Information on Result #1203322
Digital (21, 32, 419431)-net over F128, using net defined by OOA based on linear OOA(12832, 419431, F128, 11, 11) (dual of [(419431, 11), 4613709, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12832, 2097156, F128, 11) (dual of [2097156, 2097124, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12832, 2097160, F128, 11) (dual of [2097160, 2097128, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(12831, 2097153, F128, 11) (dual of [2097153, 2097122, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(12825, 2097153, F128, 9) (dual of [2097153, 2097128, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 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([0,5]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12832, 2097160, F128, 11) (dual of [2097160, 2097128, 12]-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 (28, 39, 427559)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 2 | (45, 56, 419431)-net in base 16 | [i] | Base Change | |