Information on Result #523847
There is no (3, 61, 65)-net in base 16, because extracting embedded orthogonal array would yield OA(1661, 65, S16, 58), but
- the linear programming bound shows that M ≥ 159214 122701 309768 707410 104386 945873 298246 228915 255775 554254 178010 880553 254912 / 5487 > 1661 [i]
Mode: Bound.
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 (3, 62, 65)-net in base 16 | [i] | m-Reduction | |
| 2 | No (3, 63, 65)-net in base 16 | [i] | ||
| 3 | No (3, 64, 65)-net in base 16 | [i] | ||
| 4 | No (3, 65, 65)-net in base 16 | [i] | ||
| 5 | No (3, 66, 65)-net in base 16 | [i] | ||
| 6 | No (3, 67, 65)-net in base 16 | [i] | ||
| 7 | No (3, 68, 65)-net in base 16 | [i] | ||
| 8 | No (3, 69, 65)-net in base 16 | [i] | ||
| 9 | No (3, 70, 65)-net in base 16 | [i] | ||
| 10 | No (3, 71, 65)-net in base 16 | [i] | ||
| 11 | No (3, 72, 65)-net in base 16 | [i] | ||
| 12 | No (3, 73, 65)-net in base 16 | [i] | ||
| 13 | No (3, 74, 65)-net in base 16 | [i] | ||
| 14 | No (3, 75, 65)-net in base 16 | [i] | ||
| 15 | No (3, 76, 65)-net in base 16 | [i] | ||
| 16 | No (3, 77, 65)-net in base 16 | [i] | ||
| 17 | No (3, 78, 65)-net in base 16 | [i] | ||
| 18 | No (3, 79, 65)-net in base 16 | [i] | ||
| 19 | No (3, 80, 65)-net in base 16 | [i] | ||
| 20 | No (3, 81, 65)-net in base 16 | [i] | ||
| 21 | No (3, 82, 65)-net in base 16 | [i] | ||
| 22 | No (3, 83, 65)-net in base 16 | [i] | ||
| 23 | No (3, 84, 65)-net in base 16 | [i] | ||
| 24 | No (3, 85, 65)-net in base 16 | [i] | ||
| 25 | No (3, 86, 65)-net in base 16 | [i] | ||
| 26 | No (3, 87, 65)-net in base 16 | [i] | ||
| 27 | No (3, 88, 65)-net in base 16 | [i] | ||
| 28 | No (3, 89, 65)-net in base 16 | [i] | ||
| 29 | No (3, 90, 65)-net in base 16 | [i] | ||
| 30 | No (3, 91, 65)-net in base 16 | [i] | ||
| 31 | No (3, 92, 65)-net in base 16 | [i] | ||
| 32 | No (3, 93, 65)-net in base 16 | [i] | ||
| 33 | No (3, 94, 65)-net in base 16 | [i] | ||
| 34 | No (3, 95, 65)-net in base 16 | [i] | ||
| 35 | No (3, 96, 65)-net in base 16 | [i] | ||
| 36 | No (3, 97, 65)-net in base 16 | [i] | ||
| 37 | No (3, 98, 65)-net in base 16 | [i] | ||
| 38 | No (3, 99, 65)-net in base 16 | [i] | ||
| 39 | No (3, 100, 65)-net in base 16 | [i] | ||
| 40 | No (3, 101, 65)-net in base 16 | [i] | ||
| 41 | No (3, 102, 65)-net in base 16 | [i] | ||
| 42 | No (3, 103, 65)-net in base 16 | [i] | ||
| 43 | No (3, 104, 65)-net in base 16 | [i] | ||
| 44 | No (3, 105, 65)-net in base 16 | [i] | ||
| 45 | No (3, 106, 65)-net in base 16 | [i] | ||
| 46 | No (3, 107, 65)-net in base 16 | [i] | ||
| 47 | No (3, 108, 65)-net in base 16 | [i] | ||
| 48 | No (3, 109, 65)-net in base 16 | [i] | ||
| 49 | No (3, 110, 65)-net in base 16 | [i] | ||
| 50 | No (3, 111, 65)-net in base 16 | [i] | ||
| 51 | No (3, 112, 65)-net in base 16 | [i] | ||
| 52 | No (3, 113, 65)-net in base 16 | [i] | ||
| 53 | No (3, 114, 65)-net in base 16 | [i] | ||
| 54 | No (3, 115, 65)-net in base 16 | [i] | ||
| 55 | No (3, 116, 65)-net in base 16 | [i] | ||
| 56 | No (3, 117, 65)-net in base 16 | [i] | ||
| 57 | No (3, 118, 65)-net in base 16 | [i] | ||
| 58 | No (3, 119, 65)-net in base 16 | [i] | ||
| 59 | No (3, 120, 65)-net in base 16 | [i] | ||
| 60 | No (3, 121, 65)-net in base 16 | [i] | ||
| 61 | No (3, 122, 65)-net in base 16 | [i] | ||
| 62 | No (3, 123, 65)-net in base 16 | [i] | ||
| 63 | No (3, 124, 65)-net in base 16 | [i] | ||
| 64 | No (3, 125, 65)-net in base 16 | [i] | ||
| 65 | No (3, 126, 65)-net in base 16 | [i] | ||
| 66 | No (3, 127, 65)-net in base 16 | [i] | ||
| 67 | No (3, 128, 65)-net in base 16 | [i] | ||
| 68 | No (3, 129, 65)-net in base 16 | [i] | ||
| 69 | No (3, 130, 65)-net in base 16 | [i] | ||
| 70 | No (3, m, 65)-net in base 16 for arbitrarily large m | [i] | m-Reduction from Arbitrarily Large Net | |