Information on Result #1858377
There is no (34, 1730)-sequence in base 49, because net from sequence would yield (34, m, 1731)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (34, 3459, 1731)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493459, 1731, S49, 2, 3425), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 227609 560196 747052 028421 458959 412955 940781 807451 813332 146234 213702 858549 470083 460670 958229 561547 153369 762931 509271 982890 822190 503243 083627 635832 931499 403328 503834 534091 893426 529562 966069 650199 760593 263584 180043 826246 807054 603807 864483 215734 112817 873664 102027 143327 088786 016631 838950 691399 385366 760029 355087 297802 572606 486029 157028 315751 317029 503752 559519 705264 392556 816206 982521 568307 867499 818973 721303 257901 956947 684331 741544 168408 958900 275683 834526 455657 779678 150972 649924 443552 178478 040843 519884 234562 446352 186530 148848 991586 530949 415490 990384 632631 663409 360503 132940 932114 477846 348225 506696 042911 129035 409680 331135 626527 779368 796302 111533 007686 527082 216509 915758 366539 241382 490974 588989 097058 046447 264428 959094 140039 025868 780698 578152 282251 769455 052147 852483 123956 399717 043788 680494 349394 568532 852641 375018 144702 399421 452104 067627 993035 206586 328225 753757 686548 350580 005664 533832 205365 990302 504589 147204 653710 847797 285242 950380 929778 416701 943411 819712 414330 650902 499237 461080 574823 169772 356925 943768 285724 038250 782379 836941 798633 681670 225776 990449 793602 202964 789349 526673 661250 844697 027815 644480 711407 353121 538564 567598 069507 544883 895068 914564 143573 910591 420357 764198 062098 510862 283634 539389 898500 497222 915302 690809 906395 191261 078099 327229 015897 388875 135701 803440 923764 521703 698311 149379 833060 960034 406455 396931 835035 350621 258752 879727 454002 769943 887052 748218 321967 787973 246337 262652 253830 767458 403781 476676 935509 659110 083205 880611 350375 148234 333569 640218 970040 539937 890602 655162 416467 067650 809847 522995 053696 324402 275990 295792 920928 301201 846094 442834 000598 881765 753021 380680 810866 178064 201860 459450 226998 716409 853993 870438 735986 704032 201454 616580 327012 316990 596653 969360 296950 671349 181464 258015 368252 311204 511262 910727 988116 488742 745996 509580 952377 345014 893524 987344 837308 958450 241399 787720 280445 865063 041295 345522 115860 042510 466068 276351 158499 902465 456860 850299 210015 910279 162427 739268 362307 805937 425237 109867 605315 207531 072133 853746 201493 374821 410421 294478 655546 720457 811820 493803 462606 924585 369511 799591 468954 483964 171553 671974 310834 960123 054698 291829 823247 525494 414991 249596 324249 919720 429358 107097 861149 724065 912046 052631 432291 336223 815280 373184 939581 941647 033540 675098 341800 523562 270748 645551 071354 116624 017993 581287 618465 377571 273534 512460 530166 185116 009962 461140 549193 841594 838732 257915 920760 062831 556212 123370 775734 883720 179386 857372 830589 154244 790051 204604 309287 662240 878423 147328 474512 381483 580870 013374 536600 188605 852737 273777 316006 373858 223098 998705 107328 351978 713823 894363 245891 287480 331844 613475 494074 744918 241712 344490 002412 947282 544263 586049 063711 341635 046092 111903 586928 234064 226329 270451 141499 891545 144844 316618 301639 529218 146873 290310 723155 792661 489523 475672 800902 397051 532592 734991 278869 075566 581175 365195 780744 994954 810204 182102 987064 292064 815299 141187 488470 651413 807988 481491 016309 809804 548429 127656 314538 601610 418049 839605 985428 072425 578363 712559 878009 695574 947456 137350 534460 807913 497885 489987 550223 275802 820548 887308 800783 531699 866508 211431 