Information on Result #1857219
There is no (107, 446)-sequence in base 5, because net from sequence would yield (107, m, 447)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (107, 1783, 447)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51783, 447, S5, 4, 1676), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 915275 377743 246870 913866 144501 883151 145048 440249 413883 996685 743426 099929 742585 160561 144027 299707 872347 094500 680092 282531 751637 638498 369733 938702 520749 712998 702506 027885 954592 578557 689531 039119 955276 696355 350500 596806 352492 310299 526602 108518 995321 941861 563044 269494 092353 326713 498076 050757 033651 086487 104645 603068 461070 113873 725600 907376 637404 255038 815901 082684 024255 254514 451415 386893 183019 228679 102307 569355 300093 451752 729986 645233 059103 988307 828401 408947 738528 622468 311015 991426 254955 265116 138576 964088 670487 599954 774993 612349 853768 378469 853030 758962 896453 772597 376605 981523 231837 038863 334112 726687 859973 734861 727709 490782 885307 643036 800499 335166 048759 734120 777310 007642 854798 021657 512922 758987 228907 304198 244065 419551 693161 863669 837047 530754 204319 866390 732435 745494 518127 258779 379186 952870 631243 044050 686385 068424 903862 433145 458002 335053 898709 114408 848922 055320 951122 588134 158750 106300 008065 562569 332122 412070 624531 518958 266386 245902 830233 009836 622973 540438 686617 094800 674234 635444 593911 627636 287120 074710 850590 542529 174409 975092 488213 456410 617205 072239 136171 571706 654478 677715 458556 336492 486671 958726 417402 192648 681123 141059 691147 010464 676762 865146 948765 833284 156397 589012 001531 391879 584263 999234 997034 003258 331580 354933 976195 752620 697021 484375 / 559 > 51783 [i]
- extracting embedded OOA [i] would yield OOA(51783, 447, S5, 4, 1676), 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 (107, 446)-sequence in base 5 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (107, m, 446)-net in base 5 with m > ∞ | [i] | ||
| 3 | No digital (107, 446)-sequence over F5 (for arbitrarily large k) | [i] | ||
| 4 | No digital (107, m, 446)-net over F5 with m > ∞ | [i] | ||