MinT - Best Known (38, 38+30, s)-Nets in Base 3

Best Known (38, 38+30, s)-Nets in Base 3

(38, 38+30, 60)-Net over F₃ — Constructive and digital

Digital (38, 68, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 34, 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]

(38, 38+30, 453)-Net in Base 3 — Upper bound on s

There is no (38, 68, 454)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 286 431344 391932 919334 089576 547017 > 3⁶⁸ [i]