Information on Result #1856539
There is no (200, 211)-sequence in base 2, because net from sequence would yield (200, m, 212)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (200, 1474, 212)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21474, 212, S2, 7, 1274), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 719 170794 843990 166734 688893 457449 385510 221806 933510 608403 806359 799390 528475 867679 003360 022603 585089 803259 595628 835589 050373 871614 686588 415827 443444 001294 201116 212906 298232 642351 595171 259922 459936 655680 621445 637257 770674 088188 501705 451724 831457 397130 832956 914770 751962 865303 857066 406538 629165 991556 682571 885824 218291 930812 568475 222926 864244 647425 956374 048238 875019 564476 858523 229962 951909 707901 920288 089526 793617 129102 639517 712188 066848 525237 878784 / 1275 > 21474 [i]
- extracting embedded OOA [i] would yield OOA(21474, 212, S2, 7, 1274), but
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 (200, 211)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (200, m, 211)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (200, 211)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (200, m, 211)-net over F2 with m > ∞ | [i] | ||