Information on Result #1195080
Digital (44, 56, 174763)-net over F16, using net defined by OOA based on linear OOA(1656, 174763, F16, 12, 12) (dual of [(174763, 12), 2097100, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(1656, 1048578, F16, 12) (dual of [1048578, 1048522, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(1656, 1048581, F16, 12) (dual of [1048581, 1048525, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1651, 1048576, F16, 11) (dual of [1048576, 1048525, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(1656, 1048581, F16, 12) (dual of [1048581, 1048525, 13]-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 (50, 62, 174780)-net over F16 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (51, 63, 174787)-net over F16 | [i] | ||
| 3 | Digital (52, 64, 174796)-net over F16 | [i] | ||
| 4 | Digital (53, 65, 174801)-net over F16 | [i] | ||
| 5 | Digital (54, 66, 174808)-net over F16 | [i] | ||