Information on Result #548485
There is no linear OA(3219, 227, F3, 147) (dual of [227, 8, 148]-code), because residual code would yield linear OA(372, 79, F3, 49) (dual of [79, 7, 50]-code), but
- 1 times truncation [i] would yield linear OA(371, 78, F3, 48) (dual of [78, 7, 49]-code), but
- residual code [i] would yield linear OA(323, 29, F3, 16) (dual of [29, 6, 17]-code), but
- 1 times truncation [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- 1 times truncation [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- residual code [i] would yield linear OA(323, 29, F3, 16) (dual of [29, 6, 17]-code), 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(3220, 228, F3, 148) (dual of [228, 8, 149]-code) | [i] | Truncation | |
| 2 | No linear OA(3221, 229, F3, 149) (dual of [229, 8, 150]-code) | [i] | ||
| 3 | No linear OOA(3220, 227, F3, 2, 148) (dual of [(227, 2), 234, 149]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3221, 227, F3, 2, 149) (dual of [(227, 2), 233, 150]-NRT-code) | [i] | ||
| 5 | No linear OOA(3222, 227, F3, 2, 150) (dual of [(227, 2), 232, 151]-NRT-code) | [i] | ||
| 6 | No linear OOA(3223, 227, F3, 2, 151) (dual of [(227, 2), 231, 152]-NRT-code) | [i] | ||
| 7 | No linear OOA(3224, 227, F3, 2, 152) (dual of [(227, 2), 230, 153]-NRT-code) | [i] | ||
| 8 | No linear OOA(3225, 227, F3, 2, 153) (dual of [(227, 2), 229, 154]-NRT-code) | [i] | ||
| 9 | No linear OOA(3226, 227, F3, 2, 154) (dual of [(227, 2), 228, 155]-NRT-code) | [i] | ||
| 10 | No linear OOA(3227, 227, F3, 2, 155) (dual of [(227, 2), 227, 156]-NRT-code) | [i] | ||
| 11 | No linear OOA(3228, 227, F3, 2, 156) (dual of [(227, 2), 226, 157]-NRT-code) | [i] | ||
| 12 | No linear OOA(3229, 227, F3, 2, 157) (dual of [(227, 2), 225, 158]-NRT-code) | [i] | ||
| 13 | No linear OOA(3230, 227, F3, 2, 158) (dual of [(227, 2), 224, 159]-NRT-code) | [i] | ||
| 14 | No linear OOA(3231, 227, F3, 2, 159) (dual of [(227, 2), 223, 160]-NRT-code) | [i] | ||
| 15 | No linear OOA(3232, 227, F3, 2, 160) (dual of [(227, 2), 222, 161]-NRT-code) | [i] | ||
| 16 | No linear OOA(3233, 227, F3, 2, 161) (dual of [(227, 2), 221, 162]-NRT-code) | [i] | ||
| 17 | No linear OOA(3234, 227, F3, 2, 162) (dual of [(227, 2), 220, 163]-NRT-code) | [i] | ||
| 18 | No linear OOA(3235, 227, F3, 2, 163) (dual of [(227, 2), 219, 164]-NRT-code) | [i] | ||
| 19 | No linear OOA(3236, 227, F3, 2, 164) (dual of [(227, 2), 218, 165]-NRT-code) | [i] | ||
| 20 | No linear OOA(3237, 227, F3, 2, 165) (dual of [(227, 2), 217, 166]-NRT-code) | [i] | ||
| 21 | No linear OOA(3238, 227, F3, 2, 166) (dual of [(227, 2), 216, 167]-NRT-code) | [i] | ||
| 22 | No linear OOA(3239, 227, F3, 2, 167) (dual of [(227, 2), 215, 168]-NRT-code) | [i] | ||
| 23 | No linear OOA(3240, 227, F3, 2, 168) (dual of [(227, 2), 214, 169]-NRT-code) | [i] | ||
| 24 | No linear OOA(3241, 227, F3, 2, 169) (dual of [(227, 2), 213, 170]-NRT-code) | [i] | ||
| 25 | No linear OOA(3242, 227, F3, 2, 170) (dual of [(227, 2), 212, 171]-NRT-code) | [i] | ||
| 26 | No linear OOA(3243, 227, F3, 2, 171) (dual of [(227, 2), 211, 172]-NRT-code) | [i] | ||
| 27 | No linear OOA(3244, 227, F3, 2, 172) (dual of [(227, 2), 210, 173]-NRT-code) | [i] | ||
| 28 | No linear OOA(3245, 227, F3, 2, 173) (dual of [(227, 2), 209, 174]-NRT-code) | [i] | ||
| 29 | No linear OOA(3246, 227, F3, 2, 174) (dual of [(227, 2), 208, 175]-NRT-code) | [i] | ||
| 30 | No linear OOA(3247, 227, F3, 2, 175) (dual of [(227, 2), 207, 176]-NRT-code) | [i] | ||
| 31 | No linear OOA(3248, 227, F3, 2, 176) (dual of [(227, 2), 206, 177]-NRT-code) | [i] | ||
| 32 | No linear OOA(3249, 227, F3, 2, 177) (dual of [(227, 2), 205, 178]-NRT-code) | [i] | ||
| 33 | No linear OOA(3250, 227, F3, 2, 178) (dual of [(227, 2), 204, 179]-NRT-code) | [i] | ||
| 34 | No linear OOA(3219, 227, F3, 2, 147) (dual of [(227, 2), 235, 148]-NRT-code) | [i] | Depth Reduction | |
| 35 | No linear OOA(3219, 227, F3, 3, 147) (dual of [(227, 3), 462, 148]-NRT-code) | [i] | ||
| 36 | No linear OOA(3219, 227, F3, 4, 147) (dual of [(227, 4), 689, 148]-NRT-code) | [i] | ||
| 37 | No linear OOA(3219, 227, F3, 5, 147) (dual of [(227, 5), 916, 148]-NRT-code) | [i] | ||
| 38 | No digital (72, 219, 227)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |