Information on Result #1858378
There is no (35, 1778)-sequence in base 49, because net from sequence would yield (35, m, 1779)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (35, 3555, 1779)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493555, 1779, S49, 2, 3520), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 350946 556021 122004 888389 626803 484694 466131 615295 015314 831507 703878 747542 099771 460560 832251 313551 119713 772955 047006 783104 097503 633899 948242 284120 626017 954097 890775 644482 668940 756119 702747 106141 994576 784886 908206 150961 034706 831357 245850 751837 832116 446575 525903 822806 618234 328987 575123 838125 694132 870612 116168 048366 986313 259908 281318 684775 739538 564991 086135 000165 903535 813184 353805 866639 863576 885434 639802 803761 688097 111696 409893 780140 295361 195469 135416 832268 213513 971887 420684 717978 353116 288990 524901 867332 933512 555726 642664 288081 501395 920855 667232 066523 567023 787167 741366 185425 990026 925706 248836 979724 330778 461595 726539 245493 859716 561402 623661 394517 960843 489756 141843 425291 005998 972546 325549 178080 281694 303791 800541 792849 183253 111094 567103 901365 024864 793854 154442 950475 659925 286484 104091 853235 075056 581953 835837 391562 296217 498898 794330 529117 293998 099541 167529 004800 964506 945935 462677 418106 396022 270827 440232 769946 465354 044800 920501 824375 989881 201997 829244 229466 620794 593652 963400 933528 232257 319040 476824 351651 922199 391708 447887 552015 801592 299486 412865 889761 002833 633434 392661 296831 092981 968442 867690 529890 594892 689118 831115 714371 845519 349314 681909 813602 315142 918704 441067 224134 709107 230599 427516 999380 104801 788247 173511 331111 671264 730172 546154 000169 556286 871298 500297 949251 724467 056880 879302 043359 924737 252566 499698 021197 925779 280393 070130 975605 633611 464218 255497 084591 504874 542026 497672 004930 810324 807477 857430 080786 109031 062101 024993 997168 625374 341575 617939 065104 520228 982991 317871 593668 272797 936171 274003 265742 916183 743671 088966 580551 082324 744451 458322 084677 101939 244296 242807 720332 562528 197122 848177 228460 600740 014064 346765 791208 457052 140744 282225 380784 691246 449344 782341 679559 823943 785745 144163 062479 454834 498931 728666 251213 736957 305859 495342 733102 244990 667109 153970 742635 005514 124866 664124 063606 641029 836996 892122 543119 026101 964145 070752 264811 741856 818583 441213 325317 404628 638133 746893 518263 510274 141444 497790 968043 412499 380865 249687 640369 393102 890747 819627 146976 785932 200329 752489 504742 443003 998351 565155 915365 627810 485513 727163 787740 729758 352710 418157 694538 701800 784164 591526 392457 141505 129168 109866 764195 373273 989406 968258 452387 802851 203227 679793 221357 244361 009284 719187 108608 938024 106747 365805 142551 796806 480514 391582 024506 119628 802703 104921 524300 550115 126749 659132 414705 520452 109626 683990 533006 531227 783203 350592 883506 790321 742305 262637 922363 404076 188586 075030 855287 953941 971250 655178 683562 967870 621693 032441 565472 639745 339127 880047 136294 255716 247462 140062 402466 702688 331501 820042 568825 948483 718046 428587 177526 051084 644287 038258 756979 615596 984561 962116 381715 149753 056245 303807 159115 932695 561047 477447 916737 445922 536617 997344 032955 655168 689605 173456 953796 436249 013807 853320 803175 681056 527198 262261 552035 691798 217753 172296 217415 886286 713036 612087 548206 612877 418082 673235 347892 708378 156524 066047 442951 962972 272163 900023 976362 880330 484718 575066 281486 706468 147574 142900 077233 295959 928851 754374 573822 819632 419656 644645 499091 550910 966962 249145 500956 304796 990217 636259 370396 264562 024621 570252 293950 799242 609268 500315 279554 837571 722008 189470 579296 