{
  "abstract": "Tight 2 s $2 s$ 2 s -designs are the 2 s $2 s$ 2 s - ( v , k , λ ) $(v, k, \\lambda )$ left parenthesis v comma k comma lamda right parenthesis designs whose sizes achieve the Fisher type lower bound ( v s ) ${v \\choose s}$ StartBinomialOrMatrix v Choose s EndBinomialOrMatrix . Symmetric 2 $2$ 2 -designs, the Witt 4 $4$ 4 - ( 23 , 7 , 1 ) $(23, 7, 1)$ left parenthesis 23 comma 7 comma 1 right parenthesis design and the Witt 4 $4$ 4 - ( 23 , 16 , 52 ) $(23, 16, 52)$ left parenthesis 23 comma 16 comma 52 right parenthesis design are tight designs. It has been widely conjectured since the 1970s that there are no other nontrivial tight designs. In this paper, we give a proof of this conjecture. In the proof, an upper bound v ≪ s $v \\ll s$ v much less than s is shown by analyzing the parameters of the designs and the coefficients of the Wilson polynomials, and a lower bound v ≫ s ( ln ⁡ s ) 2 $v \\gg s (\\ln s)^2$ v much greater than s left parenthesis ln s right parenthesis squared is shown by using estimates on prime gaps.",
  "abstract_shown": true,
  "affiliations": [
    "Southern University of Science and Technology"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ziqing Xiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8k7aznfmg35cp.bib",
  "cited_by": 0,
  "doi": "10.1017/fms.2026.10287",
  "fulltext_url": null,
  "id": "8k7aznfmg35cp",
  "issns": [
    "2050-5094"
  ],
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  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Finite Group Theory Research"
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  "pdf_url": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/1513E2E739D686A82DE84CA500926518/S2050509426102874a.pdf/div-class-title-classification-of-tight-span-class-inlineformula-span-class-alternatives-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-2s-span-span-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-png-data-type-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20261014030459722-0108-s2050509426102874-s2050509426102874-inline1-png-span-span-designs-with-span-class-inlineformula-span-class-alternatives-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-s-geq-2-span-span-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-png-data-type-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20261014030459722-0108-s2050509426102874-s2050509426102874-inline2-png-span-span-div.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": "Cambridge University Press (CUP)",
  "ris": "https://research.draconitic.com/paper/8k7aznfmg35cp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "10.1017/fms.2026.10287",
      "source": "crossref",
      "url": "https://www.cambridge.org/core/product/identifier/S2050509426102874/type/journal_article"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Finite Group Theory Research",
      "subfield": "combinatorics"
    }
  ],
  "title": "Classification of tight 2 s $2s$ 2 s-designs with s ≥ 2 $s \\geq 2$ s greater than or equals 2",
  "title_text": "Classification of tight 2 s 2s 2 s-designs with s ≥ 2 s ≥ 2 s greater than or equals 2",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/8k7aznfmg35cp",
  "venue": "Forum of Mathematics, Sigma",
  "versions": []
}