Information on Result #1208012
Digital (168, 179, 6710997)-net over F3, using (u, u+v)-construction based on
- digital (10, 15, 117)-net over F3, using
- net defined by OOA [i] based on linear OOA(315, 117, F3, 5, 5) (dual of [(117, 5), 570, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(315, 117, F3, 4, 5) (dual of [(117, 4), 453, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(34, 40, F3, 4, 2) (dual of [(40, 4), 156, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(34, 40, F3, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
- appending kth column [i] based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- appending kth column [i] based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(34, 40, F3, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
- linear OOA(311, 77, F3, 4, 5) (dual of [(77, 4), 297, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 11, 77)-net over F3, using
- linear OOA(34, 40, F3, 4, 2) (dual of [(40, 4), 156, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(315, 117, F3, 4, 5) (dual of [(117, 4), 453, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(315, 117, F3, 5, 5) (dual of [(117, 5), 570, 6]-NRT-code), using
- digital (153, 164, 6710880)-net over F3, using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8141, large, F81, 11) (dual of [large, large−41, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8141, 8388601, F81, 11) (dual of [8388601, 8388560, 12]-code), using
- net defined by OOA [i] based on linear OOA(8141, 1677720, F81, 11, 11) (dual of [(1677720, 11), 18454879, 12]-NRT-code), using
- trace code for nets [i] based on digital (30, 41, 1677720)-net over F81, 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 | Linear OOA(3179, 6710997, F3, 5, 11) (dual of [(6710997, 5), 33554806, 12]-NRT-code) | [i] | Extracting Embedded OOA | |