{
  "id": "1511.03869",
  "version": "v1",
  "published": "2015-11-12T11:56:34.000Z",
  "updated": "2015-11-12T11:56:34.000Z",
  "title": "An improved bound for the star discrepancy of sequences in the unit interval",
  "authors": [
    "Gerhard Larcher",
    "Florian Puchhammer"
  ],
  "comment": "14 pages, 8 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 $N D^{*}_N\\geq c\\cdot \\log N$ holds for infinitely many $N$. Let $c^{*}$ be the supremum of all such $c$ with this property. We show $c^{*}>0.065664679\\ldots$, thereby slightly improving the estimates known until now.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-12T11:56:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38",
      "11K06"
    ],
    "keywords": [
      "star discrepancy",
      "unit interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}