Best Known (52−17, 52, s)-Nets in Base 16
(52−17, 52, 1030)-Net over F16 — Constructive and digital
Digital (35, 52, 1030)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (8, 16, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 8, 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, 8, 257)-net over F256, using
- digital (19, 36, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
- digital (8, 16, 514)-net over F16, using
(52−17, 52, 4335)-Net over F16 — Digital
Digital (35, 52, 4335)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1652, 4335, F16, 17) (dual of [4335, 4283, 18]-code), using
- 233 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 15 times 0, 1, 55 times 0, 1, 156 times 0) [i] based on linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 233 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 15 times 0, 1, 55 times 0, 1, 156 times 0) [i] based on linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using
(52−17, 52, large)-Net in Base 16 — Upper bound on s
There is no (35, 52, large)-net in base 16, because
- 15 times m-reduction [i] would yield (35, 37, large)-net in base 16, but