MinT - Best Known (8, 8+53, s)-Nets in Base 81

Best Known (8, 8+53, s)-Nets in Base 81

(8, 8+53, 172)-Net over F₈₁ — Constructive and digital

Digital (8, 61, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 61, 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, 8+53, 226)-Net over F₈₁ — Digital

Digital (8, 61, 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, 8+53, 3332)-Net in Base 81 — Upper bound on s

There is no (8, 61, 3333)-net in base 81, because

1 times m-reduction [i] would yield (8, 60, 3333)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3 249165 970206 094069 647609 973179 313187 693955 176724 603297 040170 048309 796397 136370 623202 962322 553897 441568 759149 812641 > 81⁶⁰ [i]