MinT - Best Known (41, 41+85, s)-Nets in Base 9

Best Known (41, 41+85, s)-Nets in Base 9

(41, 41+85, 81)-Net over F₉ — Constructive and digital

Digital (41, 126, 81)-net over F₉, using

t-expansion [i] based on digital (32, 126, 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+85, 140)-Net over F₉ — Digital

Digital (41, 126, 140)-net over F₉, using

t-expansion [i] based on digital (39, 126, 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+85, 1402)-Net in Base 9 — Upper bound on s

There is no (41, 126, 1403)-net in base 9, because

1 times m-reduction [i] would yield (41, 125, 1403)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 194328 881168 006983 578290 776201 821942 638197 234491 983069 649320 796942 755443 316616 596645 401278 824599 143001 671542 208997 845489 > 9¹²⁵ [i]