MinT - Best Known (228−52, 228, s)-Nets in Base 3

Best Known (228−52, 228, s)-Nets in Base 3

(228−52, 228, 640)-Net over F₃ — Constructive and digital

Digital (176, 228, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 57, 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]

(228−52, 228, 1374)-Net over F₃ — Digital

Digital (176, 228, 1374)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−52, 228, 80558)-Net in Base 3 — Upper bound on s

There is no (176, 228, 80559)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 077147 726032 398226 007097 206196 474678 732025 222930 854515 651769 690257 748237 312362 193386 561119 280227 645567 104813 > 3²²⁸ [i]