Best Known (118−33, 118, s)-Nets in Base 16
(118−33, 118, 1095)-Net over F16 — Constructive and digital
Digital (85, 118, 1095)-net over F16, using
- 161 times duplication [i] based on digital (84, 117, 1095)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 17, 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 (16, 32, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 16, 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, 16, 257)-net over F256, using
- digital (35, 68, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 34, 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, 34, 258)-net over F256, using
- digital (6, 17, 65)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(118−33, 118, 2047)-Net in Base 16 — Constructive
(85, 118, 2047)-net in base 16, using
- net defined by OOA [i] based on OOA(16118, 2047, S16, 33, 33), using
- OOA 16-folding and stacking with additional row [i] based on OA(16118, 32753, S16, 33), using
- discarding factors based on OA(16118, 32768, S16, 33), using
- discarding parts of the base [i] based on linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- discarding parts of the base [i] based on linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using
- discarding factors based on OA(16118, 32768, S16, 33), using
- OOA 16-folding and stacking with additional row [i] based on OA(16118, 32753, S16, 33), using
(118−33, 118, 23511)-Net over F16 — Digital
Digital (85, 118, 23511)-net over F16, using
(118−33, 118, large)-Net in Base 16 — Upper bound on s
There is no (85, 118, large)-net in base 16, because
- 31 times m-reduction [i] would yield (85, 87, large)-net in base 16, but