Best Known (107−53, 107, s)-Nets in Base 16
(107−53, 107, 514)-Net over F16 — Constructive and digital
Digital (54, 107, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (54, 108, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 54, 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
- trace code for nets [i] based on digital (0, 54, 257)-net over F256, using
(107−53, 107, 57042)-Net in Base 16 — Upper bound on s
There is no (54, 107, 57043)-net in base 16, because
- 1 times m-reduction [i] would yield (54, 106, 57043)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 43 334318 378509 397281 807571 913414 584510 938621 957316 986963 959649 281909 257570 883289 785146 723942 967872 743377 367559 935782 570084 719896 > 16106 [i]