MinT - Best Known (7, 39, s)-Nets in Base 81

Best Known (7, 39, s)-Nets in Base 81

(7, 39, 172)-Net over F₈₁ — Constructive and digital

Digital (7, 39, 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]

(7, 39, 190)-Net over F₈₁ — Digital

Digital (7, 39, 190)-net over F₈₁, using

t-expansion [i] based on digital (6, 39, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(7, 39, 3806)-Net in Base 81 — Upper bound on s

There is no (7, 39, 3807)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 270 508321 631582 260395 607996 823136 498858 923370 377439 608658 975206 616187 656961 > 81³⁹ [i]