Information on Result #1192186
Digital (63, 82, 3642)-net over F8, using net defined by OOA based on linear OOA(882, 3642, F8, 19, 19) (dual of [(3642, 19), 69116, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(882, 32779, F8, 19) (dual of [32779, 32697, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(882, 32780, F8, 19) (dual of [32780, 32698, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(881, 32769, F8, 19) (dual of [32769, 32688, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(882, 32780, F8, 19) (dual of [32780, 32698, 20]-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 (64, 83, 3642)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (65, 84, 3642)-net over F8 | [i] | ||
| 3 | Digital (66, 85, 3642)-net over F8 | [i] | ||
| 4 | Digital (77, 96, 3670)-net over F8 | [i] | (u, u+v)-Construction for Nets | |