Information on Result #548491
There is no linear OA(458, 64, F4, 44) (dual of [64, 6, 45]-code), because residual code would yield linear OA(414, 19, F4, 11) (dual of [19, 5, 12]-code), but
- 1 times truncation [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
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(459, 65, F4, 45) (dual of [65, 6, 46]-code) | [i] | Truncation | |
| 2 | No linear OOA(459, 64, F4, 2, 45) (dual of [(64, 2), 69, 46]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(460, 64, F4, 2, 46) (dual of [(64, 2), 68, 47]-NRT-code) | [i] | ||
| 4 | No linear OOA(461, 64, F4, 2, 47) (dual of [(64, 2), 67, 48]-NRT-code) | [i] | ||
| 5 | No linear OOA(462, 64, F4, 2, 48) (dual of [(64, 2), 66, 49]-NRT-code) | [i] | ||
| 6 | No linear OOA(463, 64, F4, 2, 49) (dual of [(64, 2), 65, 50]-NRT-code) | [i] | ||
| 7 | No linear OOA(464, 64, F4, 2, 50) (dual of [(64, 2), 64, 51]-NRT-code) | [i] | ||
| 8 | No linear OOA(465, 64, F4, 2, 51) (dual of [(64, 2), 63, 52]-NRT-code) | [i] | ||
| 9 | No linear OOA(466, 64, F4, 2, 52) (dual of [(64, 2), 62, 53]-NRT-code) | [i] | ||
| 10 | No linear OOA(467, 64, F4, 2, 53) (dual of [(64, 2), 61, 54]-NRT-code) | [i] | ||
| 11 | No linear OOA(468, 64, F4, 2, 54) (dual of [(64, 2), 60, 55]-NRT-code) | [i] | ||
| 12 | No linear OOA(469, 64, F4, 2, 55) (dual of [(64, 2), 59, 56]-NRT-code) | [i] | ||
| 13 | No linear OOA(470, 64, F4, 2, 56) (dual of [(64, 2), 58, 57]-NRT-code) | [i] | ||
| 14 | No linear OOA(471, 64, F4, 2, 57) (dual of [(64, 2), 57, 58]-NRT-code) | [i] | ||
| 15 | No linear OOA(472, 64, F4, 2, 58) (dual of [(64, 2), 56, 59]-NRT-code) | [i] | ||
| 16 | No linear OOA(473, 64, F4, 2, 59) (dual of [(64, 2), 55, 60]-NRT-code) | [i] | ||
| 17 | No linear OOA(474, 64, F4, 2, 60) (dual of [(64, 2), 54, 61]-NRT-code) | [i] | ||
| 18 | No linear OOA(475, 64, F4, 2, 61) (dual of [(64, 2), 53, 62]-NRT-code) | [i] | ||
| 19 | No linear OOA(476, 64, F4, 2, 62) (dual of [(64, 2), 52, 63]-NRT-code) | [i] | ||
| 20 | No linear OOA(477, 64, F4, 2, 63) (dual of [(64, 2), 51, 64]-NRT-code) | [i] | ||
| 21 | No linear OOA(478, 64, F4, 2, 64) (dual of [(64, 2), 50, 65]-NRT-code) | [i] | ||
| 22 | No linear OOA(479, 64, F4, 2, 65) (dual of [(64, 2), 49, 66]-NRT-code) | [i] | ||
| 23 | No linear OOA(480, 64, F4, 2, 66) (dual of [(64, 2), 48, 67]-NRT-code) | [i] | ||
| 24 | No linear OOA(481, 64, F4, 2, 67) (dual of [(64, 2), 47, 68]-NRT-code) | [i] | ||
| 25 | No linear OOA(482, 64, F4, 2, 68) (dual of [(64, 2), 46, 69]-NRT-code) | [i] | ||
