MinT - Information on Result #1838705

Information on Result #1838705

OOA(128⁶², 2097664, S₁₂₈, 4, 15), using (u,Â u+v)-construction based on

OOA(128¹², 514, S₁₂₈, 4, 7), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁴, 16385, F₁₂₈, 4, 3) (dual of [(16385, 4), 65536, 4]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(128⁴, 16385, F₁₂₈, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(128⁴, 16385, F₁₂₈, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁴, 16385, F₁₂₈, 3) (dual of [16385, 16381, 4]-code or 16385-cap in PG(3,128)), using
        ovoid in PG(3,Â 128) [i]
  2. OOA(128⁸, 257, S₁₂₈, 4, 7), using
    - extracting embedded OOA [i] based on (1, 8, 257)-net in base 128, using
      - base change [i] based on digital (0, 7, 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]
OOA(128⁵⁰, 2097150, S₁₂₈, 4, 15), using
- OOA 4-folding [i] based on OA(128⁵⁰, 8388600, S₁₂₈, 15), using
  - discarding factors based on OA(128⁵⁰, large, S₁₂₈, 15), using
    - discarding parts of the base [i] 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.

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.