Best Known (22, 22+33, s)-Nets in Base 2
(22, 22+33, 21)-Net over F2 — Constructive and digital
Digital (22, 55, 21)-net over F2, using
- t-expansion [i] based on digital (21, 55, 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, 22+33, 50)-Net in Base 2 — Upper bound on s
There is no (22, 55, 51)-net in base 2, because
- 1 times m-reduction [i] would yield (22, 54, 51)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 22311 613216 406231 > 254 [i]