Information on Result #547564
There is no linear OA(748, 52, F7, 42) (dual of [52, 4, 43]-code), because residual code would yield linear OA(76, 9, F7, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,7)), 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(749, 53, F7, 43) (dual of [53, 4, 44]-code) | [i] | Truncation | |
| 2 | No linear OA(750, 54, F7, 44) (dual of [54, 4, 45]-code) | [i] | ||
| 3 | No linear OA(751, 55, F7, 45) (dual of [55, 4, 46]-code) | [i] | ||
| 4 | No linear OA(752, 56, F7, 46) (dual of [56, 4, 47]-code) | [i] | ||
| 5 | No linear OA(753, 57, F7, 47) (dual of [57, 4, 48]-code) | [i] | ||
| 6 | No linear OA(754, 58, F7, 48) (dual of [58, 4, 49]-code) | [i] | ||
| 7 | No linear OOA(749, 52, F7, 2, 43) (dual of [(52, 2), 55, 44]-NRT-code) | [i] | m-Reduction for OOAs | |
| 8 | No linear OOA(750, 52, F7, 2, 44) (dual of [(52, 2), 54, 45]-NRT-code) | [i] | ||
| 9 | No linear OOA(751, 52, F7, 2, 45) (dual of [(52, 2), 53, 46]-NRT-code) | [i] | ||
| 10 | No linear OOA(752, 52, F7, 2, 46) (dual of [(52, 2), 52, 47]-NRT-code) | [i] | ||
| 11 | No linear OOA(753, 52, F7, 2, 47) (dual of [(52, 2), 51, 48]-NRT-code) | [i] | ||
| 12 | No linear OOA(754, 52, F7, 2, 48) (dual of [(52, 2), 50, 49]-NRT-code) | [i] | ||
| 13 | No linear OOA(755, 52, F7, 2, 49) (dual of [(52, 2), 49, 50]-NRT-code) | [i] | ||
| 14 | No linear OOA(756, 52, F7, 2, 50) (dual of [(52, 2), 48, 51]-NRT-code) | [i] | ||
| 15 | No linear OOA(757, 52, F7, 2, 51) (dual of [(52, 2), 47, 52]-NRT-code) | [i] | ||
| 16 | No linear OOA(758, 52, F7, 2, 52) (dual of [(52, 2), 46, 53]-NRT-code) | [i] | ||
| 17 | No linear OOA(759, 52, F7, 2, 53) (dual of [(52, 2), 45, 54]-NRT-code) | [i] | ||
| 18 | No linear OOA(760, 52, F7, 2, 54) (dual of [(52, 2), 44, 55]-NRT-code) | [i] | ||
| 19 | No linear OOA(761, 52, F7, 2, 55) (dual of [(52, 2), 43, 56]-NRT-code) | [i] | ||
| 20 | No linear OOA(762, 52, F7, 2, 56) (dual of [(52, 2), 42, 57]-NRT-code) | [i] | ||
| 21 | No linear OOA(763, 52, F7, 2, 57) (dual of [(52, 2), 41, 58]-NRT-code) | [i] | ||
| 22 | No linear OOA(764, 52, F7, 2, 58) (dual of [(52, 2), 40, 59]-NRT-code) | [i] | ||
| 23 | No linear OOA(765, 52, F7, 2, 59) (dual of [(52, 2), 39, 60]-NRT-code) | [i] | ||
| 24 | No linear OOA(766, 52, F7, 2, 60) (dual of [(52, 2), 38, 61]-NRT-code) | [i] | ||
| 25 | No linear OOA(767, 52, F7, 2, 61) (dual of [(52, 2), 37, 62]-NRT-code) | [i] | ||
| 26 | No linear OOA(768, 52, F7, 2, 62) (dual of [(52, 2), 36, 63]-NRT-code) | [i] | ||
| 27 | No linear OOA(769, 52, F7, 2, 63) (dual of [(52, 2), 35, 64]-NRT-code) | [i] | ||
| 28 | No linear OOA(770, 52, F7, 2, 64) (dual of [(52, 2), 34, 65]-NRT-code) | [i] | ||
| 29 | No linear OOA(771, 52, F7, 2, 65) (dual of [(52, 2), 33, 66]-NRT-code) | [i] | ||
