MinT - Information on Result #3148972

Information on Result #3148972

There is no digital (49, 209, 205)-net over F₄, because 12 times m-reduction would yield digital (49, 197, 205)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4¹⁹⁷, 205, F₄, 148) (dual of [205, 8, 149]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4¹⁹⁶, 201, F₄, 148) (dual of [201, 5, 149]-code), but
    - residual code [i] would yield linear OA(4⁴⁸, 52, F₄, 37) (dual of [52, 4, 38]-code), but
      - 1 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, 205, 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.