Information on Result #523878
There is no (4, 77, 81)-net in base 16, because extracting embedded orthogonal array would yield OA(1677, 81, S16, 73), but
- the linear programming bound shows that M ≥ 20 058253 259194 796242 490750 709498 450326 191022 155255 442417 783937 598455 532112 408827 665059 378347 638784 / 37999 > 1677 [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 (4, 78, 81)-net in base 16 | [i] | m-Reduction | |
| 2 | No (4, 79, 81)-net in base 16 | [i] | ||
| 3 | No (4, 80, 81)-net in base 16 | [i] | ||
| 4 | No (4, 81, 81)-net in base 16 | [i] | ||
| 5 | No (4, 82, 81)-net in base 16 | [i] | ||
| 6 | No (4, 83, 81)-net in base 16 | [i] | ||
| 7 | No (4, 84, 81)-net in base 16 | [i] | ||
| 8 | No (4, 85, 81)-net in base 16 | [i] | ||
| 9 | No (4, 86, 81)-net in base 16 | [i] | ||
| 10 | No (4, 87, 81)-net in base 16 | [i] | ||
| 11 | No (4, 88, 81)-net in base 16 | [i] | ||
| 12 | No (4, 89, 81)-net in base 16 | [i] | ||
| 13 | No (4, 90, 81)-net in base 16 | [i] | ||
| 14 | No (4, 91, 81)-net in base 16 | [i] | ||
| 15 | No (4, 92, 81)-net in base 16 | [i] | ||
| 16 | No (4, 93, 81)-net in base 16 | [i] | ||
| 17 | No (4, 94, 81)-net in base 16 | [i] | ||
| 18 | No (4, 95, 81)-net in base 16 | [i] | ||
| 19 | No (4, 96, 81)-net in base 16 | [i] | ||
| 20 | No (4, 97, 81)-net in base 16 | [i] | ||
| 21 | No (4, 98, 81)-net in base 16 | [i] | ||
| 22 | No (4, 99, 81)-net in base 16 | [i] | ||
| 23 | No (4, 100, 81)-net in base 16 | [i] | ||
| 24 | No (4, 101, 81)-net in base 16 | [i] | ||
| 25 | No (4, 102, 81)-net in base 16 | [i] | ||
| 26 | No (4, 103, 81)-net in base 16 | [i] | ||
| 27 | No (4, 104, 81)-net in base 16 | [i] | ||
| 28 | No (4, 105, 81)-net in base 16 | [i] | ||
| 29 | No (4, 106, 81)-net in base 16 | [i] | ||
| 30 | No (4, 107, 81)-net in base 16 | [i] | ||
| 31 | No (4, 108, 81)-net in base 16 | [i] | ||
| 32 | No (4, 109, 81)-net in base 16 | [i] | ||
| 33 | No (4, 110, 81)-net in base 16 | [i] | ||
| 34 | No (4, 111, 81)-net in base 16 | [i] | ||
| 35 | No (4, 112, 81)-net in base 16 | [i] | ||
| 36 | No (4, 113, 81)-net in base 16 | [i] | ||
| 37 | No (4, 114, 81)-net in base 16 | [i] | ||
| 38 | No (4, 115, 81)-net in base 16 | [i] | ||
| 39 | No (4, 116, 81)-net in base 16 | [i] | ||
| 40 | No (4, 117, 81)-net in base 16 | [i] | ||
| 41 | No (4, 118, 81)-net in base 16 | [i] | ||
| 42 | No (4, 119, 81)-net in base 16 | [i] | ||
| 43 | No (4, 120, 81)-net in base 16 | [i] | ||
| 44 | No (4, 121, 81)-net in base 16 | [i] | ||
| 45 | No (4, 122, 81)-net in base 16 | [i] | ||
| 46 | No (4, 123, 81)-net in base 16 | [i] | ||
| 47 | No (4, 124, 81)-net in base 16 | [i] | ||
| 48 | No (4, 125, 81)-net in base 16 | [i] | ||
| 49 | No (4, 126, 81)-net in base 16 | [i] | ||
| 50 | No (4, 127, 81)-net in base 16 | [i] | ||
| 51 | No (4, 128, 81)-net in base 16 | [i] | ||
| 52 | No (4, 129, 81)-net in base 16 | [i] | ||
| 53 | No (4, 130, 81)-net in base 16 | [i] | ||
| 54 | No (4, m, 81)-net in base 16 for arbitrarily large m | [i] | m-Reduction from Arbitrarily Large Net | |