Best Known (42, 42+142, s)-Nets in Base 2
(42, 42+142, 33)-Net over F2 — Constructive and digital
Digital (42, 184, 33)-net over F2, using
- t-expansion [i] based on digital (39, 184, 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+142, 55)-Net in Base 2 — Upper bound on s
There is no (42, 184, 56)-net in base 2, because
- 23 times m-reduction [i] would yield (42, 161, 56)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2161, 56, S2, 3, 119), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 46 768052 394588 893382 517914 646921 056628 989841 375232 / 15 > 2161 [i]
- extracting embedded OOA [i] would yield OOA(2161, 56, S2, 3, 119), but