MinT - Best Known (22, 77, s)-Nets in Base 128

Best Known (22, 77, s)-Nets in Base 128

Digital (22, 77, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 77, 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 (22, 77, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 77, 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]

(22, 77, 513)-net in base 128, using

128⁵ times duplication [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 (22, 77, 73440)-net in base 128, because

1 times m-reduction [i] would yield (22, 76, 73440)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14060 768937 015923 564102 194116 457144 791293 237731 295011 439897 793056 973949 729903 470436 763342 704416 605363 036785 579395 888252 378440 916148 648758 591502 186819 294477 366587 > 128⁷⁶ [i]