MinT - Best Known (39, 39+75, s)-Nets in Base 2

Best Known (39, 39+75, s)-Nets in Base 2

(39, 39+75, 33)-Net over F₂ — Constructive and digital

Digital (39, 114, 33)-net over F₂, using

net from sequence [i] based on digital (39, 32)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]

(39, 39+75, 75)-Net in Base 2 — Upper bound on s

There is no (39, 114, 76)-net in base 2, because

1 times m-reduction [i] would yield (39, 113, 76)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10712 798135 560147 298538 819018 608060 > 2¹¹³ [i]