MinT - Best Known (11, 11+34, s)-Nets in Base 81

Best Known (11, 11+34, s)-Nets in Base 81

(11, 11+34, 172)-Net over F₈₁ — Constructive and digital

Digital (11, 45, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 45, 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]

(11, 11+34, 244)-Net over F₈₁ — Digital

Digital (11, 45, 244)-net over F₈₁, using

t-expansion [i] based on digital (9, 45, 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]

(11, 11+34, 10101)-Net in Base 81 — Upper bound on s

There is no (11, 45, 10102)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 76 275506 109547 882002 007261 090012 001369 747783 660972 952686 369081 865629 516122 051264 989921 > 81⁴⁵ [i]