MinT - Information on Result #2709070

Information on Result #2709070

OOA(8¹²⁷, 5592916, S₈, 3, 14), using 8¹ times duplication based on OOA(8¹²⁶, 5592916, S₈, 3, 14), using

(u,Â u+v)-construction [i] based on
1. OOA(8²⁰, 514, S₈, 3, 7), using
  - extracting embedded OOA [i] based on (13, 20, 514)-net in base 8, using
    - base change [i] based on digital (8, 15, 514)-net over F₁₆, using
      - 1 times m-reduction [i] based on digital (8, 16, 514)-net over F₁₆, using
        trace code for nets [i] based on digital (0, 8, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
2. linear OOA(8¹⁰⁶, 5592402, F₈, 3, 14) (dual of [(5592402, 3), 16777100, 15]-NRT-code), using
  - trace code [i] based on linear OOA(64⁵³, 2796201, F₆₄, 3, 14) (dual of [(2796201, 3), 8388550, 15]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(64⁵³, large, F₆₄, 14) (dual of [large, large−53, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.