Information on Result #548640
There is no linear OA(735, 45, F7, 30) (dual of [45, 10, 31]-code), because construction Y1 would yield
- linear OA(734, 37, F7, 30) (dual of [37, 3, 31]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(710, 45, F7, 8) (dual of [45, 35, 9]-code), but
- discarding factors / shortening the dual code would yield linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), but
- construction Y1 [i] would yield
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(732, 42, F7, 28) (dual of [42, 10, 29]-code), but
- discarding factors / shortening the dual code would yield linear OA(732, 38, F7, 28) (dual of [38, 6, 29]-code), but
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), 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(736, 46, F7, 31) (dual of [46, 10, 32]-code) | [i] | Truncation | |
| 2 | No linear OA(737, 47, F7, 32) (dual of [47, 10, 33]-code) | [i] | ||
| 3 | No linear OA(738, 48, F7, 33) (dual of [48, 10, 34]-code) | [i] | ||
| 4 | No linear OOA(736, 45, F7, 2, 31) (dual of [(45, 2), 54, 32]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(737, 45, F7, 2, 32) (dual of [(45, 2), 53, 33]-NRT-code) | [i] | ||
| 6 | No linear OOA(738, 45, F7, 2, 33) (dual of [(45, 2), 52, 34]-NRT-code) | [i] | ||
| 7 | No linear OOA(739, 45, F7, 2, 34) (dual of [(45, 2), 51, 35]-NRT-code) | [i] | ||
| 8 | No linear OOA(741, 45, F7, 2, 36) (dual of [(45, 2), 49, 37]-NRT-code) | [i] | ||
| 9 | No linear OOA(742, 45, F7, 2, 37) (dual of [(45, 2), 48, 38]-NRT-code) | [i] | ||
| 10 | No linear OOA(743, 45, F7, 2, 38) (dual of [(45, 2), 47, 39]-NRT-code) | [i] | ||
| 11 | No linear OOA(744, 45, F7, 2, 39) (dual of [(45, 2), 46, 40]-NRT-code) | [i] | ||
| 12 | No linear OOA(745, 45, F7, 2, 40) (dual of [(45, 2), 45, 41]-NRT-code) | [i] | ||
| 13 | No linear OOA(746, 45, F7, 2, 41) (dual of [(45, 2), 44, 42]-NRT-code) | [i] | ||
| 14 | No linear OOA(747, 45, F7, 2, 42) (dual of [(45, 2), 43, 43]-NRT-code) | [i] | ||
| 15 | No linear OOA(748, 45, F7, 2, 43) (dual of [(45, 2), 42, 44]-NRT-code) | [i] | ||
| 16 | No linear OOA(749, 45, F7, 2, 44) (dual of [(45, 2), 41, 45]-NRT-code) | [i] | ||
| 17 | No linear OOA(750, 45, F7, 2, 45) (dual of [(45, 2), 40, 46]-NRT-code) | [i] | ||
| 18 | No linear OOA(751, 45, F7, 2, 46) (dual of [(45, 2), 39, 47]-NRT-code) | [i] | ||
| 19 | No linear OOA(752, 45, F7, 2, 47) (dual of [(45, 2), 38, 48]-NRT-code) | [i] | ||
| 20 | No linear OOA(753, 45, F7, 2, 48) (dual of [(45, 2), 37, 49]-NRT-code) | [i] | ||
| 21 | No linear OOA(754, 45, F7, 2, 49) (dual of [(45, 2), 36, 50]-NRT-code) | [i] | ||
| 22 | No linear OOA(755, 45, F7, 2, 50) (dual of [(45, 2), 35, 51]-NRT-code) | [i] | ||
