MinT - Best Known (8, 68, s)-Nets in Base 81

Best Known (8, 68, s)-Nets in Base 81

(8, 68, 172)-Net over F₈₁ — Constructive and digital

Digital (8, 68, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 68, 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]

(8, 68, 226)-Net over F₈₁ — Digital

Digital (8, 68, 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]

(8, 68, 3173)-Net in Base 81 — Upper bound on s

There is no (8, 68, 3174)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5999 421587 732392 697659 990771 751704 559620 478725 739096 982458 775346 260970 158427 727310 903180 545713 815820 077788 387469 554259 790890 017601 > 81⁶⁸ [i]