MinT - Best Known (70−28, 70, s)-Nets in Base 3

Best Known (70−28, 70, s)-Nets in Base 3

(70−28, 70, 72)-Net over F₃ — Constructive and digital

Digital (42, 70, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 35, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(70−28, 70, 81)-Net over F₃ — Digital

Digital (42, 70, 81)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−28, 70, 721)-Net in Base 3 — Upper bound on s

There is no (42, 70, 722)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2542 837933 038352 389080 767412 669037 > 3⁷⁰ [i]