Information on Result #1203796
Digital (19, 38, 1821)-net over F128, using net defined by OOA based on linear OOA(12838, 1821, F128, 19, 19) (dual of [(1821, 19), 34561, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(12838, 16390, F128, 19) (dual of [16390, 16352, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 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
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 (20, 38, 1821)-net over F128 | [i] | t-Expansion | |
| 2 | Digital (20, 39, 1821)-net over F128 | [i] | Net Duplication | |
| 3 | Digital (21, 40, 1821)-net over F128 | [i] | ||
| 4 | Digital (22, 41, 1821)-net over F128 | [i] | ||
| 5 | Digital (19, 37, 1821)-net over F128 | [i] | m-Reduction | |
| 6 | Digital (29, 48, 1971)-net over F128 | [i] | (u, u+v)-Construction for Nets | |