Information on Result #548605
There is no linear OA(3193, 203, F3, 129) (dual of [203, 10, 130]-code), because construction Y1 would yield
- linear OA(3192, 199, F3, 129) (dual of [199, 7, 130]-code), but
- residual code [i] would yield linear OA(363, 69, F3, 43) (dual of [69, 6, 44]-code), but
- OA(310, 203, 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(3194, 204, F3, 130) (dual of [204, 10, 131]-code) | [i] | Truncation | |
| 2 | No linear OA(3195, 205, F3, 131) (dual of [205, 10, 132]-code) | [i] | ||
| 3 | No linear OOA(3194, 203, F3, 2, 130) (dual of [(203, 2), 212, 131]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3195, 203, F3, 2, 131) (dual of [(203, 2), 211, 132]-NRT-code) | [i] | ||
| 5 | No linear OOA(3197, 203, F3, 2, 133) (dual of [(203, 2), 209, 134]-NRT-code) | [i] | ||
| 6 | No linear OOA(3198, 203, F3, 2, 134) (dual of [(203, 2), 208, 135]-NRT-code) | [i] | ||
| 7 | No linear OOA(3200, 203, F3, 2, 136) (dual of [(203, 2), 206, 137]-NRT-code) | [i] | ||
| 8 | No linear OOA(3201, 203, F3, 2, 137) (dual of [(203, 2), 205, 138]-NRT-code) | [i] | ||
| 9 | No linear OOA(3202, 203, F3, 2, 138) (dual of [(203, 2), 204, 139]-NRT-code) | [i] | ||
| 10 | No linear OOA(3203, 203, F3, 2, 139) (dual of [(203, 2), 203, 140]-NRT-code) | [i] | ||
| 11 | No linear OOA(3204, 203, F3, 2, 140) (dual of [(203, 2), 202, 141]-NRT-code) | [i] | ||
| 12 | No linear OOA(3205, 203, F3, 2, 141) (dual of [(203, 2), 201, 142]-NRT-code) | [i] | ||
| 13 | No linear OOA(3206, 203, F3, 2, 142) (dual of [(203, 2), 200, 143]-NRT-code) | [i] | ||
| 14 | No linear OOA(3207, 203, F3, 2, 143) (dual of [(203, 2), 199, 144]-NRT-code) | [i] | ||
| 15 | No linear OOA(3208, 203, F3, 2, 144) (dual of [(203, 2), 198, 145]-NRT-code) | [i] | ||
| 16 | No linear OOA(3209, 203, F3, 2, 145) (dual of [(203, 2), 197, 146]-NRT-code) | [i] | ||
| 17 | No linear OOA(3210, 203, F3, 2, 146) (dual of [(203, 2), 196, 147]-NRT-code) | [i] | ||
| 18 | No linear OOA(3211, 203, F3, 2, 147) (dual of [(203, 2), 195, 148]-NRT-code) | [i] | ||
| 19 | No linear OOA(3212, 203, F3, 2, 148) (dual of [(203, 2), 194, 149]-NRT-code) | [i] | ||
| 20 | No linear OOA(3213, 203, F3, 2, 149) (dual of [(203, 2), 193, 150]-NRT-code) | [i] | ||
| 21 | No linear OOA(3214, 203, F3, 2, 150) (dual of [(203, 2), 192, 151]-NRT-code) | [i] | ||
| 22 | No linear OOA(3215, 203, F3, 2, 151) (dual of [(203, 2), 191, 152]-NRT-code) | [i] | ||
| 23 | No linear OOA(3216, 203, F3, 2, 152) (dual of [(203, 2), 190, 153]-NRT-code) | [i] | ||
| 24 | No linear OOA(3217, 203, F3, 2, 153) (dual of [(203, 2), 189, 154]-NRT-code) | [i] | ||
| 25 | No linear OOA(3218, 203, F3, 2, 154) (dual of [(203, 2), 188, 155]-NRT-code) | [i] | ||
| 26 | No linear OOA(3219, 203, F3, 2, 155) (dual of [(203, 2), 187, 156]-NRT-code) | [i] | ||
| 27 | No linear OOA(3220, 203, F3, 2, 156) (dual of [(203, 2), 186, 157]-NRT-code) | [i] | ||
| 28 | No linear OOA(3221, 203, F3, 2, 157) (dual of [(203, 2), 185, 158]-NRT-code) | [i] | ||
| 29 | No linear OOA(3222, 203, F3, 2, 158) (dual of [(203, 2), 184, 159]-NRT-code) | [i] | ||
