MinT - Best Known (74−66, 74, s)-Nets in Base 81

Best Known (74−66, 74, s)-Nets in Base 81

(74−66, 74, 172)-Net over F₈₁ — Constructive and digital

Digital (8, 74, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 74, 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]

(74−66, 74, 226)-Net over F₈₁ — Digital

Digital (8, 74, 226)-net over F₈₁, using

net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
  - a curve from the manYPoints database [i]

(74−66, 74, 3116)-Net in Base 81 — Upper bound on s

There is no (8, 74, 3117)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 1705 249188 557293 325922 991232 774978 835082 091980 230671 617265 142274 013038 051351 353897 100998 875093 667665 403292 210349 984648 273344 640477 314119 614481 > 81⁷⁴ [i]