Information on Result #547974
There is no linear OA(732, 37, F7, 28) (dual of [37, 5, 29]-code), because construction Y1 would yield
- OA(731, 33, S7, 28), but
- the (dual) Plotkin bound shows that M ≥ 5522 138371 219603 231526 496005 / 29 > 731 [i]
- OA(75, 37, S7, 4), but
- discarding factors would yield OA(75, 31, S7, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 16927 > 75 [i]
- discarding factors would yield OA(75, 31, S7, 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(733, 38, F7, 29) (dual of [38, 5, 30]-code) | [i] | Truncation | |
| 2 | No linear OOA(733, 37, F7, 2, 29) (dual of [(37, 2), 41, 30]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(735, 37, F7, 2, 31) (dual of [(37, 2), 39, 32]-NRT-code) | [i] | ||
| 4 | No linear OOA(736, 37, F7, 2, 32) (dual of [(37, 2), 38, 33]-NRT-code) | [i] | ||
| 5 | No linear OOA(737, 37, F7, 2, 33) (dual of [(37, 2), 37, 34]-NRT-code) | [i] | ||
| 6 | No linear OOA(738, 37, F7, 2, 34) (dual of [(37, 2), 36, 35]-NRT-code) | [i] | ||
| 7 | No linear OOA(739, 37, F7, 2, 35) (dual of [(37, 2), 35, 36]-NRT-code) | [i] | ||
| 8 | No linear OOA(740, 37, F7, 2, 36) (dual of [(37, 2), 34, 37]-NRT-code) | [i] | ||
| 9 | No linear OOA(741, 37, F7, 2, 37) (dual of [(37, 2), 33, 38]-NRT-code) | [i] | ||
| 10 | No linear OOA(742, 37, F7, 2, 38) (dual of [(37, 2), 32, 39]-NRT-code) | [i] | ||
| 11 | No linear OOA(743, 37, F7, 2, 39) (dual of [(37, 2), 31, 40]-NRT-code) | [i] | ||
| 12 | No linear OOA(744, 37, F7, 2, 40) (dual of [(37, 2), 30, 41]-NRT-code) | [i] | ||
| 13 | No linear OOA(745, 37, F7, 2, 41) (dual of [(37, 2), 29, 42]-NRT-code) | [i] | ||
| 14 | No linear OOA(746, 37, F7, 2, 42) (dual of [(37, 2), 28, 43]-NRT-code) | [i] | ||
| 15 | No linear OOA(747, 37, F7, 2, 43) (dual of [(37, 2), 27, 44]-NRT-code) | [i] | ||
| 16 | No linear OOA(748, 37, F7, 2, 44) (dual of [(37, 2), 26, 45]-NRT-code) | [i] | ||
| 17 | No linear OOA(749, 37, F7, 2, 45) (dual of [(37, 2), 25, 46]-NRT-code) | [i] | ||
| 18 | No linear OOA(750, 37, F7, 2, 46) (dual of [(37, 2), 24, 47]-NRT-code) | [i] | ||
| 19 | No linear OOA(751, 37, F7, 2, 47) (dual of [(37, 2), 23, 48]-NRT-code) | [i] | ||
| 20 | No linear OOA(752, 37, F7, 2, 48) (dual of [(37, 2), 22, 49]-NRT-code) | [i] | ||
| 21 | No linear OOA(753, 37, F7, 2, 49) (dual of [(37, 2), 21, 50]-NRT-code) | [i] | ||
| 22 | No linear OOA(754, 37, F7, 2, 50) (dual of [(37, 2), 20, 51]-NRT-code) | [i] | ||
| 23 | No linear OOA(755, 37, F7, 2, 51) (dual of [(37, 2), 19, 52]-NRT-code) | [i] | ||
| 24 | No linear OOA(756, 37, F7, 2, 52) (dual of [(37, 2), 18, 53]-NRT-code) | [i] | ||
| 25 | No linear OOA(757, 37, F7, 2, 53) (dual of [(37, 2), 17, 54]-NRT-code) | [i] | ||
| 26 | No linear OOA(758, 37, F7, 2, 54) (dual of [(37, 2), 16, 55]-NRT-code) | [i] | ||
| 27 | No linear OOA(759, 37, F7, 2, 55) (dual of [(37, 2), 15, 56]-NRT-code) | [i] | ||
| 28 | No linear OOA(760, 37, F7, 2, 56) (dual of [(37, 2), 14, 57]-NRT-code) | [i] | ||
| 29 | No linear OOA(761, 37, F7, 2, 57) (dual of [(37, 2), 13, 58]-NRT-code) | [i] | ||
| 30 | No linear OOA(762, 37, F7, 2, 58) (dual of [(37, 2), 12, 59]-NRT-code) | [i] | ||
| 31 | No linear OOA(763, 37, F7, 2, 59) (dual of [(37, 2), 11, 60]-NRT-code) | [i] | ||
| 32 | No linear OOA(764, 37, F7, 2, 60) (dual of [(37, 2), 10, 61]-NRT-code) | [i] | ||
| 33 | No linear OOA(765, 37, F7, 2, 61) (dual of [(37, 2), 9, 62]-NRT-code) | [i] | ||
| 34 | No linear OOA(766, 37, F7, 2, 62) (dual of [(37, 2), 8, 63]-NRT-code) | [i] | ||
| 35 | No linear OOA(767, 37, F7, 2, 63) (dual of [(37, 2), 7, 64]-NRT-code) | [i] | ||
