MinT - Best Known (166−62, 166, s)-Nets in Base 3

Best Known (166−62, 166, s)-Nets in Base 3

(166−62, 166, 148)-Net over F₃ — Constructive and digital

Digital (104, 166, 148)-net over F₃, using

8 times m-reduction [i] based on digital (104, 174, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 87, 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]

(166−62, 166, 194)-Net over F₃ — Digital

Digital (104, 166, 194)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−62, 166, 2197)-Net in Base 3 — Upper bound on s

There is no (104, 166, 2198)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 004937 460044 029821 770528 181372 575690 331344 600483 282650 071675 984204 824943 991529 > 3¹⁶⁶ [i]