MinT - Best Known (164, 246, s)-Nets in Base 3

Best Known (164, 246, s)-Nets in Base 3

(164, 246, 164)-Net over F₃ — Constructive and digital

Digital (164, 246, 164)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (7, 48, 16)-net over F₃, using
  - net from sequence [i] based on digital (7, 15)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, 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]

(164, 246, 381)-Net over F₃ — Digital

Digital (164, 246, 381)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 246, 5842)-Net in Base 3 — Upper bound on s

There is no (164, 246, 5843)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2357 848976 312104 826402 588173 368819 554964 721841 518633 658964 749211 606966 925151 535605 063050 605669 017597 882260 700574 825495 > 3²⁴⁶ [i]