MinT - Best Known (27, 27+39, s)-Nets in Base 27

Best Known (27, 27+39, s)-Nets in Base 27

Digital (27, 66, 128)-net over F₂₇, using

(27, 66, 172)-net in base 27, using

14 times m-reduction [i] based on (27, 80, 172)-net in base 27, using
- base change [i] based on digital (7, 60, 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 (27, 66, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 66, 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]

(27, 66, 244)-net in base 27, using

6 times m-reduction [i] based on (27, 72, 244)-net in base 27, using
- base change [i] based on digital (9, 54, 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 (27, 66, 24035)-net in base 27, because

1 times m-reduction [i] would yield (27, 65, 24035)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1093 395122 498511 986419 583998 586623 467161 568451 628113 242562 030740 986216 470895 844346 320114 328035 > 27⁶⁵ [i]