Information on Result #1852038
There is no (22, m, 152)-net in base 7 for arbitrarily large m, because m-reduction would yield (22, 452, 152)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7452, 152, S7, 3, 430), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 008999 018872 994671 643058 056421 817552 816176 154794 306246 388371 773779 788778 593966 979956 420926 333885 375929 479526 374758 225093 672371 196092 275354 442327 630191 452450 057262 372967 920954 346764 954828 900107 767706 377889 628617 182108 502497 342162 868862 489019 484094 461079 810987 447448 859094 319269 080922 350418 747502 928314 210213 959146 375089 122404 037386 323858 088140 855387 712716 767425 460529 519852 547942 398223 / 431 > 7452 [i]
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 (22, 151)-sequence in base 7 | [i] | Net from Sequence | |
| 2 | No (22, 22+k, 152)-net in base 7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (22, m, 152)-net in base 7 with unbounded m | [i] | ||
| 4 | No digital (22, 22+k, 152)-net over F7 for arbitrarily large k | [i] | ||
| 5 | No digital (22, m, 152)-net over F7 with unbounded m | [i] | ||