Information on Result #548019
There is no linear OA(940, 45, F9, 36) (dual of [45, 5, 37]-code), because construction Y1 would yield
- OA(939, 41, S9, 36), but
- the (dual) Plotkin bound shows that M ≥ 739 044147 071729 616580 416051 031916 488005 / 37 > 939 [i]
- OA(95, 45, 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(941, 46, F9, 37) (dual of [46, 5, 38]-code) | [i] | Truncation | |
| 2 | No linear OA(942, 47, F9, 38) (dual of [47, 5, 39]-code) | [i] | ||
| 3 | No linear OA(943, 48, F9, 39) (dual of [48, 5, 40]-code) | [i] | ||
| 4 | No linear OA(944, 49, F9, 40) (dual of [49, 5, 41]-code) | [i] | ||
| 5 | No linear OOA(941, 45, F9, 2, 37) (dual of [(45, 2), 49, 38]-NRT-code) | [i] | m-Reduction for OOAs | |
| 6 | No linear OOA(942, 45, F9, 2, 38) (dual of [(45, 2), 48, 39]-NRT-code) | [i] | ||
| 7 | No linear OOA(943, 45, F9, 2, 39) (dual of [(45, 2), 47, 40]-NRT-code) | [i] | ||
| 8 | No linear OOA(944, 45, F9, 2, 40) (dual of [(45, 2), 46, 41]-NRT-code) | [i] | ||
| 9 | No linear OOA(945, 45, F9, 2, 41) (dual of [(45, 2), 45, 42]-NRT-code) | [i] | ||
| 10 | No linear OOA(946, 45, F9, 2, 42) (dual of [(45, 2), 44, 43]-NRT-code) | [i] | ||
| 11 | No linear OOA(947, 45, F9, 2, 43) (dual of [(45, 2), 43, 44]-NRT-code) | [i] | ||
| 12 | No linear OOA(948, 45, F9, 2, 44) (dual of [(45, 2), 42, 45]-NRT-code) | [i] | ||
| 13 | No linear OOA(949, 45, F9, 2, 45) (dual of [(45, 2), 41, 46]-NRT-code) | [i] | ||
| 14 | No linear OOA(950, 45, F9, 2, 46) (dual of [(45, 2), 40, 47]-NRT-code) | [i] | ||
| 15 | No linear OOA(951, 45, F9, 2, 47) (dual of [(45, 2), 39, 48]-NRT-code) | [i] | ||
| 16 | No linear OOA(952, 45, F9, 2, 48) (dual of [(45, 2), 38, 49]-NRT-code) | [i] | ||
| 17 | No linear OOA(953, 45, F9, 2, 49) (dual of [(45, 2), 37, 50]-NRT-code) | [i] | ||
| 18 | No linear OOA(954, 45, F9, 2, 50) (dual of [(45, 2), 36, 51]-NRT-code) | [i] | ||
| 19 | No linear OOA(955, 45, F9, 2, 51) (dual of [(45, 2), 35, 52]-NRT-code) | [i] | ||
| 20 | No linear OOA(956, 45, F9, 2, 52) (dual of [(45, 2), 34, 53]-NRT-code) | [i] | ||
| 21 | No linear OOA(957, 45, F9, 2, 53) (dual of [(45, 2), 33, 54]-NRT-code) | [i] | ||
| 22 | No linear OOA(958, 45, F9, 2, 54) (dual of [(45, 2), 32, 55]-NRT-code) | [i] | ||
| 23 | No linear OOA(959, 45, F9, 2, 55) (dual of [(45, 2), 31, 56]-NRT-code) | [i] | ||
| 24 | No linear OOA(960, 45, F9, 2, 56) (dual of [(45, 2), 30, 57]-NRT-code) | [i] | ||
| 25 | No linear OOA(961, 45, F9, 2, 57) (dual of [(45, 2), 29, 58]-NRT-code) | [i] | ||
| 26 | No linear OOA(962, 45, F9, 2, 58) (dual of [(45, 2), 28, 59]-NRT-code) | [i] | ||
| 27 | No linear OOA(963, 45, F9, 2, 59) (dual of [(45, 2), 27, 60]-NRT-code) | [i] | ||
| 28 | No linear OOA(964, 45, F9, 2, 60) (dual of [(45, 2), 26, 61]-NRT-code) | [i] | ||
| 29 | No linear OOA(965, 45, F9, 2, 61) (dual of [(45, 2), 25, 62]-NRT-code) | [i] | ||
| 30 | No linear OOA(966, 45, F9, 2, 62) (dual of [(45, 2), 24, 63]-NRT-code) | [i] | ||
| 31 | No linear OOA(967, 45, F9, 2, 63) (dual of [(45, 2), 23, 64]-NRT-code) | [i] | ||
