Best Known (3, 3+15, s)-Nets in Base 16
(3, 3+15, 38)-Net over F16 — Constructive and digital
Digital (3, 18, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
(3, 3+15, 185)-Net in Base 16 — Upper bound on s
There is no (3, 18, 186)-net in base 16, because
- 1 times m-reduction [i] would yield (3, 17, 186)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 296 922658 156912 900756 > 1617 [i]