MinT - Best Known (30, 82, s)-Nets in Base 27

Best Known (30, 82, s)-Nets in Base 27

Digital (30, 82, 114)-net over F₂₇, using

(30, 82, 172)-net in base 27, using

10 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, 82, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 82, 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, 82, 244)-net in base 27, using

2 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, 82, 13249)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2354 754859 379803 912146 380632 088498 763982 426970 940867 758536 691402 700010 889643 360894 941581 618948 512997 398341 369263 032825 > 27⁸² [i]