MinT - Best Known (24, 24+29, s)-Nets in Base 27

Best Known (24, 24+29, s)-Nets in Base 27

Digital (24, 53, 140)-net over F₂₇, using

(24, 53, 172)-net in base 27, using

15 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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 (24, 53, 229)-net over F₂₇, using

(24, 53, 244)-net in base 27, using

7 times m-reduction [i] based on (24, 60, 244)-net in base 27, using
- base change [i] based on digital (9, 45, 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 (24, 53, 48186)-net in base 27, because

1 times m-reduction [i] would yield (24, 52, 48186)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 269 773202 156766 360788 561092 285314 991980 338707 244633 773764 173433 218517 869213 > 27⁵² [i]