MinT - Best Known (135, 135+99, s)-Nets in Base 3

Best Known (135, 135+99, s)-Nets in Base 3

(135, 135+99, 148)-Net over F₃ — Constructive and digital

Digital (135, 234, 148)-net over F₃, using

2 times m-reduction [i] based on digital (135, 236, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 118, 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]

(135, 135+99, 183)-Net over F₃ — Digital

Digital (135, 234, 183)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+99, 1726)-Net in Base 3 — Upper bound on s

There is no (135, 234, 1727)-net in base 3, because

1 times m-reduction [i] would yield (135, 233, 1727)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1501 579640 074787 417533 308543 115534 357766 618293 821602 859907 907322 559343 145889 355361 235210 566288 154829 691429 760287 > 3²³³ [i]