MinT - Best Known (68, 68+30, s)-Nets in Base 3

Best Known (68, 68+30, s)-Nets in Base 3

(68, 68+30, 148)-Net over F₃ — Constructive and digital

Digital (68, 98, 148)-net over F₃, using

4 times m-reduction [i] based on digital (68, 102, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 51, 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]

(68, 68+30, 233)-Net over F₃ — Digital

Digital (68, 98, 233)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+30, 4192)-Net in Base 3 — Upper bound on s

There is no (68, 98, 4193)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57448 651604 697349 384507 920324 293519 971874 835435 > 3⁹⁸ [i]