MinT - Information on Result #3149077

Information on Result #3149077

There is no digital (50, 241, 210)-net over F₄, because 39 times m-reduction would yield digital (50, 202, 210)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4²⁰², 210, F₄, 152) (dual of [210, 8, 153]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4²⁰¹, 206, F₄, 152) (dual of [206, 5, 153]-code), but
    - residual code [i] would yield linear OA(4⁴⁹, 53, F₄, 38) (dual of [53, 4, 39]-code), but
      - 2 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, 210, 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.