Best Known (34, 34+13, s)-Nets in Base 16
(34, 34+13, 1542)-Net over F16 — Constructive and digital
Digital (34, 47, 1542)-net over F16, using
- 161 times duplication [i] based on digital (33, 46, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 8, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 4, 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, 4, 257)-net over F256, using
- digital (6, 12, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 6, 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, 6, 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 (4, 8, 514)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(34, 34+13, 5461)-Net in Base 16 — Constructive
(34, 47, 5461)-net in base 16, using
- net defined by OOA [i] based on OOA(1647, 5461, S16, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(1647, 32767, S16, 13), using
- discarding factors based on OA(1647, 32771, S16, 13), using
- discarding parts of the base [i] based on linear OA(3237, 32771, F32, 13) (dual of [32771, 32734, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(3237, 32768, F32, 13) (dual of [32768, 32731, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3234, 32768, F32, 12) (dual of [32768, 32734, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(3237, 32771, F32, 13) (dual of [32771, 32734, 14]-code), using
- discarding factors based on OA(1647, 32771, S16, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(1647, 32767, S16, 13), using
(34, 34+13, 18346)-Net over F16 — Digital
Digital (34, 47, 18346)-net over F16, using
(34, 34+13, large)-Net in Base 16 — Upper bound on s
There is no (34, 47, large)-net in base 16, because
- 11 times m-reduction [i] would yield (34, 36, large)-net in base 16, but