Best Known (35, 35+14, s)-Nets in Base 16
(35, 35+14, 1285)-Net over F16 — Constructive and digital
Digital (35, 49, 1285)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (3, 7, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(3,256) in PG(6,16)) 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
- base reduction for projective spaces (embedding PG(3,256) in PG(6,16)) 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 (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 (see above)
- trace code for nets [i] based on digital (0, 14, 257)-net over F256, using
- digital (3, 7, 257)-net over F16, using
(35, 35+14, 2341)-Net in Base 16 — Constructive
(35, 49, 2341)-net in base 16, using
- base change [i] based on digital (14, 28, 2341)-net over F128, using
- net defined by OOA [i] based on linear OOA(12828, 2341, F128, 14, 14) (dual of [(2341, 14), 32746, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12828, 16387, F128, 14) (dual of [16387, 16359, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 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 factors / shortening the dual code based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12828, 16387, F128, 14) (dual of [16387, 16359, 15]-code), using
- net defined by OOA [i] based on linear OOA(12828, 2341, F128, 14, 14) (dual of [(2341, 14), 32746, 15]-NRT-code), using
(35, 35+14, 13066)-Net over F16 — Digital
Digital (35, 49, 13066)-net over F16, using
(35, 35+14, large)-Net in Base 16 — Upper bound on s
There is no (35, 49, large)-net in base 16, because
- 12 times m-reduction [i] would yield (35, 37, large)-net in base 16, but