| 30 | No linear OOA(3223, 203, F3, 2, 159) (dual of [(203, 2), 183, 160]-NRT-code) | [i] | ||
| 31 | No linear OOA(3224, 203, F3, 2, 160) (dual of [(203, 2), 182, 161]-NRT-code) | [i] | ||
| 32 | No linear OOA(3225, 203, F3, 2, 161) (dual of [(203, 2), 181, 162]-NRT-code) | [i] | ||
| 33 | No linear OOA(3226, 203, F3, 2, 162) (dual of [(203, 2), 180, 163]-NRT-code) | [i] | ||
| 34 | No linear OOA(3227, 203, F3, 2, 163) (dual of [(203, 2), 179, 164]-NRT-code) | [i] | ||
| 35 | No linear OOA(3228, 203, F3, 2, 164) (dual of [(203, 2), 178, 165]-NRT-code) | [i] | ||
| 36 | No linear OOA(3229, 203, F3, 2, 165) (dual of [(203, 2), 177, 166]-NRT-code) | [i] | ||
| 37 | No linear OOA(3230, 203, F3, 2, 166) (dual of [(203, 2), 176, 167]-NRT-code) | [i] | ||
| 38 | No linear OOA(3231, 203, F3, 2, 167) (dual of [(203, 2), 175, 168]-NRT-code) | [i] | ||
| 39 | No linear OOA(3232, 203, F3, 2, 168) (dual of [(203, 2), 174, 169]-NRT-code) | [i] | ||
| 40 | No linear OOA(3233, 203, F3, 2, 169) (dual of [(203, 2), 173, 170]-NRT-code) | [i] | ||
| 41 | No linear OOA(3234, 203, F3, 2, 170) (dual of [(203, 2), 172, 171]-NRT-code) | [i] | ||
| 42 | No linear OOA(3235, 203, F3, 2, 171) (dual of [(203, 2), 171, 172]-NRT-code) | [i] | ||
| 43 | No linear OOA(3236, 203, F3, 2, 172) (dual of [(203, 2), 170, 173]-NRT-code) | [i] | ||
| 44 | No linear OOA(3237, 203, F3, 2, 173) (dual of [(203, 2), 169, 174]-NRT-code) | [i] | ||
| 45 | No linear OOA(3238, 203, F3, 2, 174) (dual of [(203, 2), 168, 175]-NRT-code) | [i] | ||
| 46 | No linear OOA(3239, 203, F3, 2, 175) (dual of [(203, 2), 167, 176]-NRT-code) | [i] | ||
| 47 | No linear OOA(3240, 203, F3, 2, 176) (dual of [(203, 2), 166, 177]-NRT-code) | [i] | ||
| 48 | No linear OOA(3241, 203, F3, 2, 177) (dual of [(203, 2), 165, 178]-NRT-code) | [i] | ||
| 49 | No linear OOA(3242, 203, F3, 2, 178) (dual of [(203, 2), 164, 179]-NRT-code) | [i] | ||
| 50 | No linear OOA(3243, 203, F3, 2, 179) (dual of [(203, 2), 163, 180]-NRT-code) | [i] | ||
| 51 | No linear OOA(3244, 203, F3, 2, 180) (dual of [(203, 2), 162, 181]-NRT-code) | [i] | ||
| 52 | No linear OOA(3245, 203, F3, 2, 181) (dual of [(203, 2), 161, 182]-NRT-code) | [i] | ||
| 53 | No linear OOA(3246, 203, F3, 2, 182) (dual of [(203, 2), 160, 183]-NRT-code) | [i] | ||
| 54 | No linear OOA(3247, 203, F3, 2, 183) (dual of [(203, 2), 159, 184]-NRT-code) | [i] | ||
| 55 | No linear OOA(3248, 203, F3, 2, 184) (dual of [(203, 2), 158, 185]-NRT-code) | [i] | ||
| 56 | No linear OOA(3249, 203, F3, 2, 185) (dual of [(203, 2), 157, 186]-NRT-code) | [i] | ||
| 57 | No linear OOA(3250, 203, F3, 2, 186) (dual of [(203, 2), 156, 187]-NRT-code) | [i] | ||
| 58 | No linear OOA(3193, 203, F3, 2, 129) (dual of [(203, 2), 213, 130]-NRT-code) | [i] | Depth Reduction | |
| 59 | No linear OOA(3193, 203, F3, 3, 129) (dual of [(203, 3), 416, 130]-NRT-code) | [i] | ||
| 60 | No linear OOA(3193, 203, F3, 4, 129) (dual of [(203, 4), 619, 130]-NRT-code) | [i] | ||
| 61 | No linear OOA(3193, 203, F3, 5, 129) (dual of [(203, 5), 822, 130]-NRT-code) | [i] | ||
| 62 | No digital (64, 193, 203)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |