Best Known (55, 85, s)-Nets in Base 16
(55, 85, 583)-Net over F16 — Constructive and digital
Digital (55, 85, 583)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 21, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (34, 64, 518)-net over F16, using
- trace code for nets [i] based on digital (2, 32, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 32, 259)-net over F256, using
- digital (6, 21, 65)-net over F16, using
(55, 85, 594)-Net in Base 16 — Constructive
(55, 85, 594)-net in base 16, using
- 1 times m-reduction [i] based on (55, 86, 594)-net in base 16, using
- (u, u+v)-construction [i] based on
- (9, 24, 80)-net in base 16, using
- base change [i] based on digital (1, 16, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- base change [i] based on digital (1, 16, 80)-net over F64, using
- digital (31, 62, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 31, 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, 31, 257)-net over F256, using
- (9, 24, 80)-net in base 16, using
- (u, u+v)-construction [i] based on
(55, 85, 3071)-Net over F16 — Digital
Digital (55, 85, 3071)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1685, 3071, F16, 30) (dual of [3071, 2986, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(1685, 4096, F16, 30) (dual of [4096, 4011, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(1685, 4096, F16, 30) (dual of [4096, 4011, 31]-code), using
(55, 85, 2851154)-Net in Base 16 — Upper bound on s
There is no (55, 85, 2851155)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 239752 200571 748967 657406 423466 824279 583370 335653 675723 288286 965245 961907 911203 817246 555563 309208 567376 > 1685 [i]