Best Known (43, s)-Sequences in Base 49
(43, 343)-Sequence over F49 — Constructive and digital
Digital (43, 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
(43, 2161)-Sequence in Base 49 — Upper bound on s
There is no (43, 2162)-sequence in base 49, because
- net from sequence [i] would yield (43, m, 2163)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (43, 4323, 2163)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(494323, 2163, S49, 2, 4280), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 89 519590 657249 491639 485362 918883 235693 702633 639138 493383 038196 175115 931122 318374 465868 436704 221564 232069 271012 715423 323126 413737 290517 699264 151669 992375 185832 966636 534415 801941 242751 913121 497062 900038 611544 845362 331154 638554 781212 960491 132661 408915 788287 117560 182649 952761 021357 354982 266375 991257 977540 283746 487528 678237 225443 751047 668765 115597 918331 703355 246364 355467 365800 673854 212563 046727 015795 657843 401341 250757 380343 689203 867392 805891 941602 960931 784287 141124 090004 304581 127601 047735 183155 081702 080108 554955 459853 583560 747826 621808 312033 644349 530813 436834 563175 320357 338682 668721 741103 770653 755756 882992 255803 096344 608681 132332 227359 447943 167461 510618 361317 068640 845559 277849 364058 069728 818019 744687 522014 123945 920854 752144 142442 509677 074702 660634 785735 741622 306209 779178 614515 904879 463857 550859 098084 440301 909830 849516 234691 418496 615374 780116 914778 045675 245245 816556 670001 617182 047119 432880 673368 022518 902257 653500 028914 607018 996567 658781 369273 026718 788491 105189 066401 083915 222593 667721 713324 745210 219625 895244 511225 659526 824370 228985 718404 022720 262049 120385 370247 500349 658277 552914 194165 767474 121896 640631 015578 646696 680415 413678 297012 419661 711594 617039 455830 979628 599196 484507 145412 580422 712554 769640 603098 198304 317033 368608 998306 078247 347991 042931 509431 755596 060172 694721 838203 998776 225495 128800 168538 497657 408167 912771 661185 246577 363302 424855 442344 341749 360459 371536 685006 356431 117624 637948 385650 219083 821418 307308 346449 944998 829079 955513 790194 197807 897658 684720 328825 028639 010800 206722 990303 711166 719000 252949 889851 233398 904836 059192 478184 229797 986269 532476 246117 450674 779721 765539 100902 663877 648858 410482 300163 663014 988214 143096 418081 553296 717005 993274 135492 874051 462324 540341 484279 840181 845626 643957 347303 319723 295183 648661 778844 477445 139574 629833 320586 516977 758605 100454 769681 045221 804480 684245 475887 768103 627152 426904 033731 615801 911408 217572 670315 529683 581155 498942 531886 372499 601777 093993 425739 803534 070709 644135 032500 266396 406368 002795 533574 946916 391535 344041 212453 622901 213645 175389 462130 811233 493742 082067 491088 632709 061617 550896 518954 534849 995209 942991 935153 730033 583151 943715 875862 829333 177162 078064 501406 635530 953480 388771 342393 784562 977629 229801 588501 893446 765721 051874 514905 861515 894136 032904 874041 520118 953167 940550 875874 727093 228844 703221 116080 742031 646646 937401 045901 378694 970917 821910 910976 705353 933815 254793 260002 808132 743539 854015 214438 926747 473994 625439 952350 857357 553528 404520 985873 224928 798947 445025 379133 409431 214386 097442 035878 609947 221818 151403 578679 613623 947343 687672 224472 134617 779172 866418 085880 175652 677865 695771 707317 094566 637274 637145 504906 712610 988263 817135 248796 839615 822864 853693 851868 116463 527413 846758 706589 207667 621717 097097 798396 652750 828517 395919 246397 127928 455046 280262 347355 007447 100028 288281 150421 182958 726210 732082 845878 876580 218436 124871 055259 297196 189769 397637 577542 193986 180104 612341 857737 059457 893134 226578 652304 075651 441768 912899 430868 038400 741847 199956 215675 762925 573086 324841 321259 864619 482856 399503 666773 201009 482732 760513 346980 262827 378774 848864 954438 021084 783776 810602 207227 770369 703723 279497 485350 669436 861991 278125 655947 572411 514825 706074 122642 640439 880062 979269 455628 024687 624518 996592 884151 812759 052565 522988 838639 603122 944301 146610 566469 863486 936226 746361 662169 019133 067120 338412 016011 014044 339775 888745 496317 170677 172239 871790 296645 893768 250030 268750 226266 031812 716085 723630 952799 291187 686241 809923 484805 314806 132756 774485 209008 933560 270417 101700 422809 503484 092677 868361 174736 296638 236694 984758 356034 999540 321918 867710 317933 310358 125641 