MinT - Best Known (90−41, 90, s)-Nets in Base 3

Best Known (90−41, 90, s)-Nets in Base 3

(90−41, 90, 60)-Net over F₃ — Constructive and digital

Digital (49, 90, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 45, 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]

(90−41, 90, 67)-Net over F₃ — Digital

Digital (49, 90, 67)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−41, 90, 532)-Net in Base 3 — Upper bound on s

There is no (49, 90, 533)-net in base 3, because

1 times m-reduction [i] would yield (49, 89, 533)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 996919 156432 248161 375734 674520 537191 140497 > 3⁸⁹ [i]