MinT - Best Known (72−32, 72, s)-Nets in Base 3

Best Known (72−32, 72, s)-Nets in Base 3

(72−32, 72, 60)-Net over F₃ — Constructive and digital

Digital (40, 72, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 36, 30)-net over F₉, using
- net from sequence [i] based on digital (4, 29)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [i]

(72−32, 72, 61)-Net over F₃ — Digital

Digital (40, 72, 61)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−32, 72, 461)-Net in Base 3 — Upper bound on s

There is no (40, 72, 462)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22720 497877 169658 589475 179405 414305 > 3⁷² [i]