670021 236601 680015 585925 706773 034281 194397 980428 058334 057111 425305 698553 870553 429657 497806 369544 902090 471975 646246 488683 177205 886602 294827 198327 422514 506087 808805 038261 776474 227416 224190 027007 441170 003192 737183 928410 387626 190887 675506 140220 808463 999887 356121 264726 070919 731545 483768 015698 238776 056371 560855 993763 770220 126570 803748 808812 990583 074381 101372 726967 332348 774526 425633 264444 638989 455311 897943 004240 623821 456495 854680 428596 578281 155628 228729 811781 800076 473598 498999 747070 677541 971716 839509 071901 588515 508948 911697 334501 923141 147702 017754 339307 600532 176378 199207 926878 148635 743909 741467 526532 325279 976572 041510 525865 715621 717968 398268 987183 363033 964749 117257 912073 323659 660542 045810 013638 332517 927402 427544 785853 774383 210644 746445 740487 941031 125824 792672 662490 219248 676775 177371 007980 480465 180970 927318 788395 231147 605807 945138 882869 367065 852432 990892 887648 958794 984285 381155 898066 346219 592671 987273 126720 926535 054301 606610 646106 645367 384980 994178 560039 864669 911392 892977 861308 780026 628904 158932 388644 387921 960186 469780 112824 004888 032145 967136 534943 648895 335819 582145 007911 624648 978482 827715 256201 467965 098042 426943 722400 557065 083789 875548 154151 350952 680136 033887 272876 601444 361453 435034 707686 836185 968661 790099 812635 520830 658471 013329 041967 137946 207298 979630 369708 156357 438162 270185 406468 208401 069473 932204 310757 317722 998390 575302 741084 624933 218075 008260 944017 298486 234328 692107 233405 677262 066181 609266 626723 612468 105320 994467 501687 938904 659212 627617 999048 244296 522595 652728 243881 654054 106109 069760 135100 539993 157448 075487 710774 020949 003936 649066 291370 973190 886430 595123 338459 358104 533046 880885 114361 902203 313897 594813 914635 426028 649527 222374 953766 634235 985313 944996 462347 123964 470190 237172 834710 777248 609129 330946 607565 154299 374452 170037 951126 251224 917964 992380 543175 675200 257074 004881 325414 930462 357992 684325 706453 248506 448044 949606 375472 513973 836013 696127 484191 659505 640881 894266 281641 173412 906251 945396 961984 259116 375481 895073 836829 719490 654367 111533 339950 451193 855533 280104 674823 345965 403597 753946 317897 080978 920841 925977 655917 492911 938125 005571 350563 852388 147496 911846 746573 305209 526096 840415 447152 292177 686306 336109 012224 675138 353292 101645 062993 485818 533165 152393 165278 572725 904170 748207 235151 545624 139294 628610 983994 611884 041738 448132 420601 236341 556794 431043 776044 103845 202736 438880 273542 362131 765146 996945 347115 112922 483232 652549 763905 413314 911650 548062 601392 441534 060020 174296 522583 362399 751624 765247 577692 528209 928066 987747 314898 692542 228436 068970 687719 822603 578738 315661 695328 641684 686070 806574 927317 538527 270295 054140 851564 955126 667127 543992 942851 998916 607843 273006 599353 235691 802033 938233 443969 495490 721320 938232 047125 518703 280490 619432 657530 768187 751679 857738 369769 977057 293389 303084 574319 303610 124779 525591 488705 537115 418969 426862 593657 013065 106428 513122 185549 797255 294000 972638 084917 395375 144240 643192 493578 037320 222639 508220 073798 247490 418478 760581 262182 555150 422123 631143 821386 418451 947550 019013 232055 938838 048709 566264 957248 562951 912994 288346 997435 727883 310555 917086 712965 866798 696679 856754 844984 344869 700683 726372 776862 051683 506508 499673 836442 319880 253425 603669 348592 596161 843896 296234 643393 913903 157048 761565 010386 431168 144935 653748 788455 420958 153211 405571 135869 761917 502095 224749 444545 069015 081885 035226 632328 368479 680539 059228 410105 957893 140755 589624 612224 822722 136876 860779 441807 958032 615380 597111 354725 820713 840027 926771 792135 621494 742777 309844 586994 693934 621038 469277 531246 341431 281004 171464 189424 148591 361116 847008 985978 517290 186046 386424 139909 495607 336054 400925 348382 438309 746898 994416 051542 291321 255624 160421 729384 880368 489418 657040 643073 756468 752308 113951 154276 519551 081982 404964 639994 563852 129298 971253 636976 972706 845836 911312 151136 498015 647478 642955 287145 707553 328529 815638 107702 989353 215009 801934 628831 840764 997261 699780 693724 111139 771166 161086 684250 222847 208035 / 1427 > 494323 [i]
- extracting embedded OOA [i] would yield OOA(494323, 2163, S49, 2, 4280), but
- m-reduction [i] would yield (43, 4323, 2163)-net in base 49, but