Information on Result #548022
There is no linear OA(950, 55, F9, 45) (dual of [55, 5, 46]-code), because construction Y1 would yield
- OA(949, 51, S9, 45), but
- the (dual) Plotkin bound shows that M ≥ 1 546132 562196 033993 109383 389296 863818 106322 566003 / 23 > 949 [i]
- OA(95, 55, S9, 4), but
- discarding factors would yield OA(95, 44, S9, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 60897 > 95 [i]
- discarding factors would yield OA(95, 44, S9, 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(951, 56, F9, 46) (dual of [56, 5, 47]-code) | [i] | Truncation | |
| 2 | No linear OA(952, 57, F9, 47) (dual of [57, 5, 48]-code) | [i] | ||
| 3 | No linear OOA(951, 55, F9, 2, 46) (dual of [(55, 2), 59, 47]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(952, 55, F9, 2, 47) (dual of [(55, 2), 58, 48]-NRT-code) | [i] | ||
| 5 | No linear OOA(953, 55, F9, 2, 48) (dual of [(55, 2), 57, 49]-NRT-code) | [i] | ||
| 6 | No linear OOA(954, 55, F9, 2, 49) (dual of [(55, 2), 56, 50]-NRT-code) | [i] | ||
| 7 | No linear OOA(955, 55, F9, 2, 50) (dual of [(55, 2), 55, 51]-NRT-code) | [i] | ||
| 8 | No linear OOA(956, 55, F9, 2, 51) (dual of [(55, 2), 54, 52]-NRT-code) | [i] | ||
| 9 | No linear OOA(957, 55, F9, 2, 52) (dual of [(55, 2), 53, 53]-NRT-code) | [i] | ||
| 10 | No linear OOA(958, 55, F9, 2, 53) (dual of [(55, 2), 52, 54]-NRT-code) | [i] | ||
| 11 | No linear OOA(959, 55, F9, 2, 54) (dual of [(55, 2), 51, 55]-NRT-code) | [i] | ||
| 12 | No linear OOA(960, 55, F9, 2, 55) (dual of [(55, 2), 50, 56]-NRT-code) | [i] | ||
| 13 | No linear OOA(961, 55, F9, 2, 56) (dual of [(55, 2), 49, 57]-NRT-code) | [i] | ||
| 14 | No linear OOA(962, 55, F9, 2, 57) (dual of [(55, 2), 48, 58]-NRT-code) | [i] | ||
| 15 | No linear OOA(963, 55, F9, 2, 58) (dual of [(55, 2), 47, 59]-NRT-code) | [i] | ||
| 16 | No linear OOA(964, 55, F9, 2, 59) (dual of [(55, 2), 46, 60]-NRT-code) | [i] | ||
| 17 | No linear OOA(965, 55, F9, 2, 60) (dual of [(55, 2), 45, 61]-NRT-code) | [i] | ||
| 18 | No linear OOA(966, 55, F9, 2, 61) (dual of [(55, 2), 44, 62]-NRT-code) | [i] | ||
| 19 | No linear OOA(967, 55, F9, 2, 62) (dual of [(55, 2), 43, 63]-NRT-code) | [i] | ||
| 20 | No linear OOA(968, 55, F9, 2, 63) (dual of [(55, 2), 42, 64]-NRT-code) | [i] | ||
| 21 | No linear OOA(969, 55, F9, 2, 64) (dual of [(55, 2), 41, 65]-NRT-code) | [i] | ||
| 22 | No linear OOA(970, 55, F9, 2, 65) (dual of [(55, 2), 40, 66]-NRT-code) | [i] | ||
| 23 | No linear OOA(971, 55, F9, 2, 66) (dual of [(55, 2), 39, 67]-NRT-code) | [i] | ||
