MinT - Information on Result #1837771

Information on Result #1837771

OOA(128¹², 513, S₁₂₈, 4, 7), using OOA stacking with additional row based on OOA(128¹², 514, S₁₂₈, 3, 7), using

(u,Â u+v)-construction [i] based on
1. linear OOA(128⁴, 16385, F₁₂₈, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(128⁴, 16385, F₁₂₈, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁴, 16385, F₁₂₈, 3) (dual of [16385, 16381, 4]-code or 16385-cap in PG(3,128)), using
      - ovoid in PG(3,Â 128) [i]
2. OOA(128⁸, 257, S₁₂₈, 3, 7), using
  - extracting embedded OOA [i] based on (1, 8, 257)-net in base 128, using
    - base change [i] based on digital (0, 7, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

Mode: Constructive.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.