MinT - Best Known (41, 41+62, s)-Nets in Base 9

Best Known (41, 41+62, s)-Nets in Base 9

(41, 41+62, 81)-Net over F₉ — Constructive and digital

Digital (41, 103, 81)-net over F₉, using

t-expansion [i] based on digital (32, 103, 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+62, 140)-Net over F₉ — Digital

Digital (41, 103, 140)-net over F₉, using

t-expansion [i] based on digital (39, 103, 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+62, 2279)-Net in Base 9 — Upper bound on s

There is no (41, 103, 2280)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 193 854677 922157 533393 017723 764855 042024 539034 357888 170078 916165 341279 174167 441874 525073 178071 205313 > 9¹⁰³ [i]