MinT - Best Known (45−18, 45, s)-Nets in Base 3

Best Known (45−18, 45, s)-Nets in Base 3

(45−18, 45, 60)-Net over F₃ — Constructive and digital

Digital (27, 45, 60)-net over F₃, using

1 times m-reduction [i] based on digital (27, 46, 60)-net over F₃, using
- trace code for nets [i] based on digital (4, 23, 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]

(45−18, 45, 495)-Net in Base 3 — Upper bound on s

There is no (27, 45, 496)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2983 976089 968780 740321 > 3⁴⁵ [i]