238724 822968 664217 056230 194310 656896 336476 578565 531683 157642 421365 038457 677193 538706 253145 838418 173300 376745 972316 586372 117190 064068 155491 094476 794613 109444 690192 635503 546658 168220 602115 161681 666158 104605 172417 820231 140222 833752 501176 318810 784652 804974 391296 731130 484155 933048 808979 738978 790683 523140 540273 401430 093695 013024 009340 632435 049736 202595 381744 578599 584625 193315 720463 975179 875025 139509 848640 802153 195112 746941 492719 842814 756264 536159 041855 334188 088946 769747 252459 847727 170370 284733 436671 219832 619036 563497 695797 986613 652743 041106 274315 235585 725937 239299 541564 781176 726504 657040 404079 171287 808735 555021 347536 003301 782052 866995 761982 655259 939236 058337 672379 189370 985490 742297 052679 407457 273926 701171 922705 976523 828768 982515 960142 506505 950096 929817 620534 398144 456916 640883 109374 114334 620990 576298 574522 240499 649526 875406 637243 995932 394028 581291 646497 514619 575475 599290 829181 162398 096572 295213 694591 003764 764189 476551 123092 121386 214326 663595 174304 221724 488091 166701 345314 167932 671166 398511 484737 044710 440892 824020 297000 606546 904694 174498 083986 128508 828415 552516 511470 351708 242915 935302 051167 579536 442098 731251 933728 492742 891607 521687 734128 963497 431622 265179 477171 561913 515986 376539 778116 354899 991405 852118 567778 170104 217044 644448 841773 519890 300591 367055 072993 706863 050171 060376 729359 997877 729928 853007 091129 197622 256381 921230 366624 577242 849069 354464 025742 490893 946140 272697 104135 689797 188274 994159 760810 617623 010911 892405 831022 288778 267337 014323 703792 199705 856915 782694 920741 602512 645650 207864 717836 511643 163314 171942 308804 963244 595959 952949 171562 346939 157398 488008 526243 046251 482237 377932 099617 660498 241541 590454 709462 944588 393281 454301 874285 745930 653941 610499 506313 556468 588187 383788 581007 222149 608526 278178 248686 380954 922902 385433 106319 921626 235441 744683 305359 050212 743573 010652 780849 066093 935758 684652 547997 953933 593308 116806 122185 802416 114911 985101 641739 492410 408302 772677 233218 884005 695913 823553 337259 952959 939994 870496 831134 200887 640323 647794 246531 946223 636740 461332 851128 145721 462763 699072 750200 397058 296276 262731 754549 817988 111441 694151 793775 316981 832242 630363 591756 019593 278277 227498 329558 155861 513396 831538 305997 497661 524813 455493 334397 935281 624746 598827 414551 564768 027831 142744 760971 831018 114758 474891 732892 338808 947117 452782 225494 175150 316778 482218 119227 334662 847894 845716 353366 153234 946484 311199 654164 221998 639894 121504 825830 909382 393590 866063 214014 879100 668081 796099 213909 348637 967462 275359 740462 298488 949275 566857 732258 075282 874243 348522 866948 352635 763588 595054 474208 117911 574411 250636 899384 076949 065389 039209 755514 197583 838051 138806 557219 982217 188179 177096 457065 850518 827395 564920 891197 457317 405085 054362 610780 575018 073599 610919 824365 523293 621518 094858 890400 611120 088306 522253 053662 689243 517922 949961 085403 839891 160809 182067 725933 095153 245797 875486 149638 004382 979917 918529 531054 967194 682274 689560 233959 667051 858625 132311 929938 450036 109193 987813 912019 803501 241035 904453 502246 597772 874861 659472 704880 042347 585608 955222 963644 217891 023575 261959 / 503 > 493555 [i]
- extracting embedded OOA [i] would yield OOA(493555, 1779, S49, 2, 3520), 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 (35, 1778)-sequence in base 49 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (35, m, 1778)-net in base 49 with m > ∞ | [i] | ||
| 3 | No digital (35, 1778)-sequence over F49 (for arbitrarily large k) | [i] | ||
| 4 | No digital (35, m, 1778)-net over F49 with m > ∞ | [i] | ||