Information on Result #1208196
Digital (219, 232, 5598961)-net over F3, using (u, u+v)-construction based on
- digital (30, 36, 6561)-net over F3, using
- net defined by OOA [i] based on linear OOA(336, 6561, F3, 6, 6) (dual of [(6561, 6), 39330, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(336, 6561, F3, 5, 6) (dual of [(6561, 5), 32769, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(336, 19683, F3, 6) (dual of [19683, 19647, 7]-code), using
- 1 times truncation [i] based on linear OA(337, 19684, F3, 7) (dual of [19684, 19647, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(337, 19684, F3, 7) (dual of [19684, 19647, 8]-code), using
- OA 3-folding and stacking [i] based on linear OA(336, 19683, F3, 6) (dual of [19683, 19647, 7]-code), using
- appending kth column [i] based on linear OOA(336, 6561, F3, 5, 6) (dual of [(6561, 5), 32769, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(336, 6561, F3, 6, 6) (dual of [(6561, 6), 39330, 7]-NRT-code), using
- digital (183, 196, 5592400)-net over F3, using
- trace code for nets [i] based on digital (85, 98, 2796200)-net over F9, using
- net defined by OOA [i] based on linear OOA(998, 2796200, F9, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(998, 8388601, F9, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(998, 8388602, F9, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- trace code [i] based on linear OOA(8149, 4194301, F81, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
- OOA 2-folding [i] based on linear OA(8149, 8388602, F81, 13) (dual of [8388602, 8388553, 14]-code), using
- trace code [i] based on linear OOA(8149, 4194301, F81, 2, 13) (dual of [(4194301, 2), 8388553, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(998, 8388602, F9, 2, 13) (dual of [(8388602, 2), 16777106, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(998, 8388601, F9, 2, 13) (dual of [(8388601, 2), 16777104, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(998, 2796200, F9, 14, 13) (dual of [(2796200, 14), 39146702, 14]-NRT-code), using
- trace code for nets [i] based on digital (85, 98, 2796200)-net over F9, 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(3232, 5598961, F3, 5, 13) (dual of [(5598961, 5), 27994573, 14]-NRT-code) | [i] | Extracting Embedded OOA | |