Information on Result #1208181
Digital (199, 212, 5592446)-net over F3, using (u, u+v)-construction based on
- digital (10, 16, 46)-net over F3, using
- net defined by OOA [i] based on linear OOA(316, 46, F3, 6, 6) (dual of [(46, 6), 260, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(316, 46, F3, 5, 6) (dual of [(46, 5), 214, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(33, 4, F3, 5, 3) (dual of [(4, 5), 17, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;17,3) [i]
- linear OOA(313, 42, F3, 5, 6) (dual of [(42, 5), 197, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 13, 42)-net over F3, using
- linear OOA(33, 4, F3, 5, 3) (dual of [(4, 5), 17, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(316, 46, F3, 5, 6) (dual of [(46, 5), 214, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(316, 46, F3, 6, 6) (dual of [(46, 6), 260, 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(3212, 5592446, F3, 5, 13) (dual of [(5592446, 5), 27962018, 14]-NRT-code) | [i] | Extracting Embedded OOA | |