Best Known (43, 43+17, s)-Nets in Base 16
(43, 43+17, 1542)-Net over F16 — Constructive and digital
Digital (43, 60, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 10, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 5, 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, 5, 257)-net over F256, using
- digital (8, 16, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 8, 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, 8, 257)-net over F256, using
- digital (17, 34, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 17, 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, 17, 257)-net over F256, using
- digital (5, 10, 514)-net over F16, using
(43, 43+17, 2048)-Net in Base 16 — Constructive
(43, 60, 2048)-net in base 16, using
- 162 times duplication [i] based on (41, 58, 2048)-net in base 16, using
- net defined by OOA [i] based on OOA(1658, 2048, S16, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(1658, 16385, S16, 17), using
- discarding factors based on OA(1658, 16386, S16, 17), using
- discarding parts of the base [i] based on linear OA(12833, 16386, F128, 17) (dual of [16386, 16353, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(12831, 16384, F128, 16) (dual of [16384, 16353, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(16) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(12833, 16386, F128, 17) (dual of [16386, 16353, 18]-code), using
- discarding factors based on OA(1658, 16386, S16, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(1658, 16385, S16, 17), using
- net defined by OOA [i] based on OOA(1658, 2048, S16, 17, 17), using
(43, 43+17, 14864)-Net over F16 — Digital
Digital (43, 60, 14864)-net over F16, using
(43, 43+17, large)-Net in Base 16 — Upper bound on s
There is no (43, 60, large)-net in base 16, because
- 15 times m-reduction [i] would yield (43, 45, large)-net in base 16, but