MinT - Best Known (70−30, 70, s)-Nets in Base 3

Best Known (70−30, 70, s)-Nets in Base 3

(70−30, 70, 64)-Net over F₃ — Constructive and digital

Digital (40, 70, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 35, 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]

(70−30, 70, 66)-Net over F₃ — Digital

Digital (40, 70, 66)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−30, 70, 526)-Net in Base 3 — Upper bound on s

There is no (40, 70, 527)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2517 658459 547076 390262 574517 501987 > 3⁷⁰ [i]