MinT - Best Known (45, 45+15, s)-Nets in Base 4

Best Known (45, 45+15, s)-Nets in Base 4

(45, 45+15, 1028)-Net over F₄ — Constructive and digital

Digital (45, 60, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 15, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(45, 45+15, 133747)-Net in Base 4 — Upper bound on s

There is no (45, 60, 133748)-net in base 4, because

1 times m-reduction [i] would yield (45, 59, 133748)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 332315 457950 461203 299445 283177 932148 > 4⁵⁹ [i]