Best Known (86−43, 86, s)-Nets in Base 16
(86−43, 86, 514)-Net over F16 — Constructive and digital
Digital (43, 86, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 43, 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
(86−43, 86, 43261)-Net in Base 16 — Upper bound on s
There is no (43, 86, 43262)-net in base 16, because
- 1 times m-reduction [i] would yield (43, 85, 43262)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 239823 354159 973167 842292 810978 570019 272611 417445 452482 271565 001478 874307 512710 940819 693873 247130 236781 > 1685 [i]