Information on Result #1193288
Digital (59, 68, 4194301)-net over F9, using net defined by OOA based on linear OOA(968, 4194301, F9, 10, 9) (dual of [(4194301, 10), 41942942, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(968, large, F9, 2, 9), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- OOA 2-folding [i] based on linear OA(8133, 8388602, F81, 9) (dual of [8388602, 8388569, 10]-code), using
- trace code [i] based on linear OOA(8133, 4194301, F81, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(966, 8388602, F9, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-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 (60, 69, 4194301)-net over F9 | [i] | Net Duplication | |
| 2 | Digital (84, 93, 8388602)-net over F9 | [i] | (u, u+v)-Construction for Nets | |
| 3 | (83, 92, 8388602)-net in base 9 | [i] | ||