Best Known (95−34, 95, s)-Nets in Base 16
(95−34, 95, 583)-Net over F16 — Constructive and digital
Digital (61, 95, 583)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 23, 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 (38, 72, 518)-net over F16, using
- trace code for nets [i] based on digital (2, 36, 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, 36, 259)-net over F256, using
- digital (6, 23, 65)-net over F16, using
(95−34, 95, 594)-Net in Base 16 — Constructive
(61, 95, 594)-net in base 16, using
- (u, u+v)-construction [i] based on
- (10, 27, 80)-net in base 16, using
- base change [i] based on digital (1, 18, 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, 18, 80)-net over F64, using
- digital (34, 68, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 34, 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, 34, 257)-net over F256, using
- (10, 27, 80)-net in base 16, using
(95−34, 95, 2920)-Net over F16 — Digital
Digital (61, 95, 2920)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1695, 2920, F16, 34) (dual of [2920, 2825, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(1695, 4100, F16, 34) (dual of [4100, 4005, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(1694, 4099, F16, 34) (dual of [4099, 4005, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(1694, 4096, F16, 34) (dual of [4096, 4002, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(1691, 4096, F16, 33) (dual of [4096, 4005, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(1694, 4099, F16, 34) (dual of [4099, 4005, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(1695, 4100, F16, 34) (dual of [4100, 4005, 35]-code), using
(95−34, 95, 2563056)-Net in Base 16 — Upper bound on s
There is no (61, 95, 2563057)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 462633 005694 749836 365400 789528 586815 191069 430021 892754 456768 677248 693711 008717 667493 692177 490776 062690 314834 216336 > 1695 [i]