MinT - Information on Result #599864

Information on Result #599864

There is no digital (2, 13, 53)-net over F₉, because extracting embedded orthogonal array would yield linear OA(9¹³, 53, F₉, 11) (dual of [53, 40, 12]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(9¹², 17, F₉, 11) (dual of [17, 5, 12]-code), but
  - â€œMPaâ€ bound on codes from Brouwerâ€™s database [i]
2. linear OA(9⁴⁰, 53, F₉, 36) (dual of [53, 13, 37]-code), but
  - discarding factors / shortening the dual code would yield linear OA(9⁴⁰, 48, F₉, 36) (dual of [48, 8, 37]-code), but
    - residual code [i] would yield linear OA(9⁴, 11, F₉, 4) (dual of [11, 7, 5]-code or 11-arc in PG(3,9)), but
      - bound for MDS codes [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.