Information on Result #1192442
Digital (141, 162, 1677720)-net over F8, using net defined by OOA based on linear OOA(8162, 1677720, F8, 22, 21) (dual of [(1677720, 22), 36909678, 22]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8162, 8388601, F8, 2, 21) (dual of [(8388601, 2), 16777040, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8162, 8388602, F8, 2, 21) (dual of [(8388602, 2), 16777042, 22]-NRT-code), using
- trace code [i] based on linear OOA(6481, 4194301, F64, 2, 21) (dual of [(4194301, 2), 8388521, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6481, 8388602, F64, 21) (dual of [8388602, 8388521, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- OOA 2-folding [i] based on linear OA(6481, 8388602, F64, 21) (dual of [8388602, 8388521, 22]-code), using
- trace code [i] based on linear OOA(6481, 4194301, F64, 2, 21) (dual of [(4194301, 2), 8388521, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8162, 8388602, F8, 2, 21) (dual of [(8388602, 2), 16777042, 22]-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 (142, 162, 1677720)-net over F8 | [i] | t-Expansion | |
| 2 | Digital (142, 163, 1677720)-net over F8 | [i] | Net Duplication | |
| 3 | Digital (143, 164, 1677720)-net over F8 | [i] | ||
| 4 | Digital (144, 165, 1677720)-net over F8 | [i] | ||
| 5 | Digital (145, 166, 1677720)-net over F8 | [i] | ||
| 6 | Digital (146, 167, 1677720)-net over F8 | [i] | ||
| 7 | Digital (147, 168, 1677720)-net over F8 | [i] | ||
| 8 | Digital (148, 169, 1677720)-net over F8 | [i] | ||
| 9 | Digital (149, 170, 1677720)-net over F8 | [i] | ||
| 10 | Digital (150, 171, 1677720)-net over F8 | [i] | ||
| 11 | Digital (141, 161, 1677720)-net over F8 | [i] | m-Reduction | |
| 12 | Digital (151, 172, 1677729)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 13 | Digital (152, 173, 1677734)-net over F8 | [i] | ||