Information on Result #1850916
There is no (41, m, 138)-net in base 4 for arbitrarily large m, because m-reduction would yield (41, 547, 138)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4547, 138, S4, 4, 506), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 59 425560 645910 630905 884124 990717 921563 902855 803263 824051 497735 550591 822807 998080 881523 590364 033077 591306 279900 423082 302703 294424 251652 818623 805523 999752 750658 250215 309902 957701 550030 630720 478197 104912 577302 226397 243493 156503 068559 920929 376390 888476 665893 948828 900870 559790 117517 802383 038493 146955 037678 505795 160026 650958 668255 723520 / 169 > 4547 [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 (41, 137)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (41, 41+k, 138)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (41, m, 138)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (41, 41+k, 138)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (41, m, 138)-net over F4 with unbounded m | [i] | ||