Information on Result #547632
There is no linear OA(1634, 51, F16, 32) (dual of [51, 17, 33]-code), because residual code would yield OA(162, 18, S16, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 271 > 162 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(1635, 52, F16, 33) (dual of [52, 17, 34]-code) | [i] | Truncation | |
| 2 | No linear OA(1636, 53, F16, 34) (dual of [53, 17, 35]-code) | [i] | ||
| 3 | No linear OA(1637, 54, F16, 35) (dual of [54, 17, 36]-code) | [i] | ||
| 4 | No linear OA(1638, 55, F16, 36) (dual of [55, 17, 37]-code) | [i] | ||
| 5 | No linear OA(1639, 56, F16, 37) (dual of [56, 17, 38]-code) | [i] | ||
| 6 | No linear OA(1640, 57, F16, 38) (dual of [57, 17, 39]-code) | [i] | ||
| 7 | No linear OA(1641, 58, F16, 39) (dual of [58, 17, 40]-code) | [i] | ||
| 8 | No linear OA(1642, 59, F16, 40) (dual of [59, 17, 41]-code) | [i] | ||
| 9 | No linear OA(1643, 60, F16, 41) (dual of [60, 17, 42]-code) | [i] | ||
| 10 | No linear OA(1644, 61, F16, 42) (dual of [61, 17, 43]-code) | [i] | ||
| 11 | No linear OOA(1635, 51, F16, 2, 33) (dual of [(51, 2), 67, 34]-NRT-code) | [i] | m-Reduction for OOAs | |
| 12 | No linear OOA(1636, 51, F16, 2, 34) (dual of [(51, 2), 66, 35]-NRT-code) | [i] | ||
| 13 | No linear OOA(1637, 51, F16, 2, 35) (dual of [(51, 2), 65, 36]-NRT-code) | [i] | ||
| 14 | No linear OOA(1638, 51, F16, 2, 36) (dual of [(51, 2), 64, 37]-NRT-code) | [i] | ||
| 15 | No linear OOA(1639, 51, F16, 2, 37) (dual of [(51, 2), 63, 38]-NRT-code) | [i] | ||
| 16 | No linear OOA(1640, 51, F16, 2, 38) (dual of [(51, 2), 62, 39]-NRT-code) | [i] | ||
| 17 | No linear OOA(1641, 51, F16, 2, 39) (dual of [(51, 2), 61, 40]-NRT-code) | [i] | ||
| 18 | No linear OOA(1642, 51, F16, 2, 40) (dual of [(51, 2), 60, 41]-NRT-code) | [i] | ||
| 19 | No linear OOA(1643, 51, F16, 2, 41) (dual of [(51, 2), 59, 42]-NRT-code) | [i] | ||
| 20 | No linear OOA(1644, 51, F16, 2, 42) (dual of [(51, 2), 58, 43]-NRT-code) | [i] | ||
| 21 | No linear OOA(1634, 51, F16, 2, 32) (dual of [(51, 2), 68, 33]-NRT-code) | [i] | Depth Reduction | |
| 22 | No digital (2, 34, 51)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |
| 23 | No linear OA(1632, 66, F16, 30) (dual of [66, 34, 31]-code) | [i] | Construction Y1 (Bound) | |