MinT - Best Known (50−22, 50, s)-Nets in Base 2

Best Known (50−22, 50, s)-Nets in Base 2

(50−22, 50, 28)-Net over F₂ — Constructive and digital

Digital (28, 50, 28)-net over F₂, using

trace code for nets [i] based on digital (3, 25, 14)-net over F₄, using
- net from sequence [i] based on digital (3, 13)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]

(50−22, 50, 99)-Net in Base 2 — Upper bound on s

There is no (28, 50, 100)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1173 056597 910076 > 2⁵⁰ [i]