Information on Result #547906
There is no linear OA(4197, 205, F4, 148) (dual of [205, 8, 149]-code), because construction Y1 would yield
- linear OA(4196, 201, F4, 148) (dual of [201, 5, 149]-code), but
- residual code [i] would yield linear OA(448, 52, F4, 37) (dual of [52, 4, 38]-code), but
- 1 times truncation [i] would yield linear OA(447, 51, F4, 36) (dual of [51, 4, 37]-code), but
- residual code [i] would yield linear OA(448, 52, F4, 37) (dual of [52, 4, 38]-code), but
- OA(48, 205, 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(4198, 206, F4, 149) (dual of [206, 8, 150]-code) | [i] | Truncation | |
| 2 | No linear OA(4199, 207, F4, 150) (dual of [207, 8, 151]-code) | [i] | ||
| 3 | No linear OA(4200, 208, F4, 151) (dual of [208, 8, 152]-code) | [i] | ||
| 4 | No linear OOA(4198, 205, F4, 2, 149) (dual of [(205, 2), 212, 150]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4199, 205, F4, 2, 150) (dual of [(205, 2), 211, 151]-NRT-code) | [i] | ||
| 6 | No linear OOA(4200, 205, F4, 2, 151) (dual of [(205, 2), 210, 152]-NRT-code) | [i] | ||
| 7 | No linear OOA(4201, 205, F4, 2, 152) (dual of [(205, 2), 209, 153]-NRT-code) | [i] | ||
| 8 | No linear OOA(4202, 205, F4, 2, 153) (dual of [(205, 2), 208, 154]-NRT-code) | [i] | ||
| 9 | No linear OOA(4203, 205, F4, 2, 154) (dual of [(205, 2), 207, 155]-NRT-code) | [i] | ||
| 10 | No linear OOA(4204, 205, F4, 2, 155) (dual of [(205, 2), 206, 156]-NRT-code) | [i] | ||
| 11 | No linear OOA(4205, 205, F4, 2, 156) (dual of [(205, 2), 205, 157]-NRT-code) | [i] | ||
| 12 | No linear OOA(4206, 205, F4, 2, 157) (dual of [(205, 2), 204, 158]-NRT-code) | [i] | ||
| 13 | No linear OOA(4207, 205, F4, 2, 158) (dual of [(205, 2), 203, 159]-NRT-code) | [i] | ||
| 14 | No linear OOA(4208, 205, F4, 2, 159) (dual of [(205, 2), 202, 160]-NRT-code) | [i] | ||
| 15 | No linear OOA(4209, 205, F4, 2, 160) (dual of [(205, 2), 201, 161]-NRT-code) | [i] | ||
| 16 | No linear OOA(4210, 205, F4, 2, 161) (dual of [(205, 2), 200, 162]-NRT-code) | [i] | ||
| 17 | No linear OOA(4211, 205, F4, 2, 162) (dual of [(205, 2), 199, 163]-NRT-code) | [i] | ||
| 18 | No linear OOA(4212, 205, F4, 2, 163) (dual of [(205, 2), 198, 164]-NRT-code) | [i] | ||
| 19 | No linear OOA(4213, 205, F4, 2, 164) (dual of [(205, 2), 197, 165]-NRT-code) | [i] | ||
| 20 | No linear OOA(4214, 205, F4, 2, 165) (dual of [(205, 2), 196, 166]-NRT-code) | [i] | ||
| 21 | No linear OOA(4215, 205, F4, 2, 166) (dual of [(205, 2), 195, 167]-NRT-code) | [i] | ||
| 22 | No linear OOA(4216, 205, F4, 2, 167) (dual of [(205, 2), 194, 168]-NRT-code) | [i] | ||
| 23 | No linear OOA(4217, 205, F4, 2, 168) (dual of [(205, 2), 193, 169]-NRT-code) | [i] | ||
| 24 | No linear OOA(4218, 205, F4, 2, 169) (dual of [(205, 2), 192, 170]-NRT-code) | [i] | ||
| 25 | No linear OOA(4219, 205, F4, 2, 170) (dual of [(205, 2), 191, 171]-NRT-code) | [i] | ||
| 26 | No linear OOA(4220, 205, F4, 2, 171) (dual of [(205, 2), 190, 172]-NRT-code) | [i] | ||
| 27 | No linear OOA(4221, 205, F4, 2, 172) (dual of [(205, 2), 189, 173]-NRT-code) | [i] | ||
| 28 | No linear OOA(4222, 205, F4, 2, 173) (dual of [(205, 2), 188, 174]-NRT-code) | [i] | ||
| 29 | No linear OOA(4223, 205, F4, 2, 174) (dual of [(205, 2), 187, 175]-NRT-code) | [i] | ||
| 30 | No linear OOA(4224, 205, F4, 2, 175) (dual of [(205, 2), 186, 176]-NRT-code) | [i] | ||
| 31 | No linear OOA(4225, 205, F4, 2, 176) (dual of [(205, 2), 185, 177]-NRT-code) | [i] | ||
| 32 | No linear OOA(4226, 205, F4, 2, 177) (dual of [(205, 2), 184, 178]-NRT-code) | [i] | ||
