Information on Result #1185372
Digital (157, 184, 4544)-net over F3, using net defined by OOA based on linear OOA(3184, 4544, F3, 27, 27) (dual of [(4544, 27), 122504, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3184, 59073, F3, 27) (dual of [59073, 58889, 28]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3182, 59071, F3, 27) (dual of [59071, 58889, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(3181, 59050, F3, 27) (dual of [59050, 58869, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(31, 21, F3, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3182, 59071, F3, 27) (dual of [59071, 58889, 28]-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 (158, 185, 4544)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (159, 186, 4544)-net over F3 | [i] | ||
| 3 | Digital (160, 187, 4544)-net over F3 | [i] | ||