Information on Result #1858400
There is no (1, 130)-sequence in base 64, because net from sequence would yield (1, m, 131)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (1, 129, 131)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64129, 131, S64, 128), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 359114 106063 703798 370219 984742 410466 332205 126109 989319 225557 147754 704702 203399 726411 277962 562135 973685 197744 935448 875852 478791 860694 279747 355800 678568 677946 181447 581781 401213 133886 609947 027230 004277 244697 462656 003657 100713 230572 978176 / 43 > 64129 [i]
- extracting embedded OOA [i] would yield OA(64129, 131, S64, 128), 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 (1, 130)-sequence in base 64 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (1, m, 130)-net in base 64 with m > ∞ | [i] | ||
| 3 | No digital (1, 130)-sequence over F64 (for arbitrarily large k) | [i] | ||
| 4 | No digital (1, m, 130)-net over F64 with m > ∞ | [i] | ||