Information on Result #1858128
There is no (87, 2323)-sequence in base 27, because net from sequence would yield (87, m, 2324)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (87, 4645, 2324)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274645, 2324, S27, 2, 4558), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24950 637694 324445 714900 873912 095449 252490 859151 675548 368336 920897 143042 676018 910447 319309 289839 400941 546721 972509 468813 724187 800521 850800 699395 689089 047972 131630 075649 383508 046427 754607 332592 756150 715532 500004 021991 641924 620900 907910 661423 967747 384843 346011 645162 203361 344365 618267 550476 928360 325283 078641 382990 909281 782956 997027 543884 661428 943956 584664 813191 816863 242721 460779 071787 037633 475774 048553 341013 671769 609133 751040 816860 899262 190290 574584 011388 603561 716799 874657 395567 730400 081542 663264 053167 747277 265927 760702 003488 151476 440951 822770 058728 989072 024550 294624 048446 657358 932622 924199 448288 846432 320317 696009 294602 508065 321985 208741 558851 475613 300487 339189 293936 804493 434439 373977 683391 675307 056510 150661 356072 507444 937456 054516 923657 592734 709258 367525 291551 198809 087170 477275 152608 986372 617764 621504 555782 959639 838112 667611 263581 316053 311945 498225 975076 470911 306482 199868 726459 297038 219568 672082 835527 303588 399553 905273 791836 494139 580021 868127 512754 299509 072989 884509 638159 164363 694075 696818 439828 931535 073178 568024 789471 773602 644503 471542 392401 303576 310084 123129 953310 626183 433594 257128 114118 527354 861740 474734 563243 978669 464211 767286 972537 165482 115154 502578 749801 620987 069396 858832 870289 812543 208204 811143 442768 023984 604933 120334 266439 619247 354698 284170 773302 010251 553604 323123 456121 247038 145443 123054 710923 525502 214213 197838 127780 580749 653204 682409 525348 679462 162695 652113 382671 807798 984199 310865 561654 847144 125849 328911 130278 488972 135662 760809 558637 991068 169244 726857 745927 365339 672160 720278 272354 328032 767135 827408 032944 963154 736549 550774 819136 116586 419900 190377 799157 507073 142230 158680 198550 407815 248714 497016 146000 319714 738087 145556 414736 486094 521017 941086 564482 673010 758062 102463 971351 239349 360370 010853 611465 100658 025127 168762 337091 236923 993577 636264 558850 279860 458527 144494 512009 801802 500973 408485 306861 811249 742843 163009 442291 802615 608255 131081 724533 360565 603897 494844 292079 388413 067482 268198 395004 357276 537266 836992 735623 683627 973126 517631 737891 657499 863264 939484 302803 492317 220138 610166 833552 640531 391992 848203 340382 395354 134676 330119 285424 640994 135980 241550 215632 731502 011500 081025 928391 301185 323128 503380 258618 502152 124894 235135 791980 605482 894136 668359 105129 458566 801113 072223 411618 680729 560455 155169 311891 010647 033240 530776 359694 052860 344394 881436 353748 470384 747212 369067 229266 687007 188255 114560 330428 879117 436725 673122 751068 579731 370996 949441 804086 495048 839320 574926 047237 519012 703408 013786 342999 038055 533625 609286 688913 908641 030441 224293 038515 482932 084381 164191 663983 118887 519351 847523 508311 723050 836105 595862 405411 429138 493817 992378 096855 621450 910178 682472 225458 759265 725899 301300 059131 379556 951693 225735 009296 017691 502242 081099 415592 012594 227450 233863 585581 427093 861657 089041 291193 216702 351416 371907 527430 307796 026075 408825 546430 734063 102220 562185 001122 798777 479046 965347 335620 014166 783253 690109 710505 600324 618924 257623 095701 731213 094361 641618 190605 120688 248635 434241 230815 327307 939130 744267 200870 790643 920847 004625 249126 483834 188733 029603 250988 492369 769670 175476 330709 642066 063059 052733 639925 942419 122225 583870 368976 280109 697976 458001 539546 701676 159872 234961 463797 506144 449290 335064 989731 649177 278020 760461 000055 649960 803922 782527 202636 865416 627030 049122 796898 608291 160745 437844 114537 829786 333612 815155 342713 388006 668806 844866 541205 410322 815050 214339 247042 419617 245779 764953 808956 995794 705669 572514 025937 047726 947724 047254 379582 680110 982617 