MinT - Best Known (54−37, 54, s)-Nets in Base 2

Best Known (54−37, 54, s)-Nets in Base 2

(54−37, 54, 17)-Net over F₂ — Constructive and digital

Digital (17, 54, 17)-net over F₂, using

t-expansion [i] based on digital (15, 54, 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]

(54−37, 54, 36)-Net in Base 2 — Upper bound on s

There is no (17, 54, 37)-net in base 2, because

1 times m-reduction [i] would yield (17, 53, 37)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12063 701803 046300 > 2⁵³ [i]