Information on Result #1856874
There is no (23, 81)-sequence in base 4, because net from sequence would yield (23, m, 82)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (23, 242, 82)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4242, 82, S4, 3, 219), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2896 982654 693240 790722 122229 248058 331734 699076 393093 227997 297658 532344 973624 742495 471644 063642 920549 236319 392080 665346 046975 721430 379528 764237 283328 / 55 > 4242 [i]
- extracting embedded OOA [i] would yield OOA(4242, 82, S4, 3, 219), but
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 (23, 81)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (23, m, 81)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (23, 81)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (23, m, 81)-net over F4 with m > ∞ | [i] | ||