Best Known (211−149, 211, s)-Nets in Base 2
(211−149, 211, 43)-Net over F2 — Constructive and digital
Digital (62, 211, 43)-net over F2, using
- t-expansion [i] based on digital (59, 211, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(211−149, 211, 44)-Net over F2 — Digital
Digital (62, 211, 44)-net over F2, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 62 and N(F) ≥ 44, using
(211−149, 211, 91)-Net in Base 2 — Upper bound on s
There is no (62, 211, 92)-net in base 2, because
- 34 times m-reduction [i] would yield (62, 177, 92)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2177, 92, S2, 2, 115), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 129982 163463 555433 433388 108601 236734 474956 488734 408704 / 29 > 2177 [i]
- extracting embedded OOA [i] would yield OOA(2177, 92, S2, 2, 115), but