Best Known (56, 56+133, s)-Nets in Base 2
(56, 56+133, 42)-Net over F2 — Constructive and digital
Digital (56, 189, 42)-net over F2, using
- t-expansion [i] based on digital (54, 189, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
(56, 56+133, 83)-Net in Base 2 — Upper bound on s
There is no (56, 189, 84)-net in base 2, because
- 28 times m-reduction [i] would yield (56, 161, 84)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2161, 84, S2, 2, 105), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 187 072209 578355 573530 071658 587684 226515 959365 500928 / 53 > 2161 [i]
- extracting embedded OOA [i] would yield OOA(2161, 84, S2, 2, 105), but