{
  "id": "1801.02152",
  "version": "v1",
  "published": "2018-01-07T07:34:12.000Z",
  "updated": "2018-01-07T07:34:12.000Z",
  "title": "Characterization of matrices $B$ such that $(I,B,B^2)$ generates a digital net with $t$-value zero",
  "authors": [
    "Hiroki Kajiura",
    "Makoto Matsumoto",
    "Kosuke Suzuki"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study $3$-dimensional digital nets over $\\mathbb{F}_2$ generated by matrices $(I,B,B^2)$ where $I$ is the identity matrix and $B$ is a square matrix. We give a characterization of $B$ for which the $t$-value of the digital net is $0$. As a corollary, we prove that such $B$ satisfies $B^3=I$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-07T07:34:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K31",
      "11K38"
    ],
    "keywords": [
      "value zero",
      "characterization",
      "dimensional digital nets",
      "identity matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}