Information on Result #547911
There is no linear OA(4207, 215, F4, 156) (dual of [215, 8, 157]-code), because construction Y1 would yield
- linear OA(4206, 211, F4, 156) (dual of [211, 5, 157]-code), but
- residual code [i] would yield linear OA(450, 54, F4, 39) (dual of [54, 4, 40]-code), but
- 3 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(450, 54, F4, 39) (dual of [54, 4, 40]-code), but
- OA(48, 215, 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(4208, 216, F4, 157) (dual of [216, 8, 158]-code) | [i] | Truncation | |
| 2 | No linear OA(4209, 217, F4, 158) (dual of [217, 8, 159]-code) | [i] | ||
| 3 | No linear OA(4210, 218, F4, 159) (dual of [218, 8, 160]-code) | [i] | ||
| 4 | No linear OOA(4208, 215, F4, 2, 157) (dual of [(215, 2), 222, 158]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4209, 215, F4, 2, 158) (dual of [(215, 2), 221, 159]-NRT-code) | [i] | ||
| 6 | No linear OOA(4210, 215, F4, 2, 159) (dual of [(215, 2), 220, 160]-NRT-code) | [i] | ||
| 7 | No linear OOA(4212, 215, F4, 2, 161) (dual of [(215, 2), 218, 162]-NRT-code) | [i] | ||
| 8 | No linear OOA(4213, 215, F4, 2, 162) (dual of [(215, 2), 217, 163]-NRT-code) | [i] | ||
| 9 | No linear OOA(4214, 215, F4, 2, 163) (dual of [(215, 2), 216, 164]-NRT-code) | [i] | ||
| 10 | No linear OOA(4215, 215, F4, 2, 164) (dual of [(215, 2), 215, 165]-NRT-code) | [i] | ||
| 11 | No linear OOA(4216, 215, F4, 2, 165) (dual of [(215, 2), 214, 166]-NRT-code) | [i] | ||
| 12 | No linear OOA(4217, 215, F4, 2, 166) (dual of [(215, 2), 213, 167]-NRT-code) | [i] | ||
| 13 | No linear OOA(4218, 215, F4, 2, 167) (dual of [(215, 2), 212, 168]-NRT-code) | [i] | ||
| 14 | No linear OOA(4219, 215, F4, 2, 168) (dual of [(215, 2), 211, 169]-NRT-code) | [i] | ||
| 15 | No linear OOA(4220, 215, F4, 2, 169) (dual of [(215, 2), 210, 170]-NRT-code) | [i] | ||
| 16 | No linear OOA(4221, 215, F4, 2, 170) (dual of [(215, 2), 209, 171]-NRT-code) | [i] | ||
| 17 | No linear OOA(4222, 215, F4, 2, 171) (dual of [(215, 2), 208, 172]-NRT-code) | [i] | ||
| 18 | No linear OOA(4223, 215, F4, 2, 172) (dual of [(215, 2), 207, 173]-NRT-code) | [i] | ||
| 19 | No linear OOA(4224, 215, F4, 2, 173) (dual of [(215, 2), 206, 174]-NRT-code) | [i] | ||
| 20 | No linear OOA(4225, 215, F4, 2, 174) (dual of [(215, 2), 205, 175]-NRT-code) | [i] | ||
| 21 | No linear OOA(4226, 215, F4, 2, 175) (dual of [(215, 2), 204, 176]-NRT-code) | [i] | ||
| 22 | No linear OOA(4227, 215, F4, 2, 176) (dual of [(215, 2), 203, 177]-NRT-code) | [i] | ||
| 23 | No linear OOA(4228, 215, F4, 2, 177) (dual of [(215, 2), 202, 178]-NRT-code) | [i] | ||
| 24 | No linear OOA(4229, 215, F4, 2, 178) (dual of [(215, 2), 201, 179]-NRT-code) | [i] | ||
| 25 | No linear OOA(4230, 215, F4, 2, 179) (dual of [(215, 2), 200, 180]-NRT-code) | [i] | ||
| 26 | No linear OOA(4231, 215, F4, 2, 180) (dual of [(215, 2), 199, 181]-NRT-code) | [i] | ||
| 27 | No linear OOA(4232, 215, F4, 2, 181) (dual of [(215, 2), 198, 182]-NRT-code) | [i] | ||
