MinT - Information on Result #3143186

Information on Result #3143186

There is no digital (4, 14, 19)-net over F₃, because 1 times m-reduction would yield digital (4, 13, 19)-net over F₃, but

extracting embedded orthogonal array [i] would yield linear OA(3¹³, 19, F₃, 9) (dual of [19, 6, 10]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹², 15, F₃, 9) (dual of [15, 3, 10]-code), but
    - Griesmer bound [i]
  2. OA(3⁶, 19, S₃, 4), but
    - the linear programming bound shows that MÂ â‰¥ 51975 / 67 > 3⁶ [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.