MinT - Best Known (174, 174+50, s)-Nets in Base 3

Best Known (174, 174+50, s)-Nets in Base 3

(174, 174+50, 640)-Net over F₃ — Constructive and digital

Digital (174, 224, 640)-net over F₃, using

t-expansion [i] based on digital (173, 224, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 56, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(174, 174+50, 1474)-Net over F₃ — Digital

Digital (174, 224, 1474)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 174+50, 95827)-Net in Base 3 — Upper bound on s

There is no (174, 224, 95828)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75022 240352 840602 160988 664581 172645 919385 576309 888962 689374 164323 535310 835127 528246 679947 540945 594652 788649 > 3²²⁴ [i]