MinT - Information on Result #1228254

Information on Result #1228254

Digital (53, 68, 1198650)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (4, 11, 279)-net over F₁₂₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 8, 150)-net over F₁₂₈, using
    - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]
digital (42, 57, 1198371)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁵⁷, 1198371, F₁₂₈, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(128⁵⁷, 8388598, F₁₂₈, 15) (dual of [8388598, 8388541, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁵⁷, large, F₁₂₈, 15) (dual of [large, large−57, 16]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [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.