MinT - Information on Result #3147578

Information on Result #3147578

There is no digital (21, 103, 92)-net over F₄, because 18 times m-reduction would yield digital (21, 85, 92)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4⁸⁵, 92, F₄, 64) (dual of [92, 7, 65]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4⁸⁴, 88, F₄, 64) (dual of [88, 4, 65]-code), but
    - Griesmer bound [i]
  2. OA(4⁷, 92, S₄, 4), but
    - discarding factors would yield OA(4⁷, 61, S₄, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 16654 > 4⁷ [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.