MinT - Information on Result #3144093

Information on Result #3144093

There is no digital (30, 123, 99)-net over F₃, because 30 times m-reduction would yield digital (30, 93, 99)-net over F₃, but

extracting embedded orthogonal array [i] would yield linear OA(3⁹³, 99, F₃, 63) (dual of [99, 6, 64]-code), but
- residual code [i] would yield linear OA(3³⁰, 35, F₃, 21) (dual of [35, 5, 22]-code), but
  - residual code [i] would yield linear OA(3⁹, 13, F₃, 7) (dual of [13, 4, 8]-code), but
    - 1 times truncation [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.