MinT - Best Known (188−47, 188, s)-Nets in Base 4

Best Known (188−47, 188, s)-Nets in Base 4

(188−47, 188, 1028)-Net over F₄ — Constructive and digital

Digital (141, 188, 1028)-net over F₄, using

trace code for nets [i] based on digital (0, 47, 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]

(188−47, 188, 1755)-Net over F₄ — Digital

Digital (141, 188, 1755)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−47, 188, 246780)-Net in Base 4 — Upper bound on s

There is no (141, 188, 246781)-net in base 4, because

1 times m-reduction [i] would yield (141, 187, 246781)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38478 620197 259668 928584 424886 902790 428468 992745 443649 464009 828185 772000 451336 098177 459979 521263 298236 981096 984856 > 4¹⁸⁷ [i]