{
  "abstract": "We construct a symmetric conference matrix of order $86$, the smallest order for which existence was open. Equivalently, there exist a conference graph with parameters $(85,42,20,21)$, a regular two-graph on $86$ points, and a real equiangular tight frame of $86$ vectors in $\\mathbb{R}^{43}$. The matrix is a $12\\times12$ array of $7\\times7$ circulants with two border rows, and it admits a group of automorphisms of order $21$. Its $86$ descendants give exactly ten nonisomorphic strongly regular graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08893",
  "author_total": 1,
  "authors": [
    {
      "name": "Harshit Verma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddp2rjzsw057w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08893",
  "fulltext_url": null,
  "id": "ddp2rjzsw057w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08893",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7221037321",
  "pdf_url": "https://arxiv.org/pdf/2610.08893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddp2rjzsw057w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.08893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A symmetric conference matrix of order 86",
  "title_text": "A symmetric conference matrix of order 86",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/ddp2rjzsw057w",
  "venue": "arXiv",
  "versions": []
}