Best Known (69, 69+26, s)-Nets in Base 16
(69, 69+26, 1542)-Net over F16 — Constructive and digital
Digital (69, 95, 1542)-net over F16, using
- 161 times duplication [i] based on digital (68, 94, 1542)-net over F16, using
- generalized (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 (13, 26, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 13, 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, 13, 257)-net over F256, using
- digital (26, 52, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 26, 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, 26, 257)-net over F256, using
- digital (8, 16, 514)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(69, 69+26, 2520)-Net in Base 16 — Constructive
(69, 95, 2520)-net in base 16, using
- base change [i] based on digital (50, 76, 2520)-net over F32, using
- net defined by OOA [i] based on linear OOA(3276, 2520, F32, 26, 26) (dual of [(2520, 26), 65444, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3276, 32760, F32, 26) (dual of [32760, 32684, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3276, 32760, F32, 26) (dual of [32760, 32684, 27]-code), using
- net defined by OOA [i] based on linear OOA(3276, 2520, F32, 26, 26) (dual of [(2520, 26), 65444, 27]-NRT-code), using
(69, 69+26, 25551)-Net over F16 — Digital
Digital (69, 95, 25551)-net over F16, using
(69, 69+26, large)-Net in Base 16 — Upper bound on s
There is no (69, 95, large)-net in base 16, because
- 24 times m-reduction [i] would yield (69, 71, large)-net in base 16, but