MinT - Best Known (71−38, 71, s)-Nets in Base 8

Best Known (71−38, 71, s)-Nets in Base 8

(71−38, 71, 74)-Net over F₈ — Constructive and digital

Digital (33, 71, 74)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (0, 19, 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, 52, 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]

(71−38, 71, 101)-Net over F₈ — Digital

Digital (33, 71, 101)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−38, 71, 2672)-Net in Base 8 — Upper bound on s

There is no (33, 71, 2673)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13206 340540 856231 790445 337708 425431 475347 714090 362673 836925 009184 > 8⁷¹ [i]