Information on Result #547971
There is no linear OA(724, 29, F7, 21) (dual of [29, 5, 22]-code), because construction Y1 would yield
- OA(723, 25, S7, 21), but
- the (dual) Plotkin bound shows that M ≥ 383 162462 761132 828802 / 11 > 723 [i]
- OA(75, 29, S7, 4), but
- the linear programming bound shows that M ≥ 3 384381 / 197 > 75 [i]
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(725, 30, F7, 22) (dual of [30, 5, 23]-code) | [i] | Truncation | |
| 2 | No linear OA(726, 31, F7, 23) (dual of [31, 5, 24]-code) | [i] | ||
| 3 | No linear OOA(725, 29, F7, 2, 22) (dual of [(29, 2), 33, 23]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(726, 29, F7, 2, 23) (dual of [(29, 2), 32, 24]-NRT-code) | [i] | ||
| 5 | No linear OOA(727, 29, F7, 2, 24) (dual of [(29, 2), 31, 25]-NRT-code) | [i] | ||
| 6 | No linear OOA(728, 29, F7, 2, 25) (dual of [(29, 2), 30, 26]-NRT-code) | [i] | ||
| 7 | No linear OOA(729, 29, F7, 2, 26) (dual of [(29, 2), 29, 27]-NRT-code) | [i] | ||
| 8 | No linear OOA(730, 29, F7, 2, 27) (dual of [(29, 2), 28, 28]-NRT-code) | [i] | ||
| 9 | No linear OOA(731, 29, F7, 2, 28) (dual of [(29, 2), 27, 29]-NRT-code) | [i] | ||
| 10 | No linear OOA(732, 29, F7, 2, 29) (dual of [(29, 2), 26, 30]-NRT-code) | [i] | ||
| 11 | No linear OOA(733, 29, F7, 2, 30) (dual of [(29, 2), 25, 31]-NRT-code) | [i] | ||
| 12 | No linear OOA(734, 29, F7, 2, 31) (dual of [(29, 2), 24, 32]-NRT-code) | [i] | ||
| 13 | No linear OOA(735, 29, F7, 2, 32) (dual of [(29, 2), 23, 33]-NRT-code) | [i] | ||
| 14 | No linear OOA(736, 29, F7, 2, 33) (dual of [(29, 2), 22, 34]-NRT-code) | [i] | ||
| 15 | No linear OOA(737, 29, F7, 2, 34) (dual of [(29, 2), 21, 35]-NRT-code) | [i] | ||
| 16 | No linear OOA(738, 29, F7, 2, 35) (dual of [(29, 2), 20, 36]-NRT-code) | [i] | ||
| 17 | No linear OOA(739, 29, F7, 2, 36) (dual of [(29, 2), 19, 37]-NRT-code) | [i] | ||
| 18 | No linear OOA(740, 29, F7, 2, 37) (dual of [(29, 2), 18, 38]-NRT-code) | [i] | ||
| 19 | No linear OOA(741, 29, F7, 2, 38) (dual of [(29, 2), 17, 39]-NRT-code) | [i] | ||
| 20 | No linear OOA(742, 29, F7, 2, 39) (dual of [(29, 2), 16, 40]-NRT-code) | [i] | ||
| 21 | No linear OOA(743, 29, F7, 2, 40) (dual of [(29, 2), 15, 41]-NRT-code) | [i] | ||
| 22 | No linear OOA(744, 29, F7, 2, 41) (dual of [(29, 2), 14, 42]-NRT-code) | [i] | ||
| 23 | No linear OOA(745, 29, F7, 2, 42) (dual of [(29, 2), 13, 43]-NRT-code) | [i] | ||
| 24 | No linear OOA(746, 29, F7, 2, 43) (dual of [(29, 2), 12, 44]-NRT-code) | [i] | ||
| 25 | No linear OOA(747, 29, F7, 2, 44) (dual of [(29, 2), 11, 45]-NRT-code) | [i] | ||
| 26 | No linear OOA(748, 29, F7, 2, 45) (dual of [(29, 2), 10, 46]-NRT-code) | [i] | ||
| 27 | No linear OOA(749, 29, F7, 2, 46) (dual of [(29, 2), 9, 47]-NRT-code) | [i] | ||
| 28 | No linear OOA(750, 29, F7, 2, 47) (dual of [(29, 2), 8, 48]-NRT-code) | [i] | ||
| 29 | No linear OOA(751, 29, F7, 2, 48) (dual of [(29, 2), 7, 49]-NRT-code) | [i] | ||
| 30 | No linear OOA(752, 29, F7, 2, 49) (dual of [(29, 2), 6, 50]-NRT-code) | [i] | ||
| 31 | No linear OOA(753, 29, F7, 2, 50) (dual of [(29, 2), 5, 51]-NRT-code) | [i] | ||
