Information on Result #547982
There is no linear OA(827, 34, F8, 24) (dual of [34, 7, 25]-code), because construction Y1 would yield
- OA(826, 28, S8, 24), but
- the (dual) Plotkin bound shows that M ≥ 9 671406 556917 033397 649408 / 25 > 826 [i]
- OA(87, 34, S8, 6), but
- discarding factors would yield OA(87, 32, S8, 6), but
- the linear programming bound shows that M ≥ 3784 900608 / 1729 > 87 [i]
- discarding factors would yield OA(87, 32, S8, 6), 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(828, 35, F8, 25) (dual of [35, 7, 26]-code) | [i] | Truncation | |
| 2 | No linear OA(829, 36, F8, 26) (dual of [36, 7, 27]-code) | [i] | ||
| 3 | No linear OOA(828, 34, F8, 2, 25) (dual of [(34, 2), 40, 26]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(829, 34, F8, 2, 26) (dual of [(34, 2), 39, 27]-NRT-code) | [i] | ||
| 5 | No linear OOA(830, 34, F8, 2, 27) (dual of [(34, 2), 38, 28]-NRT-code) | [i] | ||
| 6 | No linear OOA(832, 34, F8, 2, 29) (dual of [(34, 2), 36, 30]-NRT-code) | [i] | ||
| 7 | No linear OOA(833, 34, F8, 2, 30) (dual of [(34, 2), 35, 31]-NRT-code) | [i] | ||
| 8 | No linear OOA(834, 34, F8, 2, 31) (dual of [(34, 2), 34, 32]-NRT-code) | [i] | ||
| 9 | No linear OOA(835, 34, F8, 2, 32) (dual of [(34, 2), 33, 33]-NRT-code) | [i] | ||
| 10 | No linear OOA(836, 34, F8, 2, 33) (dual of [(34, 2), 32, 34]-NRT-code) | [i] | ||
| 11 | No linear OOA(837, 34, F8, 2, 34) (dual of [(34, 2), 31, 35]-NRT-code) | [i] | ||
| 12 | No linear OOA(838, 34, F8, 2, 35) (dual of [(34, 2), 30, 36]-NRT-code) | [i] | ||
| 13 | No linear OOA(839, 34, F8, 2, 36) (dual of [(34, 2), 29, 37]-NRT-code) | [i] | ||
| 14 | No linear OOA(840, 34, F8, 2, 37) (dual of [(34, 2), 28, 38]-NRT-code) | [i] | ||
| 15 | No linear OOA(841, 34, F8, 2, 38) (dual of [(34, 2), 27, 39]-NRT-code) | [i] | ||
| 16 | No linear OOA(842, 34, F8, 2, 39) (dual of [(34, 2), 26, 40]-NRT-code) | [i] | ||
| 17 | No linear OOA(843, 34, F8, 2, 40) (dual of [(34, 2), 25, 41]-NRT-code) | [i] | ||
| 18 | No linear OOA(844, 34, F8, 2, 41) (dual of [(34, 2), 24, 42]-NRT-code) | [i] | ||
| 19 | No linear OOA(845, 34, F8, 2, 42) (dual of [(34, 2), 23, 43]-NRT-code) | [i] | ||
| 20 | No linear OOA(846, 34, F8, 2, 43) (dual of [(34, 2), 22, 44]-NRT-code) | [i] | ||
| 21 | No linear OOA(847, 34, F8, 2, 44) (dual of [(34, 2), 21, 45]-NRT-code) | [i] | ||
| 22 | No linear OOA(848, 34, F8, 2, 45) (dual of [(34, 2), 20, 46]-NRT-code) | [i] | ||
| 23 | No linear OOA(849, 34, F8, 2, 46) (dual of [(34, 2), 19, 47]-NRT-code) | [i] | ||
| 24 | No linear OOA(850, 34, F8, 2, 47) (dual of [(34, 2), 18, 48]-NRT-code) | [i] | ||
| 25 | No linear OOA(851, 34, F8, 2, 48) (dual of [(34, 2), 17, 49]-NRT-code) | [i] | ||
| 26 | No linear OOA(852, 34, F8, 2, 49) (dual of [(34, 2), 16, 50]-NRT-code) | [i] | ||
| 27 | No linear OOA(853, 34, F8, 2, 50) (dual of [(34, 2), 15, 51]-NRT-code) | [i] | ||
| 28 | No linear OOA(854, 34, F8, 2, 51) (dual of [(34, 2), 14, 52]-NRT-code) | [i] | ||
| 29 | No linear OOA(855, 34, F8, 2, 52) (dual of [(34, 2), 13, 53]-NRT-code) | [i] | ||
| 30 | No linear OOA(856, 34, F8, 2, 53) (dual of [(34, 2), 12, 54]-NRT-code) | [i] | ||
| 31 | No linear OOA(857, 34, F8, 2, 54) (dual of [(34, 2), 11, 55]-NRT-code) | [i] | ||
| 32 | No linear OOA(858, 34, F8, 2, 55) (dual of [(34, 2), 10, 56]-NRT-code) | [i] | ||
