Best Known (41, s)-Sequences in Base 49
(41, 343)-Sequence over F49 — Constructive and digital
Digital (41, 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
(41, 2065)-Sequence in Base 49 — Upper bound on s
There is no (41, 2066)-sequence in base 49, because
- net from sequence [i] would yield (41, m, 2067)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (41, 4131, 2067)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(494131, 2067, S49, 2, 4090), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 83 097212 481734 750505 770630 852050 112185 626519 936239 774495 882218 747127 885181 037863 391542 821894 557306 790786 146716 903502 172534 103744 545046 797823 084270 370970 468829 060310 807907 034476 986470 026504 067711 021374 713870 737560 726875 781181 733127 005011 846071 070807 075054 505967 498151 130428 761137 493364 800684 127249 022517 839854 870762 119455 172517 953434 136464 245649 535719 593592 514941 660889 278505 151129 081136 739502 902357 455223 677614 991752 484395 349080 286147 610231 819854 726673 807675 047123 507788 518620 686054 265513 991114 494726 529364 414972 918709 971747 898706 352357 042190 356068 339840 559226 137141 878557 897067 852705 087381 624186 852978 196184 433194 688406 740926 859374 786879 196776 761077 104635 917770 751108 076439 643401 605684 430998 456741 768657 071847 899413 349319 378314 383047 594310 467770 325277 152615 056244 537128 716122 489075 771444 575747 236348 188697 940319 640453 742044 392670 273503 973197 957432 060628 945590 233101 566087 774045 517107 800290 733912 772470 542140 273283 115986 486427 037996 076685 827236 431323 891068 568594 525529 284071 747235 002705 021292 732662 954981 481104 091347 137540 938459 765588 980009 516914 935000 736648 900887 261920 897580 770501 126663 748100 637944 109709 433582 859873 313337 979086 508502 825524 423550 855782 177498 646042 973271 236018 745972 692652 751425 645821 145140 952743 308153 145789 014890 320137 106672 046477 666997 926137 047759 594689 979163 461099 677404 345197 496678 677935 203758 593260 605532 618484 059560 941737 691318 991872 026367 748924 827291 327492 842232 831991 843416 335427 368755 101231 670368 549841 448381 823831 719792 254211 693585 914339 311093 917419 193773 971484 784015 083779 092677 294275 757844 859006 404636 732596 621450 959916 947428 232758 067663 539674 112075 838912 089732 124591 569393 988002 985574 047939 898655 178187 989228 950890 806708 438658 426669 116885 608232 490426 684016 624120 588552 465419 762678 462312 639263 374176 691147 070971 749015 228510 330035 684916 045114 429354 495814 639788 785930 222084 833773 438015 888180 562043 443938 176300 622097 314643 136306 986467 625378 976832 889357 933180 687390 394798 345230 431240 171967 042333 117683 666049 870434 936044 277903 557512 462020 845765 743819 989260 058350 877288 681288 743618 567713 668621 277045 697151 353488 769938 502561 961890 923731 661436 197998 098616 982370 501620 832705 646383 635024 275958 203941 856792 102846 435841 855296 138399 869396 009138 362351 662223 472824 267984 427584 442792 378942 139065 229599 346325 646260 285790 393185 064915 770919 579484 187886 657504 606477 102433 383963 155286 344639 877509 470903 074180 286581 369816 250095 329864 554930 066042 938347 196242 152873 420776 734844 086049 153480 169166 779572 199577 478426 537254 692801 080953 724619 444828 847776 042225 506745 477195 996421 073304 845481 444325 204727 235823 512596 895111 393941 458602 662953 448032 049383 024908 015713 539675 372561 910755 833177 638059 716107 381152 916532 443327 732658 646456 482905 202853 036654 266360 077902 022134 928433 088088 069397 671433 823905 810163 182281 376777 421420 628774 519636 860331 298648 970691 800594 715829 551763 588490 276293 596899 414118 622620 191135 860202 347708 758271 294980 739986 075933 145270 999249 718639 315842 277767 167798 192502 148561 615914 028872 493272 915801 012177 287980 831264 794985 818321 570913 999063 009432 071513 136649 804291 937979 790069 671401 562730 034133 725636 903962 585724 002388 135494 195565 779817 560938 670484 311207 031296 430393 047071 021235 670263 174011 298605 305240 121362 566472 105457 593751 646405 204977 271466 455929 545593 522885 731447 133481 535148 485470 135413 320710 874808 120117 608634 015562 624031 793335 880334 190255 658149 318421 100411 309122 939653 293901 306852 949902 987279 757380 642291 379780 376923 143914 