{
  "id": "1806.07491",
  "version": "v1",
  "published": "2018-06-19T22:52:32.000Z",
  "updated": "2018-06-19T22:52:32.000Z",
  "title": "Group divisible designs with block size 4 and type g^u m^1 - II",
  "authors": [
    "Anthony D. Forbes"
  ],
  "comment": "106 pages, including 91-page Appendix. Abridged submitted for publication",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the necessary conditions for the existence of 4-GDDs of type g^u m^1 are sufficient for g congruent to 0 (mod h), h = 39, 51, 57, 69, 87, 93, and for g = 13, 17, 19, 23, 25, 29, 31 and 35. More generally, we show that for all g congruent to 3 (mod 6), the possible exceptions occur only when u = 8 and g is not divisible by any of 9, 15, 21, 33, 39, 51, 57, 69, 87 or 93. Consequently we are able to extend the known spectrum for g congruent to 1 and g congruent to 5 (mod 6). Also we complete the spectrum for 4-GDDs of type (3a)^4 (6a)^1 (3b)^1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-19T22:52:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05"
    ],
    "keywords": [
      "group divisible designs",
      "block size",
      "exceptions occur",
      "necessary conditions",
      "sufficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 106,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}