Information on Result #547987
There is no linear OA(836, 41, F8, 32) (dual of [41, 5, 33]-code), because construction Y1 would yield
- OA(835, 37, S8, 32), but
- the (dual) Plotkin bound shows that M ≥ 1622 592768 292133 633915 780102 881280 / 33 > 835 [i]
- OA(85, 41, S8, 4), but
- discarding factors would yield OA(85, 37, S8, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 32894 > 85 [i]
- discarding factors would yield OA(85, 37, S8, 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(837, 42, F8, 33) (dual of [42, 5, 34]-code) | [i] | Truncation | |
| 2 | No linear OA(838, 43, F8, 34) (dual of [43, 5, 35]-code) | [i] | ||
| 3 | No linear OA(839, 44, F8, 35) (dual of [44, 5, 36]-code) | [i] | ||
| 4 | No linear OOA(837, 41, F8, 2, 33) (dual of [(41, 2), 45, 34]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(838, 41, F8, 2, 34) (dual of [(41, 2), 44, 35]-NRT-code) | [i] | ||
| 6 | No linear OOA(839, 41, F8, 2, 35) (dual of [(41, 2), 43, 36]-NRT-code) | [i] | ||
| 7 | No linear OOA(840, 41, F8, 2, 36) (dual of [(41, 2), 42, 37]-NRT-code) | [i] | ||
| 8 | No linear OOA(841, 41, F8, 2, 37) (dual of [(41, 2), 41, 38]-NRT-code) | [i] | ||
| 9 | No linear OOA(842, 41, F8, 2, 38) (dual of [(41, 2), 40, 39]-NRT-code) | [i] | ||
| 10 | No linear OOA(843, 41, F8, 2, 39) (dual of [(41, 2), 39, 40]-NRT-code) | [i] | ||
| 11 | No linear OOA(844, 41, F8, 2, 40) (dual of [(41, 2), 38, 41]-NRT-code) | [i] | ||
| 12 | No linear OOA(845, 41, F8, 2, 41) (dual of [(41, 2), 37, 42]-NRT-code) | [i] | ||
| 13 | No linear OOA(846, 41, F8, 2, 42) (dual of [(41, 2), 36, 43]-NRT-code) | [i] | ||
| 14 | No linear OOA(847, 41, F8, 2, 43) (dual of [(41, 2), 35, 44]-NRT-code) | [i] | ||
| 15 | No linear OOA(848, 41, F8, 2, 44) (dual of [(41, 2), 34, 45]-NRT-code) | [i] | ||
| 16 | No linear OOA(849, 41, F8, 2, 45) (dual of [(41, 2), 33, 46]-NRT-code) | [i] | ||
| 17 | No linear OOA(850, 41, F8, 2, 46) (dual of [(41, 2), 32, 47]-NRT-code) | [i] | ||
| 18 | No linear OOA(851, 41, F8, 2, 47) (dual of [(41, 2), 31, 48]-NRT-code) | [i] | ||
| 19 | No linear OOA(852, 41, F8, 2, 48) (dual of [(41, 2), 30, 49]-NRT-code) | [i] | ||
| 20 | No linear OOA(853, 41, F8, 2, 49) (dual of [(41, 2), 29, 50]-NRT-code) | [i] | ||
| 21 | No linear OOA(854, 41, F8, 2, 50) (dual of [(41, 2), 28, 51]-NRT-code) | [i] | ||
| 22 | No linear OOA(855, 41, F8, 2, 51) (dual of [(41, 2), 27, 52]-NRT-code) | [i] | ||
| 23 | No linear OOA(856, 41, F8, 2, 52) (dual of [(41, 2), 26, 53]-NRT-code) | [i] | ||
| 24 | No linear OOA(857, 41, F8, 2, 53) (dual of [(41, 2), 25, 54]-NRT-code) | [i] | ||
| 25 | No linear OOA(858, 41, F8, 2, 54) (dual of [(41, 2), 24, 55]-NRT-code) | [i] | ||
| 26 | No linear OOA(859, 41, F8, 2, 55) (dual of [(41, 2), 23, 56]-NRT-code) | [i] | ||
