MinT - Best Known (29, 29+34, s)-Nets in Base 128

Best Known (29, 29+34, s)-Nets in Base 128

(29, 29+34, 480)-Net over F₁₂₈ — Constructive and digital

Digital (29, 63, 480)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (3, 20, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]
2. digital (9, 43, 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]

(29, 29+34, 545)-Net in Base 128 — Constructive

(29, 63, 545)-net in base 128, using

(u,Â u+v)-construction [i] based on
1. (3, 20, 257)-net in base 128, using
  - 4 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. digital (9, 43, 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]

(29, 29+34, 1109)-Net over F₁₂₈ — Digital

Digital (29, 63, 1109)-net over F₁₂₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(29, 29+34, 3640933)-Net in Base 128 — Upper bound on s

There is no (29, 63, 3640934)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 5 678438 734295 887062 603499 011154 609691 241723 453387 171629 609258 870459 616432 855200 543580 824570 926812 269807 798338 761510 071962 101026 239902 > 128⁶³ [i]