High-accuracy semidefinite programming bounds for kissing numbers

Hans Mittelmann, Frank Vallentin

Research output: Contribution to journalArticle

23 Scopus citations

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 ≤ 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 + 7680q3 + 4320q4 + 276480q5 + 61440q6 + ・・・.

Original languageEnglish (US)
Pages (from-to)175-179
Number of pages5
JournalExperimental Mathematics
Volume19
Issue number2
DOIs
StatePublished - 2010

Keywords

  • Average theta series
  • Extremal modular form
  • Kissing number
  • Semidefinite programming

ASJC Scopus subject areas

  • Mathematics(all)

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