MinT - Information on Result #1217630

Information on Result #1217630

Digital (126, 143, 2097182)-net over F₉, using (u,Â u+v)-construction based on

digital (5, 13, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]
digital (113, 130, 2097150)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹³⁰, 2097150, F₉, 18, 17) (dual of [(2097150, 18), 37748570, 18]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OOA(9¹³⁰, 8388601, F₉, 2, 17) (dual of [(8388601, 2), 16777072, 18]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹³⁰, 8388602, F₉, 2, 17) (dual of [(8388602, 2), 16777074, 18]-NRT-code), using
      - trace code [i] based on linear OOA(81⁶⁵, 4194301, F₈₁, 2, 17) (dual of [(4194301, 2), 8388537, 18]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁶⁵, 8388602, F₈₁, 17) (dual of [8388602, 8388537, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁶⁵, large, F₈₁, 17) (dual of [large, large−65, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’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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