Best Known (19, 19+39, s)-Nets in Base 2
(19, 19+39, 20)-Net over F2 — Constructive and digital
Digital (19, 58, 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+39, 40)-Net in Base 2 — Upper bound on s
There is no (19, 58, 41)-net in base 2, because
- 1 times m-reduction [i] would yield (19, 57, 41)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 196042 634824 197648 > 257 [i]