Information on Result #548596
There is no linear OA(3162, 171, F3, 108) (dual of [171, 9, 109]-code), because construction Y1 would yield
- linear OA(3161, 167, F3, 108) (dual of [167, 6, 109]-code), but
- residual code [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- residual code [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
- residual code [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- OA(39, 171, 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(3163, 172, F3, 109) (dual of [172, 9, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(3164, 173, F3, 110) (dual of [173, 9, 111]-code) | [i] | ||
| 3 | No linear OOA(3163, 171, F3, 2, 109) (dual of [(171, 2), 179, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3164, 171, F3, 2, 110) (dual of [(171, 2), 178, 111]-NRT-code) | [i] | ||
| 5 | No linear OOA(3166, 171, F3, 2, 112) (dual of [(171, 2), 176, 113]-NRT-code) | [i] | ||
| 6 | No linear OOA(3167, 171, F3, 2, 113) (dual of [(171, 2), 175, 114]-NRT-code) | [i] | ||
| 7 | No linear OOA(3168, 171, F3, 2, 114) (dual of [(171, 2), 174, 115]-NRT-code) | [i] | ||
| 8 | No linear OOA(3169, 171, F3, 2, 115) (dual of [(171, 2), 173, 116]-NRT-code) | [i] | ||
| 9 | No linear OOA(3170, 171, F3, 2, 116) (dual of [(171, 2), 172, 117]-NRT-code) | [i] | ||
| 10 | No linear OOA(3171, 171, F3, 2, 117) (dual of [(171, 2), 171, 118]-NRT-code) | [i] | ||
| 11 | No linear OOA(3172, 171, F3, 2, 118) (dual of [(171, 2), 170, 119]-NRT-code) | [i] | ||
| 12 | No linear OOA(3173, 171, F3, 2, 119) (dual of [(171, 2), 169, 120]-NRT-code) | [i] | ||
| 13 | No linear OOA(3174, 171, F3, 2, 120) (dual of [(171, 2), 168, 121]-NRT-code) | [i] | ||
| 14 | No linear OOA(3175, 171, F3, 2, 121) (dual of [(171, 2), 167, 122]-NRT-code) | [i] | ||
| 15 | No linear OOA(3176, 171, F3, 2, 122) (dual of [(171, 2), 166, 123]-NRT-code) | [i] | ||
| 16 | No linear OOA(3177, 171, F3, 2, 123) (dual of [(171, 2), 165, 124]-NRT-code) | [i] | ||
| 17 | No linear OOA(3178, 171, F3, 2, 124) (dual of [(171, 2), 164, 125]-NRT-code) | [i] | ||
| 18 | No linear OOA(3179, 171, F3, 2, 125) (dual of [(171, 2), 163, 126]-NRT-code) | [i] | ||
| 19 | No linear OOA(3180, 171, F3, 2, 126) (dual of [(171, 2), 162, 127]-NRT-code) | [i] | ||
| 20 | No linear OOA(3181, 171, F3, 2, 127) (dual of [(171, 2), 161, 128]-NRT-code) | [i] | ||
| 21 | No linear OOA(3182, 171, F3, 2, 128) (dual of [(171, 2), 160, 129]-NRT-code) | [i] | ||
| 22 | No linear OOA(3183, 171, F3, 2, 129) (dual of [(171, 2), 159, 130]-NRT-code) | [i] | ||
| 23 | No linear OOA(3184, 171, F3, 2, 130) (dual of [(171, 2), 158, 131]-NRT-code) | [i] | ||
| 24 | No linear OOA(3185, 171, F3, 2, 131) (dual of [(171, 2), 157, 132]-NRT-code) | [i] | ||
| 25 | No linear OOA(3186, 171, F3, 2, 132) (dual of [(171, 2), 156, 133]-NRT-code) | [i] | ||
| 26 | No linear OOA(3187, 171, F3, 2, 133) (dual of [(171, 2), 155, 134]-NRT-code) | [i] | ||
| 27 | No linear OOA(3188, 171, F3, 2, 134) (dual of [(171, 2), 154, 135]-NRT-code) | [i] | ||
| 28 | No linear OOA(3189, 171, F3, 2, 135) (dual of [(171, 2), 153, 136]-NRT-code) | [i] | ||
| 29 | No linear OOA(3190, 171, F3, 2, 136) (dual of [(171, 2), 152, 137]-NRT-code) | [i] | ||
