MinT - Best Known (181, 181+76, s)-Nets in Base 4

Best Known (181, 181+76, s)-Nets in Base 4

(181, 181+76, 531)-Net over F₄ — Constructive and digital

Digital (181, 257, 531)-net over F₄, using

t-expansion [i] based on digital (179, 257, 531)-net over F₄, using
- 1 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(181, 181+76, 1092)-Net over F₄ — Digital

Digital (181, 257, 1092)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+76, 59058)-Net in Base 4 — Upper bound on s

There is no (181, 257, 59059)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53661 599849 328413 120118 347948 002398 901839 206653 496560 452860 656896 505661 887526 151355 763244 023563 751750 057552 026839 013705 264818 744229 315989 049820 984055 970540 > 4²⁵⁷ [i]