Information on Result #1208111
Digital (224, 236, 7186723)-net over F3, using (u, u+v)-construction based on
- digital (50, 56, 1594323)-net over F3, using
- net defined by OOA [i] based on linear OOA(356, 1594323, F3, 6, 6) (dual of [(1594323, 6), 9565882, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(356, 1594323, F3, 5, 6) (dual of [(1594323, 5), 7971559, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(356, 4782969, F3, 6) (dual of [4782969, 4782913, 7]-code), using
- 1 times truncation [i] based on linear OA(357, 4782970, F3, 7) (dual of [4782970, 4782913, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, 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(357, 4782970, F3, 7) (dual of [4782970, 4782913, 8]-code), using
- OA 3-folding and stacking [i] based on linear OA(356, 4782969, F3, 6) (dual of [4782969, 4782913, 7]-code), using
- appending kth column [i] based on linear OOA(356, 1594323, F3, 5, 6) (dual of [(1594323, 5), 7971559, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(356, 1594323, F3, 6, 6) (dual of [(1594323, 6), 9565882, 7]-NRT-code), using
- digital (168, 180, 5592400)-net over F3, using
- trace code for nets [i] based on digital (78, 90, 2796200)-net over F9, using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- trace code for nets [i] based on digital (78, 90, 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(3236, 7186723, F3, 5, 12) (dual of [(7186723, 5), 35933379, 13]-NRT-code) | [i] | Extracting Embedded OOA | |