Information on Result #1856824
There is no (224, 462)-sequence in base 3, because net from sequence would yield (224, m, 463)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (224, 2771, 463)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32771, 463, S3, 6, 2547), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 163906 189182 712180 674415 902474 657987 078097 818106 396677 067710 996558 202251 550019 104056 147390 613427 962823 638821 392978 679549 288474 264477 719414 342363 266970 954217 604239 892926 419936 491063 037691 636247 633231 956070 804675 504818 908364 770798 525688 050720 520349 713698 180459 525632 172921 398774 900350 639709 041029 629576 030175 152222 948284 357646 667422 155075 998342 958436 531106 711034 874363 087539 350280 234160 862232 413332 364723 508799 944342 093787 376533 157397 439445 261815 312566 663326 983861 905925 488829 510306 718360 396441 705415 515225 175426 470007 169102 682692 478450 914876 910973 728511 432784 362535 891853 798826 660694 908173 133798 277411 572755 017966 293601 826522 909030 806951 727783 097971 933869 466342 296303 174521 849221 199321 524345 530571 080176 096442 666370 584524 734360 502134 696226 261263 083210 081497 020970 322318 735233 955667 671288 301722 169571 098297 394112 491296 664428 418828 884310 775230 721457 079537 271581 202660 401324 530714 362489 525183 941241 377665 660033 760562 836009 568462 267677 218339 264710 421294 800352 015305 266614 783946 295106 604515 482124 197467 415362 860928 388374 318317 032032 328910 531145 796277 148079 893272 669538 122575 062388 879727 440884 964733 726150 050659 468685 541872 253386 685161 364335 497555 203303 455529 883377 167352 755369 014304 774541 583503 269000 482528 265843 458518 999968 378502 650053 276012 573964 590131 963470 268316 725646 948652 322552 120339 962398 180312 954482 941480 751692 908081 482271 / 1274 > 32771 [i]
- extracting embedded OOA [i] would yield OOA(32771, 463, S3, 6, 2547), 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 (224, 462)-sequence in base 3 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (224, m, 462)-net in base 3 with m > ∞ | [i] | ||
| 3 | No digital (224, 462)-sequence over F3 (for arbitrarily large k) | [i] | ||
| 4 | No digital (224, m, 462)-net over F3 with m > ∞ | [i] | ||