Information on Result #1856658
There is no (58, 128)-sequence in base 3, because net from sequence would yield (58, m, 129)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (58, 510, 129)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3510, 129, S3, 4, 452), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 367143 646813 489387 003627 305718 372040 052627 849470 463242 453506 214949 146868 181895 203000 340849 165934 557733 411564 256597 136270 597916 672925 325876 797862 769095 844151 308650 452540 820590 172783 184125 740074 424299 824593 696603 255244 038588 520731 776910 176294 287379 / 151 > 3510 [i]
- extracting embedded OOA [i] would yield OOA(3510, 129, S3, 4, 452), 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 (58, 128)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (58, m, 128)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (58, 128)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (58, m, 128)-net over F3 with m > ∞ | [i] | ||