Best Known (5, 10, s)-Nets in Base 16
(5, 10, 514)-Net over F16 — Constructive and digital
Digital (5, 10, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 5, 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
(5, 10, 24714)-Net in Base 16 — Upper bound on s
There is no (5, 10, 24715)-net in base 16, because
- 1 times m-reduction [i] would yield (5, 9, 24715)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 68722 034701 > 169 [i]