MinT - Best Known (25, 68, s)-Nets in Base 81

Best Known (25, 68, s)-Nets in Base 81

(25, 68, 370)-Net over F₈₁ — Constructive and digital

Digital (25, 68, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 68, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(25, 68, 392)-Net over F₈₁ — Digital

Digital (25, 68, 392)-net over F₈₁, using

net from sequence [i] based on digital (25, 391)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 25 and N(F) ≥ 392, using
  - a curve from the manYPoints database [i]

(25, 68, 133151)-Net in Base 81 — Upper bound on s

There is no (25, 68, 133152)-net in base 81, because

1 times m-reduction [i] would yield (25, 67, 133152)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 73 883979 451773 309344 207795 128870 245904 475550 520091 402616 911317 534927 721586 101635 141253 470953 294008 041144 758103 199552 454114 767361 > 81⁶⁷ [i]