Best Known (42, 42+204, s)-Nets in Base 2
(42, 42+204, 33)-Net over F2 — Constructive and digital
Digital (42, 246, 33)-net over F2, using
- t-expansion [i] based on digital (39, 246, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(42, 42+204, 52)-Net in Base 2 — Upper bound on s
There is no (42, 246, 53)-net in base 2, because
- 42 times m-reduction [i] would yield (42, 204, 53)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2204, 53, S2, 4, 162), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4525 137532 633316 615926 165252 032713 888702 523630 492344 624208 674816 / 163 > 2204 [i]
- extracting embedded OOA [i] would yield OOA(2204, 53, S2, 4, 162), but