MinT - Best Known (50, 50+36, s)-Nets in Base 2

Best Known (50, 50+36, s)-Nets in Base 2

(50, 50+36, 42)-Net over F₂ — Constructive and digital

Digital (50, 86, 42)-net over F₂, using

trace code for nets [i] based on digital (7, 43, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(50, 50+36, 43)-Net over F₂ — Digital

Digital (50, 86, 43)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+36, 182)-Net in Base 2 — Upper bound on s

There is no (50, 86, 183)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 83 419280 786025 635792 371945 > 2⁸⁶ [i]