Information on Result #1185626
Digital (191, 224, 3692)-net over F3, using net defined by OOA based on linear OOA(3224, 3692, F3, 33, 33) (dual of [(3692, 33), 121612, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3224, 59073, F3, 33) (dual of [59073, 58849, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3222, 59071, F3, 33) (dual of [59071, 58849, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(3221, 59050, F3, 33) (dual of [59050, 58829, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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([0,16]) ⊂ C([0,15]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3222, 59071, F3, 33) (dual of [59071, 58849, 34]-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 (192, 225, 3692)-net over F3 | [i] | Net Duplication | |
| 2 | Digital (193, 226, 3692)-net over F3 | [i] | ||
| 3 | Digital (194, 227, 3692)-net over F3 | [i] | ||
| 4 | Digital (195, 228, 3692)-net over F3 | [i] | ||