MinT - Best Known (237−124, 237, s)-Nets in Base 3

Best Known (237−124, 237, s)-Nets in Base 3

(237−124, 237, 74)-Net over F₃ — Constructive and digital

Digital (113, 237, 74)-net over F₃, using

t-expansion [i] based on digital (107, 237, 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]

(237−124, 237, 120)-Net over F₃ — Digital

Digital (113, 237, 120)-net over F₃, using

net from sequence [i] based on digital (113, 119)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(237−124, 237, 738)-Net in Base 3 — Upper bound on s

There is no (113, 237, 739)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 129000 469801 190400 519823 089891 519914 725908 261748 671960 329253 601779 275739 521680 446780 290839 011270 046036 455926 828589 > 3²³⁷ [i]