Information on Result #1856985
There is no (134, 418)-sequence in base 4, because net from sequence would yield (134, m, 419)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (134, 2089, 419)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42089, 419, S4, 5, 1955), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 914114 207548 172030 992359 713703 193388 899393 558759 035967 574070 065343 287535 005219 310746 367884 194031 870591 617579 830238 579816 260710 141231 848927 359341 973736 858337 449659 097326 021008 974073 902594 454108 626424 747980 748864 818845 753250 583881 233493 671120 440173 275262 803729 610430 473685 915694 612920 730051 411461 177361 655882 486673 366662 346843 009882 973969 089531 102042 486211 902588 255874 759957 461320 611064 694995 744393 932250 999595 448522 054508 490848 507011 066639 268403 442257 989963 308146 153818 912637 011540 100833 743572 002505 322265 474624 279522 125839 183495 023250 164744 071081 437684 403565 922199 693456 819879 239561 944088 832009 426592 256522 237701 982726 053200 580841 365494 865119 515501 545187 243147 638427 544445 662390 826864 387806 233258 108940 448560 423715 294174 218639 834507 100922 262025 848120 224102 722972 549352 791813 745687 669590 298844 483428 903093 278849 833381 697306 935967 575504 806731 779121 760773 520977 252692 719144 796771 118824 456308 335876 724459 980512 076499 807435 187816 658851 082976 195382 000302 822070 242639 531137 314267 573359 372676 409515 722644 414759 463844 980022 423544 932964 897529 360978 395014 368330 143028 363578 842086 544837 955304 740860 751049 334992 717860 573368 593510 129423 529823 684331 382878 127945 187765 804157 326971 926109 912694 294934 471699 474757 986645 260087 505586 192139 467557 453655 341628 103764 432007 808589 758464 / 163 > 42089 [i]
- extracting embedded OOA [i] would yield OOA(42089, 419, S4, 5, 1955), 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 (134, 418)-sequence in base 4 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (134, m, 418)-net in base 4 with m > ∞ | [i] | ||
| 3 | No digital (134, 418)-sequence over F4 (for arbitrarily large k) | [i] | ||
| 4 | No digital (134, m, 418)-net over F4 with m > ∞ | [i] | ||