MinT - Information on Result #1213417

Information on Result #1213417

Digital (86, 97, 1678326)-net over F₅, using (u,Â u+v)-construction based on

digital (11, 16, 606)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5¹⁶, 606, F₅, 6, 5) (dual of [(606, 6), 3620, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(5¹⁶, 607, F₅, 2, 5) (dual of [(607, 2), 1198, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(5², 6, F₅, 2, 2) (dual of [(6, 2), 10, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;10,5) [i]
      2. linear OOA(5¹⁴, 601, F₅, 2, 5) (dual of [(601, 2), 1188, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
        trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]
digital (70, 81, 1677720)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁸¹, 1677720, F₅, 11, 11) (dual of [(1677720, 11), 18454839, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(5⁸¹, 8388601, F₅, 11) (dual of [8388601, 8388520, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁸¹, large, F₅, 11) (dual of [large, large−81, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Mode: Constructive and linear.

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