Information on Result #1850931
There is no (46, m, 153)-net in base 4 for arbitrarily large m, because m-reduction would yield (46, 607, 153)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4607, 153, S4, 4, 561), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 115 664102 639503 896631 830525 630571 815702 819129 682066 847627 847714 319962 991548 974951 693565 438529 810906 006280 799466 342060 048274 551933 980423 471435 719639 890637 195039 709535 000640 819382 889984 124079 679091 534258 117211 147071 567490 760048 289929 233300 770718 934078 254963 512902 503103 385976 458788 715029 563422 617054 672250 938457 367383 670313 103946 764806 458257 488588 382856 279242 623617 597440 / 281 > 4607 [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 (46, 152)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (46, 46+k, 153)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (46, m, 153)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (46, 46+k, 153)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (46, m, 153)-net over F4 with unbounded m | [i] | ||