MinT - Information on Result #1844092

Information on Result #1844092

(44, 58, 1198885)-net in base 128, using (u,Â u+v)-construction based on

(5, 12, 514)-net in base 128, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 4, 16385)-net over F₁₂₈, using
    - net defined by OOA [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. (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]
(32, 46, 1198371)-net in base 128, using
- net defined by OOA [i] based on OOA(128⁴⁶, 1198371, S₁₂₈, 14, 14), using
  - OA 7-folding and stacking [i] based on OA(128⁴⁶, 8388597, S₁₂₈, 14), using
    - discarding factors based on OA(128⁴⁶, large, S₁₂₈, 14), using
      - discarding parts of the base [i] based on linear OA(256⁴⁰, large, F₂₅₆, 14) (dual of [large, large−40, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’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, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.