Best Known (22, 22+53, s)-Nets in Base 2
(22, 22+53, 21)-Net over F2 — Constructive and digital
Digital (22, 75, 21)-net over F2, using
- t-expansion [i] based on digital (21, 75, 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+53, 36)-Net in Base 2 — Upper bound on s
There is no (22, 75, 37)-net in base 2, because
- 7 times m-reduction [i] would yield (22, 68, 37)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(268, 37, S2, 2, 46), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 14167 099448 608935 641088 / 47 > 268 [i]
- extracting embedded OOA [i] would yield OOA(268, 37, S2, 2, 46), but