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arXiv · 2606.10421

Sets of equiangular lines in dimension $18$ constructed from $A_5^3 \oplus A_1^4$

Akihiro Munemasa·Ferenc Szöllősi·Kiyoto Yoshino
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Abstract

In 2023, Greaves, Syatriadi, and Yatsyna found a set of $57$ equiangular lines in $\mathbb{R}^{18}$, breaking the previous record. In 2025, Lin, Munemasa, Taniguchi, and Yoshino constructed a large number of sets of $57$ equiangular lines in $\mathbb{R}^{18}$ as affine equiangular sets in an integral overlattice of $A_9^2 \oplus A_1$. In this paper, we construct further sets of $57$ equiangular lines in $\mathbb{R}^{18}$ from Latin squares of order $6$ and Pasch configurations, realized as affine equiangular sets in an integral overlattice of $A_5^3 \oplus A_1^4$. Unlike the previously known examples, these sets are not strongly maximal. Moreover, some of them have only five distinct Seidel eigenvalues, fewer than any previously known examples.

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Akihiro Munemasa, Ferenc Szöllősi, Kiyoto Yoshino. 2026-06-09. Sets of equiangular lines in dimension $18$ constructed from $A_5^3 \oplus A_1^4$. https://arxiv.org/abs/2606.10421

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