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Sets of equiangular lines in dimension $18$ constructed from A53 ⊕ A14

  • 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 ℝ18, breaking the previous record. In 2025, Lin, Munemasa, Taniguchi, and Yoshino constructed a large number of sets of $57$ equiangular lines in ℝ18 as affine equiangular sets in an integral overlattice of A92 ⊕ A1. In this paper, we construct further sets of $57$ equiangular lines in ℝ18 from Latin squares of order $6$ and Pasch configurations, realized as affine equiangular sets in an integral overlattice of A53 ⊕ A14. 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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Cite

BibTeXRIS
BibTeX
@misc{munemasa2026sets,
  title = {{Sets of equiangular lines in dimension $18$ constructed from $A_5^3 \oplus A_1^4$}},
  author = {Akihiro Munemasa and Ferenc Szöllősi and Kiyoto Yoshino},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.10421},
  eprint = {2606.10421},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.10421},
}
RIS
TY  - UNPB
TI  - Sets of equiangular lines in dimension $18$ constructed from A_5^3 ⊕ A_1^4
AU  - Akihiro Munemasa
AU  - Ferenc Szöllősi
AU  - Kiyoto Yoshino
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2606.10421
UR  - https://arxiv.org/abs/2606.10421
AB  - In 2023, Greaves, Syatriadi, and Yatsyna found a set of $57$ equiangular lines in ℝ^18, breaking the previous record. In 2025, Lin, Munemasa, Taniguchi, and Yoshino constructed a large number of sets of $57$ equiangular lines in ℝ^18 as affine equiangular sets in an integral overlattice of A_9^2 ⊕ A_1. In this paper, we construct further sets of $57$ equiangular lines in ℝ^18 from Latin squares of order $6$ and Pasch configurations, realized as affine equiangular sets in an integral overlattice of A_5^3 ⊕ 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.
ER  -