Best Known (38, 52, s)-Nets in Base 16
(38, 52, 1544)-Net over F16 — Constructive and digital
Digital (38, 52, 1544)-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 (7, 14, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 7, 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, 7, 257)-net over F256, using
- digital (16, 30, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 15, 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, 15, 258)-net over F256, using
- digital (4, 8, 514)-net over F16, using
(38, 52, 4682)-Net in Base 16 — Constructive
(38, 52, 4682)-net in base 16, using
- net defined by OOA [i] based on OOA(1652, 4682, S16, 14, 14), using
- OA 7-folding and stacking [i] based on OA(1652, 32774, S16, 14), using
- discarding factors based on OA(1652, 32775, S16, 14), using
- discarding parts of the base [i] based on linear OA(3241, 32775, F32, 14) (dual of [32775, 32734, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding parts of the base [i] based on linear OA(3241, 32775, F32, 14) (dual of [32775, 32734, 15]-code), using
- discarding factors based on OA(1652, 32775, S16, 14), using
- OA 7-folding and stacking [i] based on OA(1652, 32774, S16, 14), using
(38, 52, 24769)-Net over F16 — Digital
Digital (38, 52, 24769)-net over F16, using
(38, 52, large)-Net in Base 16 — Upper bound on s
There is no (38, 52, large)-net in base 16, because
- 12 times m-reduction [i] would yield (38, 40, large)-net in base 16, but