Information on Result #1202512
Digital (31, 46, 75922)-net over F81, using net defined by OOA based on linear OOA(8146, 75922, F81, 15, 15) (dual of [(75922, 15), 1138784, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8146, 531455, F81, 15) (dual of [531455, 531409, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8146, 531457, F81, 15) (dual of [531457, 531411, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,5]) [i] based on
- linear OA(8143, 531442, F81, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(8131, 531442, F81, 11) (dual of [531442, 531411, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-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([0,7]) ⊂ C([0,5]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8146, 531457, F81, 15) (dual of [531457, 531411, 16]-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, 47, 75922)-net over F81 | [i] | Net Duplication | |