415009 961067 151678 482889 304114 657965 939250 933005 648262 320934 851396 604553 932854 806988 676749 570208 238513 425629 329137 358271 811962 418777 532984 452104 169502 172871 803624 818663 554715 815887 742122 005931 041003 524723 852887 022222 171785 688199 848618 766542 130611 305456 771861 173430 537374 728930 732775 066892 547031 373180 782322 897554 701494 775277 180218 327173 710959 182305 936068 334408 721388 792555 173482 742231 105042 462579 760936 793036 084694 546172 795616 131625 139830 965044 816647 314156 995812 683402 766211 292016 796432 630182 354298 106639 900178 405113 177502 535372 313355 782793 210198 557510 751430 724472 388529 386309 088998 536215 090466 431454 651189 218669 439565 022141 605540 777677 309072 942445 904060 845234 073935 839718 110410 014805 219618 658844 425898 536197 110529 747182 408782 362574 208910 610566 274891 986689 647506 208129 874619 256138 471044 526496 161999 394229 325824 573952 680572 491846 212372 132208 057419 791622 540989 329593 965188 770915 095924 555967 160105 461997 307483 004391 952732 599168 320846 526695 633085 608896 134282 686665 050187 733653 728703 389650 517587 875910 710924 007582 784207 699445 900972 828215 474285 686288 143084 708646 266293 324732 507466 302373 718906 196847 935827 010949 602339 294820 182462 017871 666512 936346 979274 385858 429828 552425 688747 032479 098157 900155 284800 596827 779795 355739 486625 728926 025536 048245 350007 660140 575472 976995 028201 380229 214742 711568 339795 413461 581428 719697 568760 908576 377743 016916 255298 642031 609346 288415 566769 428448 098027 820775 143497 789206 705735 202548 983716 546730 348253 707462 171596 594268 436838 758484 978723 127340 476415 278940 091241 157505 583725 582323 368430 151692 526690 352495 686478 903364 350814 649437 006070 461276 180051 522029 776122 415881 644552 779090 714204 077825 587797 796975 872236 132211 808546 812699 276170 345629 817385 924366 608109 736591 016374 016350 173233 908646 994143 195476 181545 038720 989314 953353 312967 346732 152316 637245 365978 947390 853607 287396 609643 573007 391130 009307 830697 785776 794801 454025 113835 827647 954599 666732 850368 307120 533490 854827 104959 819851 007278 687020 571637 302986 376115 055521 202819 199037 847068 995064 474472 894223 630132 045391 899874 745453 332146 715897 997403 653516 161595 484185 402787 960507 916962 544251 620953 578880 096164 259438 835513 222965 835446 722507 881722 530686 789148 810271 937464 908477 704866 871096 716590 403454 142516 453449 645657 736938 351569 676252 603478 976972 630797 559005 212023 243280 109006 991592 560038 778646 722781 814799 028994 798499 665763 481192 025874 070728 623686 134554 547175 960389 953885 892187 391208 918616 716230 528177 755906 378005 774892 340959 708408 959054 611156 382473 243791 111186 708897 619280 714892 727116 286440 715143 384463 216061 641436 601509 247818 832509 603032 617915 422813 563861 742475 839311 438272 251142 678505 044368 556667 624723 983242 522172 677881 078281 610525 847254 993030 620511 842592 552568 735854 084067 690159 593218 674600 218958 597901 592599 274893 199756 205151 690087 916085 600640 889860 762587 723374 684301 705546 359824 982014 568235 686635 885848 154325 819702 091055 860321 203012 507223 462532 866439 844050 954099 580740 686118 138508 095971 745010 799409 234661 288019 / 571 > 493459 [i]
- extracting embedded OOA [i] would yield OOA(493459, 1731, S49, 2, 3425), 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 (34, 1730)-sequence in base 49 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (34, m, 1730)-net in base 49 with m > ∞ | [i] | ||
| 3 | No digital (34, 1730)-sequence over F49 (for arbitrarily large k) | [i] | ||
| 4 | No digital (34, m, 1730)-net over F49 with m > ∞ | [i] | ||