Information on Result #1857437
There is no (23, 182)-sequence in base 8, because net from sequence would yield (23, m, 183)-net in base 8 for arbitrarily large m, but
- m-reduction [i] would yield (23, 363, 183)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8363, 183, S8, 2, 340), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 493751 205676 606832 657637 388003 341351 342351 984601 249759 303922 831140 906849 978490 894135 364952 776388 077492 317102 964182 918059 870391 017703 287924 391838 953561 052929 408714 392469 141974 975760 213967 734352 914224 009940 361286 312896 587817 539484 210967 572044 974784 288658 049638 355661 532419 763860 122064 288222 480274 006045 437296 761179 689817 015542 874112 / 341 > 8363 [i]
- extracting embedded OOA [i] would yield OOA(8363, 183, S8, 2, 340), 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, 182)-sequence in base 8 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (23, m, 182)-net in base 8 with m > ∞ | [i] | ||
| 3 | No digital (23, 182)-sequence over F8 (for arbitrarily large k) | [i] | ||
| 4 | No digital (23, m, 182)-net over F8 with m > ∞ | [i] | ||