Information on Result #1179526
Digital (12, 16, 16386)-net over F8, using net defined by OOA based on linear OOA(816, 16386, F8, 4, 4) (dual of [(16386, 4), 65528, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(816, 16386, F8, 3, 4) (dual of [(16386, 3), 49142, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(816, 32772, F8, 4) (dual of [32772, 32756, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(816, 32773, F8, 4) (dual of [32773, 32757, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(816, 32768, F8, 4) (dual of [32768, 32752, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(811, 32768, F8, 3) (dual of [32768, 32757, 4]-code or 32768-cap in PG(10,8)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 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(816, 32773, F8, 4) (dual of [32773, 32757, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(816, 32772, F8, 4) (dual of [32772, 32756, 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 (66, 74, 4210686)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (73, 82, 4210686)-net over F8 | [i] | ||
| 3 | Digital (145, 158, 5608795)-net over F8 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (146, 159, 5608851)-net over F8 | [i] | ||
| 5 | Digital (138, 150, 5608795)-net over F8 | [i] | ||
| 6 | Digital (139, 151, 5608851)-net over F8 | [i] | ||
| 7 | Digital (157, 171, 4809870)-net over F8 | [i] | ||
| 8 | Digital (142, 155, 5608786)-net over F8 | [i] | ||
| 9 | Digital (135, 147, 5608786)-net over F8 | [i] | ||