MinT - Best Known (34−12, 34, s)-Nets in Base 3

Best Known (34−12, 34, s)-Nets in Base 3

(34−12, 34, 64)-Net over F₃ — Constructive and digital

Digital (22, 34, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 17, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(34−12, 34, 78)-Net over F₃ — Digital

Digital (22, 34, 78)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(34−12, 34, 751)-Net in Base 3 — Upper bound on s

There is no (22, 34, 752)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16791 355894 538145 > 3³⁴ [i]