Information on Result #1202924
Digital (31, 54, 599)-net over F81, using net defined by OOA based on linear OOA(8154, 599, F81, 23, 23) (dual of [(599, 23), 13723, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8154, 6590, F81, 23) (dual of [6590, 6536, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8154, 6591, F81, 23) (dual of [6591, 6537, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,6]) [i] based on
- linear OA(8145, 6562, F81, 23) (dual of [6562, 6517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8125, 6562, F81, 13) (dual of [6562, 6537, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- construction X applied to C([0,11]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8154, 6591, F81, 23) (dual of [6591, 6537, 24]-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 (32, 55, 599)-net over F81 | [i] | Net Duplication | |
| 2 | Digital (31, 53, 599)-net over F81 | [i] | m-Reduction | |