Information on Result #1850292
There is no (59, m, 131)-net in base 3 for arbitrarily large m, because m-reduction would yield (59, 518, 131)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3518, 131, S3, 4, 459), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1774 926975 495066 008096 378028 392386 598262 846236 066312 140648 650519 365207 180525 252735 599647 808383 565940 318146 622275 024913 421026 370424 993835 951967 941410 133140 456542 356771 983396 552091 096136 562406 778745 770320 433126 726074 062416 868946 489296 647754 386077 521614 / 115 > 3518 [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 (59, 130)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (59, 59+k, 131)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (59, m, 131)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (59, 59+k, 131)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (59, m, 131)-net over F3 with unbounded m | [i] | ||