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arxiv: 2606.10421 · v1 · pith:NRFXV5TTnew · submitted 2026-06-09 · 🧮 math.CO

Sets of equiangular lines in dimension 18 constructed from A₅³ oplus A₁⁴

classification 🧮 math.CO
keywords equiangularsetslinesmathbboplusaffineconstructedexamples
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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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