Information on Result #547666
There is no linear OA(2728, 81, F27, 27) (dual of [81, 53, 28]-code), because dual of a near-MDS code is again a near-MDS code would yield linear OA(2753, 81, F27, 52) (dual of [81, 28, 53]-code), but
- discarding factors / shortening the dual code would yield linear OA(2753, 56, F27, 52) (dual of [56, 3, 53]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2729, 82, F27, 28) (dual of [82, 53, 29]-code) | [i] | Truncation | |
| 2 | No linear OA(2730, 83, F27, 29) (dual of [83, 53, 30]-code) | [i] | ||
| 3 | No linear OA(2731, 84, F27, 30) (dual of [84, 53, 31]-code) | [i] | ||
| 4 | No linear OA(2732, 85, F27, 31) (dual of [85, 53, 32]-code) | [i] | ||
| 5 | No linear OA(2733, 86, F27, 32) (dual of [86, 53, 33]-code) | [i] | ||
| 6 | No linear OA(2734, 87, F27, 33) (dual of [87, 53, 34]-code) | [i] | ||
| 7 | No linear OA(2735, 88, F27, 34) (dual of [88, 53, 35]-code) | [i] | ||
| 8 | No linear OA(2736, 89, F27, 35) (dual of [89, 53, 36]-code) | [i] | ||
| 9 | No linear OA(2737, 90, F27, 36) (dual of [90, 53, 37]-code) | [i] | ||
| 10 | No linear OA(2738, 91, F27, 37) (dual of [91, 53, 38]-code) | [i] | ||
| 11 | No linear OA(2739, 92, F27, 38) (dual of [92, 53, 39]-code) | [i] | ||
| 12 | No linear OA(2740, 93, F27, 39) (dual of [93, 53, 40]-code) | [i] | ||
| 13 | No linear OA(2741, 94, F27, 40) (dual of [94, 53, 41]-code) | [i] | ||
| 14 | No linear OA(2742, 95, F27, 41) (dual of [95, 53, 42]-code) | [i] | ||
| 15 | No linear OA(2743, 96, F27, 42) (dual of [96, 53, 43]-code) | [i] | ||
| 16 | No linear OA(2744, 97, F27, 43) (dual of [97, 53, 44]-code) | [i] | ||
| 17 | No linear OA(2745, 98, F27, 44) (dual of [98, 53, 45]-code) | [i] | ||
| 18 | No linear OA(2746, 99, F27, 45) (dual of [99, 53, 46]-code) | [i] | ||
| 19 | No linear OA(2747, 100, F27, 46) (dual of [100, 53, 47]-code) | [i] | ||
| 20 | No linear OA(2748, 101, F27, 47) (dual of [101, 53, 48]-code) | [i] | ||
| 21 | No linear OA(2749, 102, F27, 48) (dual of [102, 53, 49]-code) | [i] | ||
| 22 | No linear OA(2750, 103, F27, 49) (dual of [103, 53, 50]-code) | [i] | ||
| 23 | No linear OA(2751, 104, F27, 50) (dual of [104, 53, 51]-code) | [i] | ||
| 24 | No linear OA(2752, 105, F27, 51) (dual of [105, 53, 52]-code) | [i] | ||
| 25 | No linear OOA(2729, 81, F27, 2, 28) (dual of [(81, 2), 133, 29]-NRT-code) | [i] | m-Reduction for OOAs | |
| 26 | No linear OOA(2730, 81, F27, 2, 29) (dual of [(81, 2), 132, 30]-NRT-code) | [i] | ||
| 27 | No linear OOA(2731, 81, F27, 2, 30) (dual of [(81, 2), 131, 31]-NRT-code) | [i] | ||
| 28 | No linear OOA(2732, 81, F27, 2, 31) (dual of [(81, 2), 130, 32]-NRT-code) | [i] | ||
| 29 | No linear OOA(2733, 81, F27, 2, 32) (dual of [(81, 2), 129, 33]-NRT-code) | [i] | ||
| 30 | No linear OOA(2734, 81, F27, 2, 33) (dual of [(81, 2), 128, 34]-NRT-code) | [i] | ||
| 31 | No linear OOA(2735, 81, F27, 2, 34) (dual of [(81, 2), 127, 35]-NRT-code) | [i] | ||
| 32 | No linear OOA(2736, 81, F27, 2, 35) (dual of [(81, 2), 126, 36]-NRT-code) | [i] | ||
| 33 | No linear OOA(2737, 81, F27, 2, 36) (dual of [(81, 2), 125, 37]-NRT-code) | [i] | ||
| 34 | No linear OOA(2738, 81, F27, 2, 37) (dual of [(81, 2), 124, 38]-NRT-code) | [i] | ||
| 35 | No linear OOA(2739, 81, F27, 2, 38) (dual of [(81, 2), 123, 39]-NRT-code) | [i] | ||
| 36 | No linear OOA(2740, 81, F27, 2, 39) (dual of [(81, 2), 122, 40]-NRT-code) | [i] | ||
| 37 | No linear OOA(2741, 81, F27, 2, 40) (dual of [(81, 2), 121, 41]-NRT-code) | [i] | ||
| 38 | No linear OOA(2742, 81, F27, 2, 41) (dual of [(81, 2), 120, 42]-NRT-code) | [i] | ||
| 39 | No linear OOA(2743, 81, F27, 2, 42) (dual of [(81, 2), 119, 43]-NRT-code) | [i] | ||
| 40 | No linear OOA(2744, 81, F27, 2, 43) (dual of [(81, 2), 118, 44]-NRT-code) | [i] | ||
| 41 | No linear OOA(2745, 81, F27, 2, 44) (dual of [(81, 2), 117, 45]-NRT-code) | [i] | ||
| 42 | No linear OOA(2746, 81, F27, 2, 45) (dual of [(81, 2), 116, 46]-NRT-code) | [i] | ||
| 43 | No linear OOA(2747, 81, F27, 2, 46) (dual of [(81, 2), 115, 47]-NRT-code) | [i] | ||
| 44 | No linear OOA(2748, 81, F27, 2, 47) (dual of [(81, 2), 114, 48]-NRT-code) | [i] | ||
| 45 | No linear OOA(2749, 81, F27, 2, 48) (dual of [(81, 2), 113, 49]-NRT-code) | [i] | ||
| 46 | No linear OOA(2750, 81, F27, 2, 49) (dual of [(81, 2), 112, 50]-NRT-code) | [i] | ||
| 47 | No linear OOA(2751, 81, F27, 2, 50) (dual of [(81, 2), 111, 51]-NRT-code) | [i] | ||
| 48 | No linear OOA(2752, 81, F27, 2, 51) (dual of [(81, 2), 110, 52]-NRT-code) | [i] | ||
| 49 | No linear OOA(2728, 81, F27, 2, 27) (dual of [(81, 2), 134, 28]-NRT-code) | [i] | Depth Reduction | |
| 50 | No digital (1, 28, 81)-net over F27 | [i] | Extracting Embedded Orthogonal Array | |