MinT - Best Known (30, 30+48, s)-Nets in Base 27

Best Known (30, 30+48, s)-Nets in Base 27

Digital (30, 78, 114)-net over F₂₇, using

(30, 78, 172)-net in base 27, using

14 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 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 (30, 78, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 78, 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]

(30, 78, 244)-net in base 27, using

6 times m-reduction [i] based on (30, 84, 244)-net in base 27, using
- base change [i] based on digital (9, 63, 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 (30, 78, 16905)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 4432 762444 804547 994701 761403 122276 715042 683252 185977 428570 289491 374175 806003 086464 357448 962176 993184 852079 123361 > 27⁷⁸ [i]