MinT - Best Known (40, 40+32, s)-Nets in Base 9

Best Known (40, 40+32, s)-Nets in Base 9

(40, 40+32, 300)-Net over F₉ — Constructive and digital

Digital (40, 72, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 36, 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]

(40, 40+32, 308)-Net over F₉ — Digital

Digital (40, 72, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 36, 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]

(40, 40+32, 16722)-Net in Base 9 — Upper bound on s

There is no (40, 72, 16723)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 507 917123 504760 094257 165310 634158 275068 973360 404655 716539 769157 463425 > 9⁷² [i]