Best Known (105−52, 105, s)-Nets in Base 16
(105−52, 105, 514)-Net over F16 — Constructive and digital
Digital (53, 105, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (53, 106, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 53, 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, 53, 257)-net over F256, using
(105−52, 105, 51271)-Net in Base 16 — Upper bound on s
There is no (53, 105, 51272)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 708784 092332 910053 828804 947771 019882 555363 267566 981878 961048 724130 060963 612367 623309 485400 617017 830790 683344 757739 807555 190456 > 16105 [i]