Information on Result #1854615
There is no (6, m, 232)-net in base 32 for arbitrarily large m, because m-reduction would yield (6, 230, 232)-net in base 32, but
- extracting embedded OOA [i] would yield OA(32230, 232, S32, 224), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 915028 959542 212446 210073 198029 166515 784692 079580 211139 212505 444538 860658 949885 332594 359292 042110 194708 214048 439904 578978 845376 534722 313641 621351 480973 480043 908126 270174 759811 399026 124609 021081 575171 379977 076987 013639 537796 789356 709699 080458 003201 462073 589886 071984 887783 987366 625001 727879 234925 348475 343197 602958 922805 410768 939399 578202 691017 375744 / 225 > 32230 [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 (6, 231)-sequence in base 32 | [i] | Net from Sequence | |
| 2 | No (6, 6+k, 232)-net in base 32 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (6, m, 232)-net in base 32 with unbounded m | [i] | ||
| 4 | No digital (6, 6+k, 232)-net over F32 for arbitrarily large k | [i] | ||
| 5 | No digital (6, m, 232)-net over F32 with unbounded m | [i] | ||