Best Known (114−31, 114, s)-Nets in Base 16
(114−31, 114, 1544)-Net over F16 — Constructive and digital
Digital (83, 114, 1544)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (10, 20, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 10, 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, 10, 257)-net over F256, using
- digital (15, 30, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 15, 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, 15, 257)-net over F256, using
- digital (33, 64, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 32, 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, 32, 258)-net over F256, using
- digital (10, 20, 514)-net over F16, using
(114−31, 114, 2184)-Net in Base 16 — Constructive
(83, 114, 2184)-net in base 16, using
- net defined by OOA [i] based on OOA(16114, 2184, S16, 31, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(16114, 32761, S16, 31), using
- discarding factors based on OA(16114, 32771, S16, 31), using
- discarding parts of the base [i] based on linear OA(3291, 32771, F32, 31) (dual of [32771, 32680, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(3291, 32768, F32, 31) (dual of [32768, 32677, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- discarding parts of the base [i] based on linear OA(3291, 32771, F32, 31) (dual of [32771, 32680, 32]-code), using
- discarding factors based on OA(16114, 32771, S16, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(16114, 32761, S16, 31), using
(114−31, 114, 30239)-Net over F16 — Digital
Digital (83, 114, 30239)-net over F16, using
(114−31, 114, large)-Net in Base 16 — Upper bound on s
There is no (83, 114, large)-net in base 16, because
- 29 times m-reduction [i] would yield (83, 85, large)-net in base 16, but