Information on Result #1202008
Digital (7, 14, 2188)-net over F81, using net defined by OOA based on linear OOA(8114, 2188, F81, 7, 7) (dual of [(2188, 7), 15302, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(8114, 6565, F81, 7) (dual of [6565, 6551, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(819, 6562, F81, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 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
- discarding factors / shortening the dual code based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-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 (53, 67, 1200559)-net over F81 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (56, 71, 1200559)-net over F81 | [i] | ||