Best Known (179−144, 179, s)-Nets in Base 2
(179−144, 179, 24)-Net over F2 — Constructive and digital
Digital (35, 179, 24)-net over F2, using
- t-expansion [i] based on digital (33, 179, 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
(179−144, 179, 29)-Net over F2 — Digital
Digital (35, 179, 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
(179−144, 179, 44)-Net in Base 2 — Upper bound on s
There is no (35, 179, 45)-net in base 2, because
- 6 times m-reduction [i] would yield (35, 173, 45)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2173, 45, S2, 4, 138), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 819838 454778 243019 300537 094740 992155 547252 707593 027584 / 139 > 2173 [i]
- extracting embedded OOA [i] would yield OOA(2173, 45, S2, 4, 138), but