MinT - Best Known (112, 250, s)-Nets in Base 3

Best Known (112, 250, s)-Nets in Base 3

(112, 250, 74)-Net over F₃ — Constructive and digital

Digital (112, 250, 74)-net over F₃, using

t-expansion [i] based on digital (107, 250, 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]

(112, 250, 104)-Net over F₃ — Digital

Digital (112, 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]

(112, 250, 644)-Net in Base 3 — Upper bound on s

There is no (112, 250, 645)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 205136 334438 590838 568026 905394 986951 223785 419621 210178 988371 516018 704433 555052 377747 025390 443684 015638 862039 881334 569755 > 3²⁵⁰ [i]