MinT - Best Known (250−146, 250, s)-Nets in Base 3

Best Known (250−146, 250, s)-Nets in Base 3

(250−146, 250, 71)-Net over F₃ — Constructive and digital

Digital (104, 250, 71)-net over F₃, using

net from sequence [i] based on digital (104, 70)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 70)-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]

(250−146, 250, 104)-Net over F₃ — Digital

Digital (104, 250, 104)-net over F₃, using

t-expansion [i] based on 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]

(250−146, 250, 533)-Net in Base 3 — Upper bound on s

There is no (104, 250, 534)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196305 246728 622487 967286 063011 191047 476112 083135 315550 659952 653277 101760 116440 377110 809296 843466 990307 027173 991916 226845 > 3²⁵⁰ [i]