Information on Result #547882
There is no linear OA(4154, 162, F4, 116) (dual of [162, 8, 117]-code), because construction Y1 would yield
- linear OA(4153, 158, F4, 116) (dual of [158, 5, 117]-code), but
- residual code [i] would yield linear OA(437, 41, F4, 29) (dual of [41, 4, 30]-code), but
- 1 times truncation [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(48, 11, F4, 7) (dual of [11, 3, 8]-code), but
- 1 times truncation [i] would yield linear OA(436, 40, F4, 28) (dual of [40, 4, 29]-code), but
- residual code [i] would yield linear OA(437, 41, F4, 29) (dual of [41, 4, 30]-code), but
- OA(48, 162, S4, 4), but
- discarding factors would yield OA(48, 121, S4, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 65704 > 48 [i]
- discarding factors would yield OA(48, 121, S4, 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(4155, 163, F4, 117) (dual of [163, 8, 118]-code) | [i] | Truncation | |
| 2 | No linear OA(4156, 164, F4, 118) (dual of [164, 8, 119]-code) | [i] | ||
| 3 | No linear OA(4157, 165, F4, 119) (dual of [165, 8, 120]-code) | [i] | ||
| 4 | No linear OOA(4155, 162, F4, 2, 117) (dual of [(162, 2), 169, 118]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4156, 162, F4, 2, 118) (dual of [(162, 2), 168, 119]-NRT-code) | [i] | ||
| 6 | No linear OOA(4157, 162, F4, 2, 119) (dual of [(162, 2), 167, 120]-NRT-code) | [i] | ||
| 7 | No linear OOA(4158, 162, F4, 2, 120) (dual of [(162, 2), 166, 121]-NRT-code) | [i] | ||
| 8 | No linear OOA(4159, 162, F4, 2, 121) (dual of [(162, 2), 165, 122]-NRT-code) | [i] | ||
| 9 | No linear OOA(4160, 162, F4, 2, 122) (dual of [(162, 2), 164, 123]-NRT-code) | [i] | ||
| 10 | No linear OOA(4161, 162, F4, 2, 123) (dual of [(162, 2), 163, 124]-NRT-code) | [i] | ||
| 11 | No linear OOA(4162, 162, F4, 2, 124) (dual of [(162, 2), 162, 125]-NRT-code) | [i] | ||
| 12 | No linear OOA(4163, 162, F4, 2, 125) (dual of [(162, 2), 161, 126]-NRT-code) | [i] | ||
| 13 | No linear OOA(4164, 162, F4, 2, 126) (dual of [(162, 2), 160, 127]-NRT-code) | [i] | ||
| 14 | No linear OOA(4165, 162, F4, 2, 127) (dual of [(162, 2), 159, 128]-NRT-code) | [i] | ||
| 15 | No linear OOA(4166, 162, F4, 2, 128) (dual of [(162, 2), 158, 129]-NRT-code) | [i] | ||
| 16 | No linear OOA(4167, 162, F4, 2, 129) (dual of [(162, 2), 157, 130]-NRT-code) | [i] | ||
| 17 | No linear OOA(4168, 162, F4, 2, 130) (dual of [(162, 2), 156, 131]-NRT-code) | [i] | ||
| 18 | No linear OOA(4169, 162, F4, 2, 131) (dual of [(162, 2), 155, 132]-NRT-code) | [i] | ||
| 19 | No linear OOA(4170, 162, F4, 2, 132) (dual of [(162, 2), 154, 133]-NRT-code) | [i] | ||
| 20 | No linear OOA(4171, 162, F4, 2, 133) (dual of [(162, 2), 153, 134]-NRT-code) | [i] | ||
| 21 | No linear OOA(4172, 162, F4, 2, 134) (dual of [(162, 2), 152, 135]-NRT-code) | [i] | ||
| 22 | No linear OOA(4173, 162, F4, 2, 135) (dual of [(162, 2), 151, 136]-NRT-code) | [i] | ||
