Information on Result #1754694
Digital (163, 192, 2057)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2192, 2057, F2, 4, 29) (dual of [(2057, 4), 8036, 30]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2192, 8228, F2, 29) (dual of [8228, 8036, 30]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2189, 8225, F2, 29) (dual of [8225, 8036, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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([0,14]) ⊂ C([0,12]) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(2189, 8225, F2, 29) (dual of [8225, 8036, 30]-code), using
Mode: 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 (164, 193, 2057)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (165, 194, 2057)-net over F2 | [i] | ||