Information on Result #1857422
There is no (8, 73)-sequence in base 8, because net from sequence would yield (8, m, 74)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (8, 144, 74)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8144, 74, S8, 2, 136), but
- the LP bound with quadratic polynomials shows that M ≥ 1 558240 368095 897951 083068 771488 413041 331277 636361 208915 245809 524305 417174 986761 600148 465616 230526 442890 733860 560308 807367 883476 697088 / 137 > 8144 [i]
- extracting embedded OOA [i] would yield OOA(8144, 74, S8, 2, 136), 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 (8, 73)-sequence in base 8 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (8, m, 73)-net in base 8 with m > ∞ | [i] | ||
| 3 | No digital (8, 73)-sequence over F8 (for arbitrarily large k) | [i] | ||
| 4 | No digital (8, m, 73)-net over F8 with m > ∞ | [i] | ||