MinT - Best Known (20, 43, s)-Nets in Base 27

Best Known (20, 43, s)-Nets in Base 27

Digital (20, 43, 132)-net over F₂₇, using

(20, 43, 172)-net in base 27, using

9 times m-reduction [i] based on (20, 52, 172)-net in base 27, using
- base change [i] based on digital (7, 39, 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 (20, 43, 230)-net over F₂₇, using

(20, 43, 244)-net in base 27, using

1 times m-reduction [i] based on (20, 44, 244)-net in base 27, using
- base change [i] based on digital (9, 33, 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 (20, 43, 55107)-net in base 27, because

1 times m-reduction [i] would yield (20, 42, 55107)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 310073 496402 248646 450271 935898 396508 438445 610390 486515 812019 > 27⁴² [i]