MinT - Best Known (185−34, 185, s)-Nets in Base 2

Best Known (185−34, 185, s)-Nets in Base 2

(185−34, 185, 320)-Net over F₂ — Constructive and digital

Digital (151, 185, 320)-net over F₂, using

trace code for nets [i] based on digital (3, 37, 64)-net over F₃₂, using
- net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(185−34, 185, 647)-Net over F₂ — Digital

Digital (151, 185, 647)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−34, 185, 13522)-Net in Base 2 — Upper bound on s

There is no (151, 185, 13523)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49 067990 089946 088160 185707 742474 207911 595769 751368 791988 > 2¹⁸⁵ [i]