Best Known (60−15, 60, s)-Nets in Base 4
(60−15, 60, 1028)-Net over F4 — Constructive and digital
Digital (45, 60, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 15, 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
(60−15, 60, 133747)-Net in Base 4 — Upper bound on s
There is no (45, 60, 133748)-net in base 4, because
- 1 times m-reduction [i] would yield (45, 59, 133748)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 332315 457950 461203 299445 283177 932148 > 459 [i]