MinT - Best Known (22, 53, s)-Nets in Base 64

Best Known (22, 53, s)-Nets in Base 64

Digital (22, 53, 242)-net over F₆₄, using

(22, 53, 288)-net in base 64, using

38 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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, 53, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 53, 342)-net over F₆₄, using
- net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
    - a curve from the manYPoints database [i]

(22, 53, 513)-net in base 64, using

3 times m-reduction [i] based on (22, 56, 513)-net in base 64, using
- base change [i] based on digital (8, 42, 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, 53, 186138)-net in base 64, because

1 times m-reduction [i] would yield (22, 52, 186138)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 8344 255418 664765 059067 094500 414098 902917 516133 769823 598025 213777 036785 790876 801866 366817 857000 > 64⁵² [i]