MinT - Best Known (165, 165+85, s)-Nets in Base 4

Best Known (165, 165+85, s)-Nets in Base 4

(165, 165+85, 450)-Net over F₄ — Constructive and digital

Digital (165, 250, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 125, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(165, 165+85, 624)-Net over F₄ — Digital

Digital (165, 250, 624)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+85, 20384)-Net in Base 4 — Upper bound on s

There is no (165, 250, 20385)-net in base 4, because

1 times m-reduction [i] would yield (165, 249, 20385)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 819009 420776 235111 266449 485023 373621 331286 017696 308689 369564 613372 405201 758944 859456 915048 328758 459599 220227 979279 680358 549713 436019 313641 509333 864512 > 4²⁴⁹ [i]