Information on Result #1856319
There is no (4, m, 81)-net in base 16 for arbitrarily large m, because m-reduction would yield (4, 77, 81)-net in base 16, but
- extracting embedded orthogonal array [i] 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 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, 80)-sequence in base 16 | [i] | Net from Sequence | |
| 2 | No (4, 4+k, 81)-net in base 16 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (4, m, 81)-net in base 16 with unbounded m | [i] | ||