{
  "id": "2001.00185",
  "version": "v1",
  "published": "2020-01-01T10:37:52.000Z",
  "updated": "2020-01-01T10:37:52.000Z",
  "title": "A new upper bound for spherical codes",
  "authors": [
    "Naser T. Sardari",
    "Masoud Zargar"
  ],
  "comment": "Comments are welcome!",
  "categories": [
    "math.MG",
    "cs.IT",
    "math.IT",
    "math.NT"
  ],
  "abstract": "We introduce a new linear programming method for bounding the maximum number $M(n,\\theta)$ of points on a sphere in $n$-dimensional Euclidean space at an angular distance of not less than $\\theta$ from one another. We give the unique optimal solution to this linear programming problem and improve the best known upper bound of Kabatyanskii and Levenshtein. By well-known methods, this leads to new upper bounds for $\\delta_n$, the maximum packing density of an $n$-dimensional Euclidean space by equal balls.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-01T10:37:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "upper bound",
      "spherical codes",
      "dimensional euclidean space",
      "unique optimal solution",
      "maximum number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}