MinT - Information on Result #1880906

Information on Result #1880906

There is no digital (4, 4+k, 128)-net over F₂₅ for arbitrarily large k, because logical equivalence would yield digital (4, m, 128)-net over F₂₅ for arbitrarily large m, but

m-reduction [i] would yield digital (4, 104, 128)-net over F₂₅, but
- extracting embedded orthogonal array [i] would yield linear OA(25¹⁰⁴, 128, F₂₅, 100) (dual of [128, 24, 101]-code), but
  - residual code [i] would yield linear OA(25⁴, 27, F₂₅, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,25)), but
    - bound for MDS codes [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and s, k and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.