Information on Result #1194836
Digital (25, 32, 349529)-net over F16, using net defined by OOA based on linear OOA(1632, 349529, F16, 7, 7) (dual of [(349529, 7), 2446671, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(1632, 1048588, F16, 7) (dual of [1048588, 1048556, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(1631, 1048577, F16, 7) (dual of [1048577, 1048546, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(1621, 1048577, F16, 5) (dual of [1048577, 1048556, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [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 (98, 112, 2746271)-net over F16 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (103, 118, 2746271)-net over F16 | [i] | ||