MinT - Best Known (199−49, 199, s)-Nets in Base 4

Best Known (199−49, 199, s)-Nets in Base 4

(199−49, 199, 1028)-Net over F₄ — Constructive and digital

Digital (150, 199, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (150, 200, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 50, 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]

(199−49, 199, 1981)-Net over F₄ — Digital

Digital (150, 199, 1981)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−49, 199, 302836)-Net in Base 4 — Upper bound on s

There is no (150, 199, 302837)-net in base 4, because

1 times m-reduction [i] would yield (150, 198, 302837)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 161394 973145 740183 960204 345458 315016 478384 463204 230963 462786 024110 830866 591649 615067 541658 253351 003795 287378 596887 659724 > 4¹⁹⁸ [i]