MinT - Information on Result #3149158

Information on Result #3149158

There is no digital (51, 255, 215)-net over F₄, because 48 times m-reduction would yield digital (51, 207, 215)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4²⁰⁷, 215, F₄, 156) (dual of [215, 8, 157]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4²⁰⁶, 211, F₄, 156) (dual of [211, 5, 157]-code), but
    - residual code [i] would yield linear OA(4⁵⁰, 54, F₄, 39) (dual of [54, 4, 40]-code), but
      - 3 times truncation [i] would yield linear OA(4⁴⁷, 51, F₄, 36) (dual of [51, 4, 37]-code), but
        a result by Landjev, Maruta, and Hill [i]
  2. OA(4⁸, 215, S₄, 4), but
    - discarding factors would yield OA(4⁸, 121, S₄, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 65704 > 4⁸ [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.