{
  "abstract": "Possibly the most enduring lower-bound record for kissing numbers in dimensions greater than $8$ (excluding $24$) is $$ κ_{16}\\geq 4320. $$ This lower bound is attained by a shell of the famous Barnes--Wall lattice, which was discovered in 1959. Besides this configuration, at least one alternative $4320$-point kissing arrangement is currently known. Recently, it was noticed that all these configurations can be described in terms of the so-called quaternionic construction, a general type of construction that was instrumental in explaining the geometry of the $841$-point kissing arrangement in ${\\mathbb R}^{12}$. We give a simple generalization of quaternionic constructions in ${\\mathbb R}^{16}$ obtained from record configurations. They are parameterized by three Latin cubes of order $4$, six permutations of $3$-element set, and are all infinitesimally jammed. Computer-aided counting shows that there are $4\\,072\\,728\\,621$ isometry classes in this family of $4320$-point kissing arrangements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00927",
  "author_total": 1,
  "authors": [
    {
      "name": "Rustem Takhanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvvngcsad881h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00927",
  "fulltext_url": null,
  "id": "bvvngcsad881h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00927",
  "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.IT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00927",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvvngcsad881h.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00927",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00927"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Latin cubes of order $4$ and $4320$-point quaternionic constructions in ${\\mathbb R}^{16}$",
  "title_text": "Latin cubes of order $4$ and $4320$-point quaternionic constructions in ℝ^16",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/bvvngcsad881h",
  "venue": "arXiv",
  "versions": []
}