| 23 | No linear OOA(4174, 162, F4, 2, 136) (dual of [(162, 2), 150, 137]-NRT-code) | [i] | ||
| 24 | No linear OOA(4175, 162, F4, 2, 137) (dual of [(162, 2), 149, 138]-NRT-code) | [i] | ||
| 25 | No linear OOA(4176, 162, F4, 2, 138) (dual of [(162, 2), 148, 139]-NRT-code) | [i] | ||
| 26 | No linear OOA(4177, 162, F4, 2, 139) (dual of [(162, 2), 147, 140]-NRT-code) | [i] | ||
| 27 | No linear OOA(4178, 162, F4, 2, 140) (dual of [(162, 2), 146, 141]-NRT-code) | [i] | ||
| 28 | No linear OOA(4179, 162, F4, 2, 141) (dual of [(162, 2), 145, 142]-NRT-code) | [i] | ||
| 29 | No linear OOA(4180, 162, F4, 2, 142) (dual of [(162, 2), 144, 143]-NRT-code) | [i] | ||
| 30 | No linear OOA(4181, 162, F4, 2, 143) (dual of [(162, 2), 143, 144]-NRT-code) | [i] | ||
| 31 | No linear OOA(4182, 162, F4, 2, 144) (dual of [(162, 2), 142, 145]-NRT-code) | [i] | ||
| 32 | No linear OOA(4183, 162, F4, 2, 145) (dual of [(162, 2), 141, 146]-NRT-code) | [i] | ||
| 33 | No linear OOA(4184, 162, F4, 2, 146) (dual of [(162, 2), 140, 147]-NRT-code) | [i] | ||
| 34 | No linear OOA(4185, 162, F4, 2, 147) (dual of [(162, 2), 139, 148]-NRT-code) | [i] | ||
| 35 | No linear OOA(4186, 162, F4, 2, 148) (dual of [(162, 2), 138, 149]-NRT-code) | [i] | ||
| 36 | No linear OOA(4187, 162, F4, 2, 149) (dual of [(162, 2), 137, 150]-NRT-code) | [i] | ||
| 37 | No linear OOA(4188, 162, F4, 2, 150) (dual of [(162, 2), 136, 151]-NRT-code) | [i] | ||
| 38 | No linear OOA(4189, 162, F4, 2, 151) (dual of [(162, 2), 135, 152]-NRT-code) | [i] | ||
| 39 | No linear OOA(4190, 162, F4, 2, 152) (dual of [(162, 2), 134, 153]-NRT-code) | [i] | ||
| 40 | No linear OOA(4191, 162, F4, 2, 153) (dual of [(162, 2), 133, 154]-NRT-code) | [i] | ||
| 41 | No linear OOA(4192, 162, F4, 2, 154) (dual of [(162, 2), 132, 155]-NRT-code) | [i] | ||
| 42 | No linear OOA(4193, 162, F4, 2, 155) (dual of [(162, 2), 131, 156]-NRT-code) | [i] | ||
| 43 | No linear OOA(4194, 162, F4, 2, 156) (dual of [(162, 2), 130, 157]-NRT-code) | [i] | ||
| 44 | No linear OOA(4195, 162, F4, 2, 157) (dual of [(162, 2), 129, 158]-NRT-code) | [i] | ||
| 45 | No linear OOA(4196, 162, F4, 2, 158) (dual of [(162, 2), 128, 159]-NRT-code) | [i] | ||
| 46 | No linear OOA(4197, 162, F4, 2, 159) (dual of [(162, 2), 127, 160]-NRT-code) | [i] | ||
| 47 | No linear OOA(4198, 162, F4, 2, 160) (dual of [(162, 2), 126, 161]-NRT-code) | [i] | ||
| 48 | No linear OOA(4199, 162, F4, 2, 161) (dual of [(162, 2), 125, 162]-NRT-code) | [i] | ||
| 49 | No linear OOA(4200, 162, F4, 2, 162) (dual of [(162, 2), 124, 163]-NRT-code) | [i] | ||
| 50 | No linear OOA(4201, 162, F4, 2, 163) (dual of [(162, 2), 123, 164]-NRT-code) | [i] | ||
| 51 | No linear OOA(4202, 162, F4, 2, 164) (dual of [(162, 2), 122, 165]-NRT-code) | [i] | ||
| 52 | No linear OOA(4203, 162, F4, 2, 165) (dual of [(162, 2), 121, 166]-NRT-code) | [i] | ||
