MinT - Best Known (232−54, 232, s)-Nets in Base 3

Best Known (232−54, 232, s)-Nets in Base 3

(232−54, 232, 600)-Net over F₃ — Constructive and digital

Digital (178, 232, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 58, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(232−54, 232, 1285)-Net over F₃ — Digital

Digital (178, 232, 1285)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−54, 232, 68693)-Net in Base 3 — Upper bound on s

There is no (178, 232, 68694)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 217161 872604 153924 711330 566874 513239 661783 667563 288836 245254 043995 429360 089717 409963 305311 734678 387289 737009 > 3²³² [i]