{
  "id": "1111.3403",
  "version": "v1",
  "published": "2011-11-15T01:34:18.000Z",
  "updated": "2011-11-15T01:34:18.000Z",
  "title": "Upper bounds on the smallest size of a complete arc in the plane PG(2,q)",
  "authors": [
    "Daniele Bartoli",
    "Alexander A. Davydov",
    "Giorgio Faina",
    "Stefano Marcugini",
    "Fernanda Pambianco"
  ],
  "comment": "21 pages, 4 figures, 5 tables. arXiv admin note: substantial text overlap with arXiv:1011.3347",
  "categories": [
    "math.CO",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "New upper bounds on the smallest size t_{2}(2,q) of a complete arc in the projective plane PG(2,q) are obtained for q <= 9109. From these new bounds it follows that for q <= 2621 and q = 2659,2663,2683,2693,2753,2801, the relation t_{2}(2,q) < 4.5\\sqrt{q} holds. Also, for q <= 5399 and q = 5413,5417,5419,5441,5443,5471,5483,5501,5521, we have t_{2}(2,q) < 4.8\\sqrt{q}. Finally, for q <= 9067 it holds that t_{2}(2,q) < 5\\sqrt{q}. The new upper bounds are obtained by finding new small complete arcs with the help of a computer search using randomized greedy algorithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-15T01:34:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E21",
      "51E22",
      "94B05"
    ],
    "keywords": [
      "upper bounds",
      "smallest size",
      "small complete arcs",
      "projective plane pg",
      "computer search"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.3403B"
    }
  }
}