MinT - Best Known (189−53, 189, s)-Nets in Base 4

Best Known (189−53, 189, s)-Nets in Base 4

(189−53, 189, 531)-Net over F₄ — Constructive and digital

Digital (136, 189, 531)-net over F₄, using

t-expansion [i] based on digital (135, 189, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (135, 192, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(189−53, 189, 1059)-Net over F₄ — Digital

Digital (136, 189, 1059)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−53, 189, 79325)-Net in Base 4 — Upper bound on s

There is no (136, 189, 79326)-net in base 4, because

1 times m-reduction [i] would yield (136, 188, 79326)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 153939 580549 284083 487388 599355 135493 348801 831573 167200 532843 138206 011857 020992 110539 188102 119903 493276 354269 382902 > 4¹⁸⁸ [i]