MinT - Best Known (174−74, 174, s)-Nets in Base 3

Best Known (174−74, 174, s)-Nets in Base 3

(174−74, 174, 128)-Net over F₃ — Constructive and digital

Digital (100, 174, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 87, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(174−74, 174, 140)-Net over F₃ — Digital

Digital (100, 174, 140)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−74, 174, 1248)-Net in Base 3 — Upper bound on s

There is no (100, 174, 1249)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 107080 836749 434713 329712 791229 066109 149929 007070 003957 513673 683833 120246 244724 568627 > 3¹⁷⁴ [i]