Information on Result #1191090
Digital (20, 27, 2732)-net over F8, using net defined by OOA based on linear OOA(827, 2732, F8, 7, 7) (dual of [(2732, 7), 19097, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(827, 8197, F8, 7) (dual of [8197, 8170, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(826, 8196, F8, 7) (dual of [8196, 8170, 8]-code), using
- trace code [i] based on linear OA(6413, 4098, F64, 7) (dual of [4098, 4085, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6413, 4098, F64, 7) (dual of [4098, 4085, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(826, 8196, F8, 7) (dual of [8196, 8170, 8]-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 (119, 133, 2399474)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (126, 141, 2399474)-net over F8 | [i] | ||