Information on Result #548591
There is no linear OA(358, 66, F3, 39) (dual of [66, 8, 40]-code), because construction Y1 would yield
- linear OA(357, 62, F3, 39) (dual of [62, 5, 40]-code), but
- residual code [i] would yield linear OA(318, 22, F3, 13) (dual of [22, 4, 14]-code), but
- 1 times truncation [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
- residual code [i] would yield linear OA(318, 22, F3, 13) (dual of [22, 4, 14]-code), but
- OA(38, 66, S3, 4), but
- discarding factors would yield OA(38, 58, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 6729 > 38 [i]
- discarding factors would yield OA(38, 58, 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 OA(359, 67, F3, 40) (dual of [67, 8, 41]-code) | [i] | Truncation | |
| 2 | No linear OOA(359, 66, F3, 2, 40) (dual of [(66, 2), 73, 41]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(360, 66, F3, 2, 41) (dual of [(66, 2), 72, 42]-NRT-code) | [i] | ||
| 4 | No linear OOA(362, 66, F3, 2, 43) (dual of [(66, 2), 70, 44]-NRT-code) | [i] | ||
| 5 | No linear OOA(363, 66, F3, 2, 44) (dual of [(66, 2), 69, 45]-NRT-code) | [i] | ||
| 6 | No linear OOA(364, 66, F3, 2, 45) (dual of [(66, 2), 68, 46]-NRT-code) | [i] | ||
| 7 | No linear OOA(365, 66, F3, 2, 46) (dual of [(66, 2), 67, 47]-NRT-code) | [i] | ||
| 8 | No linear OOA(366, 66, F3, 2, 47) (dual of [(66, 2), 66, 48]-NRT-code) | [i] | ||
| 9 | No linear OOA(367, 66, F3, 2, 48) (dual of [(66, 2), 65, 49]-NRT-code) | [i] | ||
| 10 | No linear OOA(368, 66, F3, 2, 49) (dual of [(66, 2), 64, 50]-NRT-code) | [i] | ||
| 11 | No linear OOA(369, 66, F3, 2, 50) (dual of [(66, 2), 63, 51]-NRT-code) | [i] | ||
| 12 | No linear OOA(370, 66, F3, 2, 51) (dual of [(66, 2), 62, 52]-NRT-code) | [i] | ||
| 13 | No linear OOA(371, 66, F3, 2, 52) (dual of [(66, 2), 61, 53]-NRT-code) | [i] | ||
| 14 | No linear OOA(372, 66, F3, 2, 53) (dual of [(66, 2), 60, 54]-NRT-code) | [i] | ||
| 15 | No linear OOA(373, 66, F3, 2, 54) (dual of [(66, 2), 59, 55]-NRT-code) | [i] | ||
| 16 | No linear OOA(374, 66, F3, 2, 55) (dual of [(66, 2), 58, 56]-NRT-code) | [i] | ||
| 17 | No linear OOA(375, 66, F3, 2, 56) (dual of [(66, 2), 57, 57]-NRT-code) | [i] | ||
| 18 | No linear OOA(376, 66, F3, 2, 57) (dual of [(66, 2), 56, 58]-NRT-code) | [i] | ||
| 19 | No linear OOA(377, 66, F3, 2, 58) (dual of [(66, 2), 55, 59]-NRT-code) | [i] | ||
| 20 | No linear OOA(378, 66, F3, 2, 59) (dual of [(66, 2), 54, 60]-NRT-code) | [i] | ||
| 21 | No linear OOA(379, 66, F3, 2, 60) (dual of [(66, 2), 53, 61]-NRT-code) | [i] | ||
| 22 | No linear OOA(380, 66, F3, 2, 61) (dual of [(66, 2), 52, 62]-NRT-code) | [i] | ||
| 23 | No linear OOA(381, 66, F3, 2, 62) (dual of [(66, 2), 51, 63]-NRT-code) | [i] | ||
| 24 | No linear OOA(382, 66, F3, 2, 63) (dual of [(66, 2), 50, 64]-NRT-code) | [i] | ||
| 25 | No linear OOA(383, 66, F3, 2, 64) (dual of [(66, 2), 49, 65]-NRT-code) | [i] | ||
| 26 | No linear OOA(384, 66, F3, 2, 65) (dual of [(66, 2), 48, 66]-NRT-code) | [i] | ||
| 27 | No linear OOA(385, 66, F3, 2, 66) (dual of [(66, 2), 47, 67]-NRT-code) | [i] | ||
| 28 | No linear OOA(386, 66, F3, 2, 67) (dual of [(66, 2), 46, 68]-NRT-code) | [i] | ||
| 29 | No linear OOA(387, 66, F3, 2, 68) (dual of [(66, 2), 45, 69]-NRT-code) | [i] | ||
| 30 | No linear OOA(388, 66, F3, 2, 69) (dual of [(66, 2), 44, 70]-NRT-code) | [i] | ||
| 31 | No linear OOA(389, 66, F3, 2, 70) (dual of [(66, 2), 43, 71]-NRT-code) | [i] | ||
| 32 | No linear OOA(390, 66, F3, 2, 71) (dual of [(66, 2), 42, 72]-NRT-code) | [i] | ||
| 33 | No linear OOA(391, 66, F3, 2, 72) (dual of [(66, 2), 41, 73]-NRT-code) | [i] | ||
| 34 | No linear OOA(392, 66, F3, 2, 73) (dual of [(66, 2), 40, 74]-NRT-code) | [i] | ||
| 35 | No linear OOA(393, 66, F3, 2, 74) (dual of [(66, 2), 39, 75]-NRT-code) | [i] | ||
| 36 | No linear OOA(394, 66, F3, 2, 75) (dual of [(66, 2), 38, 76]-NRT-code) | [i] | ||
| 37 | No linear OOA(395, 66, F3, 2, 76) (dual of [(66, 2), 37, 77]-NRT-code) | [i] | ||
| 38 | No linear OOA(396, 66, F3, 2, 77) (dual of [(66, 2), 36, 78]-NRT-code) | [i] | ||
| 39 | No linear OOA(397, 66, F3, 2, 78) (dual of [(66, 2), 35, 79]-NRT-code) | [i] | ||
| 40 | No linear OOA(398, 66, F3, 2, 79) (dual of [(66, 2), 34, 80]-NRT-code) | [i] | ||
| 41 | No linear OOA(399, 66, F3, 2, 80) (dual of [(66, 2), 33, 81]-NRT-code) | [i] | ||
| 42 | No linear OOA(358, 66, F3, 2, 39) (dual of [(66, 2), 74, 40]-NRT-code) | [i] | Depth Reduction | |
| 43 | No linear OOA(358, 66, F3, 3, 39) (dual of [(66, 3), 140, 40]-NRT-code) | [i] | ||
| 44 | No linear OOA(358, 66, F3, 4, 39) (dual of [(66, 4), 206, 40]-NRT-code) | [i] | ||
| 45 | No linear OOA(358, 66, F3, 5, 39) (dual of [(66, 5), 272, 40]-NRT-code) | [i] | ||
| 46 | No digital (19, 58, 66)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |