MinT - Best Known (222−114, 222, s)-Nets in Base 3

Best Known (222−114, 222, s)-Nets in Base 3

(222−114, 222, 74)-Net over F₃ — Constructive and digital

Digital (108, 222, 74)-net over F₃, using

t-expansion [i] based on digital (107, 222, 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]

(222−114, 222, 104)-Net over F₃ — Digital

Digital (108, 222, 104)-net over F₃, using

t-expansion [i] based on digital (102, 222, 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]

(222−114, 222, 741)-Net in Base 3 — Upper bound on s

There is no (108, 222, 742)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8526 233428 658540 575087 806367 758675 925039 607301 454701 379479 324738 480359 068525 836413 722696 377997 842223 395549 > 3²²² [i]