042470 813351 648286 105295 376159 930041 349868 489062 170733 397063 810359 418209 455738 287729 922541 731089 438130 281187 403081 372256 378385 515703 928357 471016 322733 858798 601483 522094 894601 793392 851215 875385 691687 260052 495237 372369 744007 263260 909590 826776 325303 322030 643432 487053 553531 523178 630814 817562 868846 136951 196049 146114 331725 751919 627664 322075 882882 940549 017026 782055 232447 136016 420694 663045 469726 043978 014662 608033 690641 120266 594091 980900 905319 318077 808365 221309 684492 755500 121194 869866 451588 123543 093811 991791 623095 362828 065731 150174 964081 616526 279883 445864 157012 578327 192848 105427 386451 566570 828500 757400 715914 077930 684908 225038 011324 462190 670640 517230 730375 553825 775709 685591 102756 554324 736338 320066 941223 052909 037258 971755 961970 498485 775833 424165 730899 262280 645055 980973 155476 242067 340891 832299 662567 117359 874603 942991 059633 945606 345872 359028 675232 101156 383366 762374 218464 875277 828304 615675 062052 362026 683254 045637 859030 713651 712932 716499 702412 665386 784613 942846 956911 193180 024873 593157 864549 847083 606796 329189 926349 214346 086146 650787 198657 183373 799011 464339 922449 233344 153517 558334 926005 074037 281766 143896 274509 961933 132986 231486 245836 991798 185728 146537 271901 086401 861273 111589 287016 762818 924085 947688 399503 572332 530825 804611 883365 339262 142738 591531 683318 966670 063643 747390 837987 363271 583892 437875 732850 756881 189229 531840 291055 974230 648268 400807 948820 898421 721834 625540 791441 966834 651228 363538 243940 219159 960895 108053 179223 119432 365295 282548 294097 503156 050673 217322 795464 532737 550295 734524 736099 264787 372296 220938 468096 703307 314857 418342 023842 292575 158071 211957 550517 634553 846883 915197 263988 803527 599392 303655 966540 171636 484382 702727 959596 908207 706173 535202 707465 617819 168541 065268 754283 792921 197366 615351 017410 778015 067376 984721 694751 805200 606061 711830 134104 466094 093539 127083 663307 618454 979294 427113 163262 794813 516639 900345 934401 558338 799049 545751 722759 659415 088107 928580 761295 017227 718057 246259 240765 756900 885706 211552 733847 352765 609829 349460 784201 272021 358661 974153 533793 640003 024308 209460 409310 354883 143656 970241 755946 087944 716662 564513 988962 015740 454629 473073 904886 619525 185284 941604 894793 538831 849949 070188 616614 014718 213132 409669 428837 838070 130479 234250 046323 021616 090151 456708 181630 194862 408381 886468 614518 137335 780216 492534 434828 362559 811277 657729 948266 745486 448788 333139 127217 131190 909722 849565 029776 891987 533987 216016 334615 190526 516295 226354 947801 247379 175716 374493 986761 463915 828208 045210 363626 039033 629457 414887 938830 992643 546322 666895 973302 326595 095496 110116 670453 781821 877200 897254 490233 732179 471989 774630 936177 744627 636545 699105 572529 056068 981117 375514 143528 506954 529087 988774 671318 645408 453091 830395 616611 010408 154631 036923 477132 069410 205874 365728 891124 571533 283091 706836 581583 595965 047322 961855 559899 572829 979933 963511 610898 987042 551160 692545 139498 563530 739437 849641 614250 701729 456370 560686 157086 734891 297858 380022 607712 591963 675287 435874 333292 933928 087509 696678 059117 392583 311670 629208 488343 207983 834478 927099 260424 790957 179697 316281 351172 820078 205929 679118 982643 054039 649606 816123 101925 252186 269491 385079 789890 415126 210334 349984 202865 952439 849507 285643 504119 101192 378902 935833 651331 500583 121462 586064 994214 413618 380477 387907 262674 605146 898000 235489 272858 715401 649311 696990 655310 057583 966352 897059 954585 526903 369268 378277 284781 346858 792831 356841 380952 567488 336090 351181 678701 433615 246803 923290 908654 530280 076046 107856 116072 954384 807851 528884 499349 788563 159044 648409 985791 708887 688455 409166 664599 964745 707659 229969 338967 258829 791592 601158 380427 715551 832039 331030 485369 203340 952116 162378 560230 036375 390136 938048 632546 058720 368437 829868 449149 352064 607884 746053 424326 933962 492117 690664 371165 741434 336642 005863 804693 716136 948907 / 4091 > 494131 [i]
- extracting embedded OOA [i] would yield OOA(494131, 2067, S49, 2, 4090), but
- m-reduction [i] would yield (41, 4131, 2067)-net in base 49, but