Information on Result #1854798
There is no (67, m, 2146)-net in base 32 for arbitrarily large m, because m-reduction would yield (67, 4289, 2146)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324289, 2146, S32, 2, 4222), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2008 732040 747683 714576 018641 539442 211027 265190 793008 603597 356422 069432 847418 078479 053385 466325 833508 269124 595325 247026 928441 305902 257145 003252 135621 690316 816461 633406 265449 489702 125137 359370 622489 415055 226993 670922 390669 057594 659071 412588 344286 891425 017576 196051 603618 105579 714991 573551 053515 883304 965797 215080 313079 015727 061220 944887 811658 028607 461875 364948 867282 035854 404760 706040 277494 855891 561118 817512 236506 530152 967926 853673 342242 754813 422561 823317 079837 249322 361790 118029 414992 410698 209656 483715 878010 165777 128167 910653 995305 651504 129862 086380 796042 088211 061324 860545 236062 393995 422972 425282 002995 768321 084093 849256 898626 732576 279576 416163 668778 916831 447310 642293 681727 178597 479090 788644 833244 041038 210879 037167 869986 242322 866987 500566 651944 834962 422517 960796 614819 030256 800494 069235 420908 419349 867164 964901 926821 355294 155421 689562 598552 589036 241404 573897 306525 180139 756966 566785 033184 901814 536968 226694 325527 311815 554680 071426 981755 251604 964317 562312 259958 216808 309718 759451 270099 109455 190924 143761 307006 848511 640566 018370 419667 611674 256874 210513 897563 675170 085701 302367 482683 842683 423079 932771 135235 399839 800649 836851 226126 033519 650309 687183 600898 314980 729137 750716 796079 927691 603075 528576 699343 686180 970617 793751 472401 421953 524532 432854 584807 160841 736065 064830 987704 239835 311767 494756 508097 300060 846395 951428 495070 526867 215636 363495 979989 378548 958566 753836 291724 463635 760228 243193 324315 108851 983367 898752 644056 032540 726838 829022 290516 128956 509915 921628 721389 463656 688716 267581 105924 189241 986391 214999 749225 259164 427354 479971 323981 702800 031639 420796 258182 039357 964052 488679 317025 731740 843785 087471 250366 288775 174585 719739 240497 776916 272077 744889 253533 485224 525013 935881 197199 993136 868946 704650 644105 566468 788358 617762 717711 826736 392463 414255 988065 167183 655123 613636 319365 197152 410404 703323 775292 073241 846481 440200 964598 410057 953149 461133 378155 132257 762941 025367 214162 334319 397135 201102 326698 644805 368069 235530 150064 691509 070907 235182 776646 170392 404459 641195 839441 908603 061938 168259 725605 442047 664696 650690 592415 053054 423714 549645 921691 461248 965269 107905 971948 718614 294929 924609 425928 336174 988789 931829 453907 063564 838144 875282 551425 936652 043515 811124 851064 560525 667466 097291 247828 256905 594495 839213 524857 077160 543935 167373 813758 878067 823968 680486 670292 374442 020899 228579 681100 500966 008470 309396 477398 543570 089793 683639 051902 108577 025390 022737 654589 898470 035879 585836 574676 743956 789763 103278 821607 913221 040326 807659 885246 891385 629262 894067 051734 174133 652143 116934 323475 691903 322919 137504 959202 450965 186807 422748 179901 948798 203628 497188 707160 648183 537428 151217 844493 067646 050534 248207 293747 806763 084215 468905 663639 518501 855459 353676 648651 846526 490017 965793 540116 134056 653087 283368 146905 087283 899696 948415 335144 017370 640761 087593 115169 580608 227089 598830 421024 645681 078523 146881 924409 225493 140610 957950 519114 193556 998466 992321 397472 314472 494020 590447 562127 509910 458143 941503 273652 995117 571018 371419 974349 260102 405971 838132 819330 310476 367797 712708 188926 847362 623445 212082 508948 324401 686219 966139 302994 877817 121361 579879 597368 497917 049074 850088 560748 116164 507310 882793 301175 558451 324015 119743 750725 493513 221187 892985 244530 496435 523947 840422 878749 218563 537642 111337 848871 999607 544139 401355 086485 579233 814979 883999 694361 082473 907473 405902 676607 794677 852466 197059 943060 537957 171123 533040 829637 719038 