MinT - Information on Result #1228812

Information on Result #1228812

Digital (32, 44, 1398615)-net over F₂₅₆, using (u,Â u+v)-construction based on

digital (4, 10, 515)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256¹⁰, 515, F₂₅₆, 6, 6) (dual of [(515, 6), 3080, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(256¹⁰, 515, F₂₅₆, 5, 6) (dual of [(515, 5), 2565, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(256³, 257, F₂₅₆, 5, 3) (dual of [(257, 5), 1282, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(5;1282,256) [i]
      2. linear OOA(256⁷, 258, F₂₅₆, 5, 6) (dual of [(258, 5), 1283, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (1, 7, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
digital (22, 34, 1398100)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256³⁴, 1398100, F₂₅₆, 12, 12) (dual of [(1398100, 12), 16777166, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(256³⁴, 8388600, F₂₅₆, 12) (dual of [8388600, 8388566, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(256³⁴, large, F₂₅₆, 12) (dual of [large, large−34, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

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