MinT - Best Known (87, 134, s)-Nets in Base 3

Best Known (87, 134, s)-Nets in Base 3

(87, 134, 148)-Net over F₃ — Constructive and digital

Digital (87, 134, 148)-net over F₃, using

6 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]

(87, 134, 195)-Net over F₃ — Digital

Digital (87, 134, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(87, 134, 2684)-Net in Base 3 — Upper bound on s

There is no (87, 134, 2685)-net in base 3, because

1 times m-reduction [i] would yield (87, 133, 2685)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2883 918298 939207 057405 919643 373875 273121 160119 703524 147765 325307 > 3¹³³ [i]