| 23 | No linear OOA(756, 45, F7, 2, 51) (dual of [(45, 2), 34, 52]-NRT-code) | [i] | ||
| 24 | No linear OOA(757, 45, F7, 2, 52) (dual of [(45, 2), 33, 53]-NRT-code) | [i] | ||
| 25 | No linear OOA(758, 45, F7, 2, 53) (dual of [(45, 2), 32, 54]-NRT-code) | [i] | ||
| 26 | No linear OOA(759, 45, F7, 2, 54) (dual of [(45, 2), 31, 55]-NRT-code) | [i] | ||
| 27 | No linear OOA(760, 45, F7, 2, 55) (dual of [(45, 2), 30, 56]-NRT-code) | [i] | ||
| 28 | No linear OOA(761, 45, F7, 2, 56) (dual of [(45, 2), 29, 57]-NRT-code) | [i] | ||
| 29 | No linear OOA(762, 45, F7, 2, 57) (dual of [(45, 2), 28, 58]-NRT-code) | [i] | ||
| 30 | No linear OOA(763, 45, F7, 2, 58) (dual of [(45, 2), 27, 59]-NRT-code) | [i] | ||
| 31 | No linear OOA(764, 45, F7, 2, 59) (dual of [(45, 2), 26, 60]-NRT-code) | [i] | ||
| 32 | No linear OOA(765, 45, F7, 2, 60) (dual of [(45, 2), 25, 61]-NRT-code) | [i] | ||
| 33 | No linear OOA(766, 45, F7, 2, 61) (dual of [(45, 2), 24, 62]-NRT-code) | [i] | ||
| 34 | No linear OOA(767, 45, F7, 2, 62) (dual of [(45, 2), 23, 63]-NRT-code) | [i] | ||
| 35 | No linear OOA(768, 45, F7, 2, 63) (dual of [(45, 2), 22, 64]-NRT-code) | [i] | ||
| 36 | No linear OOA(769, 45, F7, 2, 64) (dual of [(45, 2), 21, 65]-NRT-code) | [i] | ||
| 37 | No linear OOA(770, 45, F7, 2, 65) (dual of [(45, 2), 20, 66]-NRT-code) | [i] | ||
| 38 | No linear OOA(771, 45, F7, 2, 66) (dual of [(45, 2), 19, 67]-NRT-code) | [i] | ||
| 39 | No linear OOA(772, 45, F7, 2, 67) (dual of [(45, 2), 18, 68]-NRT-code) | [i] | ||
| 40 | No linear OOA(773, 45, F7, 2, 68) (dual of [(45, 2), 17, 69]-NRT-code) | [i] | ||
| 41 | No linear OOA(774, 45, F7, 2, 69) (dual of [(45, 2), 16, 70]-NRT-code) | [i] | ||
| 42 | No linear OOA(775, 45, F7, 2, 70) (dual of [(45, 2), 15, 71]-NRT-code) | [i] | ||
| 43 | No linear OOA(776, 45, F7, 2, 71) (dual of [(45, 2), 14, 72]-NRT-code) | [i] | ||
| 44 | No linear OOA(777, 45, F7, 2, 72) (dual of [(45, 2), 13, 73]-NRT-code) | [i] | ||
| 45 | No linear OOA(778, 45, F7, 2, 73) (dual of [(45, 2), 12, 74]-NRT-code) | [i] | ||
| 46 | No linear OOA(779, 45, F7, 2, 74) (dual of [(45, 2), 11, 75]-NRT-code) | [i] | ||
| 47 | No linear OOA(780, 45, F7, 2, 75) (dual of [(45, 2), 10, 76]-NRT-code) | [i] | ||
| 48 | No linear OOA(735, 45, F7, 2, 30) (dual of [(45, 2), 55, 31]-NRT-code) | [i] | Depth Reduction | |
| 49 | No linear OOA(735, 45, F7, 3, 30) (dual of [(45, 3), 100, 31]-NRT-code) | [i] | ||
| 50 | No digital (5, 35, 45)-net over F7 | [i] | Extracting Embedded Orthogonal Array | |
| 51 | No linear OA(736, 94, F7, 30) (dual of [94, 58, 31]-code) | [i] | Construction Y1 (Bound) | |