MinT - Best Known (121−42, 121, s)-Nets in Base 3

Best Known (121−42, 121, s)-Nets in Base 3

(121−42, 121, 148)-Net over F₃ — Constructive and digital

Digital (79, 121, 148)-net over F₃, using

3 times m-reduction [i] based on digital (79, 124, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 62, 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]

(121−42, 121, 186)-Net over F₃ — Digital

Digital (79, 121, 186)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−42, 121, 2415)-Net in Base 3 — Upper bound on s

There is no (79, 121, 2416)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5433 902405 348101 111301 661564 921027 177189 959969 329785 690849 > 3¹²¹ [i]