Information on Result #1858381
There is no (38, 1922)-sequence in base 49, because net from sequence would yield (38, m, 1923)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (38, 3843, 1923)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493843, 1923, S49, 2, 3805), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 649683 196031 905011 396055 499055 464273 644794 758977 521090 548970 984967 673668 173014 321464 319086 209057 878021 761791 488284 300679 974586 698241 324865 370245 767320 743402 509264 619514 703716 520349 748382 262903 655580 591293 097297 982648 453456 013472 017934 907861 913377 101986 805581 013431 093593 511392 737568 989951 144531 179908 072398 309103 411625 392137 716547 634369 310056 984111 557334 872686 458443 045445 603513 212623 839862 931976 375418 057627 737566 002345 092019 896701 762369 379498 013217 276187 391877 848899 516100 339826 329620 639722 262739 194106 398710 199101 364373 334194 431179 541983 238895 485889 235967 486484 639261 983502 619763 509007 330095 637566 066090 265707 493689 603389 590334 408328 974117 845393 006804 657685 295013 588388 346936 821031 595808 539463 554824 036851 606653 826377 937049 762899 409378 808790 437649 678857 990949 483202 808476 498158 569927 987160 728618 625021 792556 629973 610739 531809 629947 483966 551780 562148 601674 077480 354459 805877 364477 033159 223903 869357 093723 875800 735478 766590 198629 804180 645860 083927 025000 476354 986479 093223 639672 298348 571093 326510 997344 933229 195097 509551 379256 435818 290387 371662 741147 245393 882678 808396 215567 252779 709774 017033 779410 240210 469704 308476 341763 828453 022057 268653 472013 464471 501971 503740 360301 259890 607930 270432 839817 247806 230925 889523 743931 928327 976033 696482 980695 410417 331329 342251 104210 405273 158504 295045 322763 857566 868415 926324 590549 008281 382972 142334 756173 708875 617359 509056 335551 810810 326961 325144 511945 575102 719417 226543 519318 868591 893494 132805 408057 197254 611059 915275 675102 372624 362497 015071 074251 263455 245216 843039 063609 950093 020403 632783 196450 527305 690219 930719 522950 271674 913797 336765 076205 673012 252901 712699 074178 698098 824689 833527 823792 827626 927776 390238 678774 894319 358138 177486 314253 414839 811501 687586 735475 395604 703114 991549 176656 584920 157351 351689 106223 868486 079288 836031 791157 522473 803047 727227 989820 891110 702589 084199 391056 298975 297664 790100 190005 257467 695244 485256 294777 484332 005438 651625 457090 612401 786541 777820 768979 107617 022957 291403 492903 219513 795402 447710 647609 063770 803937 925306 110477 361336 834475 395733 320939 303449 496255 844183 507307 475179 555935 539271 120946 407255 453671 875544 256337 457809 538009 344797 596229 940494 687666 697316 337351 664693 003093 740964 850705 845673 482032 205301 951954 457893 234248 553831 303978 435108 661146 774625 602912 020273 964635 038888 604999 566378 874107 033257 625775 232668 010770 915113 267238 680675 255594 734970 418383 882741 510872 240604 141372 859967 094721 617201 604653 675326 085277 332726 888592 278919 684079 626969 436258 316290 595256 700037 861439 450294 261097 110328 822990 140707 676172 222209 818885 926548 549604 663566 794576 582045 666425 408994 867515 782251 106521 302322 616479 476017 050013 602221 632549 985630 058775 267341 061442 513642 163601 955084 817610 080710 517155 915720 997799 285362 085922 762773 372994 061316 810450 420677 696628 134184 301047 197035 749602 103904 640537 913593 910553 778121 258126 131457 325106 087983 664354 736658 727638 370731 700813 189318 331295 260259 396018 069012 458227 895375 160570 534718 752451 172906 567820 170521 823643 499284 592785 288037 323989 485714 551729 754867 399022 926995 226549 782536 266477 279992 211636 120279 861923 968070 746596 289585 592048 041885 285686 350389 283704 392484 795469 462808 644055 996553 457796 411530 931512 208250 565619 557021 700207 829196 035820 919087 893628 332751 954045 902064 271538 074712 287973 350127 304240 294977 629043 958589 676471 826063 067959 421184 267867 813600 284517 036242 827318 653596 088913 910180 530349 529485 482492 