MinT - Best Known (101, 101+40, s)-Nets in Base 4

Best Known (101, 101+40, s)-Nets in Base 4

(101, 101+40, 531)-Net over F₄ — Constructive and digital

Digital (101, 141, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 47, 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]

(101, 101+40, 790)-Net over F₄ — Digital

Digital (101, 141, 790)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+40, 48591)-Net in Base 4 — Upper bound on s

There is no (101, 141, 48592)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 771143 555911 582267 222741 402003 182599 456570 856266 824435 956166 027207 820757 491543 355564 > 4¹⁴¹ [i]