Information on Result #1853145
There is no (101, m, 837)-net in base 9 for arbitrarily large m, because m-reduction would yield (101, 2507, 837)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92507, 837, S9, 3, 2406), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 61 026827 035277 246817 408915 022157 934232 460071 472596 140503 462665 356843 253298 554552 657115 159037 783953 904427 156680 636831 373938 371738 343190 013889 980167 973337 056622 839759 862589 610132 324901 646428 882413 343475 400155 506363 410703 171754 892826 293665 349793 909967 907646 914116 825288 284075 163219 962818 843591 636694 674619 545424 145190 874651 362794 464308 557206 142031 606289 380219 160137 799132 403026 460870 006699 972637 971961 180380 416339 491337 610714 662089 851597 012954 173351 649524 785461 340283 274210 981162 757699 255241 241291 175708 872032 350075 571187 432955 579583 386149 886584 739173 971502 176280 565579 969567 686501 025686 651741 525752 680988 611692 386565 843254 352566 804602 477770 038980 567562 017409 376050 577725 699420 165342 954804 602402 551601 782185 556609 340632 142580 492870 371867 729628 951322 394834 138991 941037 810883 987432 168510 340102 845173 185355 985068 970053 975428 231216 498012 623788 470129 156320 266423 619334 843348 594054 649194 860440 859386 991624 435288 752830 728051 803601 711614 227132 070832 485750 733533 321836 138822 084397 029310 655466 451570 300586 846451 536142 946355 152400 726215 185004 539852 177287 034471 436182 767387 924287 278998 930297 481342 924796 196519 889025 153299 131104 206327 445387 431827 145922 484861 694666 477791 873872 619659 353095 648047 952138 898510 818765 270469 812544 593061 817809 192732 062990 958320 813243 514584 512474 835987 914114 889483 936240 989139 104778 467741 787166 924405 004335 845084 348273 984015 589923 991598 596044 803880 648015 866768 148063 546416 864285 372340 541604 620880 767137 407472 638916 633973 736887 987527 325868 765617 891288 110645 802584 272920 110914 782061 204725 401883 242477 404916 877468 709533 352595 378133 673543 688038 386332 900828 891315 941328 860127 806761 482414 076610 729762 332422 885482 617925 407444 526120 195193 197000 934399 055327 606727 685969 313151 458228 404144 581152 342358 325289 340388 917943 346702 419149 541221 852443 564023 043311 803789 357016 568640 498701 951260 282600 834305 104392 528553 275316 427891 542121 513341 386585 531299 420798 431913 058184 012268 404711 433572 504438 936345 040902 047267 874727 906135 815622 085767 582865 306410 610932 783765 408760 079629 916210 982154 678438 665712 616331 075761 111557 228411 897085 880152 053763 300528 107878 815008 602362 883567 539291 251874 790268 735375 294302 063367 295154 763502 557142 589911 675744 327324 709659 812815 678772 938318 509455 735982 132538 802558 572124 783553 808573 371496 349920 724519 860770 450239 989059 070127 571726 644114 176742 405725 095924 672484 836531 179075 525488 914660 479305 231626 505815 906216 870241 751713 912604 582966 545052 576311 400931 680828 003641 598633 956612 499071 / 2407 > 92507 [i]
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 (101, 836)-sequence in base 9 | [i] | Net from Sequence | |
| 2 | No (101, 101+k, 837)-net in base 9 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (101, m, 837)-net in base 9 with unbounded m | [i] | ||
| 4 | No digital (101, 101+k, 837)-net over F9 for arbitrarily large k | [i] | ||
| 5 | No digital (101, m, 837)-net over F9 with unbounded m | [i] | ||