Information on Result #1858261
There is no (69, 2207)-sequence in base 32, because net from sequence would yield (69, m, 2208)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (69, 4413, 2208)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324413, 2208, S32, 2, 4344), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1726 451101 915591 147968 733852 825815 768175 952858 730671 667984 033615 601878 889210 767719 761598 917697 689640 582291 312527 305271 618489 326302 298764 933118 986208 522288 675787 707144 900248 696015 645219 664775 483903 472284 686088 209984 845772 185659 801848 269947 976327 599605 274042 845111 764080 131031 410733 616699 674990 067939 487293 993733 350284 866096 664417 495845 309331 503514 597906 482242 210034 888057 554497 014617 868624 172191 012145 014233 869819 352082 566108 688868 030280 186707 104932 699473 900927 039480 971482 139319 956434 123080 759860 109447 178448 629266 502498 869821 546821 100727 171803 837311 978369 733045 236736 632513 216493 552174 311642 789101 328716 609726 518082 700215 112092 420236 480302 118839 504068 233828 265234 541322 005092 401177 561792 332882 588623 147610 707216 746248 759843 706907 716675 732473 307937 922740 884977 999656 579563 512704 959338 142869 189436 585395 357798 391053 686819 103015 475068 284387 573706 985638 726408 598458 733274 193509 902780 062387 377971 442527 801543 124165 373753 188303 702292 316039 905896 525817 550864 448358 682146 133019 636077 619759 301894 754796 288361 405130 997427 993964 448013 921177 756869 789683 195905 558779 083180 559021 204421 981116 336908 532371 747599 606600 758439 028585 961306 208198 066564 684676 883366 430951 871603 074561 610981 604311 089708 387898 579570 860787 093059 963176 791387 289957 280101 287292 975571 672198 101294 595224 035882 659603 138631 381810 941038 072252 709703 144904 278751 679773 227748 215435 333138 920345 417071 861934 775738 078566 011155 958722 423837 041395 503306 034994 791460 622972 441974 068867 205791 325432 356498 804464 323290 800621 879419 480532 900667 198028 979845 474341 066167 528486 261525 208688 427603 690747 467806 371531 351058 611872 664943 311083 788883 273063 648685 945597 228893 281038 541715 794881 057133 799260 198581 490675 448209 243147 157791 500485 081580 140533 576117 279316 655222 159961 503374 342664 400727 560637 166191 666982 406151 306395 307704 418339 595917 535881 773225 939251 402384 044993 989502 750895 291931 537098 410127 511465 780151 287846 036303 168722 781021 576030 952883 880543 668390 185747 707353 632885 794942 629563 721973 496930 834072 350738 744534 063010 425023 581023 126932 406202 138638 986122 050354 663671 662709 121774 288485 285948 584734 973696 437380 496132 652377 980227 048504 292454 229780 261354 079829 565504 034491 479651 757851 984450 146916 194850 240876 577177 696452 808919 227987 520159 012679 469036 247319 515678 779469 893220 236459 092037 540110 002321 084400 842361 725526 631651 914503 712453 900103 949418 697812 733993 917580 727317 435495 217756 128908 645427 186963 251899 865335 264400 031904 111019 226179 150425 602204 544520 637117 020436 320749 084712 818513 143510 591615 773271 187769 352437 136882 219422 469895 523825 413919 393500 041755 026324 740319 085668 749285 987116 695310 209794 988883 237588 845470 761718 624139 060114 813186 282059 376777 405283 174729 794774 613357 298766 101310 389876 651897 027513 037840 966972 655910 450888 163447 066781 650884 887931 092149 006106 076788 780734 343493 255760 527976 817913 740412 428391 121991 994309 292152 724767 512958 156520 428473 234943 553615 154220 876081 397499 183321 064252 400844 485326 089178 344320 829295 724548 705575 393118 678004 385169 479717 972515 711132 147965 287696 146812 263543 742959 172550 312772 268455 265926 410634 979542 522205 360505 755817 934757 841647 595200 017540 601437 519407 695207 069631 174695 482118 351453 873894 085811 174686 278776 555201 510840 826001 677315 671261 521570 242416 662415 320465 610625 537730 308481 268962 278199 392165 243640 566403 401657 443947 910779 005432 052123 584988 685804 491883 166012 296867 994147 013857 328600 986356 975496 811904 100476 209797 630039 435561 566441 135654 842184 692911 996212 999635 619880 734151 314984 755257 