Information on Result #1198990
Digital (48, 57, 4194300)-net over F32, using net defined by OOA based on linear OOA(3257, 4194300, F32, 10, 9) (dual of [(4194300, 10), 41942943, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3257, 8388601, F32, 2, 9) (dual of [(8388601, 2), 16777145, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3257, 8388602, F32, 2, 9) (dual of [(8388602, 2), 16777147, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(3216, 4194301, F32, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3216, 8388602, F32, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, large, F32, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(3216, large, F32, 4) (dual of [large, large−16, 5]-code), using
- OOA 2-folding [i] based on linear OA(3216, 8388602, F32, 4) (dual of [8388602, 8388586, 5]-code), using
- linear OOA(3241, 4194301, F32, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3241, 8388602, F32, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F32, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(3241, 8388602, F32, 9) (dual of [8388602, 8388561, 10]-code), using
- linear OOA(3216, 4194301, F32, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3257, 8388602, F32, 2, 9) (dual of [(8388602, 2), 16777147, 10]-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 (49, 58, 4194300)-net over F32 | [i] | Net Duplication | |
| 2 | Digital (64, 73, 8388600)-net over F32 | [i] | (u, u+v)-Construction for Nets | |