| 36 | No linear OOA(768, 37, F7, 2, 64) (dual of [(37, 2), 6, 65]-NRT-code) | [i] | ||
| 37 | No linear OOA(769, 37, F7, 2, 65) (dual of [(37, 2), 5, 66]-NRT-code) | [i] | ||
| 38 | No linear OOA(772, 37, F7, 3, 68) (dual of [(37, 3), 39, 69]-NRT-code) | [i] | ||
| 39 | No linear OOA(773, 37, F7, 3, 69) (dual of [(37, 3), 38, 70]-NRT-code) | [i] | ||
| 40 | No linear OOA(774, 37, F7, 3, 70) (dual of [(37, 3), 37, 71]-NRT-code) | [i] | ||
| 41 | No linear OOA(775, 37, F7, 3, 71) (dual of [(37, 3), 36, 72]-NRT-code) | [i] | ||
| 42 | No linear OOA(776, 37, F7, 3, 72) (dual of [(37, 3), 35, 73]-NRT-code) | [i] | ||
| 43 | No linear OOA(777, 37, F7, 3, 73) (dual of [(37, 3), 34, 74]-NRT-code) | [i] | ||
| 44 | No linear OOA(778, 37, F7, 3, 74) (dual of [(37, 3), 33, 75]-NRT-code) | [i] | ||
| 45 | No linear OOA(779, 37, F7, 3, 75) (dual of [(37, 3), 32, 76]-NRT-code) | [i] | ||
| 46 | No linear OOA(780, 37, F7, 3, 76) (dual of [(37, 3), 31, 77]-NRT-code) | [i] | ||
| 47 | No linear OOA(781, 37, F7, 3, 77) (dual of [(37, 3), 30, 78]-NRT-code) | [i] | ||
| 48 | No linear OOA(782, 37, F7, 3, 78) (dual of [(37, 3), 29, 79]-NRT-code) | [i] | ||
| 49 | No linear OOA(783, 37, F7, 3, 79) (dual of [(37, 3), 28, 80]-NRT-code) | [i] | ||
| 50 | No linear OOA(784, 37, F7, 3, 80) (dual of [(37, 3), 27, 81]-NRT-code) | [i] | ||
| 51 | No linear OOA(785, 37, F7, 3, 81) (dual of [(37, 3), 26, 82]-NRT-code) | [i] | ||
| 52 | No linear OOA(786, 37, F7, 3, 82) (dual of [(37, 3), 25, 83]-NRT-code) | [i] | ||
| 53 | No linear OOA(787, 37, F7, 3, 83) (dual of [(37, 3), 24, 84]-NRT-code) | [i] | ||
| 54 | No linear OOA(788, 37, F7, 3, 84) (dual of [(37, 3), 23, 85]-NRT-code) | [i] | ||
| 55 | No linear OOA(789, 37, F7, 3, 85) (dual of [(37, 3), 22, 86]-NRT-code) | [i] | ||
| 56 | No linear OOA(790, 37, F7, 3, 86) (dual of [(37, 3), 21, 87]-NRT-code) | [i] | ||
| 57 | No linear OOA(791, 37, F7, 3, 87) (dual of [(37, 3), 20, 88]-NRT-code) | [i] | ||
| 58 | No linear OOA(792, 37, F7, 3, 88) (dual of [(37, 3), 19, 89]-NRT-code) | [i] | ||
| 59 | No linear OOA(793, 37, F7, 3, 89) (dual of [(37, 3), 18, 90]-NRT-code) | [i] | ||
| 60 | No linear OOA(794, 37, F7, 3, 90) (dual of [(37, 3), 17, 91]-NRT-code) | [i] | ||
| 61 | No linear OOA(795, 37, F7, 3, 91) (dual of [(37, 3), 16, 92]-NRT-code) | [i] | ||
| 62 | No linear OOA(796, 37, F7, 3, 92) (dual of [(37, 3), 15, 93]-NRT-code) | [i] | ||
| 63 | No linear OOA(797, 37, F7, 3, 93) (dual of [(37, 3), 14, 94]-NRT-code) | [i] | ||
| 64 | No linear OOA(798, 37, F7, 3, 94) (dual of [(37, 3), 13, 95]-NRT-code) | [i] | ||
| 65 | No linear OOA(799, 37, F7, 3, 95) (dual of [(37, 3), 12, 96]-NRT-code) | [i] | ||
| 66 | No linear OOA(7100, 37, F7, 3, 96) (dual of [(37, 3), 11, 97]-NRT-code) | [i] | ||
| 67 | No linear OOA(7101, 37, F7, 3, 97) (dual of [(37, 3), 10, 98]-NRT-code) | [i] | ||
| 68 | No linear OOA(7102, 37, F7, 3, 98) (dual of [(37, 3), 9, 99]-NRT-code) | [i] | ||
| 69 | No linear OOA(7103, 37, F7, 3, 99) (dual of [(37, 3), 8, 100]-NRT-code) | [i] | ||
| 70 | No linear OOA(7104, 37, F7, 3, 100) (dual of [(37, 3), 7, 101]-NRT-code) | [i] | ||
| 71 | No linear OOA(7105, 37, F7, 3, 101) (dual of [(37, 3), 6, 102]-NRT-code) | [i] | ||
| 72 | No linear OOA(7106, 37, F7, 3, 102) (dual of [(37, 3), 5, 103]-NRT-code) | [i] | ||
| 73 | No linear OOA(732, 37, F7, 2, 28) (dual of [(37, 2), 42, 29]-NRT-code) | [i] | Depth Reduction | |
| 74 | No linear OOA(732, 37, F7, 3, 28) (dual of [(37, 3), 79, 29]-NRT-code) | [i] | ||
| 75 | No digital (4, 32, 37)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |