Information on Result #548604
There is no linear OA(3179, 188, F3, 120) (dual of [188, 9, 121]-code), because construction Y1 would yield
- linear OA(3178, 184, F3, 120) (dual of [184, 6, 121]-code), but
- residual code [i] would yield linear OA(358, 63, F3, 40) (dual of [63, 5, 41]-code), but
- 1 times truncation [i] 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
- 1 times truncation [i] would yield linear OA(357, 62, F3, 39) (dual of [62, 5, 40]-code), but
- residual code [i] would yield linear OA(358, 63, F3, 40) (dual of [63, 5, 41]-code), but
- OA(39, 188, S3, 4), but
- discarding factors would yield OA(39, 100, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 20001 > 39 [i]
- discarding factors would yield OA(39, 100, 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(3180, 189, F3, 121) (dual of [189, 9, 122]-code) | [i] | Truncation | |
| 2 | No linear OA(3181, 190, F3, 122) (dual of [190, 9, 123]-code) | [i] | ||
| 3 | No linear OOA(3180, 188, F3, 2, 121) (dual of [(188, 2), 196, 122]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3181, 188, F3, 2, 122) (dual of [(188, 2), 195, 123]-NRT-code) | [i] | ||
| 5 | No linear OOA(3183, 188, F3, 2, 124) (dual of [(188, 2), 193, 125]-NRT-code) | [i] | ||
| 6 | No linear OOA(3184, 188, F3, 2, 125) (dual of [(188, 2), 192, 126]-NRT-code) | [i] | ||
| 7 | No linear OOA(3185, 188, F3, 2, 126) (dual of [(188, 2), 191, 127]-NRT-code) | [i] | ||
| 8 | No linear OOA(3186, 188, F3, 2, 127) (dual of [(188, 2), 190, 128]-NRT-code) | [i] | ||
| 9 | No linear OOA(3187, 188, F3, 2, 128) (dual of [(188, 2), 189, 129]-NRT-code) | [i] | ||
| 10 | No linear OOA(3188, 188, F3, 2, 129) (dual of [(188, 2), 188, 130]-NRT-code) | [i] | ||
| 11 | No linear OOA(3189, 188, F3, 2, 130) (dual of [(188, 2), 187, 131]-NRT-code) | [i] | ||
| 12 | No linear OOA(3190, 188, F3, 2, 131) (dual of [(188, 2), 186, 132]-NRT-code) | [i] | ||
| 13 | No linear OOA(3191, 188, F3, 2, 132) (dual of [(188, 2), 185, 133]-NRT-code) | [i] | ||
| 14 | No linear OOA(3192, 188, F3, 2, 133) (dual of [(188, 2), 184, 134]-NRT-code) | [i] | ||
| 15 | No linear OOA(3193, 188, F3, 2, 134) (dual of [(188, 2), 183, 135]-NRT-code) | [i] | ||
| 16 | No linear OOA(3194, 188, F3, 2, 135) (dual of [(188, 2), 182, 136]-NRT-code) | [i] | ||
| 17 | No linear OOA(3195, 188, F3, 2, 136) (dual of [(188, 2), 181, 137]-NRT-code) | [i] | ||
| 18 | No linear OOA(3196, 188, F3, 2, 137) (dual of [(188, 2), 180, 138]-NRT-code) | [i] | ||
| 19 | No linear OOA(3197, 188, F3, 2, 138) (dual of [(188, 2), 179, 139]-NRT-code) | [i] | ||
| 20 | No linear OOA(3198, 188, F3, 2, 139) (dual of [(188, 2), 178, 140]-NRT-code) | [i] | ||
| 21 | No linear OOA(3199, 188, F3, 2, 140) (dual of [(188, 2), 177, 141]-NRT-code) | [i] | ||
| 22 | No linear OOA(3200, 188, F3, 2, 141) (dual of [(188, 2), 176, 142]-NRT-code) | [i] | ||
| 23 | No linear OOA(3201, 188, F3, 2, 142) (dual of [(188, 2), 175, 143]-NRT-code) | [i] | ||
| 24 | No linear OOA(3202, 188, F3, 2, 143) (dual of [(188, 2), 174, 144]-NRT-code) | [i] | ||
| 25 | No linear OOA(3203, 188, F3, 2, 144) (dual of [(188, 2), 173, 145]-NRT-code) | [i] | ||
| 26 | No linear OOA(3204, 188, F3, 2, 145) (dual of [(188, 2), 172, 146]-NRT-code) | [i] | ||
| 27 | No linear OOA(3205, 188, F3, 2, 146) (dual of [(188, 2), 171, 147]-NRT-code) | [i] | ||
| 28 | No linear OOA(3206, 188, F3, 2, 147) (dual of [(188, 2), 170, 148]-NRT-code) | [i] | ||
| 29 | No linear OOA(3207, 188, F3, 2, 148) (dual of [(188, 2), 169, 149]-NRT-code) | [i] | ||
| 30 | No linear OOA(3208, 188, F3, 2, 149) (dual of [(188, 2), 168, 150]-NRT-code) | [i] | ||
| 31 | No linear OOA(3209, 188, F3, 2, 150) (dual of [(188, 2), 167, 151]-NRT-code) | [i] | ||
| 32 | No linear OOA(3210, 188, F3, 2, 151) (dual of [(188, 2), 166, 152]-NRT-code) | [i] | ||
| 33 | No linear OOA(3211, 188, F3, 2, 152) (dual of [(188, 2), 165, 153]-NRT-code) | [i] | ||
| 34 | No linear OOA(3212, 188, F3, 2, 153) (dual of [(188, 2), 164, 154]-NRT-code) | [i] | ||
| 35 | No linear OOA(3213, 188, F3, 2, 154) (dual of [(188, 2), 163, 155]-NRT-code) | [i] | ||
| 36 | No linear OOA(3214, 188, F3, 2, 155) (dual of [(188, 2), 162, 156]-NRT-code) | [i] | ||
| 37 | No linear OOA(3215, 188, F3, 2, 156) (dual of [(188, 2), 161, 157]-NRT-code) | [i] | ||
| 38 | No linear OOA(3216, 188, F3, 2, 157) (dual of [(188, 2), 160, 158]-NRT-code) | [i] | ||
| 39 | No linear OOA(3217, 188, F3, 2, 158) (dual of [(188, 2), 159, 159]-NRT-code) | [i] | ||
| 40 | No linear OOA(3218, 188, F3, 2, 159) (dual of [(188, 2), 158, 160]-NRT-code) | [i] | ||
| 41 | No linear OOA(3219, 188, F3, 2, 160) (dual of [(188, 2), 157, 161]-NRT-code) | [i] | ||
| 42 | No linear OOA(3220, 188, F3, 2, 161) (dual of [(188, 2), 156, 162]-NRT-code) | [i] | ||
| 43 | No linear OOA(3221, 188, F3, 2, 162) (dual of [(188, 2), 155, 163]-NRT-code) | [i] | ||
| 44 | No linear OOA(3222, 188, F3, 2, 163) (dual of [(188, 2), 154, 164]-NRT-code) | [i] | ||
| 45 | No linear OOA(3223, 188, F3, 2, 164) (dual of [(188, 2), 153, 165]-NRT-code) | [i] | ||
| 46 | No linear OOA(3224, 188, F3, 2, 165) (dual of [(188, 2), 152, 166]-NRT-code) | [i] | ||
| 47 | No linear OOA(3225, 188, F3, 2, 166) (dual of [(188, 2), 151, 167]-NRT-code) | [i] | ||
| 48 | No linear OOA(3226, 188, F3, 2, 167) (dual of [(188, 2), 150, 168]-NRT-code) | [i] | ||
| 49 | No linear OOA(3227, 188, F3, 2, 168) (dual of [(188, 2), 149, 169]-NRT-code) | [i] | ||
