Best Known (49, s)-Sequences in Base 49
(49, 343)-Sequence over F49 — Constructive and digital
Digital (49, 343)-sequence over F49, using
- t-expansion [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
(49, 2450)-Sequence in Base 49 — Upper bound on s
There is no (49, 2451)-sequence in base 49, because
- net from sequence [i] would yield (49, m, 2452)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (49, 4901, 2452)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(494901, 2452, S49, 2, 4852), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 32 686661 698933 948475 731461 053200 196229 597102 922619 197550 921261 539810 971465 571021 421610 979087 330060 313994 130891 192936 459915 781252 628207 553507 075418 895452 534881 960209 587403 605546 678019 481825 589451 650468 861990 894775 224888 829468 674348 459544 810870 176030 475285 921950 131636 721991 271802 879262 624454 820942 615889 983716 159770 394134 758733 846856 964753 142493 963495 247867 473932 818891 633636 768908 439158 481471 458666 122822 740208 971401 710188 707248 557487 397453 975976 680298 016440 187431 555199 300969 682058 430132 029294 430237 059866 269254 796808 809922 496122 099404 275378 896791 400177 348836 139456 069148 388506 558074 423740 588599 155573 645564 429064 179612 261228 457246 909950 839144 660855 277527 546227 748825 945762 203724 753414 313286 730184 989905 457289 205593 856826 554818 582649 131107 944491 124538 037682 330513 864259 028319 816120 688625 273061 933214 433485 950516 845402 346492 198636 737019 709603 817484 667495 360138 519333 715309 322678 334399 883719 611273 723723 601323 674960 005966 301073 620580 946825 317414 358876 989128 675817 101876 745832 120224 723378 535819 501624 576813 679864 452122 298881 851451 238199 011843 541598 518870 746992 579132 756907 146717 565708 178853 601257 228520 601581 770725 549563 472610 519096 814159 405656 050918 170746 297393 375691 794306 455708 286145 711610 452593 364895 977505 385973 290527 408257 092859 761039 275206 288706 578637 558488 197778 550463 678233 397525 609798 864260 770072 751189 540074 114853 377829 076319 243611 515473 704787 209433 197749 319075 438813 418538 215542 633122 884527 969125 249748 621806 790216 931290 228991 796679 514054 115747 349060 912983 796676 149927 882935 717025 666110 707231 284106 796772 504174 854440 677630 866111 279151 589157 750394 604869 039612 892598 671652 461675 019216 894836 521172 535492 065361 412524 186825 630142 038804 943562 800676 201758 810307 458475 820854 995785 335966 853918 835751 129677 155916 381781 372591 305746 500423 296929 471121 888719 891986 101172 211854 913946 369783 205052 719297 392189 408067 341271 593217 732841 293727 554166 486713 419417 901532 678059 910432 357950 521743 039272 733325 660525 521084 784261 375057 977122 701878 159911 982874 922966 317590 717777 794307 011663 181606 558500 670309 213596 734343 087471 298131 635198 612171 417849 262538 732366 266243 965521 472038 189436 424918 821164 474577 734756 968711 048758 395915 151269 892177 173993 058894 909840 787775 020944 487239 377730 153202 087191 476486 583415 546497 968599 090322 198301 329764 333304 121663 228104 658294 775270 244062 959118 319831 481931 414340 122347 527900 999417 082685 736426 480587 630740 456024 995460 180702 268852 727063 602746 567783 421138 427460 654183 969640 463011 133513 665965 980520 793929 921897 434570 672826 304865 863401 167484 140506 420659 040925 969640 994916 058853 867286 380155 831716 687795 731757 415227 983933 308216 550595 294354 261014 270418 194800 169258 539434 847857 214566 393678 073959 142103 297770 682613 752051 083856 298072 202412 644507 244972 326819 416456 942375 201223 307204 373974 385687 447529 153431 289354 543763 783084 386262 391330 566562 826655 502384 849612 346759 338676 442868 871659 434041 653766 929149 310674 130546 880316 452738 384321 458085 838899 144288 405205 097923 143267 809808 035093 055906 056781 482376 829968 914331 123226 140711 050401 509075 334674 512886 735013 938690 153517 155826 346629 688725 919730 503861 331583 621813 395530 038274 370867 400857 495345 956900 827511 971900 890768 669848 426490 575068 961201 971408 400962 060510 993613 015850 054750 311453 624459 690974 557119 517492 018622 171185 858361 058495 317189 107107 432838 720762 720943 230166 554529 123048 088152 784965 875585 534757 111553 076028 183687 353662 525995 975958 440607 087122 258798 421947 171620 737751 093918 114189 548457 229599 764918 140599 504381 741869 197938 844469 549865 366204 537190 691593 785474 153878 232275 832171 570958 279042 344300 770227 658244 172121 724996 917795 108424 600770 682970 360508 563855 989766 694953 147125 672586 741456 065231 122872 205806 357841 723353 613482 952196 516934 065803 768945 079453 015984 859498 407465 698060 085542 704597 260727 947290 070540 556414 918136 336263 106143 717628 903970 980274 810694 545095 295982 965419 475793 387614 459815 177453 110702 088826 154806 317517 073194 982889 923534 010069 695254 189704 030568 570236 754572 074012 006245 150917 673440 149542 162163 596364 297153 787352 343149 567696 901913 321038 582938 570269 925864 432521 019769 579352 814501 251499 868185 188194 240324 158473 