MinT - Best Known (8, 8+48, s)-Nets in Base 81

Best Known (8, 8+48, s)-Nets in Base 81

(8, 8+48, 172)-Net over F₈₁ — Constructive and digital

Digital (8, 56, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 56, 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+48, 226)-Net over F₈₁ — Digital

Digital (8, 56, 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+48, 3466)-Net in Base 81 — Upper bound on s

There is no (8, 56, 3467)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 75116 865061 863494 989700 325161 853551 158000 036489 355628 601364 199940 215069 549440 367849 539999 864200 079207 987841 > 81⁵⁶ [i]