MinT - Information on Result #1205583

Information on Result #1205583

Digital (129, 146, 2097230)-net over F₉, using trace code for nets based on digital (56, 73, 1048615)-net over F₈₁, using

net defined by OOA [i] based on linear OOA(81⁷³, 1048615, F₈₁, 20, 17) (dual of [(1048615, 20), 20972227, 18]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(81⁷³, 2097231, F₈₁, 4, 17) (dual of [(2097231, 4), 8388851, 18]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81⁷³, 2097232, F₈₁, 4, 17) (dual of [(2097232, 4), 8388855, 18]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(81⁸, 82, F₈₁, 4, 8) (dual of [(82, 4), 320, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;320,81) [i]
      2. linear OOA(81⁶⁵, 2097150, F₈₁, 4, 17) (dual of [(2097150, 4), 8388535, 18]-NRT-code), using
        OOA 4-folding [i] based on linear OA(81⁶⁵, 8388600, F₈₁, 17) (dual of [8388600, 8388535, 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.

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.