Best Known (89−44, 89, s)-Nets in Base 16
(89−44, 89, 514)-Net over F16 — Constructive and digital
Digital (45, 89, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (45, 90, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 45, 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, 45, 257)-net over F256, using
(89−44, 89, 44859)-Net in Base 16 — Upper bound on s
There is no (45, 89, 44860)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 146788 904668 421611 606239 539402 767209 169195 850612 703481 259899 575591 690446 463431 196763 352372 158147 180717 154926 > 1689 [i]