Information on Result #1192452
Digital (64, 86, 745)-net over F8, using net defined by OOA based on linear OOA(886, 745, F8, 22, 22) (dual of [(745, 22), 16304, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(886, 8195, F8, 22) (dual of [8195, 8109, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(886, 8196, F8, 22) (dual of [8196, 8110, 23]-code), using
- trace code [i] based on linear OA(6443, 4098, F64, 22) (dual of [4098, 4055, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(6443, 4098, F64, 22) (dual of [4098, 4055, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(886, 8196, F8, 22) (dual of [8196, 8110, 23]-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 (65, 87, 745)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (66, 88, 745)-net over F8 | [i] | ||