MinT - Best Known (250−144, 250, s)-Nets in Base 3

Best Known (250−144, 250, s)-Nets in Base 3

(250−144, 250, 73)-Net over F₃ — Constructive and digital

Digital (106, 250, 73)-net over F₃, using

net from sequence [i] based on digital (106, 72)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 72)-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]

(250−144, 250, 104)-Net over F₃ — Digital

Digital (106, 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]

(250−144, 250, 558)-Net in Base 3 — Upper bound on s

There is no (106, 250, 559)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 202113 513344 961171 681671 971520 292679 124866 858895 606533 073402 391358 243263 059742 077824 426388 576029 377914 161582 361699 202673 > 3²⁵⁰ [i]