MinT - Best Known (51, 51+36, s)-Nets in Base 2

Best Known (51, 51+36, s)-Nets in Base 2

(51, 51+36, 42)-Net over F₂ — Constructive and digital

Digital (51, 87, 42)-net over F₂, using

1 times m-reduction [i] based on digital (51, 88, 42)-net over F₂, using
- trace code for nets [i] based on digital (7, 44, 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]

(51, 51+36, 45)-Net over F₂ — Digital

Digital (51, 87, 45)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(51, 51+36, 190)-Net in Base 2 — Upper bound on s

There is no (51, 87, 191)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 165 202844 175294 703243 584019 > 2⁸⁷ [i]