Information on Result #1198022
Digital (49, 66, 66431)-net over F27, using net defined by OOA based on linear OOA(2766, 66431, F27, 17, 17) (dual of [(66431, 17), 1129261, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2766, 531449, F27, 17) (dual of [531449, 531383, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2766, 531451, F27, 17) (dual of [531451, 531385, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(2765, 531442, F27, 17) (dual of [531442, 531377, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2757, 531442, F27, 15) (dual of [531442, 531385, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 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([0,8]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2766, 531451, F27, 17) (dual of [531451, 531385, 18]-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, 67, 66431)-net over F27 | [i] | Net Duplication | |
| 2 | (61, 78, 66531)-net in base 27 | [i] | (u, u+v)-Construction for Nets | |