MinT - Best Known (181−35, 181, s)-Nets in Base 4

Best Known (181−35, 181, s)-Nets in Base 4

(181−35, 181, 1104)-Net over F₄ — Constructive and digital

Digital (146, 181, 1104)-net over F₄, using

4¹ times duplication [i] based on digital (145, 180, 1104)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (23, 40, 76)-net over F₄, using
    - trace code for nets [i] based on digital (3, 20, 38)-net over F₁₆, using
      - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
        a function field by SÃ©mirat [i]
  2. digital (105, 140, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 35, 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]

(181−35, 181, 7252)-Net over F₄ — Digital

Digital (146, 181, 7252)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−35, 181, 5669904)-Net in Base 4 — Upper bound on s

There is no (146, 181, 5669905)-net in base 4, because

1 times m-reduction [i] would yield (146, 180, 5669905)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 348545 129218 353319 089683 367398 049939 199593 180342 256760 792465 423785 890363 898345 920309 102837 495218 521520 833604 > 4¹⁸⁰ [i]