MinT - Best Known (177−54, 177, s)-Nets in Base 3

Best Known (177−54, 177, s)-Nets in Base 3

(177−54, 177, 204)-Net over F₃ — Constructive and digital

Digital (123, 177, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 59, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(177−54, 177, 378)-Net over F₃ — Digital

Digital (123, 177, 378)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−54, 177, 7304)-Net in Base 3 — Upper bound on s

There is no (123, 177, 7305)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 824683 712827 975348 392045 021608 738280 367097 998189 312688 290188 463296 461478 002316 824347 > 3¹⁷⁷ [i]