MinT - Best Known (139−100, 139, s)-Nets in Base 9

Best Known (139−100, 139, s)-Nets in Base 9

(139−100, 139, 81)-Net over F₉ — Constructive and digital

Digital (39, 139, 81)-net over F₉, using

t-expansion [i] based on digital (32, 139, 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]

(139−100, 139, 140)-Net over F₉ — Digital

Digital (39, 139, 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]

(139−100, 139, 1064)-Net in Base 9 — Upper bound on s

There is no (39, 139, 1065)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 488007 515443 985229 688846 696734 905294 758979 800946 971134 282859 317745 763566 289009 263359 349294 866956 997061 564528 889497 613631 299452 789073 > 9¹³⁹ [i]