Nonexistence of tight spherical design of harmonic index 4

Abstract

We give a new upper bound of the cardinality of a set of equiangular lines in ${\mathbb{R}}^n$ with a fixed angle $\theta$ for each $(n,\theta )$ satisfying certain conditions. Our techniques are based on semi-definite programming methods for spherical codes introduced by Bachoc--Vallentin [J.Amer.Math.Soc.2008]. As a corollary to our bound, we show the nonexistence of spherical tight designs of harmonic index 4 on $S^{n-1}$ with $n\ge 3$.

References in corpus (3)

• New upper bounds for kissing numbers from semidefinite programming
• Semidefinite programming, multivariate orthogonal polynomials, and codes in spherical caps
• Optimality and uniqueness of the (4,10,1/6) spherical code