MinT - Best Known (107, 225, s)-Nets in Base 3

Best Known (107, 225, s)-Nets in Base 3

(107, 225, 74)-Net over F₃ — Constructive and digital

Digital (107, 225, 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]

(107, 225, 104)-Net over F₃ — Digital

Digital (107, 225, 104)-net over F₃, using

t-expansion [i] based on digital (102, 225, 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]

(107, 225, 696)-Net in Base 3 — Upper bound on s

There is no (107, 225, 697)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 236014 793568 490909 202235 307579 643910 709615 833027 767795 120524 468157 848869 820869 694501 317959 770399 060318 498779 > 3²²⁵ [i]