MinT - Best Known (174−54, 174, s)-Nets in Base 3

Best Known (174−54, 174, s)-Nets in Base 3

(174−54, 174, 192)-Net over F₃ — Constructive and digital

Digital (120, 174, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 58, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(174−54, 174, 353)-Net over F₃ — Digital

Digital (120, 174, 353)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−54, 174, 6462)-Net in Base 3 — Upper bound on s

There is no (120, 174, 6463)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104821 151713 727999 186059 568952 457805 026980 133477 390918 399505 034281 164515 821824 978123 > 3¹⁷⁴ [i]