Best Known (45, s)-Sequences in Base 49
(45, 343)-Sequence over F49 — Constructive and digital
Digital (45, 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
(45, 2257)-Sequence in Base 49 — Upper bound on s
There is no (45, 2258)-sequence in base 49, because
- net from sequence [i] would yield (45, m, 2259)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (45, 4515, 2259)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(494515, 2259, S49, 2, 4470), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 867 630146 422315 505638 434283 039097 130789 436066 172376 076580 626242 826115 902659 497510 749595 099154 479183 460947 866875 205843 196422 482660 623135 784332 960833 021021 528569 635878 638757 567837 840697 159282 663844 159074 960963 360415 162593 570835 959613 347806 530954 833224 862874 070786 885704 835679 017405 958119 415515 038892 718983 799918 278546 308398 594465 173818 933375 024044 017719 234124 651884 584071 603554 032283 912414 115703 208550 262559 267349 165149 220029 175950 293578 499202 540453 760456 390826 669940 784753 033594 867063 661788 368210 599829 570504 670551 229307 250006 793063 021226 914099 080217 777545 551990 116682 957232 757159 601242 816177 845013 140277 917083 372033 915472 627007 758676 619646 279284 439106 936169 358995 066873 615790 978204 821075 631237 894217 011262 455944 985802 627042 559141 024002 467273 692640 416804 980986 514041 747938 702939 562213 970808 423656 512880 464210 149293 859458 756764 542723 312976 484572 292268 234561 089765 057299 541549 315688 567258 799994 926696 162397 069646 473358 962207 251331 914333 432192 904826 177796 702274 750724 510109 083650 750571 909864 720078 579829 794003 801876 809504 807479 819387 341861 718877 518348 526439 894458 268024 343767 830205 495618 443807 157819 023843 500834 455467 934027 299463 056990 936305 018700 554837 074260 873662 875848 393378 311746 038596 839507 265937 800236 216888 501600 035378 655330 301162 564619 470376 194731 306089 857495 709033 923542 890033 152746 470070 252859 244823 577144 958272 690095 839697 787079 246349 304419 685320 888919 954170 041284 164856 634715 369377 645246 922153 234869 159103 745975 949305 670640 795125 871482 635739 825090 037976 844063 245998 198907 011909 640293 453167 301375 394790 873225 485621 437222 126358 326193 541176 718933 038957 894480 794231 286545 847448 799950 228696 402719 982811 149576 707709 118366 008124 534003 415006 539328 786102 867487 354374 567467 773764 797488 240912 686257 916922 921341 359331 703358 700239 820979 972760 485235 161828 709647 259090 211840 515695 970177 427227 716993 976647 290975 013221 866778 291584 760181 662466 688822 923735 122476 218855 242533 253436 172552 691567 525669 546917 820133 773354 700401 910994 407675 983001 941322 973734 050259 505721 417885 486953 935926 500143 162289 372241 962273 505878 037880 125986 374441 871368 514747 519053 423816 604165 871990 550614 339381 412594 394432 904655 501316 094906 044261 856300 946277 483539 772305 870246 730697 197530 512101 401970 701857 331159 075113 488745 349112 279403 121675 277885 694936 843313 588364 361973 383665 863980 835713 342243 817664 725647 254685 000664 998048 625590 848760 279215 478560 692676 191040 460359 881067 339716 593870 621252 551763 975418 508987 127076 900111 625897 141475 162446 960999 885439 192827 140537 011805 112906 212819 563288 269805 485652 864685 194062 139462 487318 901286 471742 274616 050297 148876 901420 727124 389762 649732 709817 216452 516378 548175 208714 314543 804931 765477 811598 809820 027909 871591 745841 387481 110214 117897 671715 271082 016689 912289 997095 383293 057722 575343 557260 283606 396903 505583 838243 352938 962301 294874 971486 792621 424001 218522 257453 160977 896364 053296 598002 859535 353370 181814 906227 201128 157937 706170 548394 078804 074481 129764 345423 141254 448850 203252 445271 180533 438993 433061 316536 132213 013396 461124 065691 594790 677075 092442 289886 390097 923509 228106 561113 789975 384510 276453 400983 205854 419096 809383 556464 212742 259672 099663 549581 798020 343369 216992 431661 091161 370893 228018 718618 456599 379366 746626 602559 088284 261103 517159 422048 937921 985197 693315 915262 349929 938789 949620 979598 645648 323172 851436 654960 716425 948880 151517 678865 762610 080817 234813 951522 494924 653762 942915 558608 816669 332745 629199 738867 524847 097102 873157 044894 812762 612244 288136 181923 484875 959041 358723 241607 849280 319699 010513 462047 312604 406095 633975 143385 724285 035215 994873 834586 672198 132510 335911 597025 986987 593825 199304 966339 949036 238247 272341 401002 669122 863683 114581 738003 143072 520974 576630 558917 553135 580241 591258 413629 829475 468429 654520 239030 352704 211272 462207 734308 800357 710347 701827 