| 33 | No linear OOA(859, 34, F8, 2, 56) (dual of [(34, 2), 9, 57]-NRT-code) | [i] | ||
| 34 | No linear OOA(860, 34, F8, 2, 57) (dual of [(34, 2), 8, 58]-NRT-code) | [i] | ||
| 35 | No linear OOA(861, 34, F8, 2, 58) (dual of [(34, 2), 7, 59]-NRT-code) | [i] | ||
| 36 | No linear OOA(866, 34, F8, 3, 63) (dual of [(34, 3), 36, 64]-NRT-code) | [i] | ||
| 37 | No linear OOA(867, 34, F8, 3, 64) (dual of [(34, 3), 35, 65]-NRT-code) | [i] | ||
| 38 | No linear OOA(868, 34, F8, 3, 65) (dual of [(34, 3), 34, 66]-NRT-code) | [i] | ||
| 39 | No linear OOA(869, 34, F8, 3, 66) (dual of [(34, 3), 33, 67]-NRT-code) | [i] | ||
| 40 | No linear OOA(870, 34, F8, 3, 67) (dual of [(34, 3), 32, 68]-NRT-code) | [i] | ||
| 41 | No linear OOA(871, 34, F8, 3, 68) (dual of [(34, 3), 31, 69]-NRT-code) | [i] | ||
| 42 | No linear OOA(872, 34, F8, 3, 69) (dual of [(34, 3), 30, 70]-NRT-code) | [i] | ||
| 43 | No linear OOA(873, 34, F8, 3, 70) (dual of [(34, 3), 29, 71]-NRT-code) | [i] | ||
| 44 | No linear OOA(874, 34, F8, 3, 71) (dual of [(34, 3), 28, 72]-NRT-code) | [i] | ||
| 45 | No linear OOA(875, 34, F8, 3, 72) (dual of [(34, 3), 27, 73]-NRT-code) | [i] | ||
| 46 | No linear OOA(876, 34, F8, 3, 73) (dual of [(34, 3), 26, 74]-NRT-code) | [i] | ||
| 47 | No linear OOA(877, 34, F8, 3, 74) (dual of [(34, 3), 25, 75]-NRT-code) | [i] | ||
| 48 | No linear OOA(878, 34, F8, 3, 75) (dual of [(34, 3), 24, 76]-NRT-code) | [i] | ||
| 49 | No linear OOA(879, 34, F8, 3, 76) (dual of [(34, 3), 23, 77]-NRT-code) | [i] | ||
| 50 | No linear OOA(880, 34, F8, 3, 77) (dual of [(34, 3), 22, 78]-NRT-code) | [i] | ||
| 51 | No linear OOA(881, 34, F8, 3, 78) (dual of [(34, 3), 21, 79]-NRT-code) | [i] | ||
| 52 | No linear OOA(882, 34, F8, 3, 79) (dual of [(34, 3), 20, 80]-NRT-code) | [i] | ||
| 53 | No linear OOA(883, 34, F8, 3, 80) (dual of [(34, 3), 19, 81]-NRT-code) | [i] | ||
| 54 | No linear OOA(884, 34, F8, 3, 81) (dual of [(34, 3), 18, 82]-NRT-code) | [i] | ||
| 55 | No linear OOA(885, 34, F8, 3, 82) (dual of [(34, 3), 17, 83]-NRT-code) | [i] | ||
| 56 | No linear OOA(886, 34, F8, 3, 83) (dual of [(34, 3), 16, 84]-NRT-code) | [i] | ||
| 57 | No linear OOA(887, 34, F8, 3, 84) (dual of [(34, 3), 15, 85]-NRT-code) | [i] | ||
| 58 | No linear OOA(888, 34, F8, 3, 85) (dual of [(34, 3), 14, 86]-NRT-code) | [i] | ||
| 59 | No linear OOA(889, 34, F8, 3, 86) (dual of [(34, 3), 13, 87]-NRT-code) | [i] | ||
| 60 | No linear OOA(890, 34, F8, 3, 87) (dual of [(34, 3), 12, 88]-NRT-code) | [i] | ||
| 61 | No linear OOA(891, 34, F8, 3, 88) (dual of [(34, 3), 11, 89]-NRT-code) | [i] | ||
| 62 | No linear OOA(892, 34, F8, 3, 89) (dual of [(34, 3), 10, 90]-NRT-code) | [i] | ||
| 63 | No linear OOA(893, 34, F8, 3, 90) (dual of [(34, 3), 9, 91]-NRT-code) | [i] | ||
| 64 | No linear OOA(894, 34, F8, 3, 91) (dual of [(34, 3), 8, 92]-NRT-code) | [i] | ||
| 65 | No linear OOA(895, 34, F8, 3, 92) (dual of [(34, 3), 7, 93]-NRT-code) | [i] | ||
| 66 | No linear OOA(827, 34, F8, 2, 24) (dual of [(34, 2), 41, 25]-NRT-code) | [i] | Depth Reduction | |
| 67 | No linear OOA(827, 34, F8, 3, 24) (dual of [(34, 3), 75, 25]-NRT-code) | [i] | ||
| 68 | No digital (3, 27, 34)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |
| 69 | No linear OA(828, 77, F8, 24) (dual of [77, 49, 25]-code) | [i] | Construction Y1 (Bound) | |
| 70 | No linear OA(828, 76, F8, 24) (dual of [76, 48, 25]-code) | [i] | ||