Information on Result #548608
There is no linear OA(3229, 239, F3, 153) (dual of [239, 10, 154]-code), because construction Y1 would yield
- linear OA(3228, 235, F3, 153) (dual of [235, 7, 154]-code), but
- residual code [i] would yield linear OA(375, 81, F3, 51) (dual of [81, 6, 52]-code), but
- OA(310, 239, S3, 4), but
- discarding factors would yield OA(310, 172, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 59169 > 310 [i]
- discarding factors would yield OA(310, 172, 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(3230, 240, F3, 154) (dual of [240, 10, 155]-code) | [i] | Truncation | |
| 2 | No linear OA(3231, 241, F3, 155) (dual of [241, 10, 156]-code) | [i] | ||
| 3 | No linear OOA(3230, 239, F3, 2, 154) (dual of [(239, 2), 248, 155]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3231, 239, F3, 2, 155) (dual of [(239, 2), 247, 156]-NRT-code) | [i] | ||
| 5 | No linear OOA(3233, 239, F3, 2, 157) (dual of [(239, 2), 245, 158]-NRT-code) | [i] | ||
| 6 | No linear OOA(3234, 239, F3, 2, 158) (dual of [(239, 2), 244, 159]-NRT-code) | [i] | ||
| 7 | No linear OOA(3235, 239, F3, 2, 159) (dual of [(239, 2), 243, 160]-NRT-code) | [i] | ||
| 8 | No linear OOA(3236, 239, F3, 2, 160) (dual of [(239, 2), 242, 161]-NRT-code) | [i] | ||
| 9 | No linear OOA(3237, 239, F3, 2, 161) (dual of [(239, 2), 241, 162]-NRT-code) | [i] | ||
| 10 | No linear OOA(3238, 239, F3, 2, 162) (dual of [(239, 2), 240, 163]-NRT-code) | [i] | ||
| 11 | No linear OOA(3239, 239, F3, 2, 163) (dual of [(239, 2), 239, 164]-NRT-code) | [i] | ||
| 12 | No linear OOA(3240, 239, F3, 2, 164) (dual of [(239, 2), 238, 165]-NRT-code) | [i] | ||
| 13 | No linear OOA(3241, 239, F3, 2, 165) (dual of [(239, 2), 237, 166]-NRT-code) | [i] | ||
| 14 | No linear OOA(3242, 239, F3, 2, 166) (dual of [(239, 2), 236, 167]-NRT-code) | [i] | ||
| 15 | No linear OOA(3243, 239, F3, 2, 167) (dual of [(239, 2), 235, 168]-NRT-code) | [i] | ||
| 16 | No linear OOA(3244, 239, F3, 2, 168) (dual of [(239, 2), 234, 169]-NRT-code) | [i] | ||
| 17 | No linear OOA(3245, 239, F3, 2, 169) (dual of [(239, 2), 233, 170]-NRT-code) | [i] | ||
| 18 | No linear OOA(3246, 239, F3, 2, 170) (dual of [(239, 2), 232, 171]-NRT-code) | [i] | ||
| 19 | No linear OOA(3247, 239, F3, 2, 171) (dual of [(239, 2), 231, 172]-NRT-code) | [i] | ||
| 20 | No linear OOA(3248, 239, F3, 2, 172) (dual of [(239, 2), 230, 173]-NRT-code) | [i] | ||
| 21 | No linear OOA(3249, 239, F3, 2, 173) (dual of [(239, 2), 229, 174]-NRT-code) | [i] | ||
| 22 | No linear OOA(3250, 239, F3, 2, 174) (dual of [(239, 2), 228, 175]-NRT-code) | [i] | ||
| 23 | No linear OOA(3229, 239, F3, 2, 153) (dual of [(239, 2), 249, 154]-NRT-code) | [i] | Depth Reduction | |
| 24 | No linear OOA(3229, 239, F3, 3, 153) (dual of [(239, 3), 488, 154]-NRT-code) | [i] | ||
| 25 | No linear OOA(3229, 239, F3, 4, 153) (dual of [(239, 4), 727, 154]-NRT-code) | [i] | ||
| 26 | No linear OOA(3229, 239, F3, 5, 153) (dual of [(239, 5), 966, 154]-NRT-code) | [i] | ||
| 27 | No digital (76, 229, 239)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |