MinT - Information on Result #1227051

Information on Result #1227051

Digital (29, 46, 657)-net over F₆₄, using (u,Â u+v)-construction based on

digital (5, 13, 145)-net over F₆₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 4, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 9, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
digital (16, 33, 512)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64³³, 512, F₆₄, 17, 17) (dual of [(512, 17), 8671, 18]-NRT-code), using
  - OOA 8-folding and stacking with additional row [i] based on linear OA(64³³, 4097, F₆₄, 17) (dual of [4097, 4064, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 4097Â | 64⁴âˆ’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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