MinT - Best Known (40, 40+80, s)-Nets in Base 9

Best Known (40, 40+80, s)-Nets in Base 9

(40, 40+80, 81)-Net over F₉ — Constructive and digital

Digital (40, 120, 81)-net over F₉, using

t-expansion [i] based on digital (32, 120, 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+80, 140)-Net over F₉ — Digital

Digital (40, 120, 140)-net over F₉, using

t-expansion [i] based on digital (39, 120, 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+80, 1412)-Net in Base 9 — Upper bound on s

There is no (40, 120, 1413)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 271870 822168 824992 854745 694476 468665 190642 821115 738410 936535 653672 333138 246530 039315 633117 109640 373176 509314 753345 > 9¹²⁰ [i]