Best Known (14−7, 14, s)-Nets in Base 4
(14−7, 14, 34)-Net over F4 — Constructive and digital
Digital (7, 14, 34)-net over F4, using
- trace code for nets [i] based on digital (0, 7, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
(14−7, 14, 244)-Net in Base 4 — Upper bound on s
There is no (7, 14, 245)-net in base 4, because
- 1 times m-reduction [i] would yield (7, 13, 245)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 67 805956 > 413 [i]