| 30 | No linear OOA(3191, 171, F3, 2, 137) (dual of [(171, 2), 151, 138]-NRT-code) | [i] | ||
| 31 | No linear OOA(3192, 171, F3, 2, 138) (dual of [(171, 2), 150, 139]-NRT-code) | [i] | ||
| 32 | No linear OOA(3193, 171, F3, 2, 139) (dual of [(171, 2), 149, 140]-NRT-code) | [i] | ||
| 33 | No linear OOA(3194, 171, F3, 2, 140) (dual of [(171, 2), 148, 141]-NRT-code) | [i] | ||
| 34 | No linear OOA(3195, 171, F3, 2, 141) (dual of [(171, 2), 147, 142]-NRT-code) | [i] | ||
| 35 | No linear OOA(3196, 171, F3, 2, 142) (dual of [(171, 2), 146, 143]-NRT-code) | [i] | ||
| 36 | No linear OOA(3197, 171, F3, 2, 143) (dual of [(171, 2), 145, 144]-NRT-code) | [i] | ||
| 37 | No linear OOA(3198, 171, F3, 2, 144) (dual of [(171, 2), 144, 145]-NRT-code) | [i] | ||
| 38 | No linear OOA(3199, 171, F3, 2, 145) (dual of [(171, 2), 143, 146]-NRT-code) | [i] | ||
| 39 | No linear OOA(3200, 171, F3, 2, 146) (dual of [(171, 2), 142, 147]-NRT-code) | [i] | ||
| 40 | No linear OOA(3201, 171, F3, 2, 147) (dual of [(171, 2), 141, 148]-NRT-code) | [i] | ||
| 41 | No linear OOA(3202, 171, F3, 2, 148) (dual of [(171, 2), 140, 149]-NRT-code) | [i] | ||
| 42 | No linear OOA(3203, 171, F3, 2, 149) (dual of [(171, 2), 139, 150]-NRT-code) | [i] | ||
| 43 | No linear OOA(3204, 171, F3, 2, 150) (dual of [(171, 2), 138, 151]-NRT-code) | [i] | ||
| 44 | No linear OOA(3205, 171, F3, 2, 151) (dual of [(171, 2), 137, 152]-NRT-code) | [i] | ||
| 45 | No linear OOA(3206, 171, F3, 2, 152) (dual of [(171, 2), 136, 153]-NRT-code) | [i] | ||
| 46 | No linear OOA(3207, 171, F3, 2, 153) (dual of [(171, 2), 135, 154]-NRT-code) | [i] | ||
| 47 | No linear OOA(3208, 171, F3, 2, 154) (dual of [(171, 2), 134, 155]-NRT-code) | [i] | ||
| 48 | No linear OOA(3209, 171, F3, 2, 155) (dual of [(171, 2), 133, 156]-NRT-code) | [i] | ||
| 49 | No linear OOA(3210, 171, F3, 2, 156) (dual of [(171, 2), 132, 157]-NRT-code) | [i] | ||
| 50 | No linear OOA(3211, 171, F3, 2, 157) (dual of [(171, 2), 131, 158]-NRT-code) | [i] | ||
| 51 | No linear OOA(3212, 171, F3, 2, 158) (dual of [(171, 2), 130, 159]-NRT-code) | [i] | ||
| 52 | No linear OOA(3213, 171, F3, 2, 159) (dual of [(171, 2), 129, 160]-NRT-code) | [i] | ||
| 53 | No linear OOA(3214, 171, F3, 2, 160) (dual of [(171, 2), 128, 161]-NRT-code) | [i] | ||
| 54 | No linear OOA(3215, 171, F3, 2, 161) (dual of [(171, 2), 127, 162]-NRT-code) | [i] | ||
| 55 | No linear OOA(3216, 171, F3, 2, 162) (dual of [(171, 2), 126, 163]-NRT-code) | [i] | ||
| 56 | No linear OOA(3217, 171, F3, 2, 163) (dual of [(171, 2), 125, 164]-NRT-code) | [i] | ||
| 57 | No linear OOA(3218, 171, F3, 2, 164) (dual of [(171, 2), 124, 165]-NRT-code) | [i] | ||
| 58 | No linear OOA(3219, 171, F3, 2, 165) (dual of [(171, 2), 123, 166]-NRT-code) | [i] | ||
| 59 | No linear OOA(3220, 171, F3, 2, 166) (dual of [(171, 2), 122, 167]-NRT-code) | [i] | ||
| 60 | No linear OOA(3221, 171, F3, 2, 167) (dual of [(171, 2), 121, 168]-NRT-code) | [i] | ||
| 61 | No linear OOA(3222, 171, F3, 2, 168) (dual of [(171, 2), 120, 169]-NRT-code) | [i] | ||
| 62 | No linear OOA(3223, 171, F3, 2, 169) (dual of [(171, 2), 119, 170]-NRT-code) | [i] | ||
