MinT - Information on Result #3149815

Information on Result #3149815

There is no digital (64, 260, 265)-net over F₄, because 4 times m-reduction would yield digital (64, 256, 265)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4²⁵⁶, 265, F₄, 192) (dual of [265, 9, 193]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4²⁵⁵, 261, F₄, 192) (dual of [261, 6, 193]-code), but
    - constructionÂ Y1 [i] would yield
      1. linear OA(4²⁵⁴, 258, F₄, 192) (dual of [258, 4, 193]-code), but
        Griesmer bound [i]
      2. linear OA(4⁶, 261, F₄, 3) (dual of [261, 255, 4]-code or 261-cap in PG(5,4)), but
        discarding factors / shortening the dual code would yield linear OA(4⁶, 160, F₄, 3) (dual of [160, 154, 4]-code or 160-cap in PG(5,4)), but
        1 times Hill recurrence [i] would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
        41 is the largest size of a cap in PG(4,Â 4) [i]
  2. OA(4⁹, 265, S₄, 4), but
    - discarding factors would yield OA(4⁹, 242, S₄, 4), but
      - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 263176 > 4⁹ [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.