Information on Result #1185230
Digital (143, 168, 4923)-net over F3, using net defined by OOA based on linear OOA(3168, 4923, F3, 25, 25) (dual of [(4923, 25), 122907, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3168, 59077, F3, 25) (dual of [59077, 58909, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3167, 59076, F3, 25) (dual of [59076, 58909, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- 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(3141, 59050, F3, 21) (dual of [59050, 58909, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(36, 26, F3, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3167, 59076, F3, 25) (dual of [59076, 58909, 26]-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 (144, 168, 4923)-net over F3 | [i] | t-Expansion | |
| 2 | Digital (144, 169, 4923)-net over F3 | [i] | Net Duplication | |
| 3 | Digital (145, 170, 4923)-net over F3 | [i] | ||
| 4 | Digital (143, 167, 4923)-net over F3 | [i] | m-Reduction | |