MinT - Best Known (146−43, 146, s)-Nets in Base 3

Best Known (146−43, 146, s)-Nets in Base 3

(146−43, 146, 204)-Net over F₃ — Constructive and digital

Digital (103, 146, 204)-net over F₃, using

1 times m-reduction [i] based on digital (103, 147, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 49, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(146−43, 146, 361)-Net over F₃ — Digital

Digital (103, 146, 361)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−43, 146, 8527)-Net in Base 3 — Upper bound on s

There is no (103, 146, 8528)-net in base 3, because

1 times m-reduction [i] would yield (103, 145, 8528)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1523 885436 036560 237628 391996 304768 869135 396422 934965 729226 392970 108577 > 3¹⁴⁵ [i]