Information on Result #1850298
There is no (61, m, 135)-net in base 3 for arbitrarily large m, because m-reduction would yield (61, 534, 135)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3534, 135, S3, 4, 473), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 49117 362627 542106 424569 766777 759592 841145 602807 758577 568338 354385 898038 247528 906548 185947 296552 815440 128655 712534 888888 911192 807996 160696 178371 455245 509345 055665 936415 304928 006574 745555 215600 945614 367444 563474 858184 450839 992078 414152 895647 500432 015400 282089 / 79 > 3534 [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 (61, 134)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (61, 61+k, 135)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (61, m, 135)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (61, 61+k, 135)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (61, m, 135)-net over F3 with unbounded m | [i] | ||