MinT - Best Known (74, 132, s)-Nets in Base 3

Best Known (74, 132, s)-Nets in Base 3

(74, 132, 80)-Net over F₃ — Constructive and digital

Digital (74, 132, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 66, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(74, 132, 101)-Net over F₃ — Digital

Digital (74, 132, 101)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 132, 838)-Net in Base 3 — Upper bound on s

There is no (74, 132, 839)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 971 769231 608252 285879 908713 719330 818167 671574 296323 852982 763927 > 3¹³² [i]