{
  "id": "1406.3681",
  "version": "v2",
  "published": "2014-06-14T04:04:41.000Z",
  "updated": "2014-10-13T06:20:12.000Z",
  "title": "Enumeration of MOLS of small order",
  "authors": [
    "Judith Egan",
    "Ian M. Wanless"
  ],
  "comment": "v2 corrects some typos, including a couple of errors in tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "We report the results of a computer investigation of sets of mutually orthogonal latin squares (MOLS) of small order. For $n\\le9$ we 1. Determine the number of orthogonal mates for each species of latin square of order $n$. 2. Calculate the proportion of latin squares of order $n$ that have an orthogonal mate, and the expected number of mates when a square is chosen uniformly at random. 3. Classify all sets of MOLS of order $n$ up to various different notions of equivalence. We also provide a triple of latin squares of order 10 that is the closest to being a set of MOLS so far found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-14T04:04:41.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-13T06:20:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "small order",
      "enumeration",
      "orthogonal mate",
      "mutually orthogonal latin squares",
      "computer investigation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3681E"
    }
  }
}