Information on Result #1190694
Digital (69, 86, 14707)-net over F7, using net defined by OOA based on linear OOA(786, 14707, F7, 17, 17) (dual of [(14707, 17), 249933, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(786, 117657, F7, 17) (dual of [117657, 117571, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(786, 117663, F7, 17) (dual of [117663, 117577, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(785, 117650, F7, 17) (dual of [117650, 117565, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(773, 117650, F7, 15) (dual of [117650, 117577, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 712−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(71, 13, F7, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(786, 117663, F7, 17) (dual of [117663, 117577, 18]-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 (70, 87, 14707)-net over F7 | [i] | Net Duplication | |
| 2 | Digital (78, 95, 14720)-net over F7 | [i] | (u, u+v)-Construction for Nets | |