Best Known (164−129, 164, s)-Nets in Base 2
(164−129, 164, 24)-Net over F2 — Constructive and digital
Digital (35, 164, 24)-net over F2, using
- t-expansion [i] based on digital (33, 164, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(164−129, 164, 29)-Net over F2 — Digital
Digital (35, 164, 29)-net over F2, using
- net from sequence [i] based on digital (35, 28)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 35 and N(F) ≥ 29, using
(164−129, 164, 47)-Net in Base 2 — Upper bound on s
There is no (35, 164, 48)-net in base 2, because
- 27 times m-reduction [i] would yield (35, 137, 48)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2137, 48, S2, 3, 102), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22 300745 198530 623141 535718 272648 361505 980416 / 103 > 2137 [i]
- extracting embedded OOA [i] would yield OOA(2137, 48, S2, 3, 102), but