057280 261713 201207 780028 308940 199517 669631 782334 160042 958499 263167 946610 574382 056901 386107 554644 813893 663135 480828 478140 676406 637568 487139 006341 718930 815312 738316 722239 815892 273209 361416 483311 003141 561677 825152 783461 459670 994425 154255 885378 592651 338810 676157 093674 472372 383189 753789 571531 721108 214027 619934 597088 006221 031634 122780 388213 342149 615620 034428 500438 947291 783095 134100 719383 939835 927615 591728 793494 963249 587815 505655 964194 922957 797502 960057 871883 341438 289143 669433 405237 165380 205779 080714 854472 652017 283226 152081 167841 672095 598223 910354 940303 878136 787736 152029 402040 602310 846688 516761 990867 563222 310012 357103 622008 962627 438578 964806 278092 451365 682094 194385 994461 725910 257179 050717 697817 011954 717102 845379 548386 862993 509220 990168 672841 031610 504609 784139 542745 529417 287698 748553 517054 752455 261775 466912 159757 604577 245396 046592 874397 066732 351246 929146 889428 995246 136004 692708 867132 202436 290139 928250 318956 393552 390357 516190 402411 926407 686807 383145 512780 099966 655148 782414 801508 253295 219258 329921 967213 689974 463997 641693 600297 488544 461684 846826 139104 444328 258013 892997 438725 607795 695993 016446 544439 127282 076243 873251 715608 271913 595616 044263 846938 157255 371683 274394 517392 090927 869570 931601 936161 248674 082844 479484 880069 706632 085399 812457 443432 435274 672396 420236 948782 437659 854106 728743 253096 483204 137381 580757 800890 476780 879724 353610 734136 712822 159530 278413 793589 759490 717114 329646 948691 449637 774728 296264 319113 599185 991161 030211 446451 262415 184333 584729 142557 722463 397185 492781 594839 651820 842651 548789 660001 805445 405091 573471 645177 366158 394128 626576 083264 284304 393467 839385 618577 141467 428550 144994 938864 002734 698790 761833 947664 893136 156550 132370 370479 086736 432877 910608 518756 424742 812615 729325 833104 531006 485782 449361 471784 017070 779515 256932 062411 171529 931294 083817 192911 466159 984819 929853 934858 416197 304841 615973 647783 009164 416375 567729 121510 813881 747505 498426 306076 204727 767691 857060 964313 518039 163283 140668 377176 084967 845346 047881 783825 364000 377316 483312 985378 760401 979220 270619 658161 254194 259279 364774 285393 883826 954417 334484 481317 793448 272436 979520 239973 263476 775157 754911 036981 843626 179399 466163 121274 583094 904771 346623 530514 632600 266246 631052 979318 676604 372456 474241 997748 804963 069396 727023 365926 091712 317177 623187 782659 998581 349610 684905 403142 016511 915395 429580 869990 187348 927121 434857 748590 721047 921343 266122 410770 105134 987494 653366 382936 585866 169656 285960 550937 409274 404855 663585 876824 708104 776609 748738 309046 678061 098733 548262 875186 816951 830976 244746 461934 381105 583424 473445 626984 681009 265369 504253 675855 695762 593865 076492 413454 664685 095059 156623 817461 289576 804252 668038 765084 411082 069424 984853 663305 715998 409293 737590 119563 486544 768961 984258 843577 564258 954441 770427 174437 509448 195826 011860 307092 620287 085230 887716 643576 914035 849722 971002 499491 158240 053275 662578 847441 580009 416282 460194 067984 369726 789943 700279 273451 089662 444338 986250 436132 894497 019276 059808 198309 710794 574098 498690 977413 238446 088344 587333 420247 158979 177304 617573 339762 693522 634841 239792 997236 995874 441875 860212 675789 961793 081645 578653 260650 358960 369350 184622 938306 636816 926291 741087 680487 810293 652146 680604 525565 232704 370024 283254 593193 617425 251591 690694 434735 582465 708663 928540 030515 399084 105164 738264 937299 067955 864005 / 173 > 493843 [i]
- extracting embedded OOA [i] would yield OOA(493843, 1923, S49, 2, 3805), 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 (38, 1922)-sequence in base 49 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (38, m, 1922)-net in base 49 with m > ∞ | [i] | ||
| 3 | No digital (38, 1922)-sequence over F49 (for arbitrarily large k) | [i] | ||
| 4 | No digital (38, m, 1922)-net over F49 with m > ∞ | [i] | ||