MinT - Best Known (140, 237, s)-Nets in Base 3

Best Known (140, 237, s)-Nets in Base 3

(140, 237, 148)-Net over F₃ — Constructive and digital

Digital (140, 237, 148)-net over F₃, using

9 times m-reduction [i] based on digital (140, 246, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 123, 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]

(140, 237, 203)-Net over F₃ — Digital

Digital (140, 237, 203)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 237, 2030)-Net in Base 3 — Upper bound on s

There is no (140, 237, 2031)-net in base 3, because

1 times m-reduction [i] would yield (140, 236, 2031)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40090 789230 367925 303316 444546 869979 265555 639346 341324 311021 990102 329189 217416 634924 831998 744727 991744 616190 440865 > 3²³⁶ [i]