MinT - Information on Result #1225067

Information on Result #1225067

Digital (77, 94, 1048652)-net over F₃₂, using (u,Â u+v)-construction based on

digital (5, 13, 77)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 4, 33)-net over F₃₂, using
    - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 9, 44)-net over F₃₂, using
    - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
digital (64, 81, 1048575)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁸¹, 1048575, F₃₂, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
  - OOA 8-folding and stacking with additional row [i] based on linear OA(32⁸¹, 8388601, F₃₂, 17) (dual of [8388601, 8388520, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁸¹, large, F₃₂, 17) (dual of [large, large−81, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive and linear.

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None.