715190 705669 874467 630201 129312 514942 389901 059994 435553 408380 509264 039742 109185 218620 432533 069801 248745 031481 402326 113384 443889 997882 319612 481473 806569 426707 017801 010105 902511 333740 338144 896147 419355 598389 785263 228500 294229 376543 163888 830259 283323 420770 802983 854747 713731 814535 244075 911796 446874 418762 824428 867555 904281 300802 306960 647077 867493 695821 414524 335839 355276 282082 092897 334632 129244 503832 504032 772923 302983 361650 283091 534644 201442 787181 716662 588885 333197 964889 375715 499534 524533 258055 707032 930872 599841 810300 498981 476797 109710 437880 931786 667861 784218 476400 839339 615067 951440 169009 084111 378283 900989 538349 830027 251278 197919 967465 034366 187315 008151 187128 415184 436655 046092 458948 864365 687141 040376 281960 914471 245526 772463 813379 717170 723267 170768 543963 971100 550263 630425 818565 310696 049381 080046 711356 089163 698219 697066 102446 971599 210696 850478 883789 725717 308966 902855 141180 445096 608322 964477 889308 008286 123530 202493 954147 839861 026272 788586 387632 791680 848429 679651 656763 468761 828827 569265 520100 627733 862791 886837 664224 912962 666931 804745 095620 306124 296277 045339 800600 996303 870067 527489 977177 130653 009315 389104 832830 119200 535284 806368 528047 562035 070732 664785 065191 917801 373122 901634 593020 145343 866693 486741 177959 889325 844453 807118 456954 304762 153994 308549 568010 257103 496008 046067 189446 701571 237683 519649 794717 967169 295518 671443 778209 870772 757799 987211 091699 668379 466855 220744 847276 887184 702770 946723 061042 257646 323151 112382 867038 888331 171553 270662 783996 179673 554143 873519 164787 494557 278848 471335 976819 307972 175671 570406 507001 210508 510009 239038 291852 004564 459970 493000 202089 878516 708685 172686 408112 043249 718863 681740 365146 237456 156952 138857 161541 355672 544061 543886 348402 365700 881123 754643 538532 742347 709129 395735 103309 058461 294057 209814 791133 180326 764318 916629 382401 138791 257732 168153 365314 487209 549563 071640 428985 506150 628471 874476 219762 366420 116700 119574 626414 074539 892513 210623 992964 249528 209707 893510 908454 298013 635261 437052 682184 327522 037241 740026 470515 126368 378055 072754 999033 530129 609857 225000 181166 335695 767840 001380 632744 667509 448994 355387 390491 695377 962120 649895 696704 133896 057797 282289 398260 807134 882619 969307 237705 838448 069930 722654 657442 306041 453516 039038 494635 643900 573060 409870 502388 747402 119295 799180 258392 237000 284865 560582 450619 283484 147063 298664 355639 211418 097807 449527 106755 815207 595156 942505 405370 895431 909389 670374 271406 534886 238959 179938 497221 372002 603444 908971 375812 201836 059836 504571 530075 781393 970385 453240 267392 094539 806181 385291 522719 038805 881441 572186 205918 466088 542918 386426 419174 344041 054460 858072 159408 370514 076084 839635 094316 841896 102363 967003 064004 658993 979919 268475 500522 275654 492621 706836 420340 647245 615598 727999 733406 775256 634899 844224 952058 905473 219092 533908 184319 392200 920519 668971 668217 937099 289527 980222 853434 582516 558119 251731 722691 341984 909696 058387 789441 331644 042819 689196 796969 102233 445348 304690 029521 100769 751340 583584 459921 598385 908297 414955 296330 522464 938891 557034 394816 970012 449646 143359 805446 134113 677812 891171 025960 891302 846477 967360 238036 694798 555894 862458 643791 432720 405442 282400 863337 025763 428454 055801 180304 183017 495886 634532 996267 515209 228347 238901 423873 013544 521190 976388 038492 475882 341602 562152 335730 961650 102656 936754 599134 071261 564332 472905 147689 169336 900072 461591 379651 617312 697719 366267 893293 781693 188333 280719 280114 019763 882926 791083 918876 878447 631433 604835 998779 531390 947244 666542 310821 085122 431661 621446 046352 921504 268135 883350 292301 994817 972685 112528 101396 836410 578544 715932 896075 936415 255139 874623 895899 270945 305018 972496 982719 691947 017379 292927 918303 883927 788402 960982 624986 296187 228223 534692 929493 529136 000471 662950 924000 485677 878334 739679 747211 593439 783966 977762 565231 755100 550663 471594 683632 190632 889937 904697 075647 099047 587550 167812 271034 795212 338861 652529 711044 737350 503092 638042 735402 521920 261406 250940 377264 823468 670199 446820 850732 702550 770665 855170 424925 620722 014377 349510 005675 582450 959976 973375 390124 467496 651789 142614 765670 947372 604394 626514 973686 451497 046276 933781 684676 170162 480545 083175 905795 735730 373070 013804 952694 726129 338241 717320 816236 146595 652388 669669 432413 375322 875773 106582 257119 984089 626936 236023 636111 452176 431774 665013 824945 924909 364283 685626 954972 446186 047647 839157 577740 375091 768673 592455 859599 718728 736836 047508 985320 110893 406819 187204 151655 831449 379383 587344 514305 518427 798733 441633 759715 390232 693166 631384 409820 477749 / 4853 > 494901 [i]
- extracting embedded OOA [i] would yield OOA(494901, 2452, S49, 2, 4852), but
- m-reduction [i] would yield (49, 4901, 2452)-net in base 49, but