Information on Result #1203012
Digital (31, 58, 506)-net over F81, using net defined by OOA based on linear OOA(8158, 506, F81, 27, 27) (dual of [(506, 27), 13604, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8158, 6579, F81, 27) (dual of [6579, 6521, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- linear OA(8153, 6562, F81, 27) (dual of [6562, 6509, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(815, 17, F81, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [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 (32, 58, 506)-net over F81 | [i] | t-Expansion | |
| 2 | Digital (32, 59, 506)-net over F81 | [i] | Net Duplication | |
| 3 | Digital (31, 57, 506)-net over F81 | [i] | m-Reduction | |