MinT - Information on Result #2709135

Information on Result #2709135

OOA(8¹⁶⁹, 5592660, S₈, 3, 19), using 8¹ times duplication based on OOA(8¹⁶⁸, 5592660, S₈, 3, 19), using

(u,Â u+v)-construction [i] based on
1. OOA(8²², 258, S₈, 3, 9), using
  - extracting embedded OOA [i] based on (13, 22, 258)-net in base 8, using
    - trace code for nets [i] based on (2, 11, 129)-net in base 64, using
      - 3 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(8¹⁴⁶, 5592402, F₈, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
  - trace code [i] based on linear OOA(64⁷³, 2796201, F₆₄, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64⁷³, large, F₆₄, 19) (dual of [large, large−73, 20]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (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.