MinT - Information on Result #2709108

Information on Result #2709108

OOA(8¹⁵¹, 5592660, S₈, 3, 17), using 8¹ times duplication based on OOA(8¹⁵⁰, 5592660, S₈, 3, 17), using

(u,Â u+v)-construction [i] based on
1. OOA(8²⁰, 258, S₈, 3, 8), using
  - extracting embedded OOA [i] based on (12, 20, 258)-net in base 8, using
    - trace code for nets [i] based on (2, 10, 129)-net in base 64, using
      - 4 times m-reduction [i] based on (2, 14, 129)-net in base 64, using
        base change [i] based on digital (0, 12, 129)-net over F₁₂₈, using
        net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]
2. linear OOA(8¹³⁰, 5592402, F₈, 3, 17) (dual of [(5592402, 3), 16777076, 18]-NRT-code), using
  - trace code [i] based on linear OOA(64⁶⁵, 2796201, F₆₄, 3, 17) (dual of [(2796201, 3), 8388538, 18]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64⁶⁵, large, F₆₄, 17) (dual of [large, large−65, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: Constructive.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.