Information on Result #1198250
Digital (41, 62, 1969)-net over F27, using net defined by OOA based on linear OOA(2762, 1969, F27, 21, 21) (dual of [(1969, 21), 41287, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2762, 19691, F27, 21) (dual of [19691, 19629, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(2761, 19684, F27, 21) (dual of [19684, 19623, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2755, 19684, F27, 19) (dual of [19684, 19629, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,10]) ⊂ C([0,9]) [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 (42, 63, 1969)-net over F27 | [i] | Net Duplication | |
| 2 | Digital (43, 64, 1969)-net over F27 | [i] | ||
| 3 | Digital (41, 61, 1969)-net over F27 | [i] | m-Reduction | |
| 4 | (57, 78, 2085)-net in base 27 | [i] | (u, u+v)-Construction for Nets | |