| 27 | No linear OOA(860, 41, F8, 2, 56) (dual of [(41, 2), 22, 57]-NRT-code) | [i] | ||
| 28 | No linear OOA(861, 41, F8, 2, 57) (dual of [(41, 2), 21, 58]-NRT-code) | [i] | ||
| 29 | No linear OOA(862, 41, F8, 2, 58) (dual of [(41, 2), 20, 59]-NRT-code) | [i] | ||
| 30 | No linear OOA(863, 41, F8, 2, 59) (dual of [(41, 2), 19, 60]-NRT-code) | [i] | ||
| 31 | No linear OOA(864, 41, F8, 2, 60) (dual of [(41, 2), 18, 61]-NRT-code) | [i] | ||
| 32 | No linear OOA(865, 41, F8, 2, 61) (dual of [(41, 2), 17, 62]-NRT-code) | [i] | ||
| 33 | No linear OOA(866, 41, F8, 2, 62) (dual of [(41, 2), 16, 63]-NRT-code) | [i] | ||
| 34 | No linear OOA(867, 41, F8, 2, 63) (dual of [(41, 2), 15, 64]-NRT-code) | [i] | ||
| 35 | No linear OOA(868, 41, F8, 2, 64) (dual of [(41, 2), 14, 65]-NRT-code) | [i] | ||
| 36 | No linear OOA(869, 41, F8, 2, 65) (dual of [(41, 2), 13, 66]-NRT-code) | [i] | ||
| 37 | No linear OOA(870, 41, F8, 2, 66) (dual of [(41, 2), 12, 67]-NRT-code) | [i] | ||
| 38 | No linear OOA(871, 41, F8, 2, 67) (dual of [(41, 2), 11, 68]-NRT-code) | [i] | ||
| 39 | No linear OOA(872, 41, F8, 2, 68) (dual of [(41, 2), 10, 69]-NRT-code) | [i] | ||
| 40 | No linear OOA(873, 41, F8, 2, 69) (dual of [(41, 2), 9, 70]-NRT-code) | [i] | ||
| 41 | No linear OOA(874, 41, F8, 2, 70) (dual of [(41, 2), 8, 71]-NRT-code) | [i] | ||
| 42 | No linear OOA(875, 41, F8, 2, 71) (dual of [(41, 2), 7, 72]-NRT-code) | [i] | ||
| 43 | No linear OOA(876, 41, F8, 2, 72) (dual of [(41, 2), 6, 73]-NRT-code) | [i] | ||
| 44 | No linear OOA(877, 41, F8, 2, 73) (dual of [(41, 2), 5, 74]-NRT-code) | [i] | ||
| 45 | No linear OOA(878, 41, F8, 3, 74) (dual of [(41, 3), 45, 75]-NRT-code) | [i] | ||
| 46 | No linear OOA(879, 41, F8, 3, 75) (dual of [(41, 3), 44, 76]-NRT-code) | [i] | ||
| 47 | No linear OOA(880, 41, F8, 3, 76) (dual of [(41, 3), 43, 77]-NRT-code) | [i] | ||
| 48 | No linear OOA(881, 41, F8, 3, 77) (dual of [(41, 3), 42, 78]-NRT-code) | [i] | ||
| 49 | No linear OOA(882, 41, F8, 3, 78) (dual of [(41, 3), 41, 79]-NRT-code) | [i] | ||
| 50 | No linear OOA(883, 41, F8, 3, 79) (dual of [(41, 3), 40, 80]-NRT-code) | [i] | ||
| 51 | No linear OOA(884, 41, F8, 3, 80) (dual of [(41, 3), 39, 81]-NRT-code) | [i] | ||
| 52 | No linear OOA(885, 41, F8, 3, 81) (dual of [(41, 3), 38, 82]-NRT-code) | [i] | ||
| 53 | No linear OOA(886, 41, F8, 3, 82) (dual of [(41, 3), 37, 83]-NRT-code) | [i] | ||
| 54 | No linear OOA(887, 41, F8, 3, 83) (dual of [(41, 3), 36, 84]-NRT-code) | [i] | ||
| 55 | No linear OOA(888, 41, F8, 3, 84) (dual of [(41, 3), 35, 85]-NRT-code) | [i] | ||
| 56 | No linear OOA(889, 41, F8, 3, 85) (dual of [(41, 3), 34, 86]-NRT-code) | [i] | ||
| 57 | No linear OOA(890, 41, F8, 3, 86) (dual of [(41, 3), 33, 87]-NRT-code) | [i] | ||
