Information on Result #3182196
Digital (117, 137, 822)-net over F2, using t-expansion based on digital (116, 137, 822)-net over F2, using
- net defined by OOA [i] based on linear OOA(2137, 822, F2, 21, 21) (dual of [(822, 21), 17125, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2137, 8221, F2, 21) (dual of [8221, 8084, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2137, 8225, F2, 21) (dual of [8225, 8088, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2131, 8193, F2, 21) (dual of [8193, 8062, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2105, 8193, F2, 17) (dual of [8193, 8088, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2137, 8225, F2, 21) (dual of [8225, 8088, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2137, 8221, F2, 21) (dual of [8221, 8084, 22]-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 (118, 138, 822)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (119, 139, 822)-net over F2 | [i] | ||