MinT - Information on Result #599475

Information on Result #599475

There is no digital (46, 185, 200)-net over F₄, because extracting embedded orthogonal array would yield linear OA(4¹⁸⁵, 200, F₄, 139) (dual of [200, 15, 140]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(4¹⁸⁴, 192, F₄, 139) (dual of [192, 8, 140]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(4¹⁸³, 188, F₄, 139) (dual of [188, 5, 140]-code), but
      - the linear programming bound with additional constraints on the weights [i]
    2. OA(4⁸, 192, 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]
2. OA(4¹⁵, 200, S₄, 8), but
  - discarding factors would yield OA(4¹⁵, 135, S₄, 8), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 1082 768311 > 4¹⁵ [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.