Nonexistence of tight spherical design of harmonic index 4

2014/09/24 by Takayuki Okuda, Okuda, Takayuki, Wei-Hsuan Yu +1
Computer Science · Materials Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Quasicrystal Structures and Properties #math.MG

paper · pdf · doi:10.48550/arxiv.1409.6995

arxiv created 2014/09/24 · openalex publication_date 2014/09/24 · arxiv updated 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new upper bound of the cardinality of a set of equiangular lines in \Rⁿ with a fixed angle θ for each (n,θ) 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 ≥ 3.

Cited by

• Equiangular lines in Euclidean spaces

Related

• Equiangular Lines and Spherical Codes in Euclidean Space
• More on spherical designs of harmonic index t
• Bounds on equiangular lines and on related spherical codes
• Four-point semidefinite bound for equiangular lines
• Bounds for spherical codes