A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4

Takayuki Okuda, Wei Hsuan Yu

Research output: Contribution to journalArticlepeer-review

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Abstract

We give a new upper bound for the cardinality of a set of equiangular lines in Rn with a fixed common angle θ for each (n, θ) satisfying certain conditions. Our techniques are based on semidefinite programming methods for spherical codes introduced by Bachoc and Vallentin (2008). As a corollary to our bound, we show the nonexistence of spherical tight designs of harmonic index 4 on a sphere in Rn with n≥ 3.

Original languageEnglish
Pages (from-to)96-103
Number of pages8
JournalEuropean Journal of Combinatorics
Volume53
DOIs
StatePublished - 1 Apr 2016

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