Information on Result #524155
There is no (1, 55, 57)-net in base 27, because extracting embedded orthogonal array would yield OA(2755, 57, S27, 54), but
- the (dual) Plotkin bound shows that M ≥ 430 023359 390034 222082 732011 948356 798311 147247 214997 695270 038813 781532 497547 421283 / 55 > 2755 [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 (1, 56, 57)-net in base 27 | [i] | m-Reduction | |
| 2 | No (1, 57, 57)-net in base 27 | [i] | ||
| 3 | No (1, 58, 57)-net in base 27 | [i] | ||
| 4 | No (1, 59, 57)-net in base 27 | [i] | ||
| 5 | No (1, 60, 57)-net in base 27 | [i] | ||
| 6 | No (1, 61, 57)-net in base 27 | [i] | ||
| 7 | No (1, 62, 57)-net in base 27 | [i] | ||
| 8 | No (1, 63, 57)-net in base 27 | [i] | ||
| 9 | No (1, 64, 57)-net in base 27 | [i] | ||
| 10 | No (1, 65, 57)-net in base 27 | [i] | ||
| 11 | No (1, 66, 57)-net in base 27 | [i] | ||
| 12 | No (1, 67, 57)-net in base 27 | [i] | ||
| 13 | No (1, 68, 57)-net in base 27 | [i] | ||
| 14 | No (1, 69, 57)-net in base 27 | [i] | ||
| 15 | No (1, 70, 57)-net in base 27 | [i] | ||
| 16 | No (1, 71, 57)-net in base 27 | [i] | ||
| 17 | No (1, 72, 57)-net in base 27 | [i] | ||
| 18 | No (1, 73, 57)-net in base 27 | [i] | ||
| 19 | No (1, 74, 57)-net in base 27 | [i] | ||
| 20 | No (1, 75, 57)-net in base 27 | [i] | ||
| 21 | No (1, 76, 57)-net in base 27 | [i] | ||
| 22 | No (1, 77, 57)-net in base 27 | [i] | ||
| 23 | No (1, 78, 57)-net in base 27 | [i] | ||
| 24 | No (1, 79, 57)-net in base 27 | [i] | ||
| 25 | No (1, 80, 57)-net in base 27 | [i] | ||
| 26 | No (1, 81, 57)-net in base 27 | [i] | ||
| 27 | No (1, 82, 57)-net in base 27 | [i] | ||
| 28 | No (1, 83, 57)-net in base 27 | [i] | ||
| 29 | No (1, 84, 57)-net in base 27 | [i] | ||
| 30 | No (1, 85, 57)-net in base 27 | [i] | ||
| 31 | No (1, 86, 57)-net in base 27 | [i] | ||
| 32 | No (1, 87, 57)-net in base 27 | [i] | ||
| 33 | No (1, 88, 57)-net in base 27 | [i] | ||
| 34 | No (1, 89, 57)-net in base 27 | [i] | ||
| 35 | No (1, 90, 57)-net in base 27 | [i] | ||
| 36 | No (1, 91, 57)-net in base 27 | [i] | ||
| 37 | No (1, 92, 57)-net in base 27 | [i] | ||
| 38 | No (1, 93, 57)-net in base 27 | [i] | ||
| 39 | No (1, 94, 57)-net in base 27 | [i] | ||
| 40 | No (1, 95, 57)-net in base 27 | [i] | ||
| 41 | No (1, 96, 57)-net in base 27 | [i] | ||
| 42 | No (1, 97, 57)-net in base 27 | [i] | ||
| 43 | No (1, 98, 57)-net in base 27 | [i] | ||
| 44 | No (1, 99, 57)-net in base 27 | [i] | ||
| 45 | No (1, 100, 57)-net in base 27 | [i] | ||
| 46 | No (1, 101, 57)-net in base 27 | [i] | ||
| 47 | No (1, 102, 57)-net in base 27 | [i] | ||
| 48 | No (1, 103, 57)-net in base 27 | [i] | ||
| 49 | No (1, 104, 57)-net in base 27 | [i] | ||
| 50 | No (1, 105, 57)-net in base 27 | [i] | ||
| 51 | No (1, 106, 57)-net in base 27 | [i] | ||
| 52 | No (1, 107, 57)-net in base 27 | [i] | ||
| 53 | No (1, 108, 57)-net in base 27 | [i] | ||
| 54 | No (1, 109, 57)-net in base 27 | [i] | ||
| 55 | No (1, 110, 57)-net in base 27 | [i] | ||
| 56 | No (1, m, 57)-net in base 27 for arbitrarily large m | [i] | m-Reduction from Arbitrarily Large Net | |