Information on Result #1191094
Digital (22, 29, 2740)-net over F8, using net defined by OOA based on linear OOA(829, 2740, F8, 9, 7) (dual of [(2740, 9), 24631, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(829, 2741, F8, 3, 7) (dual of [(2741, 3), 8194, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(83, 9, F8, 3, 3) (dual of [(9, 3), 24, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;24,8) [i]
- linear OOA(826, 2732, F8, 3, 7) (dual of [(2732, 3), 8170, 8]-NRT-code), using
- OOA 3-folding [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
- OOA 3-folding [i] based on linear OA(826, 8196, F8, 7) (dual of [8196, 8170, 8]-code), using
- linear OOA(83, 9, F8, 3, 3) (dual of [(9, 3), 24, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
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 (121, 135, 2399482)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (128, 143, 2399482)-net over F8 | [i] | ||