{
  "id": "1911.12960",
  "version": "v1",
  "published": "2019-11-29T06:00:01.000Z",
  "updated": "2019-11-29T06:00:01.000Z",
  "title": "Constructions of Pairs of Orthogonal Latin Cubes",
  "authors": [
    "Vladimir N. Potapov"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We construct pairs of orthogonal latin cubes for a sequence of previously unknown orders $q_i=16(18i-1)+4$ and $q'_i=16(18i+5)+4$. The minimum new order is $84$. Keywords --- latin square, latin cube, MOLS, MDS code, block design, Steiner system",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-29T06:00:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15",
      "94B05",
      "05B05"
    ],
    "keywords": [
      "orthogonal latin cubes",
      "constructions",
      "block design",
      "mds code",
      "unknown orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}