Information on Result #1202112
Digital (9, 18, 1641)-net over F81, using net defined by OOA based on linear OOA(8118, 1641, F81, 9, 9) (dual of [(1641, 9), 14751, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(8118, 6565, F81, 9) (dual of [6565, 6547, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8118, 6567, F81, 9) (dual of [6567, 6549, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(8117, 6562, F81, 9) (dual of [6562, 6545, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8118, 6567, F81, 9) (dual of [6567, 6549, 10]-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 | (15, 24, 1641)-net in base 27 | [i] | Base Change | |