Best Known (22, 53, s)-Nets in Base 2
(22, 53, 21)-Net over F2 — Constructive and digital
Digital (22, 53, 21)-net over F2, using
- t-expansion [i] based on digital (21, 53, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(22, 53, 51)-Net in Base 2 — Upper bound on s
There is no (22, 53, 52)-net in base 2, because
- 1 times m-reduction [i] would yield (22, 52, 52)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 4831 738802 489188 > 252 [i]