Information on Result #1203096
Digital (7, 14, 5463)-net over F128, using net defined by OOA based on linear OOA(12814, 5463, F128, 7, 7) (dual of [(5463, 7), 38227, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(12814, 16390, F128, 7) (dual of [16390, 16376, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(12813, 16385, F128, 7) (dual of [16385, 16372, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(1289, 16385, F128, 5) (dual of [16385, 16376, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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([0,3]) ⊂ C([0,2]) [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 (8, 15, 5463)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (53, 67, 1203834)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (56, 71, 1203834)-net over F128 | [i] | ||
| 4 | (46, 60, 1203834)-net in base 128 | [i] | ||