MinT - Information on Result #3144595

Information on Result #3144595

There is no digital (48, 156, 154)-net over F₃, because 9 times m-reduction would yield digital (48, 147, 154)-net over F₃, but

extracting embedded orthogonal array [i] would yield linear OA(3¹⁴⁷, 154, F₃, 99) (dual of [154, 7, 100]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁴⁶, 151, F₃, 99) (dual of [151, 5, 100]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁷, 154, F₃, 3) (dual of [154, 147, 4]-code or 154-cap in PG(6,3)), but
    - discarding factors / shortening the dual code would yield linear OA(3⁷, 137, F₃, 3) (dual of [137, 130, 4]-code or 137-cap in PG(6,3)), but
      - a result by BarÃ¡t, Edel, Hill, and Storme [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.