Information on Result #547940
There is no linear OA(562, 68, F5, 50) (dual of [68, 6, 51]-code), because construction Y1 would yield
- linear OA(561, 64, F5, 50) (dual of [64, 3, 51]-code), but
- OA(56, 68, S5, 4), but
- discarding factors would yield OA(56, 45, S5, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 16021 > 56 [i]
- discarding factors would yield OA(56, 45, S5, 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(563, 69, F5, 51) (dual of [69, 6, 52]-code) | [i] | Truncation | |
| 2 | No linear OOA(563, 68, F5, 2, 51) (dual of [(68, 2), 73, 52]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(564, 68, F5, 2, 52) (dual of [(68, 2), 72, 53]-NRT-code) | [i] | ||
| 4 | No linear OOA(565, 68, F5, 2, 53) (dual of [(68, 2), 71, 54]-NRT-code) | [i] | ||
| 5 | No linear OOA(566, 68, F5, 2, 54) (dual of [(68, 2), 70, 55]-NRT-code) | [i] | ||
| 6 | No linear OOA(567, 68, F5, 2, 55) (dual of [(68, 2), 69, 56]-NRT-code) | [i] | ||
| 7 | No linear OOA(568, 68, F5, 2, 56) (dual of [(68, 2), 68, 57]-NRT-code) | [i] | ||
| 8 | No linear OOA(569, 68, F5, 2, 57) (dual of [(68, 2), 67, 58]-NRT-code) | [i] | ||
| 9 | No linear OOA(570, 68, F5, 2, 58) (dual of [(68, 2), 66, 59]-NRT-code) | [i] | ||
| 10 | No linear OOA(571, 68, F5, 2, 59) (dual of [(68, 2), 65, 60]-NRT-code) | [i] | ||
| 11 | No linear OOA(572, 68, F5, 2, 60) (dual of [(68, 2), 64, 61]-NRT-code) | [i] | ||
| 12 | No linear OOA(573, 68, F5, 2, 61) (dual of [(68, 2), 63, 62]-NRT-code) | [i] | ||
| 13 | No linear OOA(574, 68, F5, 2, 62) (dual of [(68, 2), 62, 63]-NRT-code) | [i] | ||
| 14 | No linear OOA(575, 68, F5, 2, 63) (dual of [(68, 2), 61, 64]-NRT-code) | [i] | ||
| 15 | No linear OOA(576, 68, F5, 2, 64) (dual of [(68, 2), 60, 65]-NRT-code) | [i] | ||
| 16 | No linear OOA(577, 68, F5, 2, 65) (dual of [(68, 2), 59, 66]-NRT-code) | [i] | ||
| 17 | No linear OOA(578, 68, F5, 2, 66) (dual of [(68, 2), 58, 67]-NRT-code) | [i] | ||
| 18 | No linear OOA(579, 68, F5, 2, 67) (dual of [(68, 2), 57, 68]-NRT-code) | [i] | ||
| 19 | No linear OOA(580, 68, F5, 2, 68) (dual of [(68, 2), 56, 69]-NRT-code) | [i] | ||
| 20 | No linear OOA(581, 68, F5, 2, 69) (dual of [(68, 2), 55, 70]-NRT-code) | [i] | ||
| 21 | No linear OOA(582, 68, F5, 2, 70) (dual of [(68, 2), 54, 71]-NRT-code) | [i] | ||
| 22 | No linear OOA(583, 68, F5, 2, 71) (dual of [(68, 2), 53, 72]-NRT-code) | [i] | ||
| 23 | No linear OOA(584, 68, F5, 2, 72) (dual of [(68, 2), 52, 73]-NRT-code) | [i] | ||
| 24 | No linear OOA(585, 68, F5, 2, 73) (dual of [(68, 2), 51, 74]-NRT-code) | [i] | ||
| 25 | No linear OOA(586, 68, F5, 2, 74) (dual of [(68, 2), 50, 75]-NRT-code) | [i] | ||
| 26 | No linear OOA(587, 68, F5, 2, 75) (dual of [(68, 2), 49, 76]-NRT-code) | [i] | ||
| 27 | No linear OOA(588, 68, F5, 2, 76) (dual of [(68, 2), 48, 77]-NRT-code) | [i] | ||
| 28 | No linear OOA(589, 68, F5, 2, 77) (dual of [(68, 2), 47, 78]-NRT-code) | [i] | ||
| 29 | No linear OOA(590, 68, F5, 2, 78) (dual of [(68, 2), 46, 79]-NRT-code) | [i] | ||
| 30 | No linear OOA(591, 68, F5, 2, 79) (dual of [(68, 2), 45, 80]-NRT-code) | [i] | ||
