MinT - Best Known (7, 7+66, s)-Nets in Base 81

Best Known (7, 7+66, s)-Nets in Base 81

(7, 7+66, 172)-Net over F₈₁ — Constructive and digital

Digital (7, 73, 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, 7+66, 190)-Net over F₈₁ — Digital

Digital (7, 73, 190)-net over F₈₁, using

t-expansion [i] based on digital (6, 73, 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, 7+66, 2725)-Net in Base 81 — Upper bound on s

There is no (7, 73, 2726)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 20 968460 341844 295998 051972 245858 343028 439413 859989 347013 400595 638799 143374 498285 996423 532594 205612 883886 405993 199184 782443 225684 746555 727841 > 81⁷³ [i]