{
  "id": "0809.2282",
  "version": "v2",
  "published": "2008-09-12T20:16:25.000Z",
  "updated": "2015-05-31T04:43:10.000Z",
  "title": "New lower bounds for the number of blocks in balanced incomplete block designs",
  "authors": [
    "Muhammad Ali Khan"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Bose proved the inequality $b\\geq v+r-1$ for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note we prove a new lower bound on the number of blocks $b$ that holds for all BIBDs. We further prove that for a significantly large number of BIBDs our bound is tighter than the bounds given by the inequalities of Bose and Kageyama.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-12T20:16:25.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-05-31T04:43:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B05"
    ],
    "keywords": [
      "lower bound",
      "resolvable balanced incomplete block designs",
      "significantly large number",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.2282K"
    }
  }
}