Information on Result #1857146
There is no (34, 151)-sequence in base 5, because net from sequence would yield (34, m, 152)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (34, 452, 152)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5452, 152, S5, 3, 418), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 740513 416693 355016 997209 639927 486465 744811 080605 334355 746853 524060 260535 005747 228243 825945 682713 095885 596545 888210 225649 098270 203211 474587 706072 085855 807305 467956 443740 098258 368615 839347 295399 862640 852109 336497 708544 594422 090615 478382 499485 214106 657122 640064 073074 063462 633303 926707 650788 330283 830873 668193 817138 671875 / 419 > 5452 [i]
- extracting embedded OOA [i] would yield OOA(5452, 152, S5, 3, 418), 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 (34, 151)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (34, m, 151)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (34, 151)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (34, m, 151)-net over F5 with m > ∞ | [i] | ||