MinT - Best Known (113, 189, s)-Nets in Base 3

Best Known (113, 189, s)-Nets in Base 3

(113, 189, 148)-Net over F₃ — Constructive and digital

Digital (113, 189, 148)-net over F₃, using

3 times m-reduction [i] based on digital (113, 192, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 96, 74)-net over F₉, using
  - net from sequence [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]

(113, 189, 175)-Net over F₃ — Digital

Digital (113, 189, 175)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 189, 1736)-Net in Base 3 — Upper bound on s

There is no (113, 189, 1737)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 522175 900463 729911 552772 627594 642463 349374 912870 145793 100117 993730 633878 942945 544593 286697 > 3¹⁸⁹ [i]