| 24 | No linear OOA(972, 55, F9, 2, 67) (dual of [(55, 2), 38, 68]-NRT-code) | [i] | ||
| 25 | No linear OOA(973, 55, F9, 2, 68) (dual of [(55, 2), 37, 69]-NRT-code) | [i] | ||
| 26 | No linear OOA(974, 55, F9, 2, 69) (dual of [(55, 2), 36, 70]-NRT-code) | [i] | ||
| 27 | No linear OOA(975, 55, F9, 2, 70) (dual of [(55, 2), 35, 71]-NRT-code) | [i] | ||
| 28 | No linear OOA(976, 55, F9, 2, 71) (dual of [(55, 2), 34, 72]-NRT-code) | [i] | ||
| 29 | No linear OOA(977, 55, F9, 2, 72) (dual of [(55, 2), 33, 73]-NRT-code) | [i] | ||
| 30 | No linear OOA(978, 55, F9, 2, 73) (dual of [(55, 2), 32, 74]-NRT-code) | [i] | ||
| 31 | No linear OOA(979, 55, F9, 2, 74) (dual of [(55, 2), 31, 75]-NRT-code) | [i] | ||
| 32 | No linear OOA(980, 55, F9, 2, 75) (dual of [(55, 2), 30, 76]-NRT-code) | [i] | ||
| 33 | No linear OOA(981, 55, F9, 2, 76) (dual of [(55, 2), 29, 77]-NRT-code) | [i] | ||
| 34 | No linear OOA(982, 55, F9, 2, 77) (dual of [(55, 2), 28, 78]-NRT-code) | [i] | ||
| 35 | No linear OOA(983, 55, F9, 2, 78) (dual of [(55, 2), 27, 79]-NRT-code) | [i] | ||
| 36 | No linear OOA(984, 55, F9, 2, 79) (dual of [(55, 2), 26, 80]-NRT-code) | [i] | ||
| 37 | No linear OOA(985, 55, F9, 2, 80) (dual of [(55, 2), 25, 81]-NRT-code) | [i] | ||
| 38 | No linear OOA(986, 55, F9, 2, 81) (dual of [(55, 2), 24, 82]-NRT-code) | [i] | ||
| 39 | No linear OOA(987, 55, F9, 2, 82) (dual of [(55, 2), 23, 83]-NRT-code) | [i] | ||
| 40 | No linear OOA(988, 55, F9, 2, 83) (dual of [(55, 2), 22, 84]-NRT-code) | [i] | ||
| 41 | No linear OOA(989, 55, F9, 2, 84) (dual of [(55, 2), 21, 85]-NRT-code) | [i] | ||
| 42 | No linear OOA(990, 55, F9, 2, 85) (dual of [(55, 2), 20, 86]-NRT-code) | [i] | ||
| 43 | No linear OOA(991, 55, F9, 2, 86) (dual of [(55, 2), 19, 87]-NRT-code) | [i] | ||
| 44 | No linear OOA(992, 55, F9, 2, 87) (dual of [(55, 2), 18, 88]-NRT-code) | [i] | ||
| 45 | No linear OOA(993, 55, F9, 2, 88) (dual of [(55, 2), 17, 89]-NRT-code) | [i] | ||
| 46 | No linear OOA(994, 55, F9, 2, 89) (dual of [(55, 2), 16, 90]-NRT-code) | [i] | ||
| 47 | No linear OOA(995, 55, F9, 2, 90) (dual of [(55, 2), 15, 91]-NRT-code) | [i] | ||
| 48 | No linear OOA(996, 55, F9, 2, 91) (dual of [(55, 2), 14, 92]-NRT-code) | [i] | ||
| 49 | No linear OOA(997, 55, F9, 2, 92) (dual of [(55, 2), 13, 93]-NRT-code) | [i] | ||
| 50 | No linear OOA(998, 55, F9, 2, 93) (dual of [(55, 2), 12, 94]-NRT-code) | [i] | ||
| 51 | No linear OOA(999, 55, F9, 2, 94) (dual of [(55, 2), 11, 95]-NRT-code) | [i] | ||
