{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.10421",
  "author_total": 3,
  "authors": [
    {
      "name": "Akihiro Munemasa"
    },
    {
      "name": "Ferenc Szöllősi"
    },
    {
      "name": "Kiyoto Yoshino"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/56vnx3j0vg7bh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.10421",
  "fulltext_url": null,
  "id": "56vnx3j0vg7bh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.10421",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7164208584",
  "pdf_url": "https://arxiv.org/pdf/2606.10421",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/56vnx3j0vg7bh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2606.10421",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.10421"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sets of equiangular lines in dimension $18$ constructed from $A_5^3 \\oplus A_1^4$",
  "title_text": "Sets of equiangular lines in dimension $18$ constructed from A_5^3 ⊕ A_1^4",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/56vnx3j0vg7bh",
  "venue": "arXiv",
  "versions": []
}