Information on Result #1179078
Digital (3, 7, 8193)-net over F128, using net defined by OOA based on linear OOA(1287, 8193, F128, 4, 4) (dual of [(8193, 4), 32765, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(1287, 16386, F128, 4) (dual of [16386, 16379, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(1287, 16384, F128, 4) (dual of [16384, 16377, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1285, 16384, F128, 3) (dual of [16384, 16379, 4]-code or 16384-cap in PG(4,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
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 (28, 36, 2105343)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (23, 32, 532481)-net over F128 | [i] | ||
| 3 | Digital (31, 40, 2105343)-net over F128 | [i] | ||
| 4 | Digital (64, 77, 2804393)-net over F128 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 5 | Digital (61, 73, 2804393)-net over F128 | [i] | ||