Information on Result #1850034
There is no (207, m, 219)-net in base 2 for arbitrarily large m, because m-reduction would yield (207, 1523, 219)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21523, 219, S2, 7, 1316), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 129460 140117 828898 800689 856769 098902 548989 383434 582902 660920 046043 544098 181200 367223 437183 912015 656964 345392 720164 883069 660579 036946 994831 907547 572591 789654 130895 247720 692761 096086 928013 156721 174049 321164 605791 116374 857443 539797 803730 836222 378391 541088 749863 548658 727802 364291 543446 248596 336600 603738 498896 845989 551764 831598 503889 414683 546596 439874 880206 835502 592108 472257 046449 916975 906747 332066 049828 445159 750591 879325 027739 930587 287931 706849 880014 904119 787520 / 439 > 21523 [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 (207, 218)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (207, 207+k, 219)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (207, m, 219)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (207, 207+k, 219)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (207, m, 219)-net over F2 with unbounded m | [i] | ||