MinT - Best Known (18, 18+54, s)-Nets in Base 128

Best Known (18, 18+54, s)-Nets in Base 128

Digital (18, 72, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 72, 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]

Digital (18, 72, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 72, 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]

(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]

There is no (18, 72, 35783)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 52 398456 963770 717455 823356 017950 648167 241900 397378 854180 139153 740032 472679 525871 855650 188421 719843 304720 307476 633642 543136 026174 623417 570246 890114 521760 > 128⁷² [i]