{
  "abstract": "Among lattices normalized to have packing radius one, the known shallowest depths of the deep holes in $7$-, $8$-, $9$- and $10$-dimensional lattices are $\\sqrt{7/3}$, $\\sqrt2$, $\\sqrt{5/2}$ and $\\sqrt{8/3}$, given by $E_7^*$, $E_8$, the laminated lattices $Λ_9$ and $Λ_{10}$, respectively. This paper presents new lattices in these dimensions with shallower deep holes. It also answers two problems of J. Martinet about short representatives of the classes of $Λ/2Λ$ in $7,8,9,10$ and $12$ dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22887",
  "author_total": 2,
  "authors": [
    {
      "name": "Yiming Li"
    },
    {
      "name": "Chuanming Zong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mv00afqanagr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22887",
  "fulltext_url": null,
  "id": "2mv00afqanagr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22887",
  "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.MG"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7214051699",
  "pdf_url": "https://arxiv.org/pdf/2609.22887",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mv00afqanagr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22887",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22887"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "New Lattices with Unexpected Shallow Deep Holes",
  "title_text": "New Lattices with Unexpected Shallow Deep Holes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/2mv00afqanagr",
  "venue": "arXiv",
  "versions": []
}