Best Known (74, 74+30, s)-Nets in Base 16
(74, 74+30, 1073)-Net over F16 — Constructive and digital
Digital (74, 104, 1073)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 14, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, 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, 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, 15, 257)-net over F256, using
- digital (30, 60, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 30, 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, 30, 257)-net over F256, using
- digital (4, 14, 45)-net over F16, using
(74, 74+30, 1092)-Net in Base 16 — Constructive
(74, 104, 1092)-net in base 16, using
- net defined by OOA [i] based on OOA(16104, 1092, S16, 30, 30), using
- OA 15-folding and stacking [i] based on OA(16104, 16380, S16, 30), using
- discarding factors based on OA(16104, 16386, S16, 30), using
- discarding parts of the base [i] based on linear OA(12859, 16386, F128, 30) (dual of [16386, 16327, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(29) ⊂ Ce(28) [i] based on
- discarding parts of the base [i] based on linear OA(12859, 16386, F128, 30) (dual of [16386, 16327, 31]-code), using
- discarding factors based on OA(16104, 16386, S16, 30), using
- OA 15-folding and stacking [i] based on OA(16104, 16380, S16, 30), using
(74, 74+30, 16205)-Net over F16 — Digital
Digital (74, 104, 16205)-net over F16, using
(74, 74+30, large)-Net in Base 16 — Upper bound on s
There is no (74, 104, large)-net in base 16, because
- 28 times m-reduction [i] would yield (74, 76, large)-net in base 16, but