Information on Result #1179538
Digital (19, 23, 1048584)-net over F8, using net defined by OOA based on linear OOA(823, 1048584, F8, 4, 4) (dual of [(1048584, 4), 4194313, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(823, 1048584, F8, 3, 4) (dual of [(1048584, 3), 3145729, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(823, 2097168, F8, 4) (dual of [2097168, 2097145, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(822, 2097152, F8, 4) (dual of [2097152, 2097130, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(88, 2097152, F8, 2) (dual of [2097152, 2097144, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(815, 16, F8, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,8)), using
- dual of repetition code with length 16 [i]
- linear OA(81, 16, F8, 1) (dual of [16, 15, 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(823, 2097168, F8, 4) (dual of [2097168, 2097145, 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 (73, 81, 5242884)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (80, 89, 5242884)-net over F8 | [i] | ||
| 3 | Digital (149, 162, 6640984)-net over F8 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (142, 154, 6640984)-net over F8 | [i] | ||