878287 276531 952718 479312 552813 140169 256001 729226 599452 509924 474018 527550 616493 946717 384449 194735 740231 872458 273533 189624 095238 049935 353867 087507 181494 117906 114197 884196 866739 417951 804617 664428 748880 785864 775430 087657 998088 846231 902343 766818 270980 395190 680954 098512 625320 579231 072579 341729 618513 023796 568418 239296 345176 517257 221941 110651 492142 066707 895742 071754 197434 748205 512813 657971 172819 777038 675322 928250 220682 541457 083805 593122 167188 196781 001657 669461 136162 395364 707824 109123 425555 193060 621938 047810 649198 283666 295873 050934 285322 800897 095042 450646 470163 961271 388665 427442 735588 527842 570582 105113 817514 248070 774296 942839 721719 314956 220019 107039 525080 219369 466512 509119 423700 764876 684840 828330 343422 255227 988602 273152 426304 743360 694872 189688 215414 760679 120773 485012 304538 824692 109086 794875 221425 510114 502477 700172 203474 099715 068338 703696 491285 354091 475574 656129 941767 313928 409354 531359 777902 163669 574488 119618 640812 168932 227663 966007 084765 096464 782697 622274 834205 952036 593770 217353 748119 526578 086157 934190 268879 732425 400986 561543 140451 664816 477306 503062 122672 381103 847873 286723 765384 164618 072350 780366 890185 441510 530079 100037 856427 476334 083973 382024 891744 884538 370412 859285 857084 678422 942812 643230 257826 078564 895690 538131 152831 423530 346749 818879 310075 514405 365253 161848 684582 392752 717857 390216 462646 516843 082389 677446 086279 381206 257478 065145 098984 244159 285477 028525 104515 179945 992816 240101 627417 637944 127910 315765 701845 548582 304670 412257 704318 257903 400673 963905 905865 466905 351342 720308 538989 701894 041773 317568 249255 896863 991959 394378 664239 741862 077146 572449 175906 514992 881151 358580 631187 361282 597055 680241 108110 292330 658954 196840 291717 624735 211605 540106 765996 751565 416647 917950 971360 947090 352768 624884 117297 839651 445240 197234 248553 048872 753499 949896 889851 658919 045643 630248 826247 613016 271118 597925 316060 721361 736034 283478 116417 487895 832712 235552 136150 513252 998298 764661 157416 321882 489993 101387 528234 730168 284185 999581 673307 952406 017256 990822 771065 510447 318587 544450 894512 238416 010636 516149 310440 366653 049911 040165 228222 351461 559820 847994 413946 643941 348634 483540 013355 088453 120302 659096 388412 755117 686352 774724 277346 768865 579402 722624 087625 266736 440741 841912 987563 164885 046329 711654 938191 661676 212869 616110 121738 617184 196620 361838 087913 709184 771456 521281 926378 746265 685461 453981 446757 080683 571611 610740 556373 781985 479311 462844 799977 237945 469986 038225 004008 772316 553638 762021 113490 848503 191505 816358 430774 425144 412225 212292 295649 027512 952404 153034 290487 928727 058761 092647 557550 618518 128876 671424 187768 268960 497496 544536 682147 841026 795506 675767 710355 591374 017390 214427 424423 172188 691848 009066 005049 547468 720747 006617 105346 186605 646428 925830 891578 406732 162929 764528 142714 436629 286148 756210 420159 549033 183779 870432 508686 360734 391130 908181 229147 153259 970443 847756 043741 529060 811579 695801 637794 760108 417662 834893 725442 908345 247681 934380 897073 926235 867712 780342 515653 719901 602481 636004 026530 363180 456484 893444 780480 495614 382171 156779 406793 210186 852368 128682 778668 464366 275655 111160 791778 272909 286385 081235 947639 725995 801295 758344 160632 153162 657273 004748 559257 064860 055878 409135 341809 543916 139212 866675 158442 444857 873946 485286 278668 046007 013901 151581 513445 410442 036010 609190 161595 665763 210439 035291 757970 819797 036151 858084 747635 919300 964288 525062 596553 585873 313158 646737 013103 000517 869568 / 869 > 324413 [i]
- extracting embedded OOA [i] would yield OOA(324413, 2208, S32, 2, 4344), 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 (69, 2207)-sequence in base 32 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (69, m, 2207)-net in base 32 with m > ∞ | [i] | ||
| 3 | No digital (69, 2207)-sequence over F32 (for arbitrarily large k) | [i] | ||
| 4 | No digital (69, m, 2207)-net over F32 with m > ∞ | [i] | ||