MinT - Best Known (27−9, 27, s)-Nets in Base 4

Best Known (27−9, 27, s)-Nets in Base 4

(27−9, 27, 195)-Net over F₄ — Constructive and digital

Digital (18, 27, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 9, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(27−9, 27, 6041)-Net in Base 4 — Upper bound on s

There is no (18, 27, 6042)-net in base 4, because

1 times m-reduction [i] would yield (18, 26, 6042)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4506 204999 796714 > 4²⁶ [i]