| 53 | No linear OOA(4204, 162, F4, 2, 166) (dual of [(162, 2), 120, 167]-NRT-code) | [i] | ||
| 54 | No linear OOA(4205, 162, F4, 2, 167) (dual of [(162, 2), 119, 168]-NRT-code) | [i] | ||
| 55 | No linear OOA(4206, 162, F4, 2, 168) (dual of [(162, 2), 118, 169]-NRT-code) | [i] | ||
| 56 | No linear OOA(4207, 162, F4, 2, 169) (dual of [(162, 2), 117, 170]-NRT-code) | [i] | ||
| 57 | No linear OOA(4208, 162, F4, 2, 170) (dual of [(162, 2), 116, 171]-NRT-code) | [i] | ||
| 58 | No linear OOA(4209, 162, F4, 2, 171) (dual of [(162, 2), 115, 172]-NRT-code) | [i] | ||
| 59 | No linear OOA(4210, 162, F4, 2, 172) (dual of [(162, 2), 114, 173]-NRT-code) | [i] | ||
| 60 | No linear OOA(4211, 162, F4, 2, 173) (dual of [(162, 2), 113, 174]-NRT-code) | [i] | ||
| 61 | No linear OOA(4212, 162, F4, 2, 174) (dual of [(162, 2), 112, 175]-NRT-code) | [i] | ||
| 62 | No linear OOA(4213, 162, F4, 2, 175) (dual of [(162, 2), 111, 176]-NRT-code) | [i] | ||
| 63 | No linear OOA(4214, 162, F4, 2, 176) (dual of [(162, 2), 110, 177]-NRT-code) | [i] | ||
| 64 | No linear OOA(4215, 162, F4, 2, 177) (dual of [(162, 2), 109, 178]-NRT-code) | [i] | ||
| 65 | No linear OOA(4216, 162, F4, 2, 178) (dual of [(162, 2), 108, 179]-NRT-code) | [i] | ||
| 66 | No linear OOA(4217, 162, F4, 2, 179) (dual of [(162, 2), 107, 180]-NRT-code) | [i] | ||
| 67 | No linear OOA(4218, 162, F4, 2, 180) (dual of [(162, 2), 106, 181]-NRT-code) | [i] | ||
| 68 | No linear OOA(4219, 162, F4, 2, 181) (dual of [(162, 2), 105, 182]-NRT-code) | [i] | ||
| 69 | No linear OOA(4220, 162, F4, 2, 182) (dual of [(162, 2), 104, 183]-NRT-code) | [i] | ||
| 70 | No linear OOA(4221, 162, F4, 2, 183) (dual of [(162, 2), 103, 184]-NRT-code) | [i] | ||
| 71 | No linear OOA(4222, 162, F4, 2, 184) (dual of [(162, 2), 102, 185]-NRT-code) | [i] | ||
| 72 | No linear OOA(4223, 162, F4, 2, 185) (dual of [(162, 2), 101, 186]-NRT-code) | [i] | ||
| 73 | No linear OOA(4224, 162, F4, 2, 186) (dual of [(162, 2), 100, 187]-NRT-code) | [i] | ||
| 74 | No linear OOA(4225, 162, F4, 2, 187) (dual of [(162, 2), 99, 188]-NRT-code) | [i] | ||
| 75 | No linear OOA(4226, 162, F4, 2, 188) (dual of [(162, 2), 98, 189]-NRT-code) | [i] | ||
| 76 | No linear OOA(4227, 162, F4, 2, 189) (dual of [(162, 2), 97, 190]-NRT-code) | [i] | ||
| 77 | No linear OOA(4228, 162, F4, 2, 190) (dual of [(162, 2), 96, 191]-NRT-code) | [i] | ||
| 78 | No linear OOA(4229, 162, F4, 2, 191) (dual of [(162, 2), 95, 192]-NRT-code) | [i] | ||
| 79 | No linear OOA(4230, 162, F4, 2, 192) (dual of [(162, 2), 94, 193]-NRT-code) | [i] | ||
| 80 | No linear OOA(4231, 162, F4, 2, 193) (dual of [(162, 2), 93, 194]-NRT-code) | [i] | ||
| 81 | No linear OOA(4232, 162, F4, 2, 194) (dual of [(162, 2), 92, 195]-NRT-code) | [i] | ||
| 82 | No linear OOA(4233, 162, F4, 2, 195) (dual of [(162, 2), 91, 196]-NRT-code) | [i] | ||
| 83 | No linear OOA(4234, 162, F4, 2, 196) (dual of [(162, 2), 90, 197]-NRT-code) | [i] | ||
