MinT - Best Known (250−154, 250, s)-Nets in Base 3

Best Known (250−154, 250, s)-Nets in Base 3

(250−154, 250, 64)-Net over F₃ — Constructive and digital

Digital (96, 250, 64)-net over F₃, using

t-expansion [i] based on digital (89, 250, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(250−154, 250, 96)-Net over F₃ — Digital

Digital (96, 250, 96)-net over F₃, using

t-expansion [i] based on digital (89, 250, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(250−154, 250, 449)-Net in Base 3 — Upper bound on s

There is no (96, 250, 450)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 194677 617910 520829 766140 775436 469907 689729 742251 675775 825360 224724 861870 886203 433172 553187 592772 213583 724137 550927 434061 > 3²⁵⁰ [i]