Information on Result #599731
There is no digital (12, 62, 68)-net over F5, because extracting embedded orthogonal array would yield linear OA(562, 68, F5, 50) (dual of [68, 6, 51]-code), but
- construction Y1 [i] 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, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (12, 63, 68)-net over F5 | [i] | m-Reduction | |
| 2 | No digital (12, 64, 68)-net over F5 | [i] | ||
| 3 | No digital (12, 65, 68)-net over F5 | [i] | ||
| 4 | No digital (12, 66, 68)-net over F5 | [i] | ||
| 5 | No digital (12, 67, 68)-net over F5 | [i] | ||
| 6 | No digital (12, 68, 68)-net over F5 | [i] | ||
| 7 | No digital (12, 69, 68)-net over F5 | [i] | ||
| 8 | No digital (12, 70, 68)-net over F5 | [i] | ||
| 9 | No digital (12, 71, 68)-net over F5 | [i] | ||
| 10 | No digital (12, 72, 68)-net over F5 | [i] | ||
| 11 | No digital (12, 73, 68)-net over F5 | [i] | ||
| 12 | No digital (12, 74, 68)-net over F5 | [i] | ||
| 13 | No digital (12, 75, 68)-net over F5 | [i] | ||
| 14 | No digital (12, 76, 68)-net over F5 | [i] | ||
| 15 | No digital (12, 77, 68)-net over F5 | [i] | ||
| 16 | No digital (12, 78, 68)-net over F5 | [i] | ||
| 17 | No digital (12, 79, 68)-net over F5 | [i] | ||
| 18 | No digital (12, 80, 68)-net over F5 | [i] | ||
| 19 | No digital (12, 81, 68)-net over F5 | [i] | ||
| 20 | No digital (12, 82, 68)-net over F5 | [i] | ||
| 21 | No digital (12, 83, 68)-net over F5 | [i] | ||
| 22 | No digital (12, 84, 68)-net over F5 | [i] | ||
| 23 | No digital (12, 85, 68)-net over F5 | [i] | ||
| 24 | No digital (12, 86, 68)-net over F5 | [i] | ||
| 25 | No digital (12, 87, 68)-net over F5 | [i] | ||
| 26 | No digital (12, 88, 68)-net over F5 | [i] | ||
| 27 | No digital (12, 89, 68)-net over F5 | [i] | ||
| 28 | No digital (12, 90, 68)-net over F5 | [i] | ||
| 29 | No digital (12, 91, 68)-net over F5 | [i] | ||
| 30 | No digital (12, 92, 68)-net over F5 | [i] | ||
| 31 | No digital (12, 93, 68)-net over F5 | [i] | ||
| 32 | No digital (12, 94, 68)-net over F5 | [i] | ||
| 33 | No digital (12, 95, 68)-net over F5 | [i] | ||
| 34 | No digital (12, 96, 68)-net over F5 | [i] | ||
| 35 | No digital (12, 97, 68)-net over F5 | [i] | ||
| 36 | No digital (12, 98, 68)-net over F5 | [i] | ||
| 37 | No digital (12, 99, 68)-net over F5 | [i] | ||
| 38 | No digital (12, 100, 68)-net over F5 | [i] | ||
| 39 | No digital (12, 101, 68)-net over F5 | [i] | ||
| 40 | No digital (12, 102, 68)-net over F5 | [i] | ||
| 41 | No digital (12, 103, 68)-net over F5 | [i] | ||
| 42 | No digital (12, 104, 68)-net over F5 | [i] | ||
| 43 | No digital (12, 105, 68)-net over F5 | [i] | ||
| 44 | No digital (12, 106, 68)-net over F5 | [i] | ||
| 45 | No digital (12, 107, 68)-net over F5 | [i] | ||
| 46 | No digital (12, 108, 68)-net over F5 | [i] | ||
| 47 | No digital (12, 109, 68)-net over F5 | [i] | ||
| 48 | No digital (12, 110, 68)-net over F5 | [i] | ||
| 49 | No digital (12, 111, 68)-net over F5 | [i] | ||
| 50 | No digital (12, 112, 68)-net over F5 | [i] | ||
| 51 | No digital (12, 113, 68)-net over F5 | [i] | ||
| 52 | No digital (12, 114, 68)-net over F5 | [i] | ||
| 53 | No digital (12, 115, 68)-net over F5 | [i] | ||
| 54 | No digital (12, 116, 68)-net over F5 | [i] | ||
| 55 | No digital (12, 117, 68)-net over F5 | [i] | ||
| 56 | No digital (12, 118, 68)-net over F5 | [i] | ||
| 57 | No digital (12, 119, 68)-net over F5 | [i] | ||
| 58 | No digital (12, 120, 68)-net over F5 | [i] | ||
| 59 | No digital (12, 121, 68)-net over F5 | [i] | ||
| 60 | No digital (12, 122, 68)-net over F5 | [i] | ||