Best Known (19, 19+27, s)-Nets in Base 2
(19, 19+27, 20)-Net over F2 — Constructive and digital
Digital (19, 46, 20)-net over F2, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
(19, 19+27, 45)-Net in Base 2 — Upper bound on s
There is no (19, 46, 46)-net in base 2, because
- 1 times m-reduction [i] would yield (19, 45, 46)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 37 536163 543663 > 245 [i]