MinT - Best Known (89, 142, s)-Nets in Base 3

Best Known (89, 142, s)-Nets in Base 3

(89, 142, 148)-Net over F₃ — Constructive and digital

Digital (89, 142, 148)-net over F₃, using

2 times m-reduction [i] based on digital (89, 144, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 72, 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]

(89, 142, 170)-Net over F₃ — Digital

Digital (89, 142, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 142, 2015)-Net in Base 3 — Upper bound on s

There is no (89, 142, 2016)-net in base 3, because

1 times m-reduction [i] would yield (89, 141, 2016)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19 015743 077828 508851 440901 073200 603198 257287 899171 950109 773968 949569 > 3¹⁴¹ [i]