Information on Result #1200270
Digital (16, 22, 1921603)-net over F49, using net defined by OOA based on linear OOA(4922, 1921603, F49, 6, 6) (dual of [(1921603, 6), 11529596, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(4922, 5764809, F49, 6) (dual of [5764809, 5764787, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(4922, 5764810, F49, 6) (dual of [5764810, 5764788, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(4922, 5764810, F49, 6) (dual of [5764810, 5764788, 7]-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 (38, 44, 3843206)-net over F7 | [i] | Trace Code for Nets | |
| 2 | Digital (23, 29, 3843206)-net over F49 | [i] | (u, u+v)-Construction for Nets | |