MinT - Best Known (27, 75, s)-Nets in Base 64

Best Known (27, 75, s)-Nets in Base 64

Digital (27, 75, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 75, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(27, 75, 288)-net in base 64, using

Digital (27, 75, 425)-net over F₆₄, using

t-expansion [i] based on digital (26, 75, 425)-net over F₆₄, using
- net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
    - a curve from the manYPoints database [i]

(27, 75, 513)-net in base 64, using

1 times m-reduction [i] based on (27, 76, 513)-net in base 64, using
- base change [i] based on digital (8, 57, 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 (27, 75, 68590)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2907 582312 668563 079053 959700 017927 500797 919935 173215 675555 629307 053675 770114 990824 317911 820750 514823 389233 731699 773635 365010 253220 011866 > 64⁷⁵ [i]