| 33 | No linear OOA(4227, 205, F4, 2, 178) (dual of [(205, 2), 183, 179]-NRT-code) | [i] | ||
| 34 | No linear OOA(4228, 205, F4, 2, 179) (dual of [(205, 2), 182, 180]-NRT-code) | [i] | ||
| 35 | No linear OOA(4229, 205, F4, 2, 180) (dual of [(205, 2), 181, 181]-NRT-code) | [i] | ||
| 36 | No linear OOA(4230, 205, F4, 2, 181) (dual of [(205, 2), 180, 182]-NRT-code) | [i] | ||
| 37 | No linear OOA(4231, 205, F4, 2, 182) (dual of [(205, 2), 179, 183]-NRT-code) | [i] | ||
| 38 | No linear OOA(4232, 205, F4, 2, 183) (dual of [(205, 2), 178, 184]-NRT-code) | [i] | ||
| 39 | No linear OOA(4233, 205, F4, 2, 184) (dual of [(205, 2), 177, 185]-NRT-code) | [i] | ||
| 40 | No linear OOA(4234, 205, F4, 2, 185) (dual of [(205, 2), 176, 186]-NRT-code) | [i] | ||
| 41 | No linear OOA(4235, 205, F4, 2, 186) (dual of [(205, 2), 175, 187]-NRT-code) | [i] | ||
| 42 | No linear OOA(4236, 205, F4, 2, 187) (dual of [(205, 2), 174, 188]-NRT-code) | [i] | ||
| 43 | No linear OOA(4237, 205, F4, 2, 188) (dual of [(205, 2), 173, 189]-NRT-code) | [i] | ||
| 44 | No linear OOA(4238, 205, F4, 2, 189) (dual of [(205, 2), 172, 190]-NRT-code) | [i] | ||
| 45 | No linear OOA(4239, 205, F4, 2, 190) (dual of [(205, 2), 171, 191]-NRT-code) | [i] | ||
| 46 | No linear OOA(4240, 205, F4, 2, 191) (dual of [(205, 2), 170, 192]-NRT-code) | [i] | ||
| 47 | No linear OOA(4241, 205, F4, 2, 192) (dual of [(205, 2), 169, 193]-NRT-code) | [i] | ||
| 48 | No linear OOA(4242, 205, F4, 2, 193) (dual of [(205, 2), 168, 194]-NRT-code) | [i] | ||
| 49 | No linear OOA(4243, 205, F4, 2, 194) (dual of [(205, 2), 167, 195]-NRT-code) | [i] | ||
| 50 | No linear OOA(4244, 205, F4, 2, 195) (dual of [(205, 2), 166, 196]-NRT-code) | [i] | ||
| 51 | No linear OOA(4245, 205, F4, 2, 196) (dual of [(205, 2), 165, 197]-NRT-code) | [i] | ||
| 52 | No linear OOA(4246, 205, F4, 2, 197) (dual of [(205, 2), 164, 198]-NRT-code) | [i] | ||
| 53 | No linear OOA(4247, 205, F4, 2, 198) (dual of [(205, 2), 163, 199]-NRT-code) | [i] | ||
| 54 | No linear OOA(4248, 205, F4, 2, 199) (dual of [(205, 2), 162, 200]-NRT-code) | [i] | ||
| 55 | No linear OOA(4249, 205, F4, 2, 200) (dual of [(205, 2), 161, 201]-NRT-code) | [i] | ||
| 56 | No linear OOA(4250, 205, F4, 2, 201) (dual of [(205, 2), 160, 202]-NRT-code) | [i] | ||
| 57 | No linear OOA(4251, 205, F4, 2, 202) (dual of [(205, 2), 159, 203]-NRT-code) | [i] | ||
| 58 | No linear OOA(4252, 205, F4, 2, 203) (dual of [(205, 2), 158, 204]-NRT-code) | [i] | ||
| 59 | No linear OOA(4253, 205, F4, 2, 204) (dual of [(205, 2), 157, 205]-NRT-code) | [i] | ||
| 60 | No linear OOA(4254, 205, F4, 2, 205) (dual of [(205, 2), 156, 206]-NRT-code) | [i] | ||
| 61 | No linear OOA(4255, 205, F4, 2, 206) (dual of [(205, 2), 155, 207]-NRT-code) | [i] | ||
| 62 | No linear OOA(4256, 205, F4, 2, 207) (dual of [(205, 2), 154, 208]-NRT-code) | [i] | ||
| 63 | No linear OOA(4257, 205, F4, 2, 208) (dual of [(205, 2), 153, 209]-NRT-code) | [i] | ||
| 64 | No linear OOA(4258, 205, F4, 2, 209) (dual of [(205, 2), 152, 210]-NRT-code) | [i] | ||
| 65 | No linear OOA(4259, 205, F4, 2, 210) (dual of [(205, 2), 151, 211]-NRT-code) | [i] | ||
| 66 | No linear OOA(4260, 205, F4, 2, 211) (dual of [(205, 2), 150, 212]-NRT-code) | [i] | ||
| 67 | No linear OOA(4197, 205, F4, 2, 148) (dual of [(205, 2), 213, 149]-NRT-code) | [i] | Depth Reduction | |
| 68 | No linear OOA(4197, 205, F4, 3, 148) (dual of [(205, 3), 418, 149]-NRT-code) | [i] | ||
| 69 | No digital (49, 197, 205)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 70 | No linear OA(4198, 213, F4, 148) (dual of [213, 15, 149]-code) | [i] | Construction Y1 (Bound) | |