Classification of equiangular lines with fixed angle $\arccos (1/(1+2\sqrt{2}))$

Abstract

We determine the maximum number $N_{\hat{I}}\pm (d)$ of equiangular lines with fixed angle $\arccos \hat{I}\pm$ for $\hat{I}\pm =1/(1+2\sqrt{2})$ in $d$-dimensional Euclidean space: $2,3,4,6,8,10,14,15,16,17,18,20,22$ for $d\in \{2,\dots ,14\}$, and $\max (24,\lfloor 3(d-1)/2\rfloor )$ for $d\ge 15$. This appears to be the first complete determination of $N_{\hat{I}}\pm (d)$ in all dimensions $d$ for a fixed nontrivial $\hat{I}\pm$, since the work of Lemmens and Seidel for $\hat{I}\pm =1/3$ in 1973.

14 pages, 3 figures