Information on Result #1179528
Digital (13, 17, 16390)-net over F8, using net defined by OOA based on linear OOA(817, 16390, F8, 4, 4) (dual of [(16390, 4), 65543, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(817, 16390, F8, 3, 4) (dual of [(16390, 3), 49153, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(817, 32780, F8, 4) (dual of [32780, 32763, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [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(86, 32768, F8, 2) (dual of [32768, 32762, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(811, 12, F8, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,8)), using
- dual of repetition code with length 12 [i]
- linear OA(81, 12, F8, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(817, 32780, F8, 4) (dual of [32780, 32763, 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 (67, 75, 4210690)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (74, 83, 4210690)-net over F8 | [i] | ||
| 3 | Digital (158, 172, 4809874)-net over F8 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (143, 156, 5608790)-net over F8 | [i] | ||
| 5 | Digital (136, 148, 5608790)-net over F8 | [i] | ||