MinT - Best Known (136−49, 136, s)-Nets in Base 3

Best Known (136−49, 136, s)-Nets in Base 3

(136−49, 136, 148)-Net over F₃ — Constructive and digital

Digital (87, 136, 148)-net over F₃, using

4 times m-reduction [i] based on digital (87, 140, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 70, 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]

(136−49, 136, 182)-Net over F₃ — Digital

Digital (87, 136, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−49, 136, 2343)-Net in Base 3 — Upper bound on s

There is no (87, 136, 2344)-net in base 3, because

1 times m-reduction [i] would yield (87, 135, 2344)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25974 475099 103285 187055 485034 648431 611597 080522 774200 095340 977409 > 3¹³⁵ [i]