{
  "id": "2106.01937",
  "version": "v1",
  "published": "2021-06-03T15:39:00.000Z",
  "updated": "2021-06-03T15:39:00.000Z",
  "title": "On a partition with a lower expected $\\mathcal{L}_2$-discrepancy than classical jittered sampling",
  "authors": [
    "Markus Kiderlen",
    "Florian Pausinger"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that classical jittered sampling of the $d$-dimensional unit cube does not yield the smallest expected $\\mathcal{L}_2$-discrepancy among all stratified samples with $N=m^d$ points. Our counterexample can be given explicitly and consists of convex partitioning sets of equal volume.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-03T15:39:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K38",
      "60C05",
      "05A18",
      "60D99"
    ],
    "keywords": [
      "classical jittered sampling",
      "discrepancy",
      "dimensional unit cube",
      "equal volume",
      "convex partitioning sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}