Information on Result #1191026
Digital (22, 28, 10927)-net over F8, using net defined by OOA based on linear OOA(828, 10927, F8, 6, 6) (dual of [(10927, 6), 65534, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(828, 32781, F8, 6) (dual of [32781, 32753, 7]-code), using
- 1 times code embedding in larger space [i] based on linear OA(827, 32780, F8, 6) (dual of [32780, 32753, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 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, 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(5) ⊂ Ce(3) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(827, 32780, F8, 6) (dual of [32780, 32753, 7]-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 (106, 118, 2807127)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (113, 126, 2807127)-net over F8 | [i] | ||