Best Known (25, 35, s)-Nets in Base 16
(25, 35, 1542)-Net over F16 — Constructive and digital
Digital (25, 35, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 5, 514)-net over F16, using
- s-reduction based on digital (2, 5, 629)-net over F16, using
- net defined by OOA [i] based on linear OOA(165, 629, F16, 3, 3) (dual of [(629, 3), 1882, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(165, 629, F16, 2, 3) (dual of [(629, 2), 1253, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(165, 629, F16, 3, 3) (dual of [(629, 3), 1882, 4]-NRT-code), using
- s-reduction based on digital (2, 5, 629)-net over F16, using
- digital (5, 10, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 5, 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, 5, 257)-net over F256, using
- digital (10, 20, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 10, 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, 10, 257)-net over F256, using
- digital (2, 5, 514)-net over F16, using
(25, 35, 6554)-Net in Base 16 — Constructive
(25, 35, 6554)-net in base 16, using
- base change [i] based on digital (18, 28, 6554)-net over F32, using
- net defined by OOA [i] based on linear OOA(3228, 6554, F32, 10, 10) (dual of [(6554, 10), 65512, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3228, 32770, F32, 10) (dual of [32770, 32742, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3228, 32771, F32, 10) (dual of [32771, 32743, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3225, 32768, F32, 9) (dual of [32768, 32743, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3228, 32771, F32, 10) (dual of [32771, 32743, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(3228, 32770, F32, 10) (dual of [32770, 32742, 11]-code), using
- net defined by OOA [i] based on linear OOA(3228, 6554, F32, 10, 10) (dual of [(6554, 10), 65512, 11]-NRT-code), using
(25, 35, 13320)-Net over F16 — Digital
Digital (25, 35, 13320)-net over F16, using
(25, 35, 16385)-Net in Base 16
(25, 35, 16385)-net in base 16, using
- base change [i] based on digital (18, 28, 16385)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3228, 16385, F32, 2, 10) (dual of [(16385, 2), 32742, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3228, 32770, F32, 10) (dual of [32770, 32742, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3228, 32771, F32, 10) (dual of [32771, 32743, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(3225, 32768, F32, 9) (dual of [32768, 32743, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(3228, 32771, F32, 10) (dual of [32771, 32743, 11]-code), using
- OOA 2-folding [i] based on linear OA(3228, 32770, F32, 10) (dual of [32770, 32742, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3228, 16385, F32, 2, 10) (dual of [(16385, 2), 32742, 11]-NRT-code), using
(25, 35, large)-Net in Base 16 — Upper bound on s
There is no (25, 35, large)-net in base 16, because
- 8 times m-reduction [i] would yield (25, 27, large)-net in base 16, but