Information on Result #1857671
There is no (83, 691)-sequence in base 9, because net from sequence would yield (83, m, 692)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (83, 2072, 692)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92072, 692, S9, 3, 1989), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 939710 282301 128090 641170 817104 860943 569477 105780 998432 840518 092530 104175 308664 223679 561148 229939 273816 271151 850479 839895 588407 008963 888541 772072 945553 619254 887667 426423 128469 131820 579081 677905 075612 427011 250916 781727 607259 752458 894096 526320 736458 707286 205750 783862 848805 570794 324347 342671 228994 277730 099413 678281 112317 155109 870859 053869 980800 177466 355244 037599 281342 917379 100742 405030 120026 600863 905220 942573 891097 961382 002544 051113 192133 177000 614771 170427 151259 569673 116167 268060 833107 209615 188946 521651 184694 482030 416488 398505 062223 726261 905852 892574 992153 776348 690871 659924 686329 720816 583802 662176 501436 309548 059187 391258 198083 281705 237949 661641 212298 259456 375604 221624 685208 039511 382267 988020 625859 290550 539932 697143 260476 450340 393088 559309 421055 491886 722644 730242 599366 061591 195031 477135 132284 458786 593767 684496 570732 739832 893344 771838 600761 287924 012396 276404 619564 573948 179534 266248 449667 057008 829366 882316 913902 212910 308620 901365 121468 324063 340071 670894 880687 994037 749698 007355 996637 603106 143121 813279 652932 152753 605624 188554 321716 429831 562763 456917 758068 979001 516902 058653 081473 012386 648556 421007 398118 164451 472805 351403 907374 892819 815201 989030 234165 576459 861108 088937 529614 693419 043145 941809 502878 706670 613128 584069 211249 159493 592409 323835 616562 269240 506105 188636 023731 347363 807540 825454 944712 087292 596420 841488 679901 440509 317164 347528 591200 076998 450781 517580 362114 222300 760547 378514 661518 496432 014291 649859 549971 809064 133101 608533 394763 791114 518614 560752 616150 933225 642660 379323 602821 381483 699473 084964 429108 033629 536186 958789 616668 424875 465451 735451 789365 087933 923193 473732 340878 406537 171434 084363 151739 822421 855319 612392 413291 184279 135814 050751 883157 803355 417909 907460 362825 282655 840585 970150 671174 844823 389916 464736 167796 498552 143177 636571 096172 212009 769287 903644 204094 748235 284634 189386 896873 689601 739552 692110 727944 818354 543045 634238 190015 125813 347847 165423 574805 303718 361723 255599 227166 048005 308418 611363 314776 394176 797844 798926 997196 334954 474800 616394 818700 996131 / 995 > 92072 [i]
- extracting embedded OOA [i] would yield OOA(92072, 692, S9, 3, 1989), 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 (83, 691)-sequence in base 9 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (83, m, 691)-net in base 9 with m > ∞ | [i] | ||
| 3 | No digital (83, 691)-sequence over F9 (for arbitrarily large k) | [i] | ||
| 4 | No digital (83, m, 691)-net over F9 with m > ∞ | [i] | ||