MinT - Information on Result #1229527

Information on Result #1229527

Digital (80, 103, 408)-net over F₅, using (u,Â u+v)-construction based on

digital (26, 37, 156)-net over F₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (2, 5, 52)-net over F₅, using
    - s-reduction based on digital (2, 5, 66)-net over F₅, using
      - net defined by OOA [i] based on linear OOA(5⁵, 66, F₅, 3, 3) (dual of [(66, 3), 193, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(5⁵, 66, F₅, 2, 3) (dual of [(66, 2), 127, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁵, 66, F₅, 3) (dual of [66, 61, 4]-code or 66-cap in PG(4,5)), using
        caps completed using a computer search [i]
  2. digital (5, 10, 52)-net over F₅, using
    - s-reduction based on digital (5, 10, 68)-net over F₅, using
      - linear code embedding found in a computer search [i]
  3. digital (11, 22, 52)-net over F₅, using
    - trace code for nets [i] based on digital (0, 11, 26)-net over F₂₅, using
      - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
digital (43, 66, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 33, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

Mode: Constructive and 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.