MinT - Best Known (168−68, 168, s)-Nets in Base 3

Best Known (168−68, 168, s)-Nets in Base 3

(168−68, 168, 128)-Net over F₃ — Constructive and digital

Digital (100, 168, 128)-net over F₃, using

6 times m-reduction [i] based on digital (100, 174, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 87, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(168−68, 168, 156)-Net over F₃ — Digital

Digital (100, 168, 156)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−68, 168, 1508)-Net in Base 3 — Upper bound on s

There is no (100, 168, 1509)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145 089441 052038 920137 666842 608202 313959 531253 774882 897379 415436 297099 159310 240145 > 3¹⁶⁸ [i]