Information on Result #1854369
There is no (72, m, 1932)-net in base 27 for arbitrarily large m, because m-reduction would yield (72, 3861, 1932)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273861, 1932, S27, 2, 3789), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1267 501380 636922 872709 037234 640930 808660 940415 176698 322354 584791 223694 158489 242508 747607 461129 706466 561372 594925 648072 280155 518642 530763 829725 631772 053099 191332 958548 945517 868272 919633 586163 373217 340807 736972 374281 211904 658940 638847 135028 092780 069755 473211 430911 103853 066338 323152 323399 248752 993585 198320 605382 052297 423636 259365 976788 628777 359434 707670 539448 365678 465350 543814 244544 430829 448564 975568 905184 863072 560009 549311 886091 281659 276644 899188 616273 954382 899455 471545 261194 490194 567921 548080 359570 014781 540456 543448 407786 630707 340351 699614 530451 675430 105840 236633 993750 394334 923524 183821 805824 843789 548076 747421 299377 292505 245669 680462 425357 217967 377203 413715 810473 455681 738978 618388 703679 073676 575685 469739 468709 092096 226613 898937 141274 775950 857619 109691 062257 409962 009566 204572 178050 764223 468619 434686 648428 701211 836714 568671 434902 122158 134612 505975 831661 240143 430154 651466 489670 359945 962316 071410 143917 903642 458341 504957 867356 212726 107976 665780 192366 290056 312146 842616 333075 341544 669666 894702 512840 563193 137927 454661 901626 120034 953488 356750 477036 207953 253723 185936 716350 018478 699632 362082 642742 532162 823419 212071 524191 547727 864429 513111 738006 726203 199609 732187 742565 138795 709209 982296 256667 021240 993621 411136 096164 961210 634540 412784 978467 399050 445824 480983 448766 510653 056569 514868 759624 209050 610525 134844 758640 872831 235627 403221 863854 417958 853723 966597 064749 573213 525035 880889 826406 433241 761282 205169 826767 559611 519654 346461 794154 137387 773854 583475 522348 619304 850069 273370 291059 500383 167778 096332 090810 332146 749931 309858 858493 191331 996866 407101 787553 037975 891338 876683 756078 754236 824709 156654 250704 776989 556168 793476 710926 199801 910963 867781 250252 654666 346774 567589 693442 029272 179349 219731 271354 437334 357166 910654 950642 821208 271715 184187 901095 386898 513506 177754 078113 795498 718456 875848 927274 185163 450585 040559 660020 775696 103477 491974 033773 822887 243006 712806 991423 403636 028529 281223 228081 222482 962279 753024 483099 674452 076265 707754 867943 088594 022701 985068 344885 783140 034854 824069 457581 325984 755713 112748 013334 504481 438367 125347 403746 253520 246383 817164 369176 370364 634337 098613 472052 746150 395669 070829 211232 223333 681227 370485 356234 175640 736650 212844 604735 670499 123048 461734 092922 536382 213086 838493 536938 833586 714346 804683 104628 526819 566247 143427 395411 187737 013444 697028 353715 857719 543460 343860 080935 785687 581349 442461 021707 468529 746820 696645 522839 183262 574011 071083 227896 528368 895464 589769 669427 159882 852334 547192 097105 063316 511832 930820 520686 751541 214585 366736 907796 403033 889292 042676 738589 485157 023432 526242 063508 682727 735283 009168 070195 606584 454400 656376 492414 715697 858532 359199 344982 201498 832807 743668 641895 653872 026792 322353 711924 525642 324421 343539 378748 161070 833996 411368 442534 761662 653846 709681 222414 575597 651380 714666 986424 009953 986999 513769 873724 500785 529749 387502 833965 795696 926843 648162 049915 099386 321730 733000 414857 527751 159186 839440 670424 104737 895045 988303 072248 559691 193701 760809 161104 853404 227863 386091 464581 268473 771848 265365 881305 632769 734640 532418 296473 279731 413544 211803 603050 510537 706294 515649 714196 332555 927934 342062 304432 901307 964333 381751 956976 030655 295437 569163 922457 889469 682510 251691 834397 846121 129499 640743 925027 332505 263750 094741 137498 494230 365954 586686 676783 570962 294241 904372 617499 720745 097883 849963 857819 842846 056206 248148 516527 839412 402660 965850 595206 744038 044102 608077 593585 788583 840958 456326 577984 563208 882165 924700 238209 117637 037573 878912 953443 460216 382583 963203 437504 593436 315531 451400 647610 132155 311903 864561 529459 391437 546780 217283 232496 242465 490259 046057 377220 950192 708342 722986 400956 306483 769319 045483 836966 919562 903440 279756 769211 951816 743616 776671 090947 260767 170437 143207 449331 777994 932461 286565 978629 428843 442726 613820 737536 218501 112979 328789 252068 185615 810277 481072 673906 602487 739397 339416 698976 679897 784258 169107 148521 455744 592674 465951 664279 087759 405107 788857 708415 072058 034515 227640 585903 872331 699107 597950 352959 513239 506927 043204 422427 807206 681126 796845 242089 547134 759531 679205 666908 860114 739229 452959 076956 582965 776972 755093 743388 851227 651580 579775 561644 143292 143577 609059 075018 983058 814411 550026 762245 179657 319406 477706 680384 183098 373590 283919 648444 774604 450730 037514 555571 756607 417064 664377 303164 123779 056845 741888 366544 003730 832033 504653 652207 303065 443189 703468 743444 103994 060723 165836 830819 437094 275559 656839 299938 602477 328949 993235 849030 548672 110181 811336 709155 233751 902032 941767 518722 129283 039949 825032 651166 326483 308889 592371 035989 129428 442402 215893 318247 300901 459946 277432 286033 314151 897164 598538 285073 947501 094122 520282 294822 425672 079382 647337 795535 048944 872521 360320 676736 381338 778969 798175 478330 016990 887979 066320 357479 341590 172572 569639 868408 880048 237604 952095 575121 212863 336097 407713 091918 115252 493335 262729 440181 302364 248779 335054 498486 118956 494581 104253 923012 556021 839890 850852 676240 024648 137401 202430 873662 378490 195703 265169 726839 435859 525241 189869 899638 042444 339592 070808 846404 350018 996056 599334 085592 505765 798482 736626 779386 601335 427649 148088 528698 607088 592083 896493 434644 617047 952238 755989 426984 461766 075052 629213 127080 404086 729081 585049 269133 656250 776526 475135 394438 288245 163065 916897 061947 613150 547038 274887 019111 127307 225317 162457 305086 438834 162355 788245 404390 825918 423755 214528 283518 453567 019632 214669 642762 374650 307986 918778 911973 759841 217547 098929 299098 450017 385589 722375 835497 582017 772097 941430 969197 818606 921253 650013 790993 014974 795962 210594 916267 488425 779524 500060 350637 051859 588245 601820 226154 547880 092976 465682 147268 034435 705621 827730 490415 671733 786105 577940 057826 843720 711662 511952 488820 563088 897814 542476 888173 880494 352533 540366 554297 000342 316935 / 379 > 273861 [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 (72, 1931)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (72, 72+k, 1932)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (72, m, 1932)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (72, 72+k, 1932)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (72, m, 1932)-net over F27 with unbounded m | [i] | ||