Information on Result #1193146
Digital (37, 44, 1594328)-net over F9, using net defined by OOA based on linear OOA(944, 1594328, F9, 7, 7) (dual of [(1594328, 7), 11160252, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(944, 4782985, F9, 7) (dual of [4782985, 4782941, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(943, 4782970, F9, 7) (dual of [4782970, 4782927, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(929, 4782970, F9, 5) (dual of [4782970, 4782941, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(91, 15, F9, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [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 (38, 45, 1594328)-net over F9 | [i] | Net Duplication | |
| 2 | Digital (136, 150, 3991070)-net over F9 | [i] | (u, u+v)-Construction for Nets | |