Best Known (2, ∞, s)-Nets in Base 16
(2, ∞, 33)-Net over F16 — Constructive and digital
Digital (2, m, 33)-net over F16 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
(2, ∞, 48)-Net in Base 16 — Upper bound on s
There is no (2, m, 49)-net in base 16 for arbitrarily large m, because
- m-reduction [i] would yield (2, 45, 49)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1645, 49, S16, 43), but
- the linear programming bound shows that M ≥ 79 689768 125026 220634 634045 411816 077548 174434 353547 313152 / 47 > 1645 [i]
- extracting embedded orthogonal array [i] would yield OA(1645, 49, S16, 43), but