MinT - Best Known (250−148, 250, s)-Nets in Base 3

Best Known (250−148, 250, s)-Nets in Base 3

(250−148, 250, 69)-Net over F₃ — Constructive and digital

Digital (102, 250, 69)-net over F₃, using

net from sequence [i] based on digital (102, 68)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 68)-sequence over F₉, using
  - s-reduction 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]

(250−148, 250, 104)-Net over F₃ — Digital

Digital (102, 250, 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]

(250−148, 250, 510)-Net in Base 3 — Upper bound on s

There is no (102, 250, 511)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 199000 843309 720870 240146 208433 974342 244366 472153 808740 135646 193948 402350 741412 466240 202374 882585 490146 189877 917309 600621 > 3²⁵⁰ [i]