A new relative bound for equiangular lines and nonexistence of tight spherical designs of harmonic index 4. (April 2016)

• Record Type: Journal Article
• Authors: Okuda, Takayuki; Yu, Wei-Hsuan
• Is Part Of: European journal of combinatorics. Volume 53(2016:Apr.)
• Page Start: 96
• Page End: 103
• Publication Date: 2016-04
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2015.11.003
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: We give a new upper bound for the cardinality of a set of equiangular lines in R n 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 R n with n ≥ 3 .