MinT - Best Known (96−62, 96, s)-Nets in Base 27

Best Known (96−62, 96, s)-Nets in Base 27

Digital (34, 96, 114)-net over F₂₇, using

(34, 96, 172)-net in base 27, using

12 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 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 (34, 96, 220)-net over F₂₇, using

t-expansion [i] based on digital (33, 96, 220)-net over F₂₇, using
- net from sequence [i] based on digital (33, 219)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 33 and N(F) ≥ 220, using
    - Drinfeld modules of rank 1 [i]

(34, 96, 244)-net in base 27, using

4 times m-reduction [i] based on (34, 100, 244)-net in base 27, using
- base change [i] based on digital (9, 75, 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 (34, 96, 12916)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 257622 673572 771955 998425 674660 485635 258612 750795 851767 652951 423540 796553 043287 696848 892951 894139 238714 184357 453580 219997 127051 916308 779985 > 27⁹⁶ [i]