Information on Result #1185916
Digital (44, 52, 16389)-net over F4, using net defined by OOA based on linear OOA(452, 16389, F4, 8, 8) (dual of [(16389, 8), 131060, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(452, 65556, F4, 8) (dual of [65556, 65504, 9]-code), using
- construction X applied to C([0,4]) ⊂ C([0,2]) [i] based on
- linear OA(449, 65537, F4, 9) (dual of [65537, 65488, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(433, 65537, F4, 5) (dual of [65537, 65504, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,2], and minimum distance d ≥ |{−4,−2,0,2,4}|+1 = 6 (BCH-bound) [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to C([0,4]) ⊂ 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 (220, 236, 4210689)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (231, 248, 4210689)-net over F4 | [i] | ||