MinT - Best Known (22, 22+27, s)-Nets in Base 27

Best Known (22, 22+27, s)-Nets in Base 27

Digital (22, 49, 132)-net over F₂₇, using

(22, 49, 172)-net in base 27, using

11 times m-reduction [i] based on (22, 60, 172)-net in base 27, using
- base change [i] based on digital (7, 45, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

Digital (22, 49, 209)-net over F₂₇, using

(22, 49, 244)-net in base 27, using

3 times m-reduction [i] based on (22, 52, 244)-net in base 27, using
- base change [i] based on digital (9, 39, 244)-net over F₈₁, using
  - net from sequence [i] based on digital (9, 243)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 9 and N(F) ≥ 244, using
      - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₈₁ [i]

There is no (22, 49, 42015)-net in base 27, because

1 times m-reduction [i] would yield (22, 48, 42015)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 507 578639 055610 518662 532847 859825 161292 847295 707450 563110 526748 258543 > 27⁴⁸ [i]