MinT - Best Known (29, 29+46, s)-Nets in Base 27

Best Known (29, 29+46, s)-Nets in Base 27

Digital (29, 75, 114)-net over F₂₇, using

(29, 75, 172)-net in base 27, using

13 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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 (29, 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]

(29, 75, 244)-net in base 27, using

5 times m-reduction [i] based on (29, 80, 244)-net in base 27, using
- base change [i] based on digital (9, 60, 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 (29, 75, 16853)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 225169 236163 665133 161351 839108 273001 146463 361491 773921 794907 965370 657500 982531 797748 987502 198540 169399 825443 > 27⁷⁵ [i]