| 32 | No linear OOA(968, 45, F9, 2, 64) (dual of [(45, 2), 22, 65]-NRT-code) | [i] | ||
| 33 | No linear OOA(969, 45, F9, 2, 65) (dual of [(45, 2), 21, 66]-NRT-code) | [i] | ||
| 34 | No linear OOA(970, 45, F9, 2, 66) (dual of [(45, 2), 20, 67]-NRT-code) | [i] | ||
| 35 | No linear OOA(971, 45, F9, 2, 67) (dual of [(45, 2), 19, 68]-NRT-code) | [i] | ||
| 36 | No linear OOA(972, 45, F9, 2, 68) (dual of [(45, 2), 18, 69]-NRT-code) | [i] | ||
| 37 | No linear OOA(973, 45, F9, 2, 69) (dual of [(45, 2), 17, 70]-NRT-code) | [i] | ||
| 38 | No linear OOA(974, 45, F9, 2, 70) (dual of [(45, 2), 16, 71]-NRT-code) | [i] | ||
| 39 | No linear OOA(975, 45, F9, 2, 71) (dual of [(45, 2), 15, 72]-NRT-code) | [i] | ||
| 40 | No linear OOA(976, 45, F9, 2, 72) (dual of [(45, 2), 14, 73]-NRT-code) | [i] | ||
| 41 | No linear OOA(977, 45, F9, 2, 73) (dual of [(45, 2), 13, 74]-NRT-code) | [i] | ||
| 42 | No linear OOA(978, 45, F9, 2, 74) (dual of [(45, 2), 12, 75]-NRT-code) | [i] | ||
| 43 | No linear OOA(979, 45, F9, 2, 75) (dual of [(45, 2), 11, 76]-NRT-code) | [i] | ||
| 44 | No linear OOA(980, 45, F9, 2, 76) (dual of [(45, 2), 10, 77]-NRT-code) | [i] | ||
| 45 | No linear OOA(981, 45, F9, 2, 77) (dual of [(45, 2), 9, 78]-NRT-code) | [i] | ||
| 46 | No linear OOA(982, 45, F9, 2, 78) (dual of [(45, 2), 8, 79]-NRT-code) | [i] | ||
| 47 | No linear OOA(983, 45, F9, 2, 79) (dual of [(45, 2), 7, 80]-NRT-code) | [i] | ||
| 48 | No linear OOA(984, 45, F9, 2, 80) (dual of [(45, 2), 6, 81]-NRT-code) | [i] | ||
| 49 | No linear OOA(985, 45, F9, 2, 81) (dual of [(45, 2), 5, 82]-NRT-code) | [i] | ||
| 50 | No linear OOA(986, 45, F9, 3, 82) (dual of [(45, 3), 49, 83]-NRT-code) | [i] | ||
| 51 | No linear OOA(987, 45, F9, 3, 83) (dual of [(45, 3), 48, 84]-NRT-code) | [i] | ||
| 52 | No linear OOA(988, 45, F9, 3, 84) (dual of [(45, 3), 47, 85]-NRT-code) | [i] | ||
| 53 | No linear OOA(989, 45, F9, 3, 85) (dual of [(45, 3), 46, 86]-NRT-code) | [i] | ||
| 54 | No linear OOA(990, 45, F9, 3, 86) (dual of [(45, 3), 45, 87]-NRT-code) | [i] | ||
| 55 | No linear OOA(991, 45, F9, 3, 87) (dual of [(45, 3), 44, 88]-NRT-code) | [i] | ||
| 56 | No linear OOA(992, 45, F9, 3, 88) (dual of [(45, 3), 43, 89]-NRT-code) | [i] | ||
| 57 | No linear OOA(993, 45, F9, 3, 89) (dual of [(45, 3), 42, 90]-NRT-code) | [i] | ||
| 58 | No linear OOA(994, 45, F9, 3, 90) (dual of [(45, 3), 41, 91]-NRT-code) | [i] | ||
| 59 | No linear OOA(995, 45, F9, 3, 91) (dual of [(45, 3), 40, 92]-NRT-code) | [i] | ||
| 60 | No linear OOA(996, 45, F9, 3, 92) (dual of [(45, 3), 39, 93]-NRT-code) | [i] | ||
| 61 | No linear OOA(997, 45, F9, 3, 93) (dual of [(45, 3), 38, 94]-NRT-code) | [i] | ||
| 62 | No linear OOA(998, 45, F9, 3, 94) (dual of [(45, 3), 37, 95]-NRT-code) | [i] | ||
| 63 | No linear OOA(999, 45, F9, 3, 95) (dual of [(45, 3), 36, 96]-NRT-code) | [i] | ||
| 64 | No linear OOA(9100, 45, F9, 3, 96) (dual of [(45, 3), 35, 97]-NRT-code) | [i] | ||
| 65 | No linear OOA(9101, 45, F9, 3, 97) (dual of [(45, 3), 34, 98]-NRT-code) | [i] | ||
| 66 | No linear OOA(9102, 45, F9, 3, 98) (dual of [(45, 3), 33, 99]-NRT-code) | [i] | ||
