MinT - Best Known (174−51, 174, s)-Nets in Base 4

Best Known (174−51, 174, s)-Nets in Base 4

(174−51, 174, 531)-Net over F₄ — Constructive and digital

Digital (123, 174, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 58, 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]

(174−51, 174, 816)-Net over F₄ — Digital

Digital (123, 174, 816)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−51, 174, 49725)-Net in Base 4 — Upper bound on s

There is no (123, 174, 49726)-net in base 4, because

1 times m-reduction [i] would yield (123, 173, 49726)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 354681 518118 063141 908423 616541 067913 864958 570257 755872 729592 902607 497877 499321 071982 145379 243408 204651 > 4¹⁷³ [i]