MinT - Best Known (40, 40+84, s)-Nets in Base 9

Best Known (40, 40+84, s)-Nets in Base 9

(40, 40+84, 81)-Net over F₉ — Constructive and digital

Digital (40, 124, 81)-net over F₉, using

t-expansion [i] based on digital (32, 124, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(40, 40+84, 140)-Net over F₉ — Digital

Digital (40, 124, 140)-net over F₉, using

t-expansion [i] based on digital (39, 124, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(40, 40+84, 1329)-Net in Base 9 — Upper bound on s

There is no (40, 124, 1330)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21464 891142 835628 260759 446275 261718 575403 735535 809283 796337 144878 513387 648836 843212 448999 994028 622826 491652 874972 028257 > 9¹²⁴ [i]