MinT - Information on Result #1234664

Information on Result #1234664

Digital (54, 69, 1198758)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (5, 12, 387)-net over F₁₂₈, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 2, 129)-net over F₁₂₈, using
    - kÂ =Â 2 construction [i]
  2. 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]
  3. digital (0, 7, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈ (see above)
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.

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