MinT - Information on Result #3146795

Information on Result #3146795

There is no digital (80, 250, 249)-net over F₃, because 8 times m-reduction would yield digital (80, 242, 249)-net over F₃, but

extracting embedded orthogonal array [i] would yield linear OA(3²⁴², 249, F₃, 162) (dual of [249, 7, 163]-code), but
- residual code [i] would yield linear OA(3⁸⁰, 86, F₃, 54) (dual of [86, 6, 55]-code), but
  - residual code [i] would yield linear OA(3²⁶, 31, F₃, 18) (dual of [31, 5, 19]-code), but
    - residual code [i] would yield linear OA(3⁸, 12, F₃, 6) (dual of [12, 4, 7]-code), but
      - residual code [i] would yield linear OA(3², 5, F₃, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,3)), but
        improvement by Maruta on the Griesmer bound [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.