Information on Result #1179556
Digital (10, 14, 6563)-net over F9, using net defined by OOA based on linear OOA(914, 6563, F9, 4, 4) (dual of [(6563, 4), 26238, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(914, 6563, F9, 3, 4) (dual of [(6563, 3), 19675, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(914, 13126, F9, 4) (dual of [13126, 13112, 5]-code), using
- trace code [i] based on linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(815, 6561, F81, 3) (dual of [6561, 6556, 4]-code or 6561-cap in PG(4,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- trace code [i] based on linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(914, 13126, F9, 4) (dual of [13126, 13112, 5]-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 (64, 72, 4200863)-net over F9 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (71, 80, 4200863)-net over F9 | [i] | ||
| 3 | Digital (133, 145, 5598963)-net over F9 | [i] | Generalized (u, u+v)-Construction for Nets | |