MinT - Best Known (160−40, 160, s)-Nets in Base 3

Best Known (160−40, 160, s)-Nets in Base 3

(160−40, 160, 328)-Net over F₃ — Constructive and digital

Digital (120, 160, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 40, 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]

(160−40, 160, 712)-Net over F₃ — Digital

Digital (120, 160, 712)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−40, 160, 27222)-Net in Base 3 — Upper bound on s

There is no (120, 160, 27223)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21848 047240 578370 269120 980884 251404 292910 679914 730089 577540 745158 121615 646041 > 3¹⁶⁰ [i]