Information on Result #1202724
Digital (21, 40, 730)-net over F81, using net defined by OOA based on linear OOA(8140, 730, F81, 19, 19) (dual of [(730, 19), 13830, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8140, 6571, F81, 19) (dual of [6571, 6531, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8140, 6573, F81, 19) (dual of [6573, 6533, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8129, 6562, F81, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to C([0,9]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8140, 6573, F81, 19) (dual of [6573, 6533, 20]-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 (22, 40, 730)-net over F81 | [i] | t-Expansion | |
| 2 | Digital (22, 41, 730)-net over F81 | [i] | Net Duplication | |
| 3 | Digital (23, 42, 730)-net over F81 | [i] | ||
| 4 | Digital (21, 39, 730)-net over F81 | [i] | m-Reduction | |