MinT - Best Known (146, 188, s)-Nets in Base 2

Best Known (146, 188, s)-Nets in Base 2

(146, 188, 196)-Net over F₂ — Constructive and digital

Digital (146, 188, 196)-net over F₂, using

trace code for nets [i] based on digital (5, 47, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(146, 188, 358)-Net over F₂ — Digital

Digital (146, 188, 358)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 188, 4268)-Net in Base 2 — Upper bound on s

There is no (146, 188, 4269)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 392 896671 137591 460067 607885 282029 659859 393743 012545 545820 > 2¹⁸⁸ [i]