MinT - Best Known (189−47, 189, s)-Nets in Base 4

Best Known (189−47, 189, s)-Nets in Base 4

(189−47, 189, 1028)-Net over F₄ — Constructive and digital

Digital (142, 189, 1028)-net over F₄, using

4¹ times duplication [i] based on 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]

(189−47, 189, 1808)-Net over F₄ — Digital

Digital (142, 189, 1808)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−47, 189, 262113)-Net in Base 4 — Upper bound on s

There is no (142, 189, 262114)-net in base 4, because

1 times m-reduction [i] would yield (142, 188, 262114)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 153914 933536 776801 833238 653538 872844 104760 496510 748536 544463 643943 790699 364495 748515 744256 493796 248409 308985 488592 > 4¹⁸⁸ [i]