MinT - Best Known (144, 144+47, s)-Nets in Base 3

Best Known (144, 144+47, s)-Nets in Base 3

(144, 144+47, 328)-Net over F₃ — Constructive and digital

Digital (144, 191, 328)-net over F₃, using

1 times m-reduction [i] based on digital (144, 192, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 48, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(144, 144+47, 872)-Net over F₃ — Digital

Digital (144, 191, 872)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+47, 41174)-Net in Base 3 — Upper bound on s

There is no (144, 191, 41175)-net in base 3, because

1 times m-reduction [i] would yield (144, 190, 41175)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 500119 654688 925241 842222 257687 416390 849328 992668 678644 407497 146465 485561 079537 566199 249331 > 3¹⁹⁰ [i]