Information on Result #1856785
There is no (185, 384)-sequence in base 3, because net from sequence would yield (185, m, 385)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (185, 2303, 385)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32303, 385, S3, 6, 2118), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 17462 067597 281707 374896 351567 635936 419907 862607 183866 474330 511664 987387 054351 136366 039518 414172 708872 374237 794618 623181 442070 810296 974090 766543 137155 256557 492097 618994 798087 968580 409069 290645 385538 945903 308275 223819 061177 384530 609713 532582 667046 548132 085151 507589 334527 787291 010309 913637 014665 292521 530469 061366 468935 029085 995035 494303 491451 419621 484146 917955 001455 296052 706518 979290 782891 110717 715546 624244 911913 526122 907448 550083 370092 934731 572469 869476 902741 199371 497528 610422 677838 178767 389893 488301 528896 419696 143002 375776 576023 683818 528837 352192 531467 319427 101553 808628 793916 913994 651465 489219 934327 853636 914769 930912 833069 402706 675840 124260 239204 990529 442355 691864 452809 608629 793081 291882 231345 693334 009375 360732 305275 012262 352668 217354 417830 072567 146662 352592 423308 317920 984267 449393 476913 516641 353222 105152 813675 755229 631618 955630 316861 578424 140651 549578 390643 234060 910727 005091 668705 175306 157602 306450 463210 607345 851387 127783 127254 366434 156145 894730 855633 859213 220194 966760 660336 464026 749285 244147 856813 700302 603265 803729 169842 023243 980747 642863 964226 024275 991088 339702 453542 561436 965862 958981 / 2119 > 32303 [i]
- extracting embedded OOA [i] would yield OOA(32303, 385, S3, 6, 2118), 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 (185, 384)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (185, m, 384)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (185, 384)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (185, m, 384)-net over F3 with m > ∞ | [i] | ||