MinT - Best Known (168−66, 168, s)-Nets in Base 3

Best Known (168−66, 168, s)-Nets in Base 3

(168−66, 168, 148)-Net over F₃ — Constructive and digital

Digital (102, 168, 148)-net over F₃, using

2 times m-reduction [i] based on digital (102, 170, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 85, 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]

(168−66, 168, 170)-Net over F₃ — Digital

Digital (102, 168, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−66, 168, 1735)-Net in Base 3 — Upper bound on s

There is no (102, 168, 1736)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145 971933 407395 479688 346888 561371 722087 189027 713050 608663 874414 074723 023737 333649 > 3¹⁶⁸ [i]