| 84 | No linear OOA(4235, 162, F4, 2, 197) (dual of [(162, 2), 89, 198]-NRT-code) | [i] | ||
| 85 | No linear OOA(4236, 162, F4, 2, 198) (dual of [(162, 2), 88, 199]-NRT-code) | [i] | ||
| 86 | No linear OOA(4237, 162, F4, 2, 199) (dual of [(162, 2), 87, 200]-NRT-code) | [i] | ||
| 87 | No linear OOA(4238, 162, F4, 2, 200) (dual of [(162, 2), 86, 201]-NRT-code) | [i] | ||
| 88 | No linear OOA(4239, 162, F4, 2, 201) (dual of [(162, 2), 85, 202]-NRT-code) | [i] | ||
| 89 | No linear OOA(4240, 162, F4, 2, 202) (dual of [(162, 2), 84, 203]-NRT-code) | [i] | ||
| 90 | No linear OOA(4241, 162, F4, 2, 203) (dual of [(162, 2), 83, 204]-NRT-code) | [i] | ||
| 91 | No linear OOA(4242, 162, F4, 2, 204) (dual of [(162, 2), 82, 205]-NRT-code) | [i] | ||
| 92 | No linear OOA(4243, 162, F4, 2, 205) (dual of [(162, 2), 81, 206]-NRT-code) | [i] | ||
| 93 | No linear OOA(4244, 162, F4, 2, 206) (dual of [(162, 2), 80, 207]-NRT-code) | [i] | ||
| 94 | No linear OOA(4245, 162, F4, 2, 207) (dual of [(162, 2), 79, 208]-NRT-code) | [i] | ||
| 95 | No linear OOA(4246, 162, F4, 2, 208) (dual of [(162, 2), 78, 209]-NRT-code) | [i] | ||
| 96 | No linear OOA(4247, 162, F4, 2, 209) (dual of [(162, 2), 77, 210]-NRT-code) | [i] | ||
| 97 | No linear OOA(4248, 162, F4, 2, 210) (dual of [(162, 2), 76, 211]-NRT-code) | [i] | ||
| 98 | No linear OOA(4249, 162, F4, 2, 211) (dual of [(162, 2), 75, 212]-NRT-code) | [i] | ||
| 99 | No linear OOA(4250, 162, F4, 2, 212) (dual of [(162, 2), 74, 213]-NRT-code) | [i] | ||
| 100 | No linear OOA(4251, 162, F4, 2, 213) (dual of [(162, 2), 73, 214]-NRT-code) | [i] | ||
| 101 | No linear OOA(4252, 162, F4, 2, 214) (dual of [(162, 2), 72, 215]-NRT-code) | [i] | ||
| 102 | No linear OOA(4253, 162, F4, 2, 215) (dual of [(162, 2), 71, 216]-NRT-code) | [i] | ||
| 103 | No linear OOA(4254, 162, F4, 2, 216) (dual of [(162, 2), 70, 217]-NRT-code) | [i] | ||
| 104 | No linear OOA(4255, 162, F4, 2, 217) (dual of [(162, 2), 69, 218]-NRT-code) | [i] | ||
| 105 | No linear OOA(4256, 162, F4, 2, 218) (dual of [(162, 2), 68, 219]-NRT-code) | [i] | ||
| 106 | No linear OOA(4257, 162, F4, 2, 219) (dual of [(162, 2), 67, 220]-NRT-code) | [i] | ||
| 107 | No linear OOA(4258, 162, F4, 2, 220) (dual of [(162, 2), 66, 221]-NRT-code) | [i] | ||
| 108 | No linear OOA(4259, 162, F4, 2, 221) (dual of [(162, 2), 65, 222]-NRT-code) | [i] | ||
| 109 | No linear OOA(4260, 162, F4, 2, 222) (dual of [(162, 2), 64, 223]-NRT-code) | [i] | ||
| 110 | No linear OOA(4154, 162, F4, 2, 116) (dual of [(162, 2), 170, 117]-NRT-code) | [i] | Depth Reduction | |
| 111 | No linear OOA(4154, 162, F4, 3, 116) (dual of [(162, 3), 332, 117]-NRT-code) | [i] | ||
| 112 | No digital (38, 154, 162)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 113 | No linear OA(4155, 170, F4, 116) (dual of [170, 15, 117]-code) | [i] | Construction Y1 (Bound) | |