Information on Result #1858201
There is no (9, 330)-sequence in base 32, because net from sequence would yield (9, m, 331)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (9, 329, 331)-net in base 32, but
- extracting embedded OOA [i] would yield OA(32329, 331, S32, 320), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 550662 536265 139487 336747 918215 507788 856602 474434 068973 913648 876820 927379 487137 817296 092002 115837 257842 863570 954340 366750 677225 146269 558152 396211 465868 082914 027102 713968 542359 118863 940375 628452 122921 737355 150111 873537 862957 803747 581998 043497 580718 077816 681217 646015 742085 017678 941185 582577 497983 587403 771467 313186 370758 146887 124423 798842 929260 229110 600030 930622 673428 170499 718653 924061 606905 007718 355208 175786 066005 332178 916530 215686 433868 533074 484274 332202 289953 004555 874400 361329 424107 793614 372864 / 321 > 32329 [i]
- extracting embedded OOA [i] would yield OA(32329, 331, S32, 320), 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 (9, 330)-sequence in base 32 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (9, m, 330)-net in base 32 with m > ∞ | [i] | ||
| 3 | No digital (9, 330)-sequence over F32 (for arbitrarily large k) | [i] | ||
| 4 | No digital (9, m, 330)-net over F32 with m > ∞ | [i] | ||