{
  "id": "1401.3601",
  "version": "v2",
  "published": "2014-01-15T14:18:22.000Z",
  "updated": "2015-10-19T18:56:57.000Z",
  "title": "Construction of some perfect integral lattices with minimum 4",
  "authors": [
    "Roland Bacher"
  ],
  "comment": "Final version, to appear in Journal de Th{\\'e}orie des Nombres de Bordeaux",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We construct several families of perfect sublattices with minimum $4$ of $\\mathbb Z^d$. In particular, the number of $d-$dimensional perfect integral lattices with minimum $4$ grows faster than $d^k$ for every exponent $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-15T14:18:22.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-10-19T18:56:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "construction",
      "dimensional perfect integral lattices",
      "grows faster",
      "perfect sublattices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.3601B"
    }
  }
}