102391 898616 780405 457468 675068 131319 697004 918336 760358 951363 587236 855668 595687 076063 756212 806297 691759 454931 618888 685634 066917 238868 075743 719375 137247 576401 375457 259265 479159 938524 007855 752070 459731 617024 091859 582904 366192 456342 387651 124083 152480 756875 489810 358752 070021 621172 248748 565889 265405 921693 566748 944924 257722 169368 832472 955539 138102 922853 384845 756061 330448 009227 447614 081516 614415 286169 559239 218176 917045 184965 065110 134046 498565 508074 549226 100517 120471 301233 715032 551151 678757 495982 993365 786451 888349 533531 998413 077756 042278 503388 570872 212157 894395 553223 952748 473824 654749 653843 004161 743818 803974 271532 628367 515618 688767 684973 567036 104228 085670 843730 393352 653710 736339 412684 563134 549367 249777 500191 065189 093070 766529 482283 305052 353069 480440 308000 868915 551481 615263 935045 530435 698821 553074 359333 935704 258393 159075 504950 013391 549168 557941 142528 557035 089282 401783 996327 730298 873077 810136 575320 808245 518214 195443 577176 225920 233260 478073 472925 325867 011701 423906 909774 539436 160687 650200 175362 125363 015604 316888 416638 279428 384932 484124 750425 322093 072329 537438 373378 237218 570774 934519 704478 118903 736632 716059 041111 405393 211732 928581 614830 369827 381767 600746 988556 222946 001192 485586 710146 978344 965024 647571 088518 639507 901026 451327 023198 335112 569954 043617 371364 741413 771236 814842 260192 945370 580518 233360 171989 700454 790022 857505 467513 394108 931869 698587 823770 433167 170839 601929 877360 901777 499847 046689 281733 918477 287060 946931 942257 953039 385976 972432 787643 537643 331290 657482 641688 279765 204438 143288 796432 844183 251624 403815 542978 193899 393393 414151 461046 238329 636087 145743 439626 139142 225479 271739 428975 571027 955565 091869 484816 392271 281181 911036 633473 554164 019845 685604 784547 114069 510942 436111 137468 713229 650064 859085 526251 199491 459531 456723 227798 675028 462905 721831 569650 991730 077538 667585 693832 486040 475751 886254 925476 507718 156628 580435 447073 337068 041877 578007 472683 949862 553336 887643 163456 270986 721377 214944 647091 746414 241300 000561 693648 133721 851338 436217 138714 918207 015241 577903 040591 998148 733424 795200 511561 338722 089109 321549 550749 328205 702140 214786 311812 655534 917365 466955 324041 052490 415772 687334 574780 515074 557831 034680 101695 743375 324218 564262 594424 095000 466603 643777 880529 554571 335657 499814 720398 259084 117990 182850 762420 123926 536503 642291 890183 734816 309982 037340 513466 535099 227858 923663 931939 872304 464467 255496 156086 073777 765704 205591 777665 590590 104738 966407 101019 525281 778588 691441 922793 761438 763940 294585 270741 300641 278226 725775 198113 686687 569517 363994 631280 008925 771694 855596 568872 812009 758745 486465 188278 742350 881352 862997 884869 723367 453353 722762 258853 993391 372896 455842 334823 894410 686896 217457 755372 296577 928996 993264 162687 035455 481170 324619 054688 584197 625797 931252 855641 318500 474182 055134 789218 976814 458390 207153 923685 884623 372265 683599 201712 630847 930818 205606 658523 879277 336816 548947 653688 033931 888860 251354 371212 118303 281354 907626 033202 301603 310452 055432 105729 919117 723562 810803 459815 420813 434135 520010 048872 929338 126125 498825 902446 733783 603741 284687 696296 815174 623408 121226 005292 217076 132951 184708 860715 004505 629555 104539 829100 378922 479733 496359 489632 736644 182185 341254 400841 453999 265648 415129 504261 397819 663683 655033 560808 689000 422445 906062 808384 969960 768769 137033 849052 880285 218307 775339 227132 876459 499582 044639 375035 446804 774163 848091 389676 617728 218539 697666 560413 930999 / 4559 > 274645 [i]
- extracting embedded OOA [i] would yield OOA(274645, 2324, S27, 2, 4558), 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 (87, 2323)-sequence in base 27 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (87, m, 2323)-net in base 27 with m > ∞ | [i] | ||
| 3 | No digital (87, 2323)-sequence over F27 (for arbitrarily large k) | [i] | ||
| 4 | No digital (87, m, 2323)-net over F27 with m > ∞ | [i] | ||