MinT - Best Known (4, 4+8, s)-Nets in Base 81

Best Known (4, 4+8, s)-Nets in Base 81

(4, 4+8, 164)-Net over F₈₁ — Constructive and digital

Digital (4, 12, 164)-net over F₈₁, using

(u,Â u+v)-construction [i] based on
1. digital (0, 4, 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, 8, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)

(4, 4+8, 14701)-Net in Base 81 — Upper bound on s

There is no (4, 12, 14702)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 79769 617856 382646 611841 > 81¹² [i]