MinT - Best Known (6, 16, s)-Nets in Base 81

Best Known (6, 16, s)-Nets in Base 81

(6, 16, 182)-Net over F₈₁ — Constructive and digital

Digital (6, 16, 182)-net over F₈₁, using

(u,Â u+v)-construction [i] based on
1. digital (0, 5, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]
2. digital (1, 11, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(6, 16, 190)-Net over F₈₁ — Digital

Digital (6, 16, 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]

(6, 16, 41675)-Net in Base 81 — Upper bound on s

There is no (6, 16, 41676)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3 434047 479355 138082 696068 254401 > 81¹⁶ [i]