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arXiv · 1311.3219

New bounds for equiangular lines

Alexander Barg·Wei-Hsuan Yu
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Abstract

A set of lines in $\mathbb{R}^n$ is called equiangular if the angle between each pair of lines is the same. We address the question of determining the maximum size of equiangular line sets in $\mathbb{R}^n$, using semidefinite programming to improve the upper bounds on this quantity. Improvements are obtained in dimensions $24 \leq n \leq 136$. In particular, we show that the maximum number of equiangular lines in $\mathbb{R}^n$ is $276$ for all $24 \leq n \leq 41$ and is 344 for $n=43.$ This provides a partial resolution of the conjecture set forth by Lemmens and Seidel (1973).

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Alexander Barg, Wei-Hsuan Yu. 2014-05-26. New bounds for equiangular lines. https://arxiv.org/abs/1311.3219

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