New bounds for equiangular lines
Alexander Barg, Wei-Hsuan Yu · Contemporary mathematics - American Mathematical Society · 2014
A set of lines in R n \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 R n , \mathbb {R}^n, using semidefinite programming to improve the upper bounds on this quantity. Improvements are obtained in dimensions 24 ≤ n ≤ 136 24 \leq n \leq 136 . In particular, we show that the maximum number of equiangular lines in R n \mathbb {R}^n is 276 276 for all 24 ≤ n ≤ 41 24 \leq n \leq 41 and is 344 for n = 43. n=43. This provides a partial resolution of the conjecture set forth by Lemmens and Seidel (1973).