| 63 | No linear OOA(3224, 171, F3, 2, 170) (dual of [(171, 2), 118, 171]-NRT-code) | [i] | ||
| 64 | No linear OOA(3225, 171, F3, 2, 171) (dual of [(171, 2), 117, 172]-NRT-code) | [i] | ||
| 65 | No linear OOA(3226, 171, F3, 2, 172) (dual of [(171, 2), 116, 173]-NRT-code) | [i] | ||
| 66 | No linear OOA(3227, 171, F3, 2, 173) (dual of [(171, 2), 115, 174]-NRT-code) | [i] | ||
| 67 | No linear OOA(3228, 171, F3, 2, 174) (dual of [(171, 2), 114, 175]-NRT-code) | [i] | ||
| 68 | No linear OOA(3229, 171, F3, 2, 175) (dual of [(171, 2), 113, 176]-NRT-code) | [i] | ||
| 69 | No linear OOA(3230, 171, F3, 2, 176) (dual of [(171, 2), 112, 177]-NRT-code) | [i] | ||
| 70 | No linear OOA(3231, 171, F3, 2, 177) (dual of [(171, 2), 111, 178]-NRT-code) | [i] | ||
| 71 | No linear OOA(3232, 171, F3, 2, 178) (dual of [(171, 2), 110, 179]-NRT-code) | [i] | ||
| 72 | No linear OOA(3233, 171, F3, 2, 179) (dual of [(171, 2), 109, 180]-NRT-code) | [i] | ||
| 73 | No linear OOA(3234, 171, F3, 2, 180) (dual of [(171, 2), 108, 181]-NRT-code) | [i] | ||
| 74 | No linear OOA(3235, 171, F3, 2, 181) (dual of [(171, 2), 107, 182]-NRT-code) | [i] | ||
| 75 | No linear OOA(3236, 171, F3, 2, 182) (dual of [(171, 2), 106, 183]-NRT-code) | [i] | ||
| 76 | No linear OOA(3237, 171, F3, 2, 183) (dual of [(171, 2), 105, 184]-NRT-code) | [i] | ||
| 77 | No linear OOA(3238, 171, F3, 2, 184) (dual of [(171, 2), 104, 185]-NRT-code) | [i] | ||
| 78 | No linear OOA(3239, 171, F3, 2, 185) (dual of [(171, 2), 103, 186]-NRT-code) | [i] | ||
| 79 | No linear OOA(3240, 171, F3, 2, 186) (dual of [(171, 2), 102, 187]-NRT-code) | [i] | ||
| 80 | No linear OOA(3241, 171, F3, 2, 187) (dual of [(171, 2), 101, 188]-NRT-code) | [i] | ||
| 81 | No linear OOA(3242, 171, F3, 2, 188) (dual of [(171, 2), 100, 189]-NRT-code) | [i] | ||
| 82 | No linear OOA(3243, 171, F3, 2, 189) (dual of [(171, 2), 99, 190]-NRT-code) | [i] | ||
| 83 | No linear OOA(3244, 171, F3, 2, 190) (dual of [(171, 2), 98, 191]-NRT-code) | [i] | ||
| 84 | No linear OOA(3245, 171, F3, 2, 191) (dual of [(171, 2), 97, 192]-NRT-code) | [i] | ||
| 85 | No linear OOA(3246, 171, F3, 2, 192) (dual of [(171, 2), 96, 193]-NRT-code) | [i] | ||
| 86 | No linear OOA(3247, 171, F3, 2, 193) (dual of [(171, 2), 95, 194]-NRT-code) | [i] | ||
| 87 | No linear OOA(3248, 171, F3, 2, 194) (dual of [(171, 2), 94, 195]-NRT-code) | [i] | ||
| 88 | No linear OOA(3249, 171, F3, 2, 195) (dual of [(171, 2), 93, 196]-NRT-code) | [i] | ||
| 89 | No linear OOA(3250, 171, F3, 2, 196) (dual of [(171, 2), 92, 197]-NRT-code) | [i] | ||
| 90 | No linear OOA(3162, 171, F3, 2, 108) (dual of [(171, 2), 180, 109]-NRT-code) | [i] | Depth Reduction | |
| 91 | No linear OOA(3162, 171, F3, 3, 108) (dual of [(171, 3), 351, 109]-NRT-code) | [i] | ||
| 92 | No linear OOA(3162, 171, F3, 4, 108) (dual of [(171, 4), 522, 109]-NRT-code) | [i] | ||
| 93 | No linear OOA(3162, 171, F3, 5, 108) (dual of [(171, 5), 693, 109]-NRT-code) | [i] | ||
| 94 | No digital (54, 162, 171)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 95 | No linear OA(3163, 177, F3, 108) (dual of [177, 14, 109]-code) | [i] | Construction Y1 (Bound) | |