MinT - Best Known (64−30, 64, s)-Nets in Base 3

Best Known (64−30, 64, s)-Nets in Base 3

(64−30, 64, 40)-Net over F₃ — Constructive and digital

Digital (34, 64, 40)-net over F₃, using

trace code for nets [i] based on digital (2, 32, 20)-net over F₉, using
- net from sequence [i] based on digital (2, 19)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
    - a function field by GarcÃa and Quoos [i]

(64−30, 64, 49)-Net over F₃ — Digital

Digital (34, 64, 49)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−30, 64, 334)-Net in Base 3 — Upper bound on s

There is no (34, 64, 335)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 516058 054742 880350 073928 473891 > 3⁶⁴ [i]