MinT - Best Known (105−64, 105, s)-Nets in Base 9

Best Known (105−64, 105, s)-Nets in Base 9

(105−64, 105, 81)-Net over F₉ — Constructive and digital

Digital (41, 105, 81)-net over F₉, using

t-expansion [i] based on digital (32, 105, 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]

(105−64, 105, 140)-Net over F₉ — Digital

Digital (41, 105, 140)-net over F₉, using

t-expansion [i] based on digital (39, 105, 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]

(105−64, 105, 2142)-Net in Base 9 — Upper bound on s

There is no (41, 105, 2143)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15738 769388 970940 405304 738177 275355 474036 028468 842314 970091 054138 744577 785966 697634 799085 190919 560961 > 9¹⁰⁵ [i]