Best Known (46, 46+19, s)-Nets in Base 16
(46, 46+19, 1066)-Net over F16 — Constructive and digital
Digital (46, 65, 1066)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (3, 9, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (9, 18, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 9, 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, 9, 257)-net over F256, using
- digital (19, 38, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 19, 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, 19, 257)-net over F256, using
- digital (3, 9, 38)-net over F16, using
(46, 46+19, 1820)-Net in Base 16 — Constructive
(46, 65, 1820)-net in base 16, using
- net defined by OOA [i] based on OOA(1665, 1820, S16, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(1665, 16381, S16, 19), using
- discarding factors based on OA(1665, 16386, S16, 19), using
- discarding parts of the base [i] based on linear OA(12837, 16386, F128, 19) (dual of [16386, 16349, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(12837, 16384, F128, 19) (dual of [16384, 16347, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- discarding parts of the base [i] based on linear OA(12837, 16386, F128, 19) (dual of [16386, 16349, 20]-code), using
- discarding factors based on OA(1665, 16386, S16, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(1665, 16381, S16, 19), using
(46, 46+19, 11236)-Net over F16 — Digital
Digital (46, 65, 11236)-net over F16, using
(46, 46+19, large)-Net in Base 16 — Upper bound on s
There is no (46, 65, large)-net in base 16, because
- 17 times m-reduction [i] would yield (46, 48, large)-net in base 16, but