MinT - Best Known (109, 236, s)-Nets in Base 3

Best Known (109, 236, s)-Nets in Base 3

(109, 236, 74)-Net over F₃ — Constructive and digital

Digital (109, 236, 74)-net over F₃, using

t-expansion [i] based on digital (107, 236, 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]

(109, 236, 104)-Net over F₃ — Digital

Digital (109, 236, 104)-net over F₃, using

t-expansion [i] based on digital (102, 236, 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]

(109, 236, 671)-Net in Base 3 — Upper bound on s

There is no (109, 236, 672)-net in base 3, because

1 times m-reduction [i] would yield (109, 235, 672)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13993 531071 420342 280827 839649 503996 456136 758139 412578 112062 877992 089924 871130 787823 880629 403915 915535 355152 170881 > 3²³⁵ [i]