Information on Result #1202936
Digital (47, 70, 48314)-net over F81, using net defined by OOA based on linear OOA(8170, 48314, F81, 23, 23) (dual of [(48314, 23), 1111152, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8170, 531455, F81, 23) (dual of [531455, 531385, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8170, 531457, F81, 23) (dual of [531457, 531387, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(8167, 531442, F81, 23) (dual of [531442, 531375, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,11]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8170, 531457, F81, 23) (dual of [531457, 531387, 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 (48, 71, 48314)-net over F81 | [i] | Net Duplication | |
| 2 | Digital (49, 72, 48314)-net over F81 | [i] | ||
| 3 | Digital (47, 69, 48314)-net over F81 | [i] | m-Reduction | |