| 52 | No linear OOA(9100, 55, F9, 2, 95) (dual of [(55, 2), 10, 96]-NRT-code) | [i] | ||
| 53 | No linear OOA(9101, 55, F9, 2, 96) (dual of [(55, 2), 9, 97]-NRT-code) | [i] | ||
| 54 | No linear OOA(9102, 55, F9, 2, 97) (dual of [(55, 2), 8, 98]-NRT-code) | [i] | ||
| 55 | No linear OOA(9103, 55, F9, 2, 98) (dual of [(55, 2), 7, 99]-NRT-code) | [i] | ||
| 56 | No linear OOA(9104, 55, F9, 2, 99) (dual of [(55, 2), 6, 100]-NRT-code) | [i] | ||
| 57 | No linear OOA(9105, 55, F9, 2, 100) (dual of [(55, 2), 5, 101]-NRT-code) | [i] | ||
| 58 | No linear OOA(9106, 55, F9, 3, 101) (dual of [(55, 3), 59, 102]-NRT-code) | [i] | ||
| 59 | No linear OOA(9107, 55, F9, 3, 102) (dual of [(55, 3), 58, 103]-NRT-code) | [i] | ||
| 60 | No linear OOA(9108, 55, F9, 3, 103) (dual of [(55, 3), 57, 104]-NRT-code) | [i] | ||
| 61 | No linear OOA(9109, 55, F9, 3, 104) (dual of [(55, 3), 56, 105]-NRT-code) | [i] | ||
| 62 | No linear OOA(9110, 55, F9, 3, 105) (dual of [(55, 3), 55, 106]-NRT-code) | [i] | ||
| 63 | No linear OOA(9111, 55, F9, 3, 106) (dual of [(55, 3), 54, 107]-NRT-code) | [i] | ||
| 64 | No linear OOA(9112, 55, F9, 3, 107) (dual of [(55, 3), 53, 108]-NRT-code) | [i] | ||
| 65 | No linear OOA(9113, 55, F9, 3, 108) (dual of [(55, 3), 52, 109]-NRT-code) | [i] | ||
| 66 | No linear OOA(9114, 55, F9, 3, 109) (dual of [(55, 3), 51, 110]-NRT-code) | [i] | ||
| 67 | No linear OOA(9115, 55, F9, 3, 110) (dual of [(55, 3), 50, 111]-NRT-code) | [i] | ||
| 68 | No linear OOA(9116, 55, F9, 3, 111) (dual of [(55, 3), 49, 112]-NRT-code) | [i] | ||
| 69 | No linear OOA(9117, 55, F9, 3, 112) (dual of [(55, 3), 48, 113]-NRT-code) | [i] | ||
| 70 | No linear OOA(9118, 55, F9, 3, 113) (dual of [(55, 3), 47, 114]-NRT-code) | [i] | ||
| 71 | No linear OOA(9119, 55, F9, 3, 114) (dual of [(55, 3), 46, 115]-NRT-code) | [i] | ||
| 72 | No linear OOA(9120, 55, F9, 3, 115) (dual of [(55, 3), 45, 116]-NRT-code) | [i] | ||
| 73 | No linear OOA(9121, 55, F9, 3, 116) (dual of [(55, 3), 44, 117]-NRT-code) | [i] | ||
| 74 | No linear OOA(9122, 55, F9, 3, 117) (dual of [(55, 3), 43, 118]-NRT-code) | [i] | ||
| 75 | No linear OOA(9123, 55, F9, 3, 118) (dual of [(55, 3), 42, 119]-NRT-code) | [i] | ||
| 76 | No linear OOA(9124, 55, F9, 3, 119) (dual of [(55, 3), 41, 120]-NRT-code) | [i] | ||
| 77 | No linear OOA(9125, 55, F9, 3, 120) (dual of [(55, 3), 40, 121]-NRT-code) | [i] | ||
| 78 | No linear OOA(9126, 55, F9, 3, 121) (dual of [(55, 3), 39, 122]-NRT-code) | [i] | ||
| 79 | No linear OOA(9127, 55, F9, 3, 122) (dual of [(55, 3), 38, 123]-NRT-code) | [i] | ||
