 26 Jun 2009 14:59:47 UTC (8 KB)
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