{
  "abstract": "For all prime powers $q\\geq5$, we construct lattices $\\mathcal{L}_q\\subseteq\\mathbb{Z}^q$ with kissing numbers \\[ τ(\\mathcal{L}_q)\\geq \\left(\\frac{1}{2πe^2}+o(1)\\right)\\sqrt{q}\\,e^{2\\sqrt{q}}. \\] The same asymptotic bound holds on a set of integer dimensions of natural density $1$, and in every sufficiently large integer dimension $n$ with an additional factor $e^{-\\tfrac{1}{2}n^{1/40}}$. The construction is an extension of a previous construction by Bennett-Peikert based on Reed-Solomon codes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13608",
  "author_total": 2,
  "authors": [
    {
      "name": "Thijs Laarhoven"
    },
    {
      "name": "Scott Duke Kominers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8fv7x40dqn5ga.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13608",
  "fulltext_url": null,
  "id": "8fv7x40dqn5ga",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13608",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.MG"
    ],
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      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "1702|Coding theory and cryptography"
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  "openalex": "W7213365930",
  "pdf_url": "https://arxiv.org/pdf/2609.13608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8fv7x40dqn5ga.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2609.13608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13608"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A lattice family with kissing numbers $τ(\\mathcal{L}_n) \\ge e^{2 \\sqrt{n}}$",
  "title_text": "A lattice family with kissing numbers τ(ℒ_n) ≥ e^2 √n",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/8fv7x40dqn5ga",
  "venue": "arXiv",
  "versions": []
}