| 58 | No linear OOA(891, 41, F8, 3, 87) (dual of [(41, 3), 32, 88]-NRT-code) | [i] | ||
| 59 | No linear OOA(892, 41, F8, 3, 88) (dual of [(41, 3), 31, 89]-NRT-code) | [i] | ||
| 60 | No linear OOA(893, 41, F8, 3, 89) (dual of [(41, 3), 30, 90]-NRT-code) | [i] | ||
| 61 | No linear OOA(894, 41, F8, 3, 90) (dual of [(41, 3), 29, 91]-NRT-code) | [i] | ||
| 62 | No linear OOA(895, 41, F8, 3, 91) (dual of [(41, 3), 28, 92]-NRT-code) | [i] | ||
| 63 | No linear OOA(896, 41, F8, 3, 92) (dual of [(41, 3), 27, 93]-NRT-code) | [i] | ||
| 64 | No linear OOA(897, 41, F8, 3, 93) (dual of [(41, 3), 26, 94]-NRT-code) | [i] | ||
| 65 | No linear OOA(898, 41, F8, 3, 94) (dual of [(41, 3), 25, 95]-NRT-code) | [i] | ||
| 66 | No linear OOA(899, 41, F8, 3, 95) (dual of [(41, 3), 24, 96]-NRT-code) | [i] | ||
| 67 | No linear OOA(8100, 41, F8, 3, 96) (dual of [(41, 3), 23, 97]-NRT-code) | [i] | ||
| 68 | No linear OOA(8101, 41, F8, 3, 97) (dual of [(41, 3), 22, 98]-NRT-code) | [i] | ||
| 69 | No linear OOA(8102, 41, F8, 3, 98) (dual of [(41, 3), 21, 99]-NRT-code) | [i] | ||
| 70 | No linear OOA(8103, 41, F8, 3, 99) (dual of [(41, 3), 20, 100]-NRT-code) | [i] | ||
| 71 | No linear OOA(8104, 41, F8, 3, 100) (dual of [(41, 3), 19, 101]-NRT-code) | [i] | ||
| 72 | No linear OOA(8105, 41, F8, 3, 101) (dual of [(41, 3), 18, 102]-NRT-code) | [i] | ||
| 73 | No linear OOA(8106, 41, F8, 3, 102) (dual of [(41, 3), 17, 103]-NRT-code) | [i] | ||
| 74 | No linear OOA(8107, 41, F8, 3, 103) (dual of [(41, 3), 16, 104]-NRT-code) | [i] | ||
| 75 | No linear OOA(8108, 41, F8, 3, 104) (dual of [(41, 3), 15, 105]-NRT-code) | [i] | ||
| 76 | No linear OOA(8109, 41, F8, 3, 105) (dual of [(41, 3), 14, 106]-NRT-code) | [i] | ||
| 77 | No linear OOA(8110, 41, F8, 3, 106) (dual of [(41, 3), 13, 107]-NRT-code) | [i] | ||
| 78 | No linear OOA(8111, 41, F8, 3, 107) (dual of [(41, 3), 12, 108]-NRT-code) | [i] | ||
| 79 | No linear OOA(8112, 41, F8, 3, 108) (dual of [(41, 3), 11, 109]-NRT-code) | [i] | ||
| 80 | No linear OOA(8113, 41, F8, 3, 109) (dual of [(41, 3), 10, 110]-NRT-code) | [i] | ||
| 81 | No linear OOA(8114, 41, F8, 3, 110) (dual of [(41, 3), 9, 111]-NRT-code) | [i] | ||
| 82 | No linear OOA(8115, 41, F8, 3, 111) (dual of [(41, 3), 8, 112]-NRT-code) | [i] | ||
| 83 | No linear OOA(8116, 41, F8, 3, 112) (dual of [(41, 3), 7, 113]-NRT-code) | [i] | ||
| 84 | No linear OOA(8117, 41, F8, 3, 113) (dual of [(41, 3), 6, 114]-NRT-code) | [i] | ||
| 85 | No linear OOA(8118, 41, F8, 3, 114) (dual of [(41, 3), 5, 115]-NRT-code) | [i] | ||
| 86 | No linear OOA(836, 41, F8, 2, 32) (dual of [(41, 2), 46, 33]-NRT-code) | [i] | Depth Reduction | |
| 87 | No linear OOA(836, 41, F8, 3, 32) (dual of [(41, 3), 87, 33]-NRT-code) | [i] | ||
| 88 | No digital (4, 36, 41)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |