New bounds for equiangular lines and spherical two-distance sets

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Abstract

A set of lines in Rn is called equiangular if the angle between each pair of lines is the same. We derive new upper bounds on the cardinality of equiangular lines. Let us denote the maximum cardinality of equiangular lines in Rn with the common angle arccos α by Mα(n). We prove that M1/a (n) ≤ 1/2 (a2 - 2)(a2 - 1) for any n ∈ N in the interval a2 - 2 ≤ n ≤ 3a2 - 16 and a ≥ 3. Moreover, we discuss the relation between equiangular lines and spherical two-distance sets and we obtain the new results on the maximum spherical two-distance sets in Rn up to n ≤ 417.

Original languageEnglish
Pages (from-to)908-917
Number of pages10
JournalSIAM Journal on Discrete Mathematics
Volume31
Issue number2
DOIs
StatePublished - 2017

Keywords

  • Equiangular lines
  • Semidefinite programming
  • Two-distance set

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