| 30 | No linear OOA(772, 52, F7, 2, 66) (dual of [(52, 2), 32, 67]-NRT-code) | [i] | ||
| 31 | No linear OOA(773, 52, F7, 2, 67) (dual of [(52, 2), 31, 68]-NRT-code) | [i] | ||
| 32 | No linear OOA(774, 52, F7, 2, 68) (dual of [(52, 2), 30, 69]-NRT-code) | [i] | ||
| 33 | No linear OOA(775, 52, F7, 2, 69) (dual of [(52, 2), 29, 70]-NRT-code) | [i] | ||
| 34 | No linear OOA(776, 52, F7, 2, 70) (dual of [(52, 2), 28, 71]-NRT-code) | [i] | ||
| 35 | No linear OOA(777, 52, F7, 2, 71) (dual of [(52, 2), 27, 72]-NRT-code) | [i] | ||
| 36 | No linear OOA(778, 52, F7, 2, 72) (dual of [(52, 2), 26, 73]-NRT-code) | [i] | ||
| 37 | No linear OOA(779, 52, F7, 2, 73) (dual of [(52, 2), 25, 74]-NRT-code) | [i] | ||
| 38 | No linear OOA(780, 52, F7, 2, 74) (dual of [(52, 2), 24, 75]-NRT-code) | [i] | ||
| 39 | No linear OOA(781, 52, F7, 2, 75) (dual of [(52, 2), 23, 76]-NRT-code) | [i] | ||
| 40 | No linear OOA(782, 52, F7, 2, 76) (dual of [(52, 2), 22, 77]-NRT-code) | [i] | ||
| 41 | No linear OOA(783, 52, F7, 2, 77) (dual of [(52, 2), 21, 78]-NRT-code) | [i] | ||
| 42 | No linear OOA(784, 52, F7, 2, 78) (dual of [(52, 2), 20, 79]-NRT-code) | [i] | ||
| 43 | No linear OOA(785, 52, F7, 2, 79) (dual of [(52, 2), 19, 80]-NRT-code) | [i] | ||
| 44 | No linear OOA(786, 52, F7, 2, 80) (dual of [(52, 2), 18, 81]-NRT-code) | [i] | ||
| 45 | No linear OOA(787, 52, F7, 2, 81) (dual of [(52, 2), 17, 82]-NRT-code) | [i] | ||
| 46 | No linear OOA(788, 52, F7, 2, 82) (dual of [(52, 2), 16, 83]-NRT-code) | [i] | ||
| 47 | No linear OOA(789, 52, F7, 2, 83) (dual of [(52, 2), 15, 84]-NRT-code) | [i] | ||
| 48 | No linear OOA(790, 52, F7, 2, 84) (dual of [(52, 2), 14, 85]-NRT-code) | [i] | ||
| 49 | No linear OOA(791, 52, F7, 2, 85) (dual of [(52, 2), 13, 86]-NRT-code) | [i] | ||
| 50 | No linear OOA(792, 52, F7, 2, 86) (dual of [(52, 2), 12, 87]-NRT-code) | [i] | ||
| 51 | No linear OOA(793, 52, F7, 2, 87) (dual of [(52, 2), 11, 88]-NRT-code) | [i] | ||
| 52 | No linear OOA(794, 52, F7, 2, 88) (dual of [(52, 2), 10, 89]-NRT-code) | [i] | ||
| 53 | No linear OOA(795, 52, F7, 2, 89) (dual of [(52, 2), 9, 90]-NRT-code) | [i] | ||
| 54 | No linear OOA(796, 52, F7, 2, 90) (dual of [(52, 2), 8, 91]-NRT-code) | [i] | ||
| 55 | No linear OOA(797, 52, F7, 2, 91) (dual of [(52, 2), 7, 92]-NRT-code) | [i] | ||
| 56 | No linear OOA(798, 52, F7, 2, 92) (dual of [(52, 2), 6, 93]-NRT-code) | [i] | ||
| 57 | No linear OOA(748, 52, F7, 2, 42) (dual of [(52, 2), 56, 43]-NRT-code) | [i] | Depth Reduction | |
| 58 | No linear OOA(748, 52, F7, 3, 42) (dual of [(52, 3), 108, 43]-NRT-code) | [i] | ||
| 59 | No digital (6, 48, 52)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |
| 60 | No linear OA(749, 66, F7, 42) (dual of [66, 17, 43]-code) | [i] | Construction Y1 (Bound) | |