MinT - Best Known (47, 74, s)-Nets in Base 81

Best Known (47, 74, s)-Nets in Base 81

(47, 74, 756)-Net over F₈₁ — Constructive and digital

Digital (47, 74, 756)-net over F₈₁, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 3, 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 (0, 3, 82)-net over F₈₁ (see above)
3. digital (0, 3, 82)-net over F₈₁ (see above)
4. digital (0, 4, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
5. digital (0, 5, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
6. digital (0, 6, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
7. digital (0, 9, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
8. digital (0, 13, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)
9. digital (1, 28, 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]

(47, 74, 35662)-Net over F₈₁ — Digital

Digital (47, 74, 35662)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 74, large)-Net in Base 81 — Upper bound on s

There is no (47, 74, large)-net in base 81, because

25 times m-reduction [i] would yield (47, 49, large)-net in base 81, but
- mutually orthogonal hypercube bound [i]