New bounds for equiangular lines and spherical two-distance sets

2016/09/05 by Wei-Hsuan Yu, Yu, Wei-Hsuan · 1 citation
Engineering · Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Metric Geometry (math.MG) #Optimization and Packing Problems #Point processes and geometric inequalities #math.MG

paper · pdf · doi:10.48550/arxiv.1609.01036

arxiv created 2016/09/05 · openalex publication_date 2016/09/05 · arxiv updated 2016/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 M_α(n). We prove that M_{\frac 1 a} (n) ≤ \frac 1 2 ( a²-2) ( a²-1) for any n ∈ ℕ in the interval a² -2 ≤ n ≤ 3 a²-16 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.

Citations

• On tight spherical designs

Cited by

• A new proof of the Lemmens-Seidel conjecture
• Noncommutative Equiangular Lines: van Lint-Seidel Relative and Gerzon Universal Bounds

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