| 32 | No linear OOA(754, 29, F7, 3, 51) (dual of [(29, 3), 33, 52]-NRT-code) | [i] | ||
| 33 | No linear OOA(755, 29, F7, 3, 52) (dual of [(29, 3), 32, 53]-NRT-code) | [i] | ||
| 34 | No linear OOA(756, 29, F7, 3, 53) (dual of [(29, 3), 31, 54]-NRT-code) | [i] | ||
| 35 | No linear OOA(757, 29, F7, 3, 54) (dual of [(29, 3), 30, 55]-NRT-code) | [i] | ||
| 36 | No linear OOA(758, 29, F7, 3, 55) (dual of [(29, 3), 29, 56]-NRT-code) | [i] | ||
| 37 | No linear OOA(759, 29, F7, 3, 56) (dual of [(29, 3), 28, 57]-NRT-code) | [i] | ||
| 38 | No linear OOA(760, 29, F7, 3, 57) (dual of [(29, 3), 27, 58]-NRT-code) | [i] | ||
| 39 | No linear OOA(761, 29, F7, 3, 58) (dual of [(29, 3), 26, 59]-NRT-code) | [i] | ||
| 40 | No linear OOA(762, 29, F7, 3, 59) (dual of [(29, 3), 25, 60]-NRT-code) | [i] | ||
| 41 | No linear OOA(763, 29, F7, 3, 60) (dual of [(29, 3), 24, 61]-NRT-code) | [i] | ||
| 42 | No linear OOA(764, 29, F7, 3, 61) (dual of [(29, 3), 23, 62]-NRT-code) | [i] | ||
| 43 | No linear OOA(765, 29, F7, 3, 62) (dual of [(29, 3), 22, 63]-NRT-code) | [i] | ||
| 44 | No linear OOA(766, 29, F7, 3, 63) (dual of [(29, 3), 21, 64]-NRT-code) | [i] | ||
| 45 | No linear OOA(767, 29, F7, 3, 64) (dual of [(29, 3), 20, 65]-NRT-code) | [i] | ||
| 46 | No linear OOA(768, 29, F7, 3, 65) (dual of [(29, 3), 19, 66]-NRT-code) | [i] | ||
| 47 | No linear OOA(769, 29, F7, 3, 66) (dual of [(29, 3), 18, 67]-NRT-code) | [i] | ||
| 48 | No linear OOA(770, 29, F7, 3, 67) (dual of [(29, 3), 17, 68]-NRT-code) | [i] | ||
| 49 | No linear OOA(771, 29, F7, 3, 68) (dual of [(29, 3), 16, 69]-NRT-code) | [i] | ||
| 50 | No linear OOA(772, 29, F7, 3, 69) (dual of [(29, 3), 15, 70]-NRT-code) | [i] | ||
| 51 | No linear OOA(773, 29, F7, 3, 70) (dual of [(29, 3), 14, 71]-NRT-code) | [i] | ||
| 52 | No linear OOA(774, 29, F7, 3, 71) (dual of [(29, 3), 13, 72]-NRT-code) | [i] | ||
| 53 | No linear OOA(775, 29, F7, 3, 72) (dual of [(29, 3), 12, 73]-NRT-code) | [i] | ||
| 54 | No linear OOA(776, 29, F7, 3, 73) (dual of [(29, 3), 11, 74]-NRT-code) | [i] | ||
| 55 | No linear OOA(777, 29, F7, 3, 74) (dual of [(29, 3), 10, 75]-NRT-code) | [i] | ||
| 56 | No linear OOA(778, 29, F7, 3, 75) (dual of [(29, 3), 9, 76]-NRT-code) | [i] | ||
| 57 | No linear OOA(779, 29, F7, 3, 76) (dual of [(29, 3), 8, 77]-NRT-code) | [i] | ||
| 58 | No linear OOA(780, 29, F7, 3, 77) (dual of [(29, 3), 7, 78]-NRT-code) | [i] | ||
| 59 | No linear OOA(781, 29, F7, 3, 78) (dual of [(29, 3), 6, 79]-NRT-code) | [i] | ||
| 60 | No linear OOA(782, 29, F7, 3, 79) (dual of [(29, 3), 5, 80]-NRT-code) | [i] | ||
| 61 | No linear OOA(724, 29, F7, 2, 21) (dual of [(29, 2), 34, 22]-NRT-code) | [i] | Depth Reduction | |
| 62 | No linear OOA(724, 29, F7, 3, 21) (dual of [(29, 3), 63, 22]-NRT-code) | [i] | ||
| 63 | No digital (3, 24, 29)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |
| 64 | No linear OA(725, 56, F7, 21) (dual of [56, 31, 22]-code) | [i] | Construction Y1 (Bound) | |
| 65 | No linear OA(725, 53, F7, 21) (dual of [53, 28, 22]-code) | [i] | ||