| 67 | No linear OOA(9103, 45, F9, 3, 99) (dual of [(45, 3), 32, 100]-NRT-code) | [i] | ||
| 68 | No linear OOA(9104, 45, F9, 3, 100) (dual of [(45, 3), 31, 101]-NRT-code) | [i] | ||
| 69 | No linear OOA(9105, 45, F9, 3, 101) (dual of [(45, 3), 30, 102]-NRT-code) | [i] | ||
| 70 | No linear OOA(9106, 45, F9, 3, 102) (dual of [(45, 3), 29, 103]-NRT-code) | [i] | ||
| 71 | No linear OOA(9107, 45, F9, 3, 103) (dual of [(45, 3), 28, 104]-NRT-code) | [i] | ||
| 72 | No linear OOA(9108, 45, F9, 3, 104) (dual of [(45, 3), 27, 105]-NRT-code) | [i] | ||
| 73 | No linear OOA(9109, 45, F9, 3, 105) (dual of [(45, 3), 26, 106]-NRT-code) | [i] | ||
| 74 | No linear OOA(9110, 45, F9, 3, 106) (dual of [(45, 3), 25, 107]-NRT-code) | [i] | ||
| 75 | No linear OOA(9111, 45, F9, 3, 107) (dual of [(45, 3), 24, 108]-NRT-code) | [i] | ||
| 76 | No linear OOA(9112, 45, F9, 3, 108) (dual of [(45, 3), 23, 109]-NRT-code) | [i] | ||
| 77 | No linear OOA(9113, 45, F9, 3, 109) (dual of [(45, 3), 22, 110]-NRT-code) | [i] | ||
| 78 | No linear OOA(9114, 45, F9, 3, 110) (dual of [(45, 3), 21, 111]-NRT-code) | [i] | ||
| 79 | No linear OOA(9115, 45, F9, 3, 111) (dual of [(45, 3), 20, 112]-NRT-code) | [i] | ||
| 80 | No linear OOA(9116, 45, F9, 3, 112) (dual of [(45, 3), 19, 113]-NRT-code) | [i] | ||
| 81 | No linear OOA(9117, 45, F9, 3, 113) (dual of [(45, 3), 18, 114]-NRT-code) | [i] | ||
| 82 | No linear OOA(9118, 45, F9, 3, 114) (dual of [(45, 3), 17, 115]-NRT-code) | [i] | ||
| 83 | No linear OOA(9119, 45, F9, 3, 115) (dual of [(45, 3), 16, 116]-NRT-code) | [i] | ||
| 84 | No linear OOA(9120, 45, F9, 3, 116) (dual of [(45, 3), 15, 117]-NRT-code) | [i] | ||
| 85 | No linear OOA(9121, 45, F9, 3, 117) (dual of [(45, 3), 14, 118]-NRT-code) | [i] | ||
| 86 | No linear OOA(9122, 45, F9, 3, 118) (dual of [(45, 3), 13, 119]-NRT-code) | [i] | ||
| 87 | No linear OOA(9123, 45, F9, 3, 119) (dual of [(45, 3), 12, 120]-NRT-code) | [i] | ||
| 88 | No linear OOA(9124, 45, F9, 3, 120) (dual of [(45, 3), 11, 121]-NRT-code) | [i] | ||
| 89 | No linear OOA(9125, 45, F9, 3, 121) (dual of [(45, 3), 10, 122]-NRT-code) | [i] | ||
| 90 | No linear OOA(9126, 45, F9, 3, 122) (dual of [(45, 3), 9, 123]-NRT-code) | [i] | ||
| 91 | No linear OOA(9127, 45, F9, 3, 123) (dual of [(45, 3), 8, 124]-NRT-code) | [i] | ||
| 92 | No linear OOA(9128, 45, F9, 3, 124) (dual of [(45, 3), 7, 125]-NRT-code) | [i] | ||
| 93 | No linear OOA(9129, 45, F9, 3, 125) (dual of [(45, 3), 6, 126]-NRT-code) | [i] | ||
| 94 | No linear OOA(9130, 45, F9, 3, 126) (dual of [(45, 3), 5, 127]-NRT-code) | [i] | ||
| 95 | No linear OOA(940, 45, F9, 2, 36) (dual of [(45, 2), 50, 37]-NRT-code) | [i] | Depth Reduction | |
| 96 | No linear OOA(940, 45, F9, 3, 36) (dual of [(45, 3), 95, 37]-NRT-code) | [i] | ||
| 97 | No digital (4, 40, 45)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |
| 98 | No linear OA(941, 78, F9, 36) (dual of [78, 37, 37]-code) | [i] | Construction Y1 (Bound) | |
| 99 | No linear OA(941, 77, F9, 36) (dual of [77, 36, 37]-code) | [i] | ||