MinT - Information on Result #3147283

Information on Result #3147283

There is no digital (15, 65, 68)-net over F₄, because 2 times m-reduction would yield digital (15, 63, 68)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4⁶³, 68, F₄, 48) (dual of [68, 5, 49]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4⁶², 65, F₄, 48) (dual of [65, 3, 49]-code), but
    - Griesmer bound [i]
  2. linear OA(4⁵, 68, F₄, 3) (dual of [68, 63, 4]-code or 68-cap in PG(4,4)), but
    - discarding factors / shortening the dual code 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]

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.