MinT - Best Known (174, 174+58, s)-Nets in Base 3

Best Known (174, 174+58, s)-Nets in Base 3

(174, 174+58, 328)-Net over F₃ — Constructive and digital

Digital (174, 232, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 58, 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]

(174, 174+58, 960)-Net over F₃ — Digital

Digital (174, 232, 960)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 174+58, 38259)-Net in Base 3 — Upper bound on s

There is no (174, 232, 38260)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 391293 921442 559557 804023 291789 089210 795034 008554 817509 848212 711659 534545 225657 367740 663071 474117 033963 694153 > 3²³² [i]