Information on Result #1850889
There is no (32, m, 110)-net in base 4 for arbitrarily large m, because m-reduction would yield (32, 435, 110)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4435, 110, S4, 4, 403), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 054875 063481 616124 677859 711331 326146 029316 510093 812405 543725 714230 154498 556273 149990 616921 915800 320772 623552 815563 309832 963862 612446 544498 079601 274639 873255 874571 437476 078886 965066 542754 190312 342423 904086 653876 992402 014005 611975 088780 301577 371103 880548 449901 346816 / 101 > 4435 [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 (32, 109)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (32, 32+k, 110)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (32, m, 110)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (32, 32+k, 110)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (32, m, 110)-net over F4 with unbounded m | [i] | ||