Information on Result #1224668
Digital (48, 58, 1679705)-net over F32, using (u, u+v)-construction based on
- digital (7, 12, 1985)-net over F32, using
- net defined by OOA [i] based on linear OOA(3212, 1985, F32, 5, 5) (dual of [(1985, 5), 9913, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3212, 3971, F32, 5) (dual of [3971, 3959, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3212, 3972, F32, 5) (dual of [3972, 3960, 6]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code) (see above)
- linear OA(323, 993, F32, 2) (dual of [993, 990, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code), using
- generalized (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(3212, 3972, F32, 5) (dual of [3972, 3960, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3212, 3971, F32, 5) (dual of [3971, 3959, 6]-code), using
- net defined by OOA [i] based on linear OOA(3212, 1985, F32, 5, 5) (dual of [(1985, 5), 9913, 6]-NRT-code), using
- digital (36, 46, 1677720)-net over F32, using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(3246, large, F32, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(3246, 8388600, F32, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(3246, 1677720, F32, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (69, 79, 3359410)-net over F32 | [i] | (u, u+v)-Construction for Nets | |