MinT - Best Known (124−56, 124, s)-Nets in Base 3

Best Known (124−56, 124, s)-Nets in Base 3

(124−56, 124, 68)-Net over F₃ — Constructive and digital

Digital (68, 124, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 62, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(124−56, 124, 89)-Net over F₃ — Digital

Digital (68, 124, 89)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−56, 124, 705)-Net in Base 3 — Upper bound on s

There is no (68, 124, 706)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 147535 856626 552940 990569 635911 759387 670942 613700 485924 379673 > 3¹²⁴ [i]