MinT - Best Known (74−40, 74, s)-Nets in Base 8

Best Known (74−40, 74, s)-Nets in Base 8

(74−40, 74, 74)-Net over F₈ — Constructive and digital

Digital (34, 74, 74)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (0, 20, 9)-net over F₈, using
  - net from sequence [i] based on digital (0, 8)-sequence over F₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
      - the rational function field F₈(x) [i]
    - Niederreiter sequence [i]
2. digital (14, 54, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(74−40, 74, 100)-Net over F₈ — Digital

Digital (34, 74, 100)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−40, 74, 2591)-Net in Base 8 — Upper bound on s

There is no (34, 74, 2592)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 757500 484165 917174 553791 428350 926718 930480 560122 794737 048146 570203 > 8⁷⁴ [i]