Best Known (66−24, 66, s)-Nets in Base 32
(66−24, 66, 300)-Net over F32 — Constructive and digital
Digital (42, 66, 300)-net over F32, using
- 1 times m-reduction [i] based on digital (42, 67, 300)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 14, 98)-net over F32, using
- s-reduction based on digital (6, 14, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 8, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- generalized (u, u+v)-construction [i] based on
- s-reduction based on digital (6, 14, 99)-net over F32, using
- digital (7, 19, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (9, 34, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (6, 14, 98)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(66−24, 66, 1365)-Net in Base 32 — Constructive
(42, 66, 1365)-net in base 32, using
- net defined by OOA [i] based on OOA(3266, 1365, S32, 24, 24), using
- OA 12-folding and stacking [i] based on OA(3266, 16380, S32, 24), using
- discarding factors based on OA(3266, 16386, S32, 24), using
- discarding parts of the base [i] based on linear OA(12847, 16386, F128, 24) (dual of [16386, 16339, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12845, 16384, F128, 23) (dual of [16384, 16339, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(12847, 16386, F128, 24) (dual of [16386, 16339, 25]-code), using
- discarding factors based on OA(3266, 16386, S32, 24), using
- OA 12-folding and stacking [i] based on OA(3266, 16380, S32, 24), using
(66−24, 66, 6353)-Net over F32 — Digital
Digital (42, 66, 6353)-net over F32, using
(66−24, 66, large)-Net in Base 32 — Upper bound on s
There is no (42, 66, large)-net in base 32, because
- 22 times m-reduction [i] would yield (42, 44, large)-net in base 32, but