Information on Result #547740
There is no linear OA(340, 47, F3, 27) (dual of [47, 7, 28]-code), because construction Y1 would yield
- linear OA(339, 43, F3, 27) (dual of [43, 4, 28]-code), but
- OA(37, 47, S3, 4), but
- discarding factors would yield OA(37, 34, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 2313 > 37 [i]
- discarding factors would yield OA(37, 34, S3, 4), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(342, 47, F3, 2, 29) (dual of [(47, 2), 52, 30]-NRT-code) | [i] | m-Reduction for OOAs | |
| 2 | No linear OOA(344, 47, F3, 2, 31) (dual of [(47, 2), 50, 32]-NRT-code) | [i] | ||
| 3 | No linear OOA(345, 47, F3, 2, 32) (dual of [(47, 2), 49, 33]-NRT-code) | [i] | ||
| 4 | No linear OOA(346, 47, F3, 2, 33) (dual of [(47, 2), 48, 34]-NRT-code) | [i] | ||
| 5 | No linear OOA(347, 47, F3, 2, 34) (dual of [(47, 2), 47, 35]-NRT-code) | [i] | ||
| 6 | No linear OOA(348, 47, F3, 2, 35) (dual of [(47, 2), 46, 36]-NRT-code) | [i] | ||
| 7 | No linear OOA(349, 47, F3, 2, 36) (dual of [(47, 2), 45, 37]-NRT-code) | [i] | ||
| 8 | No linear OOA(350, 47, F3, 2, 37) (dual of [(47, 2), 44, 38]-NRT-code) | [i] | ||
| 9 | No linear OOA(351, 47, F3, 2, 38) (dual of [(47, 2), 43, 39]-NRT-code) | [i] | ||
| 10 | No linear OOA(352, 47, F3, 2, 39) (dual of [(47, 2), 42, 40]-NRT-code) | [i] | ||
| 11 | No linear OOA(353, 47, F3, 2, 40) (dual of [(47, 2), 41, 41]-NRT-code) | [i] | ||
| 12 | No linear OOA(354, 47, F3, 2, 41) (dual of [(47, 2), 40, 42]-NRT-code) | [i] | ||
| 13 | No linear OOA(355, 47, F3, 2, 42) (dual of [(47, 2), 39, 43]-NRT-code) | [i] | ||
| 14 | No linear OOA(356, 47, F3, 2, 43) (dual of [(47, 2), 38, 44]-NRT-code) | [i] | ||
| 15 | No linear OOA(357, 47, F3, 2, 44) (dual of [(47, 2), 37, 45]-NRT-code) | [i] | ||
| 16 | No linear OOA(358, 47, F3, 2, 45) (dual of [(47, 2), 36, 46]-NRT-code) | [i] | ||
| 17 | No linear OOA(359, 47, F3, 2, 46) (dual of [(47, 2), 35, 47]-NRT-code) | [i] | ||
| 18 | No linear OOA(360, 47, F3, 2, 47) (dual of [(47, 2), 34, 48]-NRT-code) | [i] | ||
| 19 | No linear OOA(361, 47, F3, 2, 48) (dual of [(47, 2), 33, 49]-NRT-code) | [i] | ||
| 20 | No linear OOA(362, 47, F3, 2, 49) (dual of [(47, 2), 32, 50]-NRT-code) | [i] | ||
| 21 | No linear OOA(363, 47, F3, 2, 50) (dual of [(47, 2), 31, 51]-NRT-code) | [i] | ||
| 22 | No linear OOA(364, 47, F3, 2, 51) (dual of [(47, 2), 30, 52]-NRT-code) | [i] | ||
| 23 | No linear OOA(365, 47, F3, 2, 52) (dual of [(47, 2), 29, 53]-NRT-code) | [i] | ||
| 24 | No linear OOA(366, 47, F3, 2, 53) (dual of [(47, 2), 28, 54]-NRT-code) | [i] | ||
| 25 | No linear OOA(367, 47, F3, 2, 54) (dual of [(47, 2), 27, 55]-NRT-code) | [i] | ||
| 26 | No linear OOA(368, 47, F3, 2, 55) (dual of [(47, 2), 26, 56]-NRT-code) | [i] | ||
| 27 | No linear OOA(369, 47, F3, 2, 56) (dual of [(47, 2), 25, 57]-NRT-code) | [i] | ||
| 28 | No linear OOA(370, 47, F3, 2, 57) (dual of [(47, 2), 24, 58]-NRT-code) | [i] | ||
| 29 | No linear OOA(371, 47, F3, 2, 58) (dual of [(47, 2), 23, 59]-NRT-code) | [i] | ||
| 30 | No linear OOA(340, 47, F3, 2, 27) (dual of [(47, 2), 54, 28]-NRT-code) | [i] | Depth Reduction | |
| 31 | No linear OOA(340, 47, F3, 3, 27) (dual of [(47, 3), 101, 28]-NRT-code) | [i] | ||
| 32 | No linear OOA(340, 47, F3, 4, 27) (dual of [(47, 4), 148, 28]-NRT-code) | [i] | ||
| 33 | No linear OOA(340, 47, F3, 5, 27) (dual of [(47, 5), 195, 28]-NRT-code) | [i] | ||
| 34 | No digital (13, 40, 47)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 35 | No linear OA(341, 55, F3, 27) (dual of [55, 14, 28]-code) | [i] | Construction Y1 (Bound) | |