MinT - Best Known (166, 248, s)-Nets in Base 3

Best Known (166, 248, s)-Nets in Base 3

(166, 248, 167)-Net over F₃ — Constructive and digital

Digital (166, 248, 167)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (9, 50, 19)-net over F₃, using
  - net from sequence [i] based on digital (9, 18)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
      - an explicitly constructive algebraic function field [i]
2. digital (116, 198, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 99, 74)-net over F₉, using
    - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
        a function field by GarcÃa and Quoos [i]

(166, 248, 393)-Net over F₃ — Digital

Digital (166, 248, 393)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 248, 6166)-Net in Base 3 — Upper bound on s

There is no (166, 248, 6167)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21235 935198 122340 167422 931829 150165 146457 977441 630241 825552 370413 794985 408384 465338 463039 893886 102989 203329 601332 023775 > 3²⁴⁸ [i]