Best Known (95−27, 95, s)-Nets in Base 16
(95−27, 95, 1093)-Net over F16 — Constructive and digital
Digital (68, 95, 1093)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 15, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, 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, 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, 13, 257)-net over F256, using
- digital (27, 54, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 27, 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, 27, 257)-net over F256, using
- digital (6, 15, 65)-net over F16, using
(95−27, 95, 1260)-Net in Base 16 — Constructive
(68, 95, 1260)-net in base 16, using
- 162 times duplication [i] based on (66, 93, 1260)-net in base 16, using
- net defined by OOA [i] based on OOA(1693, 1260, S16, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(1693, 16381, S16, 27), using
- discarding factors based on OA(1693, 16386, S16, 27), using
- discarding parts of the base [i] based on linear OA(12853, 16386, F128, 27) (dual of [16386, 16333, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(12851, 16384, F128, 26) (dual of [16384, 16333, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(12853, 16386, F128, 27) (dual of [16386, 16333, 28]-code), using
- discarding factors based on OA(1693, 16386, S16, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(1693, 16381, S16, 27), using
- net defined by OOA [i] based on OOA(1693, 1260, S16, 27, 27), using
(95−27, 95, 17668)-Net over F16 — Digital
Digital (68, 95, 17668)-net over F16, using
(95−27, 95, large)-Net in Base 16 — Upper bound on s
There is no (68, 95, large)-net in base 16, because
- 25 times m-reduction [i] would yield (68, 70, large)-net in base 16, but