{
  "abstract": "A long-standing and far-reaching conjecture of Cameron and Praeger (1993) asserts that no non-trivial block-transitive $6$-$(v,k,λ)$ designs exist. Huber (2010) reduced the Steiner case ($λ=1$) to a single infinite family of possible exceptions, where the automorphism group is $G=\\PGaL(2,p^e)$ acting on the points of the projective line, with $p\\in\\{2,3\\}$ and $e$ an odd prime power. In this paper, we resolve this final case. By combining orbit-stabiliser analysis for the action of specific involutions in $\\PGaL(2,p^e)$ with the modular arithmetic constraints derived from the design parameters, we prove that no such Steiner 6-designs can exist for any admissible $q$. This completes the proof that the Cameron-Praeger conjecture is true for the important case of non-trivial Steiner 6-designs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06081",
  "author_total": 3,
  "authors": [
    {
      "name": "Ximin Wang"
    },
    {
      "name": "Zheng Huang"
    },
    {
      "name": "Weijun Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16xgzwdf3bqdk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06081",
  "fulltext_url": null,
  "id": "16xgzwdf3bqdk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06081",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06081",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16xgzwdf3bqdk.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06081",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06081"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Cameron-Praeger conjecture for Steiner 6-designs",
  "title_text": "On the Cameron-Praeger conjecture for Steiner 6-designs",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/16xgzwdf3bqdk",
  "venue": "arXiv",
  "versions": []
}