MinT - Best Known (176−44, 176, s)-Nets in Base 3

Best Known (176−44, 176, s)-Nets in Base 3

(176−44, 176, 328)-Net over F₃ — Constructive and digital

Digital (132, 176, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 44, 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]

(176−44, 176, 767)-Net over F₃ — Digital

Digital (132, 176, 767)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−44, 176, 29681)-Net in Base 3 — Upper bound on s

There is no (132, 176, 29682)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 941150 302662 295072 902068 804445 379861 083929 635541 717981 644707 411657 559165 690604 952957 > 3¹⁷⁶ [i]