MinT - Best Known (227−120, 227, s)-Nets in Base 3

Best Known (227−120, 227, s)-Nets in Base 3

(227−120, 227, 74)-Net over F₃ — Constructive and digital

Digital (107, 227, 74)-net over F₃, using

net from sequence [i] based on digital (107, 73)-sequence over F₃, using
- base reduction for sequences [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]

(227−120, 227, 104)-Net over F₃ — Digital

Digital (107, 227, 104)-net over F₃, using

t-expansion [i] based on digital (102, 227, 104)-net over F₃, using
- net from sequence [i] based on digital (102, 103)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 102 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(227−120, 227, 682)-Net in Base 3 — Upper bound on s

There is no (107, 227, 683)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 071844 732442 095497 008426 644370 961848 098924 938438 906804 130241 525137 367919 441976 671690 536750 824574 917474 272617 > 3²²⁷ [i]