272758 272138 453704 707559 315052 397753 730798 558603 304556 099577 159869 014717 954243 172340 536567 032494 440478 626963 916543 665805 807845 305798 945710 584871 231641 005172 459933 488847 945606 132963 343504 673040 313920 711516 678808 481966 080650 910296 452417 619054 008983 683029 929922 026773 791392 417665 807351 181820 978677 526149 350442 399465 711106 044983 863949 489921 140295 723056 003549 175889 804470 077048 917227 326544 462210 312964 663952 188605 751776 213424 728554 375809 461719 545711 734714 906858 913825 449715 410817 498887 488190 112795 196630 351551 200535 586969 965668 555746 122993 346036 544311 843424 963483 197680 325034 704373 329692 436288 264539 451664 912631 076308 383575 295386 491573 369638 632252 801375 420754 990158 611189 348430 053207 939439 301094 809018 968759 034942 133108 184048 771400 614152 506919 330352 953083 884992 477882 194698 671675 115419 745815 163646 376124 770830 701721 236682 656927 954746 041727 618866 647633 516910 143749 689604 710430 627581 965340 220893 551493 995639 980111 714250 223520 836761 949371 666518 447174 980158 850709 023115 215710 621035 870164 056995 759245 985468 284882 292434 285224 830157 622339 745072 529971 993748 915345 105585 716716 089922 411837 913937 541638 829277 026997 211151 175430 721217 819834 842682 350556 706152 878589 313167 418042 695644 342942 374575 481823 719485 342478 517186 141238 438849 940779 811097 306151 441993 659201 686955 479850 612059 687618 418379 306980 723899 427471 906187 225578 414327 951915 533897 903177 137456 659239 429700 956416 477490 584984 030962 664855 788962 368575 989521 542579 112297 059361 209046 445750 950277 054637 298222 025260 874680 512174 848478 625696 405006 872547 076916 518723 011498 008943 211741 304442 904514 590096 378238 482108 365272 344998 311479 305099 802692 543885 098081 340814 125705 057010 187748 612553 094458 741004 394752 786426 274232 713399 566579 390180 833681 213060 570636 614819 057445 155786 446843 534081 593364 010283 512772 603627 770025 333999 139659 226637 356921 696277 834862 789600 370449 973294 275511 962345 588565 076652 117214 137057 127464 650719 918991 739693 803655 803013 236438 522558 926234 239917 176952 495048 373114 223711 629993 926225 755479 607083 854435 348651 846946 982200 240622 599830 124365 519063 715809 399263 052841 001115 599579 899003 417756 051740 319248 361581 401263 486827 071279 455051 445810 138090 458795 708683 033143 106316 555650 139486 701373 544618 695608 737494 632128 442051 582857 524943 775592 594753 354425 680907 340692 396647 831907 390560 223088 049712 717772 613871 212996 874043 974674 273829 567891 106913 930600 892324 367664 413220 221397 124469 097948 599371 008866 425469 030548 351506 193953 019768 217950 454011 418954 420198 018167 508422 699403 371736 377928 031988 595084 450612 203937 455505 170775 139731 248610 384950 307800 875574 021494 238118 876780 560104 788536 930368 336411 681760 565249 182134 778266 527646 101581 426977 785671 021818 038229 074093 299602 205930 420717 589876 607613 234699 504625 467341 743578 756759 853786 822381 656754 476874 358576 685497 689698 983656 236749 915301 822838 171505 776219 466459 273059 603532 306979 478394 459693 910518 076124 316242 998590 203866 060456 844467 386318 826685 644632 917913 990589 043933 591959 847079 124638 349190 105352 520978 758833 211883 979319 073152 543044 608312 550448 984505 807157 614437 259657 859591 932330 472941 121037 456202 804639 986097 429687 944697 471761 479367 758985 830883 707556 503955 544373 489706 892797 348479 877150 125876 643424 145653 377387 526877 479612 199856 817464 753179 498827 704885 675427 401333 263908 800678 222876 377088 / 4223 > 324289 [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 (67, 2145)-sequence in base 32 | [i] | Net from Sequence | |
| 2 | No (67, 67+k, 2146)-net in base 32 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (67, m, 2146)-net in base 32 with unbounded m | [i] | ||
| 4 | No digital (67, 67+k, 2146)-net over F32 for arbitrarily large k | [i] | ||
| 5 | No digital (67, m, 2146)-net over F32 with unbounded m | [i] | ||