{
  "id": "1407.2094",
  "version": "v1",
  "published": "2014-07-08T14:09:15.000Z",
  "updated": "2014-07-08T14:09:15.000Z",
  "title": "On the star discrepancy of sequences in the unit interval",
  "authors": [
    "Gerhard Larcher"
  ],
  "comment": "13 pages, 10 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "It is known that there is a constant $c > 0$ such that for every sequence $x_1, x_2, \\ldots$ in $[0,1)$ we have for the star discrepancy $D_N^*$ of the first $N$ elements of the sequence that $N D_N^* \\ge c \\cdot \\log N$ holds for infinitely many $N$. Let $c^*$ be the supremum of all such $c$ with this property. We show $c^* > 0.0646363$, thereby improving the until now known estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-08T14:09:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38"
    ],
    "keywords": [
      "star discrepancy",
      "unit interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.2094L"
    }
  }
}