MinT - Best Known (26, 67, s)-Nets in Base 27

Best Known (26, 67, s)-Nets in Base 27

Digital (26, 67, 114)-net over F₂₇, using

(26, 67, 172)-net in base 27, using

9 times m-reduction [i] based on (26, 76, 172)-net in base 27, using
- base change [i] based on digital (7, 57, 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 (26, 67, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 67, 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]

(26, 67, 244)-net in base 27, using

1 times m-reduction [i] based on (26, 68, 244)-net in base 27, using
- base change [i] based on digital (9, 51, 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 (26, 67, 16888)-net in base 27, because

1 times m-reduction [i] would yield (26, 66, 16888)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 29524 741927 323143 755585 905257 535830 062320 395695 231328 413905 188740 559755 543929 652529 829192 924609 > 27⁶⁶ [i]