Information on Result #1192632
Digital (74, 99, 683)-net over F8, using net defined by OOA based on linear OOA(899, 683, F8, 25, 25) (dual of [(683, 25), 16976, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(899, 8197, F8, 25) (dual of [8197, 8098, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(898, 8196, F8, 25) (dual of [8196, 8098, 26]-code), using
- trace code [i] based on linear OA(6449, 4098, F64, 25) (dual of [4098, 4049, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(6449, 4096, F64, 25) (dual of [4096, 4047, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6447, 4096, F64, 24) (dual of [4096, 4049, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(24) ⊂ Ce(23) [i] based on
- trace code [i] based on linear OA(6449, 4098, F64, 25) (dual of [4098, 4049, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(898, 8196, F8, 25) (dual of [8196, 8098, 26]-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 (75, 100, 683)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (76, 101, 683)-net over F8 | [i] | ||