MinT - Best Known (20, 20+54, s)-Nets in Base 128

Best Known (20, 20+54, s)-Nets in Base 128

(20, 20+54, 288)-Net over F₁₂₈ — Constructive and digital

Digital (20, 74, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 74, 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]

(20, 20+54, 386)-Net over F₁₂₈ — Digital

Digital (20, 74, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 74, 386)-net over F₁₂₈, using
- net from sequence [i] based on digital (15, 385)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
    - a curve from the manYPoints database [i]

(20, 20+54, 513)-Net in Base 128

(20, 74, 513)-net in base 128, using

128² times duplication [i] based on (18, 72, 513)-net in base 128, using
- t-expansion [i] based on (17, 72, 513)-net in base 128, using
  - base change [i] based on digital (8, 63, 513)-net over F₂₅₆, using
    - net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
        K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(20, 20+54, 51263)-Net in Base 128 — Upper bound on s

There is no (20, 74, 51264)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 858374 038442 788948 941363 238516 977222 722219 050027 762699 386235 933439 886982 595528 182276 501113 365376 148237 254383 640284 116549 867263 697409 280079 654808 514491 991661 > 128⁷⁴ [i]