| 50 | No linear OOA(3228, 188, F3, 2, 169) (dual of [(188, 2), 148, 170]-NRT-code) | [i] | ||
| 51 | No linear OOA(3229, 188, F3, 2, 170) (dual of [(188, 2), 147, 171]-NRT-code) | [i] | ||
| 52 | No linear OOA(3230, 188, F3, 2, 171) (dual of [(188, 2), 146, 172]-NRT-code) | [i] | ||
| 53 | No linear OOA(3231, 188, F3, 2, 172) (dual of [(188, 2), 145, 173]-NRT-code) | [i] | ||
| 54 | No linear OOA(3232, 188, F3, 2, 173) (dual of [(188, 2), 144, 174]-NRT-code) | [i] | ||
| 55 | No linear OOA(3233, 188, F3, 2, 174) (dual of [(188, 2), 143, 175]-NRT-code) | [i] | ||
| 56 | No linear OOA(3234, 188, F3, 2, 175) (dual of [(188, 2), 142, 176]-NRT-code) | [i] | ||
| 57 | No linear OOA(3235, 188, F3, 2, 176) (dual of [(188, 2), 141, 177]-NRT-code) | [i] | ||
| 58 | No linear OOA(3236, 188, F3, 2, 177) (dual of [(188, 2), 140, 178]-NRT-code) | [i] | ||
| 59 | No linear OOA(3237, 188, F3, 2, 178) (dual of [(188, 2), 139, 179]-NRT-code) | [i] | ||
| 60 | No linear OOA(3238, 188, F3, 2, 179) (dual of [(188, 2), 138, 180]-NRT-code) | [i] | ||
| 61 | No linear OOA(3239, 188, F3, 2, 180) (dual of [(188, 2), 137, 181]-NRT-code) | [i] | ||
| 62 | No linear OOA(3240, 188, F3, 2, 181) (dual of [(188, 2), 136, 182]-NRT-code) | [i] | ||
| 63 | No linear OOA(3241, 188, F3, 2, 182) (dual of [(188, 2), 135, 183]-NRT-code) | [i] | ||
| 64 | No linear OOA(3242, 188, F3, 2, 183) (dual of [(188, 2), 134, 184]-NRT-code) | [i] | ||
| 65 | No linear OOA(3243, 188, F3, 2, 184) (dual of [(188, 2), 133, 185]-NRT-code) | [i] | ||
| 66 | No linear OOA(3244, 188, F3, 2, 185) (dual of [(188, 2), 132, 186]-NRT-code) | [i] | ||
| 67 | No linear OOA(3245, 188, F3, 2, 186) (dual of [(188, 2), 131, 187]-NRT-code) | [i] | ||
| 68 | No linear OOA(3246, 188, F3, 2, 187) (dual of [(188, 2), 130, 188]-NRT-code) | [i] | ||
| 69 | No linear OOA(3247, 188, F3, 2, 188) (dual of [(188, 2), 129, 189]-NRT-code) | [i] | ||
| 70 | No linear OOA(3248, 188, F3, 2, 189) (dual of [(188, 2), 128, 190]-NRT-code) | [i] | ||
| 71 | No linear OOA(3249, 188, F3, 2, 190) (dual of [(188, 2), 127, 191]-NRT-code) | [i] | ||
| 72 | No linear OOA(3250, 188, F3, 2, 191) (dual of [(188, 2), 126, 192]-NRT-code) | [i] | ||
| 73 | No linear OOA(3179, 188, F3, 2, 120) (dual of [(188, 2), 197, 121]-NRT-code) | [i] | Depth Reduction | |
| 74 | No linear OOA(3179, 188, F3, 3, 120) (dual of [(188, 3), 385, 121]-NRT-code) | [i] | ||
| 75 | No linear OOA(3179, 188, F3, 4, 120) (dual of [(188, 4), 573, 121]-NRT-code) | [i] | ||
| 76 | No linear OOA(3179, 188, F3, 5, 120) (dual of [(188, 5), 761, 121]-NRT-code) | [i] | ||
| 77 | No digital (59, 179, 188)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |