Best Known (70, 70+28, s)-Nets in Base 16
(70, 70+28, 1077)-Net over F16 — Constructive and digital
Digital (70, 98, 1077)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 14, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- digital (14, 28, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 14, 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, 14, 257)-net over F256, using
- digital (28, 56, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 28, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 28, 257)-net over F256, using
- digital (5, 14, 49)-net over F16, using
(70, 70+28, 1170)-Net in Base 16 — Constructive
(70, 98, 1170)-net in base 16, using
- base change [i] based on digital (28, 56, 1170)-net over F128, using
- 1 times m-reduction [i] based on digital (28, 57, 1170)-net over F128, using
- net defined by OOA [i] based on linear OOA(12857, 1170, F128, 29, 29) (dual of [(1170, 29), 33873, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12857, 16381, F128, 29) (dual of [16381, 16324, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12857, 16381, F128, 29) (dual of [16381, 16324, 30]-code), using
- net defined by OOA [i] based on linear OOA(12857, 1170, F128, 29, 29) (dual of [(1170, 29), 33873, 30]-NRT-code), using
- 1 times m-reduction [i] based on digital (28, 57, 1170)-net over F128, using
(70, 70+28, 17107)-Net over F16 — Digital
Digital (70, 98, 17107)-net over F16, using
(70, 70+28, large)-Net in Base 16 — Upper bound on s
There is no (70, 98, large)-net in base 16, because
- 26 times m-reduction [i] would yield (70, 72, large)-net in base 16, but