MinT - Best Known (30, 30+40, s)-Nets in Base 128

Best Known (30, 30+40, s)-Nets in Base 128

(30, 30+40, 438)-Net over F₁₂₈ — Constructive and digital

Digital (30, 70, 438)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (1, 21, 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 (9, 49, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(30, 30+40, 515)-Net in Base 128 — Constructive

(30, 70, 515)-net in base 128, using

(u,Â u+v)-construction [i] based on
1. (3, 23, 257)-net in base 128, using
  - 1 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
    - base change [i] based on digital (0, 21, 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. (7, 47, 258)-net in base 128, using
  - 1 times m-reduction [i] based on (7, 48, 258)-net in base 128, using
    - base change [i] based on digital (1, 42, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(30, 30+40, 754)-Net over F₁₂₈ — Digital

Digital (30, 70, 754)-net over F₁₂₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 30+40, 1551438)-Net in Base 128 — Upper bound on s

There is no (30, 70, 1551439)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 3196 671144 384206 926286 147280 679754 865728 715436 789979 708466 534197 577671 571804 591747 955848 758285 001201 911758 609612 533578 965505 666797 200579 605725 592644 > 128⁷⁰ [i]