Best Known (7, 14, s)-Nets in Base 16
(7, 14, 514)-Net over F16 — Constructive and digital
Digital (7, 14, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 7, 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
(7, 14, 20004)-Net in Base 16 — Upper bound on s
There is no (7, 14, 20005)-net in base 16, because
- 1 times m-reduction [i] would yield (7, 13, 20005)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 4504 186279 028476 > 1613 [i]