MinT - Best Known (166−48, 166, s)-Nets in Base 4

Best Known (166−48, 166, s)-Nets in Base 4

(166−48, 166, 531)-Net over F₄ — Constructive and digital

Digital (118, 166, 531)-net over F₄, using

4¹ times duplication [i] based on digital (117, 165, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 55, 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]

(166−48, 166, 833)-Net over F₄ — Digital

Digital (118, 166, 833)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−48, 166, 47677)-Net in Base 4 — Upper bound on s

There is no (118, 166, 47678)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8751 823927 464079 023941 283737 457046 446851 624421 324527 306508 188801 203674 218648 821883 845791 640832 798401 > 4¹⁶⁶ [i]