Information on Result #1854354
There is no (67, m, 1802)-net in base 27 for arbitrarily large m, because m-reduction would yield (67, 3601, 1802)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273601, 1802, S27, 2, 3534), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1835 017433 093573 276546 505621 946415 845794 556466 181334 992789 802665 839056 996196 205735 145191 968964 416555 843368 854757 362673 471177 302108 833855 838733 144630 286209 635972 298340 144783 806901 519700 057426 890449 940351 807445 127228 504927 340908 499803 201167 251987 967124 379932 083620 531622 282057 740257 284026 445684 580885 656290 511996 937133 726997 920978 710914 188716 366340 792658 245041 577306 423270 386069 088452 628005 687297 929606 815151 149527 630020 347355 081777 374440 418771 317234 606403 343680 723947 520317 096629 246621 415358 539117 931585 975416 121779 764939 218146 268233 233307 073666 874830 393591 281861 121190 178334 468303 534630 225926 106598 458735 633142 992759 484160 313562 808351 977881 192594 398265 662513 155543 897952 621859 298095 704008 541989 525135 538863 741920 697108 308287 471003 980891 900526 387395 846877 985302 727655 565366 950773 072020 081497 572883 322469 695704 584335 575283 047207 344212 455749 352287 616038 988645 207659 923655 874492 737810 282712 443275 885211 926477 894151 096655 108614 856132 832593 149846 264574 809177 572496 322916 503903 073280 747311 671681 246690 189233 603619 397160 030997 279830 013282 455758 715620 436856 739957 033034 516983 906451 731782 444182 002385 981341 235695 265066 249530 674382 765187 105044 293789 914795 142253 184804 493432 027787 629208 570525 259347 732997 030048 961830 879133 788637 038185 914868 919908 572469 512533 125070 264744 620130 923704 575889 326379 758411 785275 645218 327835 029763 902937 862362 860632 125128 225657 605649 725622 779024 844203 511828 641114 878929 443805 666328 725017 408230 141238 322587 469726 738045 930683 790419 194036 878095 725218 387162 285726 563002 901925 859471 621818 807852 297615 291587 294837 495815 725767 569735 336156 363632 057937 229073 581251 615694 390665 699710 315448 853214 054531 883943 505093 799592 949494 063996 156900 585473 062600 093462 531489 685154 254176 149165 033910 005862 262472 217316 045108 083562 482752 362522 482638 720126 722546 258642 053759 958001 340205 076733 602681 089819 215894 647421 471466 799322 389353 242868 893336 454109 054698 266381 344913 318519 554156 129581 674068 481614 082274 288272 991886 094400 009474 224796 446868 430757 258972 060342 006099 546471 864636 608603 281686 884040 165803 710091 408413 527139 397171 372390 550671 496768 097927 919200 364586 921023 487456 138939 146577 749744 037528 508148 990978 727571 925287 380736 392582 260290 438082 251749 336816 115066 062243 682541 042987 170253 635203 660076 028473 371404 810655 875375 707877 094961 905384 252550 770191 560274 929645 846194 483451 857746 092673 385665 997027 899715 501263 444832 813850 920693 591573 724690 210019 498276 475934 545972 626904 627491 560469 825131 821190 749442 128025 906669 215655 094178 638692 848084 685780 428973 344265 568994 939157 594190 777740 544107 272499 559022 019812 777120 204226 190845 845198 377828 402030 077482 194641 684194 895767 787531 193250 629004 327176 451348 775481 169939 246329 145551 073132 275788 337479 220382 077741 266748 333128 205842 475589 750644 145323 142672 854771 615689 464909 051459 917170 219415 072971 046246 255717 996041 953551 398964 633963 306648 443871 953242 935044 845229 452173 486023 369815 888581 541586 888553 219539 316403 863261 315630 458415 088780 714857 554442 762039 311663 734660 445896 929413 327750 116611 315306 848443 322802 421302 191440 517871 429729 607097 611406 177512 601807 837516 802079 087684 112534 501943 043652 167533 843100 047348 769062 802543 707673 636194 811927 641038 770470 334021 515318 526064 418087 831823 699183 842625 850487 648249 264594 536913 563273 410800 045555 904688 101327 656252 452058 857197 847012 839605 813171 444871 536514 991894 959825 177412 235114 341237 767103 761725 832984 544540 717228 703216 781876 497623 247173 317450 026167 759560 745615 308806 718858 200979 974128 756493 229154 305732 244040 752152 837243 072204 642425 202696 337303 935560 523984 264717 858885 059099 663688 637808 451984 314115 646001 166731 065776 624250 559747 819173 436536 226627 616195 633540 055804 831513 786896 427890 456330 942413 290492 105268 487210 093582 326869 218050 381009 114450 644297 562070 327999 813298 028180 026915 202536 542285 715600 788846 574896 881298 767746 268369 761282 312471 367812 575321 743112 430120 467740 386375 008950 613581 411292 314837 259081 942911 136724 267812 192504 502234 720939 009662 673790 320279 067642 156047 313586 451327 667574 436881 818427 234671 155798 740510 218556 125182 297639 921575 448998 910610 789406 388263 855935 656504 640939 511307 685027 204065 784025 047645 462468 412572 786772 989079 936494 564420 614460 350553 106477 517773 767902 970668 609483 644577 803788 386104 616466 367847 937461 680274 016748 082320 343427 947371 695115 013115 457586 995186 183876 413348 930774 273568 623590 735708 106336 171202 949392 291695 635113 108776 745755 881123 797960 226915 976006 356298 953203 839458 997587 096697 857022 637533 399074 622398 206005 227112 864356 552282 115842 871401 754618 465215 625575 660532 801860 914919 707069 491232 010443 516584 013289 457240 388074 624391 345678 820536 541922 227262 680762 730845 681226 704644 074584 787040 942876 364310 737559 332075 746134 750157 729881 086063 191353 016540 921027 481105 518587 813114 566381 073851 302962 748683 425180 677945 493722 551320 436505 527068 931296 693625 626335 196476 198903 241815 457132 680105 807666 817821 402603 485338 337068 159523 563957 127281 730431 443061 937352 261456 938021 343641 477698 707953 512480 726290 167981 658963 948790 070441 123010 594339 648883 910631 837107 720285 922163 024662 123086 937488 645660 383589 302386 398554 822451 543829 475701 127316 447497 464537 365216 483855 951916 803683 970766 852184 423586 588288 837293 776140 036788 978048 915795 645486 186861 461104 286119 749571 258671 802528 213524 444701 268889 160203 169898 915427 189306 505996 182308 258991 519412 473731 451864 258992 104685 995964 762733 246599 / 707 > 273601 [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, 1801)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (67, 67+k, 1802)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (67, m, 1802)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (67, 67+k, 1802)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (67, m, 1802)-net over F27 with unbounded m | [i] | ||