Best Known (9, 18, s)-Nets in Base 16
(9, 18, 514)-Net over F16 — Constructive and digital
Digital (9, 18, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 9, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(9, 18, 19338)-Net in Base 16 — Upper bound on s
There is no (9, 18, 19339)-net in base 16, because
- 1 times m-reduction [i] would yield (9, 17, 19339)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 295 153903 719203 436466 > 1617 [i]