Best Known (9−4, 9, s)-Nets in Base 16
(9−4, 9, 514)-Net over F16 — Constructive and digital
Digital (5, 9, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (5, 10, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 5, 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, 5, 257)-net over F256, using
(9−4, 9, 819)-Net over F16 — Digital
Digital (5, 9, 819)-net over F16, using
(9−4, 9, 2016)-Net in Base 16 — Constructive
(5, 9, 2016)-net in base 16, using
- base change [i] based on digital (2, 6, 2016)-net over F64, using
- net defined by OOA [i] based on linear OOA(646, 2016, F64, 4, 4) (dual of [(2016, 4), 8058, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(646, 2016, F64, 3, 4) (dual of [(2016, 3), 6042, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- 1 times truncation [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(646, 4032, F64, 4) (dual of [4032, 4026, 5]-code), using
- appending kth column [i] based on linear OOA(646, 2016, F64, 3, 4) (dual of [(2016, 3), 6042, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(646, 2016, F64, 4, 4) (dual of [(2016, 4), 8058, 5]-NRT-code), using
(9−4, 9, 24714)-Net in Base 16 — Upper bound on s
There is no (5, 9, 24715)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 68722 034701 > 169 [i]