Information on Result #1179064
Digital (3, 7, 3281)-net over F81, using net defined by OOA based on linear OOA(817, 3281, F81, 4, 4) (dual of [(3281, 4), 13117, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(817, 6562, F81, 4) (dual of [6562, 6555, 5]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 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 (28, 36, 2100431)-net over F81 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (31, 40, 2100431)-net over F81 | [i] | ||
| 3 | Digital (64, 77, 2799481)-net over F81 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (61, 73, 2799481)-net over F81 | [i] | ||