Best Known (20, ∞, s)-Nets in Base 2
(20, ∞, 20)-Net over F2 — Constructive and digital
Digital (20, m, 20)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (20, 19)-sequence over F2, using
- t-expansion [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
- t-expansion [i] based on digital (19, 19)-sequence over F2, using
(20, ∞, 27)-Net in Base 2 — Upper bound on s
There is no (20, m, 28)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (20, 133, 28)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2133, 28, S2, 5, 113), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 261336 857795 280739 939871 698507 597986 398208 / 19 > 2133 [i]
- extracting embedded OOA [i] would yield OOA(2133, 28, S2, 5, 113), but