Information on Result #523472
There is no (18, 128, 144)-net in base 8, because extracting embedded orthogonal array would yield OA(8128, 144, S8, 110), but
- the linear programming bound shows that M ≥ 6109 893966 434273 613815 828543 318095 703793 603744 881950 919851 825987 742070 359262 466307 770153 217353 472069 496822 008994 926770 763501 404160 / 124 535855 141787 > 8128 [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 (18, 129, 144)-net in base 8 | [i] | m-Reduction | |
| 2 | No (18, 130, 144)-net in base 8 | [i] | ||
| 3 | No (18, 131, 144)-net in base 8 | [i] | ||
| 4 | No (18, 132, 144)-net in base 8 | [i] | ||
| 5 | No (18, 133, 144)-net in base 8 | [i] | ||
| 6 | No (18, 134, 144)-net in base 8 | [i] | ||
| 7 | No (18, 135, 144)-net in base 8 | [i] | ||
| 8 | No (18, 136, 144)-net in base 8 | [i] | ||
| 9 | No (18, 137, 144)-net in base 8 | [i] | ||
| 10 | No (18, 138, 144)-net in base 8 | [i] | ||
| 11 | No (18, 139, 144)-net in base 8 | [i] | ||
| 12 | No (18, 140, 144)-net in base 8 | [i] | ||
| 13 | No (18, 141, 144)-net in base 8 | [i] | ||
| 14 | No (18, 142, 144)-net in base 8 | [i] | ||
| 15 | No (18, 143, 144)-net in base 8 | [i] | ||
| 16 | No (18, 144, 144)-net in base 8 | [i] | ||
| 17 | No (18, 145, 144)-net in base 8 | [i] | ||
| 18 | No (18, 146, 144)-net in base 8 | [i] | ||
| 19 | No (18, 147, 144)-net in base 8 | [i] | ||
| 20 | No (18, 148, 144)-net in base 8 | [i] | ||
| 21 | No (18, 149, 144)-net in base 8 | [i] | ||
| 22 | No (18, 150, 144)-net in base 8 | [i] | ||
| 23 | No (18, 151, 144)-net in base 8 | [i] | ||
| 24 | No (18, 152, 144)-net in base 8 | [i] | ||
| 25 | No (18, 153, 144)-net in base 8 | [i] | ||
| 26 | No (18, 154, 144)-net in base 8 | [i] | ||
| 27 | No (18, 155, 144)-net in base 8 | [i] | ||
| 28 | No (18, 156, 144)-net in base 8 | [i] | ||
| 29 | No (18, 157, 144)-net in base 8 | [i] | ||
| 30 | No (18, 158, 144)-net in base 8 | [i] | ||
| 31 | No (18, 159, 144)-net in base 8 | [i] | ||
| 32 | No (18, 160, 144)-net in base 8 | [i] | ||
| 33 | No (18, 161, 144)-net in base 8 | [i] | ||
| 34 | No (18, 162, 144)-net in base 8 | [i] | ||
| 35 | No (18, 163, 144)-net in base 8 | [i] | ||
| 36 | No (18, 164, 144)-net in base 8 | [i] | ||
| 37 | No (18, 165, 144)-net in base 8 | [i] | ||
| 38 | No (18, 166, 144)-net in base 8 | [i] | ||
| 39 | No (18, 167, 144)-net in base 8 | [i] | ||
| 40 | No (18, 168, 144)-net in base 8 | [i] | ||
| 41 | No (18, 169, 144)-net in base 8 | [i] | ||
| 42 | No (18, 170, 144)-net in base 8 | [i] | ||
| 43 | No (18, 171, 144)-net in base 8 | [i] | ||
| 44 | No (18, 172, 144)-net in base 8 | [i] | ||
| 45 | No (18, 173, 144)-net in base 8 | [i] | ||
| 46 | No (18, m, 144)-net in base 8 for arbitrarily large m | [i] | m-Reduction from Arbitrarily Large Net | |