MinT - Information on Result #3147058

Information on Result #3147058

There is no digital (10, 44, 47)-net over F₄, because 2 times m-reduction would yield digital (10, 42, 47)-net over F₄, but

extracting embedded orthogonal array [i] would yield linear OA(4⁴², 47, F₄, 32) (dual of [47, 5, 33]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(4⁴¹, 44, F₄, 32) (dual of [44, 3, 33]-code), but
    - Griesmer bound [i]
  2. linear OA(4⁵, 47, F₄, 3) (dual of [47, 42, 4]-code or 47-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.