MinT - Best Known (46−31, 46, s)-Nets in Base 2

Best Known (46−31, 46, s)-Nets in Base 2

(46−31, 46, 17)-Net over F₂ — Constructive and digital

Digital (15, 46, 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]

(46−31, 46, 32)-Net in Base 2 — Upper bound on s

There is no (15, 46, 33)-net in base 2, because

1 times m-reduction [i] would yield (15, 45, 33)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 36 244458 357760 > 2⁴⁵ [i]