Best Known (211−164, 211, s)-Nets in Base 2
(211−164, 211, 34)-Net over F2 — Constructive and digital
Digital (47, 211, 34)-net over F2, using
- t-expansion [i] based on digital (45, 211, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
(211−164, 211, 36)-Net over F2 — Digital
Digital (47, 211, 36)-net over F2, using
- net from sequence [i] based on digital (47, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 47 and N(F) ≥ 36, using
(211−164, 211, 61)-Net in Base 2 — Upper bound on s
There is no (47, 211, 62)-net in base 2, because
- 32 times m-reduction [i] would yield (47, 179, 62)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2179, 62, S2, 3, 132), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 122 599643 269271 108668 667762 172024 734689 499129 774688 174080 / 133 > 2179 [i]
- extracting embedded OOA [i] would yield OOA(2179, 62, S2, 3, 132), but