MinT - Best Known (168−42, 168, s)-Nets in Base 3

Best Known (168−42, 168, s)-Nets in Base 3

(168−42, 168, 328)-Net over F₃ — Constructive and digital

Digital (126, 168, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 42, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(168−42, 168, 740)-Net over F₃ — Digital

Digital (126, 168, 740)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−42, 168, 28452)-Net in Base 3 — Upper bound on s

There is no (126, 168, 28453)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 397626 872946 036628 229133 155581 419929 570545 985194 957857 839937 647603 920234 782747 > 3¹⁶⁸ [i]