Information on Result #1205969
Digital (157, 170, 1399122)-net over F2, using (u, u+v)-construction based on
- digital (25, 31, 1022)-net over F2, using
- 1 times m-reduction [i] based on digital (25, 32, 1022)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(232, 1023, F2, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- 1 times m-reduction [i] based on digital (25, 32, 1022)-net over F2, using
- digital (126, 139, 1398100)-net over F2, using
- net defined by OOA [i] based on linear OOA(2139, 1398100, F2, 13, 13) (dual of [(1398100, 13), 18175161, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2139, 8388601, F2, 13) (dual of [8388601, 8388462, 14]-code), using
- net defined by OOA [i] based on linear OOA(2139, 1398100, F2, 13, 13) (dual of [(1398100, 13), 18175161, 14]-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 (158, 170, 1399122)-net over F2 | [i] | t-Expansion | |
| 2 | Digital (158, 171, 1399122)-net over F2 | [i] | Net Duplication | |
| 3 | Digital (159, 172, 1399122)-net over F2 | [i] | ||
| 4 | Digital (221, 234, 2798244)-net over F2 | [i] | (u, u+v)-Construction for Nets | |
| 5 | Linear OOA(2170, 1399122, F2, 6, 13) (dual of [(1399122, 6), 8394562, 14]-NRT-code) | [i] | Extracting Embedded OOA | |
| 6 | Linear OOA(2170, 1399122, F2, 7, 13) (dual of [(1399122, 7), 9793684, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(2170, 1399122, F2, 8, 13) (dual of [(1399122, 8), 11192806, 14]-NRT-code) | [i] | ||