Information on Result #1851618
There is no (26, m, 120)-net in base 5 for arbitrarily large m, because m-reduction would yield (26, 356, 120)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5356, 120, S5, 3, 330), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 323604 947840 619454 713164 082434 795472 466741 351807 611801 670303 806980 327070 984661 962357 662803 163279 124548 054904 233129 419928 970788 208892 858866 920989 805084 329599 102508 520039 105712 758908 584033 788569 229050 368528 411980 688364 035785 298256 087116 897106 170654 296875 / 331 > 5356 [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 (26, 119)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (26, 26+k, 120)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (26, m, 120)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (26, 26+k, 120)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (26, m, 120)-net over F5 with unbounded m | [i] | ||