Best Known (78, 78+29, s)-Nets in Base 16
(78, 78+29, 1544)-Net over F16 — Constructive and digital
Digital (78, 107, 1544)-net over F16, using
- 161 times duplication [i] based on digital (77, 106, 1544)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- 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 (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 (31, 60, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 30, 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, 30, 258)-net over F256, using
- digital (9, 18, 514)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(78, 78+29, 2340)-Net in Base 16 — Constructive
(78, 107, 2340)-net in base 16, using
- net defined by OOA [i] based on OOA(16107, 2340, S16, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(16107, 32761, S16, 29), using
- discarding factors based on OA(16107, 32771, S16, 29), using
- discarding parts of the base [i] based on linear OA(3285, 32771, F32, 29) (dual of [32771, 32686, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(3285, 32768, F32, 29) (dual of [32768, 32683, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(28) ⊂ Ce(27) [i] based on
- discarding parts of the base [i] based on linear OA(3285, 32771, F32, 29) (dual of [32771, 32686, 30]-code), using
- discarding factors based on OA(16107, 32771, S16, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(16107, 32761, S16, 29), using
(78, 78+29, 30100)-Net over F16 — Digital
Digital (78, 107, 30100)-net over F16, using
(78, 78+29, large)-Net in Base 16 — Upper bound on s
There is no (78, 107, large)-net in base 16, because
- 27 times m-reduction [i] would yield (78, 80, large)-net in base 16, but