MinT - Best Known (54, 54+42, s)-Nets in Base 3

Best Known (54, 54+42, s)-Nets in Base 3

(54, 54+42, 68)-Net over F₃ — Constructive and digital

Digital (54, 96, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 48, 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]

(54, 54+42, 79)-Net over F₃ — Digital

Digital (54, 96, 79)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+42, 638)-Net in Base 3 — Upper bound on s

There is no (54, 96, 639)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6503 831385 551465 554108 652244 412938 935678 980311 > 3⁹⁶ [i]