Best Known (22, 22+104, s)-Nets in Base 2
(22, 22+104, 21)-Net over F2 — Constructive and digital
Digital (22, 126, 21)-net over F2, using
- t-expansion [i] based on digital (21, 126, 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+104, 30)-Net in Base 2 — Upper bound on s
There is no (22, 126, 31)-net in base 2, because
- 9 times m-reduction [i] would yield (22, 117, 31)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2117, 31, S2, 4, 95), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 706152 372760 736557 480147 500773 933056 / 3 > 2117 [i]
- extracting embedded OOA [i] would yield OOA(2117, 31, S2, 4, 95), but