MinT - Information on Result #1228876

Information on Result #1228876

Digital (39, 54, 1198886)-net over F₂₅₆, using (u,Â u+v)-construction based on

digital (4, 11, 515)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256¹¹, 515, F₂₅₆, 7, 7) (dual of [(515, 7), 3594, 8]-NRT-code), using
  - appending kth column [i] based on linear OOA(256¹¹, 515, F₂₅₆, 6, 7) (dual of [(515, 6), 3079, 8]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(256³, 257, F₂₅₆, 6, 3) (dual of [(257, 6), 1539, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(6;1539,256) [i]
      2. linear OOA(256⁸, 258, F₂₅₆, 6, 7) (dual of [(258, 6), 1540, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (1, 8, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
digital (28, 43, 1198371)-net over F₂₅₆, using
- net defined by OOA [i] based on linear OOA(256⁴³, 1198371, F₂₅₆, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(256⁴³, 8388598, F₂₅₆, 15) (dual of [8388598, 8388555, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(256⁴³, large, F₂₅₆, 15) (dual of [large, large−43, 16]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.