MinT - Best Known (139−108, 139, s)-Nets in Base 9

Best Known (139−108, 139, s)-Nets in Base 9

(139−108, 139, 78)-Net over F₉ — Constructive and digital

Digital (31, 139, 78)-net over F₉, using

t-expansion [i] based on digital (22, 139, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(139−108, 139, 120)-Net over F₉ — Digital

Digital (31, 139, 120)-net over F₉, using

net from sequence [i] based on digital (31, 119)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
  - a curve from the manYPoints database [i]

(139−108, 139, 716)-Net in Base 9 — Upper bound on s

There is no (31, 139, 717)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 481697 727195 203241 613817 175669 380619 485511 270800 586950 360952 768563 188040 296733 802808 543853 832648 068068 873746 710365 258453 764776 596785 > 9¹³⁹ [i]