MinT - Best Known (176−51, 176, s)-Nets in Base 4

Best Known (176−51, 176, s)-Nets in Base 4

(176−51, 176, 531)-Net over F₄ — Constructive and digital

Digital (125, 176, 531)-net over F₄, using

1 times m-reduction [i] based on digital (125, 177, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 59, 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]

(176−51, 176, 865)-Net over F₄ — Digital

Digital (125, 176, 865)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−51, 176, 55560)-Net in Base 4 — Upper bound on s

There is no (125, 176, 55561)-net in base 4, because

1 times m-reduction [i] would yield (125, 175, 55561)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2294 083119 594634 744550 141432 547122 469088 726845 760916 727266 611327 648759 289668 693358 325673 451954 292796 943680 > 4¹⁷⁵ [i]