Semidefinite Programming Bounds For Spherical Three-distance Sets

2020/05/04 by Feng-Yuan Liu, Liu, Feng-Yuan, Wei-Hsuan Yu +1 · 1 citation
Computer Science · Mathematics · #Digital Image Processing Techniques #Mathematical Approximation and Integration #Point processes and geometric inequalities #math.CO

paper · pdf · doi:10.48550/arxiv.2005.01324

10 pages

arxiv created 2020/05/04 · arxiv updated 2020/05/05

Abstract

A spherical three-distance set is a finite collection X of unit vectors in ℝⁿ such that for each pair of distinct vectors has three inner product values. We use the semidefinite programming method to improve the upper bounds of spherical three-distance sets for several dimensions. We obtain better bounds in ℝ⁷, ℝ²⁰, ℝ²¹, ℝ²³, ℝ²⁴ and ℝ²⁵. In particular, we prove that maximum size of spherical three-distance sets is 2300 in \mathbb R²³.

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