| 80 | No linear OOA(9128, 55, F9, 3, 123) (dual of [(55, 3), 37, 124]-NRT-code) | [i] | ||
| 81 | No linear OOA(9129, 55, F9, 3, 124) (dual of [(55, 3), 36, 125]-NRT-code) | [i] | ||
| 82 | No linear OOA(9130, 55, F9, 3, 125) (dual of [(55, 3), 35, 126]-NRT-code) | [i] | ||
| 83 | No linear OOA(9131, 55, F9, 3, 126) (dual of [(55, 3), 34, 127]-NRT-code) | [i] | ||
| 84 | No linear OOA(9132, 55, F9, 3, 127) (dual of [(55, 3), 33, 128]-NRT-code) | [i] | ||
| 85 | No linear OOA(9133, 55, F9, 3, 128) (dual of [(55, 3), 32, 129]-NRT-code) | [i] | ||
| 86 | No linear OOA(9134, 55, F9, 3, 129) (dual of [(55, 3), 31, 130]-NRT-code) | [i] | ||
| 87 | No linear OOA(9135, 55, F9, 3, 130) (dual of [(55, 3), 30, 131]-NRT-code) | [i] | ||
| 88 | No linear OOA(9136, 55, F9, 3, 131) (dual of [(55, 3), 29, 132]-NRT-code) | [i] | ||
| 89 | No linear OOA(9137, 55, F9, 3, 132) (dual of [(55, 3), 28, 133]-NRT-code) | [i] | ||
| 90 | No linear OOA(9138, 55, F9, 3, 133) (dual of [(55, 3), 27, 134]-NRT-code) | [i] | ||
| 91 | No linear OOA(9139, 55, F9, 3, 134) (dual of [(55, 3), 26, 135]-NRT-code) | [i] | ||
| 92 | No linear OOA(9140, 55, F9, 3, 135) (dual of [(55, 3), 25, 136]-NRT-code) | [i] | ||
| 93 | No linear OOA(9141, 55, F9, 3, 136) (dual of [(55, 3), 24, 137]-NRT-code) | [i] | ||
| 94 | No linear OOA(9142, 55, F9, 3, 137) (dual of [(55, 3), 23, 138]-NRT-code) | [i] | ||
| 95 | No linear OOA(9143, 55, F9, 3, 138) (dual of [(55, 3), 22, 139]-NRT-code) | [i] | ||
| 96 | No linear OOA(9144, 55, F9, 3, 139) (dual of [(55, 3), 21, 140]-NRT-code) | [i] | ||
| 97 | No linear OOA(9145, 55, F9, 3, 140) (dual of [(55, 3), 20, 141]-NRT-code) | [i] | ||
| 98 | No linear OOA(9146, 55, F9, 3, 141) (dual of [(55, 3), 19, 142]-NRT-code) | [i] | ||
| 99 | No linear OOA(9147, 55, F9, 3, 142) (dual of [(55, 3), 18, 143]-NRT-code) | [i] | ||
| 100 | No linear OOA(9148, 55, F9, 3, 143) (dual of [(55, 3), 17, 144]-NRT-code) | [i] | ||
| 101 | No linear OOA(9149, 55, F9, 3, 144) (dual of [(55, 3), 16, 145]-NRT-code) | [i] | ||
| 102 | No linear OOA(9150, 55, F9, 3, 145) (dual of [(55, 3), 15, 146]-NRT-code) | [i] | ||
| 103 | No linear OOA(950, 55, F9, 2, 45) (dual of [(55, 2), 60, 46]-NRT-code) | [i] | Depth Reduction | |
| 104 | No linear OOA(950, 55, F9, 3, 45) (dual of [(55, 3), 115, 46]-NRT-code) | [i] | ||
| 105 | No digital (5, 50, 55)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |
| 106 | No linear OA(951, 86, F9, 45) (dual of [86, 35, 46]-code) | [i] | Construction Y1 (Bound) | |