MinT - Best Known (50, 50+14, s)-Nets in Base 128

Best Known (50, 50+14, s)-Nets in Base 128

(50, 50+14, 1198650)-Net over F₁₂₈ — Constructive and digital

Digital (50, 64, 1198650)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 11, 279)-net over F₁₂₈, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 3, 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. digital (1, 8, 150)-net over F₁₂₈, using
      - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]
2. digital (39, 53, 1198371)-net over F₁₂₈, using
  - net defined by OOA [i] based on linear OOA(128⁵³, 1198371, F₁₂₈, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
    - OA 7-folding and stacking [i] based on linear OA(128⁵³, 8388597, F₁₂₈, 14) (dual of [8388597, 8388544, 15]-code), using
      - discarding factors / shortening the dual code based on linear OA(128⁵³, large, F₁₂₈, 14) (dual of [large, large−53, 15]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9256395Â | 128⁴âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

(50, 50+14, 1264163)-Net in Base 128 — Constructive

(50, 64, 1264163)-net in base 128, using

base change [i] based on digital (42, 56, 1264163)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 16, 65792)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256¹⁶, 65792, F₂₅₆, 7, 7) (dual of [(65792, 7), 460528, 8]-NRT-code), using
      - appending kth column [i] based on linear OOA(256¹⁶, 65792, F₂₅₆, 6, 7) (dual of [(65792, 6), 394736, 8]-NRT-code), using
        generalized (u,Â u+v)-construction [i] based on
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256⁰, s, F₂₅₆, 6, 0) with arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256⁰, 257, F₂₅₆, 6, 0) (dual of [(257, 6), 1542, 1]-NRT-code) (see above)
        linear OOA(256¹, 257, F₂₅₆, 6, 1) (dual of [(257, 6), 1541, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(256¹, s, F₂₅₆, 6, 1) with arbitrarily large s, using
        appending 5 arbitrary columns [i] based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
        parity-check code [i]
        linear OOA(256¹, 257, F₂₅₆, 6, 1) (dual of [(257, 6), 1541, 2]-NRT-code) (see above)
        linear OOA(256¹, 257, F₂₅₆, 6, 1) (dual of [(257, 6), 1541, 2]-NRT-code) (see above)
        linear OOA(256¹, 257, F₂₅₆, 6, 1) (dual of [(257, 6), 1541, 2]-NRT-code) (see above)
        linear OOA(256², 257, F₂₅₆, 6, 2) (dual of [(257, 6), 1540, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(6;1540,256) [i]
        linear OOA(256³, 257, F₂₅₆, 6, 3) (dual of [(257, 6), 1539, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(6;1539,256) [i]
        linear OOA(256⁷, 257, F₂₅₆, 6, 7) (dual of [(257, 6), 1535, 8]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(6;1535,256) [i]
  2. digital (26, 40, 1198371)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256⁴⁰, 1198371, F₂₅₆, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
      - OA 7-folding and stacking [i] based on linear OA(256⁴⁰, 8388597, F₂₅₆, 14) (dual of [8388597, 8388557, 15]-code), using
        discarding factors / shortening the dual code 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]

(50, 50+14, large)-Net over F₁₂₈ — Digital

Digital (50, 64, large)-net over F₁₂₈, using

t-expansion [i] based on digital (48, 64, large)-net over F₁₂₈, using
- 2 times m-reduction [i] based on digital (48, 66, large)-net over F₁₂₈, using
  - Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+14, large)-Net in Base 128 — Upper bound on s

There is no (50, 64, large)-net in base 128, because

12 times m-reduction [i] would yield (50, 52, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]

Best Known (50, 50+14, s)-Nets in Base 128

(50, 50+14, 1198650)-Net over F128 — Constructive and digital

(50, 50+14, 1264163)-Net in Base 128 — Constructive

(50, 50+14, large)-Net over F128 — Digital

(50, 50+14, large)-Net in Base 128 — Upper bound on s

(50, 50+14, 1198650)-Net over F₁₂₈ — Constructive and digital

(50, 50+14, large)-Net over F₁₂₈ — Digital