Information on Result #1854339
There is no (62, m, 1671)-net in base 27 for arbitrarily large m, because m-reduction would yield (62, 3339, 1671)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273339, 1671, S27, 2, 3277), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 341289 982729 267604 333974 938408 427906 184886 953201 847002 594505 847446 203381 514827 567472 916276 504155 551343 497475 829354 350805 572153 726647 051221 363685 089112 258076 437280 485613 876257 812159 029020 811162 744332 805636 582530 949104 958613 922647 280603 633008 623676 668482 857267 929271 414274 765280 779386 076246 164102 901185 022132 502816 279271 327382 178765 396391 389709 362599 563518 067090 955096 831588 885573 171230 124786 710142 213510 354490 940572 463625 916396 991163 203568 411810 134396 701486 039057 853420 334859 089297 825131 749829 516275 613970 240158 128931 814861 745242 515605 573281 424644 394676 968763 439245 337753 226665 862947 588338 262702 732310 218176 047836 637645 939250 362190 433848 160063 309099 549072 753712 990466 911154 541535 160319 875076 047121 766664 501432 358933 400290 507539 950123 538335 853115 922014 072528 697520 647535 144577 968090 635376 804031 801961 350091 293810 579017 528514 138600 205078 491166 789429 002167 642850 481661 076051 686933 884822 419836 420619 130083 010214 314784 475964 871503 911851 092393 868668 557101 963918 698776 188283 808066 563161 148196 174009 910126 600459 204329 583656 523711 093840 072110 041571 838877 678261 087831 556774 050407 331146 180733 155600 069143 387588 600743 085899 905763 616465 336559 790281 041187 575706 200343 422239 365927 478829 472246 200581 369515 179562 397754 904376 016953 871596 149650 018389 955795 430794 917958 482219 711226 104372 353688 705141 454580 503439 121059 592189 366256 278184 561468 037844 384115 152410 246851 164500 555911 478817 499478 571141 205182 408315 295271 008917 387421 302066 041238 614957 276836 291376 065769 608383 100468 440268 889552 969882 635525 047255 589605 011928 897095 350977 109095 660444 318891 393060 716057 470803 405055 661261 908449 711660 887680 805402 401816 693909 491188 822323 183854 975527 477701 985357 130274 820076 801752 540178 813203 777094 706265 168960 518245 305845 627985 569219 600058 814426 794715 587806 735398 934906 510550 957430 316222 535653 116752 695844 570739 504281 459019 186122 477302 453049 293773 016692 637693 172890 451663 094533 149362 336611 492558 437395 778019 426902 195805 125150 978392 400487 159431 445282 422780 198636 174137 213677 689157 306521 533963 186984 393072 556973 484548 787209 212187 954708 646440 415656 298394 485995 008635 454945 714406 573112 267985 535594 582834 620223 935552 560504 492110 775787 579813 475313 311558 661988 246732 372206 004201 270344 730352 114048 223363 847378 736752 718712 569229 382683 491437 325550 294030 047618 494566 359653 832000 869303 149278 623409 343170 804319 642069 562482 871894 667068 518645 978931 629806 751561 880745 949776 564328 099354 967385 928550 133806 417838 554528 407627 464609 137924 851124 414063 735127 601470 239315 027878 483591 269673 567892 947564 955926 283603 973239 969551 943266 663101 940328 809698 719467 226580 462067 578951 709311 721793 075748 605748 649036 271213 328931 343105 323763 883239 158299 352722 401301 598108 748904 366044 436900 307331 598236 314516 325280 778686 262375 807241 820730 658695 574600 591047 641253 670158 059491 724455 518315 332618 491092 555537 065307 447241 038172 030562 880384 440996 998684 400212 919593 832066 991612 786071 949445 639820 309673 580071 596580 631033 884562 234960 013885 009899 373644 134996 718332 971657 050128 813931 115026 942896 302510 139706 482818 949254 306513 535094 272703 930837 228370 568930 746530 868241 006775 530398 692318 272580 502000 544332 382252 525752 771388 461139 548609 440757 628543 763765 044995 568122 626861 590325 931439 050149 430815 722833 615545 088470 788621 901372 435472 361528 747999 235520 116007 044871 895967 806263 346852 188689 514579 351586 248285 127577 332596 556837 031613 933451 396929 192204 120660 932303 034773 289256 991874 203006 681292 375588 714407 154851 339277 152506 560250 975536 794341 855457 296603 762940 369470 218483 459671 541766 935947 210321 108234 441208 732631 025368 214018 364780 925983 546729 758647 694558 674046 114949 138692 469418 974929 578000 199900 808376 135196 325083 827547 153142 580060 302278 200022 377211 615103 930790 572779 989866 683335 855870 362890 883301 585352 589013 726416 201886 160342 086213 557276 005248 623534 594056 945992 724576 554433 926030 710105 877186 709100 431654 846237 340171 175676 543785 695205 605323 600305 150297 975800 282638 036714 029717 495190 814576 222436 050807 782659 549398 126077 341987 612706 742480 454404 047330 358119 639465 604010 312930 559758 812369 189265 247385 171973 894296 945922 326571 814928 513708 128847 168431 466293 540240 685861 003480 220971 684984 364732 196062 208843 779937 934782 850198 983267 464757 492961 010916 335459 006644 314881 851712 830456 374331 413193 571983 230602 661366 691819 975895 730364 668908 737253 668130 827593 231595 848040 636861 965292 343964 227797 126220 747689 562443 033892 071491 845805 024324 039548 303790 217172 019674 345942 893236 834033 872214 634927 335167 515695 061821 697786 936480 550104 500188 855204 940827 180428 303250 280490 348822 324624 428959 255482 131166 252256 860409 233381 257664 958737 426077 249641 477111 740270 916459 120594 180310 308532 176093 319918 891561 862193 859591 384458 921782 295337 755696 077488 620688 556884 169657 017794 940862 398307 094422 465642 400105 855803 163204 884413 521469 988737 007026 106592 203778 973042 658392 570484 143767 218725 059719 012503 889818 028931 474655 258934 339330 610666 653617 928639 010788 304767 742362 360561 981825 255608 637175 058631 578563 734313 906406 / 149 > 273339 [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 (62, 1670)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (62, 62+k, 1671)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (62, m, 1671)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (62, 62+k, 1671)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (62, m, 1671)-net over F27 with unbounded m | [i] | ||