Best Known (61−22, 61, s)-Nets in Base 32
(61−22, 61, 330)-Net over F32 — Constructive and digital
Digital (39, 61, 330)-net over F32, using
- 1 times m-reduction [i] based on digital (39, 62, 330)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 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, 3, 33)-net over F32 (see above)
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 5, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 7, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 11, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 23, 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
(61−22, 61, 1489)-Net in Base 32 — Constructive
(39, 61, 1489)-net in base 32, using
- net defined by OOA [i] based on OOA(3261, 1489, S32, 22, 22), using
- OA 11-folding and stacking [i] based on OA(3261, 16379, S32, 22), using
- discarding factors based on OA(3261, 16386, S32, 22), using
- discarding parts of the base [i] based on linear OA(12843, 16386, F128, 22) (dual of [16386, 16343, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12841, 16384, F128, 21) (dual of [16384, 16343, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [i] based on
- discarding parts of the base [i] based on linear OA(12843, 16386, F128, 22) (dual of [16386, 16343, 23]-code), using
- discarding factors based on OA(3261, 16386, S32, 22), using
- OA 11-folding and stacking [i] based on OA(3261, 16379, S32, 22), using
(61−22, 61, 6606)-Net over F32 — Digital
Digital (39, 61, 6606)-net over F32, using
(61−22, 61, large)-Net in Base 32 — Upper bound on s
There is no (39, 61, large)-net in base 32, because
- 20 times m-reduction [i] would yield (39, 41, large)-net in base 32, but