Best Known (18, ∞, s)-Nets in Base 2
(18, ∞, 17)-Net over F2 — Constructive and digital
Digital (18, m, 17)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 16)-sequence over F2, using
- t-expansion [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- t-expansion [i] based on digital (15, 16)-sequence over F2, using
(18, ∞, 18)-Net over F2 — Digital
Digital (18, m, 18)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 17)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 18 and N(F) ≥ 18, using
(18, ∞, 25)-Net in Base 2 — Upper bound on s
There is no (18, m, 26)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (18, 98, 26)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(298, 26, S2, 4, 80), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 27 888313 205021 046832 927470 518272 / 81 > 298 [i]
- extracting embedded OOA [i] would yield OOA(298, 26, S2, 4, 80), but