MinT - Best Known (22, 22+28, s)-Nets in Base 64

Best Known (22, 22+28, s)-Nets in Base 64

Digital (22, 50, 257)-net over F₆₄, using

(22, 50, 288)-net in base 64, using

41 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, 50, 397)-net over F₆₄, using

(22, 50, 513)-net in base 64, using

6 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, 50, 270863)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2 037069 342168 699877 370185 148225 464503 837028 615292 184216 920532 798726 601868 922994 489344 464833 > 64⁵⁰ [i]