Information on Result #1824881
(23, 30, 6563)-net in base 9, using base change based on digital (13, 20, 6563)-net over F27, using
- net defined by OOA [i] based on linear OOA(2720, 6563, F27, 7, 7) (dual of [(6563, 7), 45921, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2720, 19690, F27, 7) (dual of [19690, 19670, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2720, 19691, F27, 7) (dual of [19691, 19671, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(2719, 19684, F27, 7) (dual of [19684, 19665, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2713, 19684, F27, 5) (dual of [19684, 19671, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 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(2720, 19691, F27, 7) (dual of [19691, 19671, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2720, 19690, F27, 7) (dual of [19690, 19670, 8]-code), using
Mode: Constructive.
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 | (122, 136, 2403305)-net in base 9 | [i] | (u, u+v)-Construction for Nets | |
| 2 | (129, 144, 2403305)-net in base 9 | [i] | ||