| 31 | No linear OOA(592, 68, F5, 2, 80) (dual of [(68, 2), 44, 81]-NRT-code) | [i] | ||
| 32 | No linear OOA(593, 68, F5, 2, 81) (dual of [(68, 2), 43, 82]-NRT-code) | [i] | ||
| 33 | No linear OOA(594, 68, F5, 2, 82) (dual of [(68, 2), 42, 83]-NRT-code) | [i] | ||
| 34 | No linear OOA(595, 68, F5, 2, 83) (dual of [(68, 2), 41, 84]-NRT-code) | [i] | ||
| 35 | No linear OOA(596, 68, F5, 2, 84) (dual of [(68, 2), 40, 85]-NRT-code) | [i] | ||
| 36 | No linear OOA(597, 68, F5, 2, 85) (dual of [(68, 2), 39, 86]-NRT-code) | [i] | ||
| 37 | No linear OOA(598, 68, F5, 2, 86) (dual of [(68, 2), 38, 87]-NRT-code) | [i] | ||
| 38 | No linear OOA(599, 68, F5, 2, 87) (dual of [(68, 2), 37, 88]-NRT-code) | [i] | ||
| 39 | No linear OOA(5100, 68, F5, 2, 88) (dual of [(68, 2), 36, 89]-NRT-code) | [i] | ||
| 40 | No linear OOA(5101, 68, F5, 2, 89) (dual of [(68, 2), 35, 90]-NRT-code) | [i] | ||
| 41 | No linear OOA(5102, 68, F5, 2, 90) (dual of [(68, 2), 34, 91]-NRT-code) | [i] | ||
| 42 | No linear OOA(5103, 68, F5, 2, 91) (dual of [(68, 2), 33, 92]-NRT-code) | [i] | ||
| 43 | No linear OOA(5104, 68, F5, 2, 92) (dual of [(68, 2), 32, 93]-NRT-code) | [i] | ||
| 44 | No linear OOA(5105, 68, F5, 2, 93) (dual of [(68, 2), 31, 94]-NRT-code) | [i] | ||
| 45 | No linear OOA(5106, 68, F5, 2, 94) (dual of [(68, 2), 30, 95]-NRT-code) | [i] | ||
| 46 | No linear OOA(5107, 68, F5, 2, 95) (dual of [(68, 2), 29, 96]-NRT-code) | [i] | ||
| 47 | No linear OOA(5108, 68, F5, 2, 96) (dual of [(68, 2), 28, 97]-NRT-code) | [i] | ||
| 48 | No linear OOA(5109, 68, F5, 2, 97) (dual of [(68, 2), 27, 98]-NRT-code) | [i] | ||
| 49 | No linear OOA(5110, 68, F5, 2, 98) (dual of [(68, 2), 26, 99]-NRT-code) | [i] | ||
| 50 | No linear OOA(5111, 68, F5, 2, 99) (dual of [(68, 2), 25, 100]-NRT-code) | [i] | ||
| 51 | No linear OOA(5112, 68, F5, 2, 100) (dual of [(68, 2), 24, 101]-NRT-code) | [i] | ||
| 52 | No linear OOA(5113, 68, F5, 2, 101) (dual of [(68, 2), 23, 102]-NRT-code) | [i] | ||
| 53 | No linear OOA(5114, 68, F5, 2, 102) (dual of [(68, 2), 22, 103]-NRT-code) | [i] | ||
| 54 | No linear OOA(5115, 68, F5, 2, 103) (dual of [(68, 2), 21, 104]-NRT-code) | [i] | ||
| 55 | No linear OOA(5116, 68, F5, 2, 104) (dual of [(68, 2), 20, 105]-NRT-code) | [i] | ||
| 56 | No linear OOA(5117, 68, F5, 2, 105) (dual of [(68, 2), 19, 106]-NRT-code) | [i] | ||
| 57 | No linear OOA(5118, 68, F5, 2, 106) (dual of [(68, 2), 18, 107]-NRT-code) | [i] | ||
| 58 | No linear OOA(5119, 68, F5, 2, 107) (dual of [(68, 2), 17, 108]-NRT-code) | [i] | ||
| 59 | No linear OOA(5120, 68, F5, 2, 108) (dual of [(68, 2), 16, 109]-NRT-code) | [i] | ||
| 60 | No linear OOA(5121, 68, F5, 2, 109) (dual of [(68, 2), 15, 110]-NRT-code) | [i] | ||
| 61 | No linear OOA(5122, 68, F5, 2, 110) (dual of [(68, 2), 14, 111]-NRT-code) | [i] | ||
| 62 | No linear OOA(562, 68, F5, 2, 50) (dual of [(68, 2), 74, 51]-NRT-code) | [i] | Depth Reduction | |
| 63 | No linear OOA(562, 68, F5, 3, 50) (dual of [(68, 3), 142, 51]-NRT-code) | [i] | ||
| 64 | No digital (12, 62, 68)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |