Best Known (2, 2+18, s)-Nets in Base 16
(2, 2+18, 33)-Net over F16 — Constructive and digital
Digital (2, 20, 33)-net over F16, 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, 2+18, 123)-Net in Base 16 — Upper bound on s
There is no (2, 20, 124)-net in base 16, because
- 4 times m-reduction [i] would yield (2, 16, 124)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 18 506952 222034 991146 > 1616 [i]