MinT - Best Known (51−34, 51, s)-Nets in Base 2

Best Known (51−34, 51, s)-Nets in Base 2

(51−34, 51, 17)-Net over F₂ — Constructive and digital

Digital (17, 51, 17)-net over F₂, using

t-expansion [i] based on digital (15, 51, 17)-net over F₂, using
- net from sequence [i] based on digital (15, 16)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]

(51−34, 51, 36)-Net in Base 2 — Upper bound on s

There is no (17, 51, 37)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2657 346140 915124 > 2⁵¹ [i]