{
  "id": "1412.8705",
  "version": "v1",
  "published": "2014-12-30T17:51:24.000Z",
  "updated": "2014-12-30T17:51:24.000Z",
  "title": "On the lower bound of the discrepancy of Halton's sequence",
  "authors": [
    "Mordechay B. Levin"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $ (H_s(n))_{n \\geq 1} $ be an $s-$dimensional Halton's sequence. Let $D_N$ be the discrepancy of the sequence $ (H_s(n))_{n = 1}^{N} $. It is known that $ND_N =O(\\ln^s N)$ as $N \\to \\infty $. In this paper we prove that this estimate is exact: $$ \\overline{\\lim}_{ N \\to \\infty} N \\ln^{-s}(N) D_N >0. $$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-30T17:51:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38"
    ],
    "keywords": [
      "lower bound",
      "discrepancy",
      "dimensional haltons sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.8705L"
    }
  }
}