{
  "id": "1510.06212",
  "version": "v1",
  "published": "2015-10-21T11:14:00.000Z",
  "updated": "2015-10-21T11:14:00.000Z",
  "title": "On the number of latin hypercubes, pairs of orthogonal latin squares and MDS codes",
  "authors": [
    "Vladimir N. Potapov"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The logarithm of the number of latin $d$-cubes of order $n$ is $\\Theta(n^d\\ln n)$. The logarithm of the number of pairs of orthogonal latin squares of order $n$ is $\\Theta(n^2\\ln n)$. Similar estimations are obtained for systems of mutually strong orthogonal latin $d$-cubes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-21T11:14:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "orthogonal latin squares",
      "latin hypercubes",
      "mds codes",
      "mutually strong orthogonal latin",
      "similar estimations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006212P"
    }
  }
}