Information on Result #1850958
There is no (55, m, 180)-net in base 4 for arbitrarily large m, because m-reduction would yield (55, 715, 180)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4715, 180, S4, 4, 660), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 23 292165 226338 150497 413837 680749 468165 158064 818907 090678 280277 145093 831671 774801 570450 532309 408343 381370 778690 973470 702023 045705 361421 179050 557263 352433 855467 757534 777884 032434 483025 797135 401934 632090 244028 777349 464485 685605 081042 699734 979180 059788 898455 170515 848758 719151 351344 977588 846016 713656 209655 862263 184840 537771 817665 060935 803432 767334 671398 366933 206983 571478 392544 010283 372701 995731 294508 790281 913243 365906 085225 962475 094016 / 661 > 4715 [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 (55, 179)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (55, 55+k, 180)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (55, m, 180)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (55, 55+k, 180)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (55, m, 180)-net over F4 with unbounded m | [i] | ||