MinT - Information on Result #1214646

Information on Result #1214646

Digital (57, 72, 2422)-net over F₇, using (u,Â u+v)-construction based on

digital (4, 11, 21)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 8)-net over F₇, using
    - net from sequence [i] based on digital (0, 7)-sequence over F₇, using
      - Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using
        the rational function field F₇(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 8, 13)-net over F₇, using
    - 5 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
digital (46, 61, 2401)-net over F₇, using
- net defined by OOA [i] based on linear OOA(7⁶¹, 2401, F₇, 15, 15) (dual of [(2401, 15), 35954, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(7⁶¹, 16808, F₇, 15) (dual of [16808, 16747, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16808Â | 7¹⁰âˆ’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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