037572 853291 212810 364395 238625 329989 164968 361334 051582 828588 056780 332196 140193 879022 811493 024430 616408 028901 820966 930475 672457 013895 583802 221538 502806 131660 692106 881847 915151 705992 695180 487429 260522 524953 566716 922407 779665 269644 055253 661245 847639 217723 031151 390264 657400 491171 771516 137007 588072 289955 167791 359710 744620 670120 747065 482824 677945 085762 444511 568791 298803 983054 976134 614675 282044 638185 303396 512247 862125 947376 450948 749111 426859 236688 845207 858848 376715 118807 083468 337484 426065 029194 461685 611987 545956 765490 045188 171518 455843 621421 518687 898092 510248 032590 435358 654634 223113 403066 956910 694192 389829 031541 743666 891679 372942 052146 091666 051390 199827 176091 908707 359433 380221 299971 614625 738764 171731 697997 516667 721184 502088 288383 757754 252472 392804 524470 025258 091470 609145 087248 095059 274938 147676 245621 942987 938922 677912 415663 670689 307898 007173 559528 861978 063789 937039 519558 968190 401163 915911 552501 545941 355653 470951 723799 470492 860927 953457 072628 638236 917530 897794 732695 968645 651134 325342 726998 395751 200608 914456 860680 868465 978223 165507 690308 110528 336352 107646 719725 538842 200998 199490 014540 184288 494070 486034 097405 766315 468717 059062 089854 019167 589560 901036 737632 844940 672134 617258 754899 571698 855209 368382 346058 100948 701128 255384 162614 375275 995202 991944 438506 324259 080404 223168 387649 088106 169160 627169 967047 174436 020127 913703 994503 374929 934011 771353 894898 848876 426573 782481 599301 071559 240812 781287 114124 964558 964505 146063 928951 439628 310937 556058 709223 722833 262356 901966 309216 276095 782516 402557 941370 910893 733758 808898 366111 355476 002886 366102 846399 511696 481895 424428 876871 356985 326977 567906 988828 507663 452238 862101 162814 968206 613880 355319 388000 378946 373458 329713 918264 287117 670103 805317 772349 942078 166684 453216 519490 010811 602897 387634 276083 796147 412675 051188 816994 097216 789705 251596 661216 130322 312153 006391 860677 960071 525256 071188 558765 615793 410152 068341 498545 816496 313932 198456 805585 496491 411180 374670 842889 554122 785466 732040 992559 553732 271046 393953 718082 496643 386170 722711 448476 872594 927941 625191 651718 606201 549780 953990 215925 952738 869668 082744 240524 737519 101074 987061 936316 726053 457997 620149 667969 479209 490207 550905 161852 021163 568040 573339 049575 938803 123875 287205 723067 721146 808253 214481 192842 380977 494426 098748 954018 027481 720384 147798 719172 170765 813489 007272 091269 704100 964591 334274 551368 191275 478057 519935 533225 960398 158676 824620 077232 114393 268175 503608 531453 311736 260902 729557 499356 309861 090389 220583 634519 885593 051634 753169 781269 213129 983331 791084 752559 098641 067104 060084 057942 123113 879347 007441 769406 539724 096905 192551 180717 757148 396456 450032 535701 968869 608092 445156 215829 549914 092971 347072 709715 787731 487977 913809 102345 006943 116773 347751 550305 952334 424780 165530 373898 904099 456135 504997 661458 906159 200810 209748 943864 331822 232035 622840 484878 804685 477775 173097 681846 796486 683428 893823 049003 369434 877131 343715 382146 283423 815391 863362 085247 510544 227906 263036 350076 045170 656286 509175 990833 097968 223649 277671 994145 680516 670167 211511 353285 535007 197259 878790 768074 573740 830459 518754 210081 383561 308088 121754 005153 891931 127520 680421 450397 962809 945581 395789 464930 142516 168554 605996 627198 820669 476835 022509 626379 756083 612463 315076 777515 363223 757852 309936 186369 691605 542947 605196 942504 465089 024022 818993 221886 937266 290015 467890 474330 501082 842027 745031 299769 974919 767567 815338 313549 194534 628712 144745 039684 250210 926199 811158 162009 114385 477730 010331 551688 207404 355843 444103 043631 858949 596734 383947 864790 709108 027152 466017 019546 795715 363247 652815 401977 152921 709498 113364 923458 838468 019134 796982 273416 108848 548972 727032 925760 959466 129275 990881 271128 411228 967032 122287 520998 515204 408642 707061 308173 127114 603614 729369 879398 941556 340766 200772 537727 452962 801688 600900 749347 642850 877323 660574 467902 990830 137563 070435 883950 078407 290318 731376 938328 309428 416766 257183 986770 727505 896168 659851 885786 709036 761841 950266 031259 813492 842534 863661 077752 260452 345246 585759 124179 065642 794837 528902 390937 997772 752124 624568 642497 394314 922475 356879 837095 608650 222048 909368 299949 055596 494370 513602 017703 / 4471 > 494515 [i]
- extracting embedded OOA [i] would yield OOA(494515, 2259, S49, 2, 4470), but
- m-reduction [i] would yield (45, 4515, 2259)-net in base 49, but