Information on Result #1195186
Digital (40, 54, 18725)-net over F16, using net defined by OOA based on linear OOA(1654, 18725, F16, 14, 14) (dual of [(18725, 14), 262096, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(1654, 131075, F16, 14) (dual of [131075, 131021, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1654, 131076, F16, 14) (dual of [131076, 131022, 15]-code), using
- trace code [i] based on linear OA(25627, 65538, F256, 14) (dual of [65538, 65511, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(25627, 65538, F256, 14) (dual of [65538, 65511, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1654, 131076, F16, 14) (dual of [131076, 131022, 15]-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 (41, 55, 18725)-net over F16 | [i] | Net Duplication | |
| 2 | Digital (47, 61, 18742)-net over F16 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (48, 62, 18749)-net over F16 | [i] | ||
| 4 | Digital (49, 63, 18758)-net over F16 | [i] | ||
| 5 | Digital (50, 64, 18763)-net over F16 | [i] | ||
| 6 | Digital (51, 65, 18770)-net over F16 | [i] | ||
| 7 | (58, 72, 18725)-net in base 8 | [i] | Base Change | |