MinT - Best Known (84−38, 84, s)-Nets in Base 9

Best Known (84−38, 84, s)-Nets in Base 9

(84−38, 84, 300)-Net over F₉ — Constructive and digital

Digital (46, 84, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 42, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(84−38, 84, 308)-Net over F₉ — Digital

Digital (46, 84, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 42, 154)-net over F₈₁, using
- net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
    - a curve from the manYPoints database [i]

(84−38, 84, 16390)-Net in Base 9 — Upper bound on s

There is no (46, 84, 16391)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 143 496706 247070 695472 451084 898528 380050 264453 847934 148239 039595 060934 615588 608297 > 9⁸⁴ [i]