Best Known (21−17, 21, s)-Nets in Base 16
(21−17, 21, 45)-Net over F16 — Constructive and digital
Digital (4, 21, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
(21−17, 21, 252)-Net in Base 16 — Upper bound on s
There is no (4, 21, 253)-net in base 16, because
- 1 times m-reduction [i] would yield (4, 20, 253)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 1 210272 781828 985733 870661 > 1620 [i]