MinT - Best Known (7, 54, s)-Nets in Base 81

Best Known (7, 54, s)-Nets in Base 81

(7, 54, 172)-Net over F₈₁ — Constructive and digital

Digital (7, 54, 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, 54, 190)-Net over F₈₁ — Digital

Digital (7, 54, 190)-net over F₈₁, using

t-expansion [i] based on digital (6, 54, 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, 54, 2934)-Net in Base 81 — Upper bound on s

There is no (7, 54, 2935)-net in base 81, because

1 times m-reduction [i] would yield (7, 53, 2935)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 141864 625257 033234 218932 062402 381164 931358 885565 972019 420169 906981 385421 325495 720292 661641 075873 176401 > 81⁵³ [i]