MinT - Best Known (41, 41+108, s)-Nets in Base 9

Best Known (41, 41+108, s)-Nets in Base 9

(41, 41+108, 81)-Net over F₉ — Constructive and digital

Digital (41, 149, 81)-net over F₉, using

t-expansion [i] based on digital (32, 149, 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]

(41, 41+108, 140)-Net over F₉ — Digital

Digital (41, 149, 140)-net over F₉, using

t-expansion [i] based on digital (39, 149, 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]

(41, 41+108, 1092)-Net in Base 9 — Upper bound on s

There is no (41, 149, 1093)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15343 414854 799178 691980 613205 378419 101934 487936 260631 604635 661864 023686 935429 444293 549857 956278 628911 036736 996162 580309 528713 047761 504215 567025 > 9¹⁴⁹ [i]