{
  "id": "1602.01307",
  "version": "v1",
  "published": "2016-02-03T14:13:05.000Z",
  "updated": "2016-02-03T14:13:05.000Z",
  "title": "On an explicit lower bound for the star discrepancy in three dimensions",
  "authors": [
    "Florian Puchhammer"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Following a result of D.~Bylik and M.T.~Lacey from 2008 it is known that there exists an absolute constant $\\eta>0$ such that the (unnormalized) $L^{\\infty}$-norm of the three-dimensional discrepancy function, i.e, the (unnormalized) star discrepancy $D^{\\ast}_N$, is bounded from below by $D_{N}^{\\ast}\\geq c (\\log N)^{1+\\eta}$, for infinitely many $N\\in\\mathbb{N}$, where $c>0$ is some constant independent of $N$. This paper builds upon their methods to verify that the above result holds with $\\eta<1/(32+4\\sqrt{41})\\approx 0.017357\\ldots$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-03T14:13:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38",
      "11K06"
    ],
    "keywords": [
      "explicit lower bound",
      "star discrepancy",
      "dimensions",
      "three-dimensional discrepancy function",
      "result holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201307P"
    }
  }
}