MinT - Best Known (168−63, 168, s)-Nets in Base 3

Best Known (168−63, 168, s)-Nets in Base 3

(168−63, 168, 148)-Net over F₃ — Constructive and digital

Digital (105, 168, 148)-net over F₃, using

8 times m-reduction [i] based on digital (105, 176, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 88, 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]

(168−63, 168, 193)-Net over F₃ — Digital

Digital (105, 168, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−63, 168, 2278)-Net in Base 3 — Upper bound on s

There is no (105, 168, 2279)-net in base 3, because

1 times m-reduction [i] would yield (105, 167, 2279)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48 416231 147681 705732 112455 812341 385579 731524 851505 190298 596759 282103 268056 805475 > 3¹⁶⁷ [i]