Best Known (34, ∞, s)-Nets in Base 2
(34, ∞, 24)-Net over F2 — Constructive and digital
Digital (34, m, 24)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (34, 23)-sequence over F2, using
- t-expansion [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
- t-expansion [i] based on digital (33, 23)-sequence over F2, using
(34, ∞, 28)-Net over F2 — Digital
Digital (34, m, 28)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (34, 27)-sequence over F2, using
- t-expansion [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
- t-expansion [i] based on digital (33, 27)-sequence over F2, using
(34, ∞, 42)-Net in Base 2 — Upper bound on s
There is no (34, m, 43)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (34, 208, 43)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2208, 43, S2, 5, 174), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 87211 741538 023920 234213 366675 539576 764085 000878 579732 757476 278272 / 175 > 2208 [i]
- extracting embedded OOA [i] would yield OOA(2208, 43, S2, 5, 174), but