MinT - Best Known (83−58, 83, s)-Nets in Base 9

Best Known (83−58, 83, s)-Nets in Base 9

(83−58, 83, 78)-Net over F₉ — Constructive and digital

Digital (25, 83, 78)-net over F₉, using

t-expansion [i] based on digital (22, 83, 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]

(83−58, 83, 96)-Net over F₉ — Digital

Digital (25, 83, 96)-net over F₉, using

net from sequence [i] based on digital (25, 95)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 25 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(83−58, 83, 767)-Net in Base 9 — Upper bound on s

There is no (25, 83, 768)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 938633 035397 281077 038380 879939 073260 169001 253001 677494 043957 530666 712186 943489 > 9⁸³ [i]