MinT - Information on Result #3147354

Information on Result #3147354

There is no digital (16, 91, 73)-net over F₄, because 23 times m-reduction would yield digital (16, 68, 73)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4⁶⁸, 73, F₄, 52) (dual of [73, 5, 53]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4⁶⁷, 70, F₄, 52) (dual of [70, 3, 53]-code), but
    - Griesmer bound [i]
  2. linear OA(4⁵, 73, F₄, 3) (dual of [73, 68, 4]-code or 73-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.