| 28 | No linear OOA(4233, 215, F4, 2, 182) (dual of [(215, 2), 197, 183]-NRT-code) | [i] | ||
| 29 | No linear OOA(4234, 215, F4, 2, 183) (dual of [(215, 2), 196, 184]-NRT-code) | [i] | ||
| 30 | No linear OOA(4235, 215, F4, 2, 184) (dual of [(215, 2), 195, 185]-NRT-code) | [i] | ||
| 31 | No linear OOA(4236, 215, F4, 2, 185) (dual of [(215, 2), 194, 186]-NRT-code) | [i] | ||
| 32 | No linear OOA(4237, 215, F4, 2, 186) (dual of [(215, 2), 193, 187]-NRT-code) | [i] | ||
| 33 | No linear OOA(4238, 215, F4, 2, 187) (dual of [(215, 2), 192, 188]-NRT-code) | [i] | ||
| 34 | No linear OOA(4239, 215, F4, 2, 188) (dual of [(215, 2), 191, 189]-NRT-code) | [i] | ||
| 35 | No linear OOA(4240, 215, F4, 2, 189) (dual of [(215, 2), 190, 190]-NRT-code) | [i] | ||
| 36 | No linear OOA(4241, 215, F4, 2, 190) (dual of [(215, 2), 189, 191]-NRT-code) | [i] | ||
| 37 | No linear OOA(4242, 215, F4, 2, 191) (dual of [(215, 2), 188, 192]-NRT-code) | [i] | ||
| 38 | No linear OOA(4243, 215, F4, 2, 192) (dual of [(215, 2), 187, 193]-NRT-code) | [i] | ||
| 39 | No linear OOA(4244, 215, F4, 2, 193) (dual of [(215, 2), 186, 194]-NRT-code) | [i] | ||
| 40 | No linear OOA(4245, 215, F4, 2, 194) (dual of [(215, 2), 185, 195]-NRT-code) | [i] | ||
| 41 | No linear OOA(4246, 215, F4, 2, 195) (dual of [(215, 2), 184, 196]-NRT-code) | [i] | ||
| 42 | No linear OOA(4247, 215, F4, 2, 196) (dual of [(215, 2), 183, 197]-NRT-code) | [i] | ||
| 43 | No linear OOA(4248, 215, F4, 2, 197) (dual of [(215, 2), 182, 198]-NRT-code) | [i] | ||
| 44 | No linear OOA(4249, 215, F4, 2, 198) (dual of [(215, 2), 181, 199]-NRT-code) | [i] | ||
| 45 | No linear OOA(4250, 215, F4, 2, 199) (dual of [(215, 2), 180, 200]-NRT-code) | [i] | ||
| 46 | No linear OOA(4251, 215, F4, 2, 200) (dual of [(215, 2), 179, 201]-NRT-code) | [i] | ||
| 47 | No linear OOA(4252, 215, F4, 2, 201) (dual of [(215, 2), 178, 202]-NRT-code) | [i] | ||
| 48 | No linear OOA(4253, 215, F4, 2, 202) (dual of [(215, 2), 177, 203]-NRT-code) | [i] | ||
| 49 | No linear OOA(4254, 215, F4, 2, 203) (dual of [(215, 2), 176, 204]-NRT-code) | [i] | ||
| 50 | No linear OOA(4255, 215, F4, 2, 204) (dual of [(215, 2), 175, 205]-NRT-code) | [i] | ||
| 51 | No linear OOA(4256, 215, F4, 2, 205) (dual of [(215, 2), 174, 206]-NRT-code) | [i] | ||
| 52 | No linear OOA(4257, 215, F4, 2, 206) (dual of [(215, 2), 173, 207]-NRT-code) | [i] | ||
| 53 | No linear OOA(4258, 215, F4, 2, 207) (dual of [(215, 2), 172, 208]-NRT-code) | [i] | ||
| 54 | No linear OOA(4259, 215, F4, 2, 208) (dual of [(215, 2), 171, 209]-NRT-code) | [i] | ||
| 55 | No linear OOA(4260, 215, F4, 2, 209) (dual of [(215, 2), 170, 210]-NRT-code) | [i] | ||
| 56 | No linear OOA(4207, 215, F4, 2, 156) (dual of [(215, 2), 223, 157]-NRT-code) | [i] | Depth Reduction | |
| 57 | No linear OOA(4207, 215, F4, 3, 156) (dual of [(215, 3), 438, 157]-NRT-code) | [i] | ||
| 58 | No digital (51, 207, 215)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |