MinT - Information on Result #1228346

Information on Result #1228346

Digital (32, 51, 2099)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (5, 14, 279)-net over F₁₂₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 4, 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, 10, 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 (18, 37, 1820)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128³⁷, 1820, F₁₂₈, 19, 19) (dual of [(1820, 19), 34543, 20]-NRT-code), using
  - OOA 9-folding and stacking with additional row [i] based on linear OA(128³⁷, 16381, F₁₂₈, 19) (dual of [16381, 16344, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(128³⁷, 16384, F₁₂₈, 19) (dual of [16384, 16347, 20]-code), using
      - an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

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