MinT - Best Known (126−42, 126, s)-Nets in Base 3

Best Known (126−42, 126, s)-Nets in Base 3

(126−42, 126, 148)-Net over F₃ — Constructive and digital

Digital (84, 126, 148)-net over F₃, using

8 times m-reduction [i] based on digital (84, 134, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 67, 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]

(126−42, 126, 217)-Net over F₃ — Digital

Digital (84, 126, 217)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−42, 126, 3143)-Net in Base 3 — Upper bound on s

There is no (84, 126, 3144)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 316841 564237 131721 825520 902125 885087 656573 605801 095307 485457 > 3¹²⁶ [i]