| 26 | No linear OOA(483, 64, F4, 2, 69) (dual of [(64, 2), 45, 70]-NRT-code) | [i] | ||
| 27 | No linear OOA(484, 64, F4, 2, 70) (dual of [(64, 2), 44, 71]-NRT-code) | [i] | ||
| 28 | No linear OOA(485, 64, F4, 2, 71) (dual of [(64, 2), 43, 72]-NRT-code) | [i] | ||
| 29 | No linear OOA(486, 64, F4, 2, 72) (dual of [(64, 2), 42, 73]-NRT-code) | [i] | ||
| 30 | No linear OOA(487, 64, F4, 2, 73) (dual of [(64, 2), 41, 74]-NRT-code) | [i] | ||
| 31 | No linear OOA(488, 64, F4, 2, 74) (dual of [(64, 2), 40, 75]-NRT-code) | [i] | ||
| 32 | No linear OOA(489, 64, F4, 2, 75) (dual of [(64, 2), 39, 76]-NRT-code) | [i] | ||
| 33 | No linear OOA(490, 64, F4, 2, 76) (dual of [(64, 2), 38, 77]-NRT-code) | [i] | ||
| 34 | No linear OOA(491, 64, F4, 2, 77) (dual of [(64, 2), 37, 78]-NRT-code) | [i] | ||
| 35 | No linear OOA(492, 64, F4, 2, 78) (dual of [(64, 2), 36, 79]-NRT-code) | [i] | ||
| 36 | No linear OOA(493, 64, F4, 2, 79) (dual of [(64, 2), 35, 80]-NRT-code) | [i] | ||
| 37 | No linear OOA(494, 64, F4, 2, 80) (dual of [(64, 2), 34, 81]-NRT-code) | [i] | ||
| 38 | No linear OOA(495, 64, F4, 2, 81) (dual of [(64, 2), 33, 82]-NRT-code) | [i] | ||
| 39 | No linear OOA(496, 64, F4, 2, 82) (dual of [(64, 2), 32, 83]-NRT-code) | [i] | ||
| 40 | No linear OOA(497, 64, F4, 2, 83) (dual of [(64, 2), 31, 84]-NRT-code) | [i] | ||
| 41 | No linear OOA(498, 64, F4, 2, 84) (dual of [(64, 2), 30, 85]-NRT-code) | [i] | ||
| 42 | No linear OOA(499, 64, F4, 2, 85) (dual of [(64, 2), 29, 86]-NRT-code) | [i] | ||
| 43 | No linear OOA(4100, 64, F4, 2, 86) (dual of [(64, 2), 28, 87]-NRT-code) | [i] | ||
| 44 | No linear OOA(4101, 64, F4, 2, 87) (dual of [(64, 2), 27, 88]-NRT-code) | [i] | ||
| 45 | No linear OOA(4102, 64, F4, 2, 88) (dual of [(64, 2), 26, 89]-NRT-code) | [i] | ||
| 46 | No linear OOA(4103, 64, F4, 2, 89) (dual of [(64, 2), 25, 90]-NRT-code) | [i] | ||
| 47 | No linear OOA(4104, 64, F4, 2, 90) (dual of [(64, 2), 24, 91]-NRT-code) | [i] | ||
| 48 | No linear OOA(4105, 64, F4, 2, 91) (dual of [(64, 2), 23, 92]-NRT-code) | [i] | ||
| 49 | No linear OOA(4106, 64, F4, 2, 92) (dual of [(64, 2), 22, 93]-NRT-code) | [i] | ||
| 50 | No linear OOA(4107, 64, F4, 2, 93) (dual of [(64, 2), 21, 94]-NRT-code) | [i] | ||
| 51 | No linear OOA(458, 64, F4, 2, 44) (dual of [(64, 2), 70, 45]-NRT-code) | [i] | Depth Reduction | |
| 52 | No linear OOA(458, 64, F4, 3, 44) (dual of [(64, 3), 134, 45]-NRT-code) | [i] | ||
| 53 | No digital (14, 58, 64)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 54 | No linear OA(4234, 241, F4, 176) (dual of [241, 7, 177]-code) | [i] | Residual Code | |