{
  "id": "1410.4315",
  "version": "v1",
  "published": "2014-10-16T07:08:00.000Z",
  "updated": "2014-10-16T07:08:00.000Z",
  "title": "Optimal order of $L_p$-discrepancy of digit shifted Hammersley point sets in dimension 2",
  "authors": [
    "Aicke Hinrichs",
    "Ralph Kritzinger",
    "Friedrich Pillichshammer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "It is well known that the two-dimensional Hammersley point set consisting of $N=2^n$ elements (also known as Roth net) does not have optimal order of $L_p$-discrepancy for $p \\in (1,\\infty)$ in the sense of the lower bounds according to Roth (for $p \\in [2,\\infty)$) and Schmidt (for $p \\in (1,2)$). On the other hand, it is also known that slight modifications of the Hammersley point set can lead to the optimal order $\\sqrt{\\log N}/N$ of $L_2$-discrepancy, where $N$ is the number of points. Among these are for example digit shifts or the symmetrization. In this paper we show that these modified Hammersley point sets also achieve optimal order of $L_p$-discrepancy for all $p \\in (1,\\infty)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-16T07:08:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38",
      "11K31"
    ],
    "keywords": [
      "digit shifted hammersley point sets",
      "optimal order",
      "discrepancy",
      "hammersley point set consisting",
      "two-dimensional hammersley point set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}