MinT - Best Known (28, 28+47, s)-Nets in Base 27

Best Known (28, 28+47, s)-Nets in Base 27

Digital (28, 75, 114)-net over F₂₇, using

(28, 75, 172)-net in base 27, using

9 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 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 (28, 75, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 75, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(28, 75, 244)-net in base 27, using

1 times m-reduction [i] based on (28, 76, 244)-net in base 27, using
- base change [i] based on digital (9, 57, 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 (28, 75, 14602)-net in base 27, because

1 times m-reduction [i] would yield (28, 74, 14602)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 8346 445775 066635 487674 408981 523727 412854 587565 412202 115933 214570 627412 391857 158698 252053 317651 836971 120025 > 27⁷⁴ [i]