Information on Result #1849707
There is no (98, m, 108)-net in base 2 for arbitrarily large m, because m-reduction would yield (98, 855, 108)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2855, 108, S2, 8, 757), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 97 057177 562787 164573 067126 687543 672703 038428 025407 981722 171883 323779 300841 541427 520344 119047 246524 091610 106360 019872 220740 793824 933955 400888 052166 601040 693908 993589 655255 188519 807931 307366 871890 472698 439642 645150 923182 623169 682730 117852 928334 233518 627012 739072 / 379 > 2855 [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 (98, 107)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (98, 98+k, 108)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (98, m, 108)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (98, 98+k, 108)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (98, m, 108)-net over F2 with unbounded m | [i] | ||