Information on Result #1205386
Digital (66, 76, 2305924)-net over F7, using trace code for nets based on digital (28, 38, 1152962)-net over F49, using
- net defined by OOA [i] based on linear OOA(4938, 1152962, F49, 10, 10) (dual of [(1152962, 10), 11529582, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4938, 5764810, F49, 10) (dual of [5764810, 5764772, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(4937, 5764801, F49, 10) (dual of [5764801, 5764764, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(9) ⊂ Ce(7) [i] based on
- OA 5-folding and stacking [i] based on linear OA(4938, 5764810, F49, 10) (dual of [5764810, 5764772, 11]-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 (67, 77, 2305924)-net over F7 | [i] | Net Duplication | |
| 2 | Digital (99, 109, 4611848)-net over F7 | [i] | (u, u+v)-Construction for Nets | |