MinT - Best Known (218−111, 218, s)-Nets in Base 3

Best Known (218−111, 218, s)-Nets in Base 3

(218−111, 218, 74)-Net over F₃ — Constructive and digital

Digital (107, 218, 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]

(218−111, 218, 104)-Net over F₃ — Digital

Digital (107, 218, 104)-net over F₃, using

t-expansion [i] based on digital (102, 218, 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]

(218−111, 218, 760)-Net in Base 3 — Upper bound on s

There is no (107, 218, 761)-net in base 3, because

1 times m-reduction [i] would yield (107, 217, 761)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 535998 095607 903181 959640 776529 987610 165357 541203 978259 382111 557494 537055 889727 521982 605348 611327 829163 > 3²¹⁷ [i]