MinT - Best Known (76−38, 76, s)-Nets in Base 9

Best Known (76−38, 76, s)-Nets in Base 9

(76−38, 76, 164)-Net over F₉ — Constructive and digital

Digital (38, 76, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 38, 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]

(76−38, 76, 6491)-Net in Base 9 — Upper bound on s

There is no (38, 76, 6492)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 336143 054550 589328 135553 030130 575597 993890 913992 214020 299690 436102 327073 > 9⁷⁶ [i]