{
  "id": "1710.06754",
  "version": "v1",
  "published": "2017-09-28T19:45:11.000Z",
  "updated": "2017-09-28T19:45:11.000Z",
  "title": "An upper bound on the minimal dispersion",
  "authors": [
    "Mario Ullrich",
    "Jan Vybíral"
  ],
  "categories": [
    "math.CA",
    "math.NA"
  ],
  "abstract": "For $\\varepsilon\\in(0,1/2)$ and a natural number $d\\ge 2$, let $N$ be a natural number with \\[ N \\,\\ge\\, 2^9\\,\\log_2(d)\\, \\left(\\frac{\\log_2(1/\\varepsilon)}{\\varepsilon}\\right)^2. \\] We prove that there is a set of $N$ points in the unit cube $[0,1]^d$, which intersects all axis-parallel boxes with volume $\\varepsilon$. That is, the dispersion of this point set is bounded from above by $\\varepsilon$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-28T19:45:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal dispersion",
      "upper bound",
      "natural number",
      "point set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}