Best Known (33, s)-Sequences in Base 49
(33, 343)-Sequence over F49 — Constructive and digital
Digital (33, 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
(33, 1681)-Sequence in Base 49 — Upper bound on s
There is no (33, 1682)-sequence in base 49, because
- net from sequence [i] would yield (33, m, 1683)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (33, 3363, 1683)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493363, 1683, S49, 2, 3330), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 759121 088348 049804 442195 852408 853713 308171 233923 592009 457878 268615 382798 059540 776027 650602 595208 406545 898314 201082 517686 989696 419335 337431 676420 226871 613819 435175 053344 634183 484461 187826 000744 974099 251325 691427 748203 663101 298784 527587 702311 355038 377411 493235 918289 560091 203597 806077 489295 285571 566650 283628 122757 800872 160706 231917 720055 158284 708213 189720 500479 126645 549849 657097 056710 141923 136984 471985 359774 728049 523128 179700 092647 919485 436193 987459 137884 879535 032807 601544 449182 657814 645756 615885 957561 433437 083011 034492 936709 082504 909697 130466 128975 279868 878411 344835 414084 918882 012030 810915 064987 371011 912214 462139 689975 586530 743367 461154 274550 198987 370342 828162 479310 683040 459599 253767 708175 530360 533560 385433 062084 022413 745411 046644 574953 035186 566615 732984 412588 077857 708006 403870 371805 495014 209053 649984 776157 684595 924842 034604 561834 344899 417288 822493 337015 295563 869890 782409 296182 390859 087040 145591 886587 960263 711046 830733 279960 556098 101365 693787 308585 675612 031092 817729 870060 680907 981916 531942 262412 138421 951953 483057 974839 501133 013113 451282 001106 200616 389795 995381 566272 994048 430194 799727 879567 941184 590371 715286 848291 789220 911712 838060 524982 621565 873487 333513 556038 434662 027555 788354 740263 028075 083477 460912 613657 056060 058856 167350 489019 116346 448583 930901 231108 587961 305847 781760 792433 059275 484051 312446 045049 719269 063007 893448 597811 924571 581325 696533 851028 665712 110466 827568 955426 126131 412939 278892 318249 151970 345581 150393 216006 371894 254326 109055 707817 322473 327015 375761 791730 082028 191705 922700 102476 601609 894759 468604 634396 288366 486637 180406 407840 322651 037790 747353 607049 529362 229996 380718 547437 356823 443411 848569 996561 565456 233427 830678 318650 283505 135418 068827 156260 591623 763008 239909 034379 485809 035948 791385 763375 963972 920572 623920 264026 561254 085314 935972 072816 436024 198466 012570 934373 787309 767234 037292 557422 631004 734653 177158 101890 704625 827074 737809 167365 685032 151805 716394 475495 066790 181312 464066 249982 727223 015440 204406 651046 742534 970140 640707 533088 183547 358343 966002 066000 609966 285923 272317 997774 549186 024668 850218 472189 468306 381245 554704 237073 190905 707145 739731 371690 873565 313914 303522 220748 875950 120591 210633 125758 197534 330275 862102 536530 140851 377748 311581 495739 578769 403567 700336 224260 173355 841873 522467 443893 857301 808051 559517 549649 111226 129573 904449 792553 642811 919200 016127 546315 366348 217986 886964 121874 545740 912638 175304 807867 137352 477923 728837 447288 532103 511165 638925 513403 457214 995714 166337 465904 698821 358134 098447 277368 393782 687726 240490 562399 879756 210608 574603 047890 931254 706938 499720 009434 111796 014996 518786 946232 155029 904580 068400 007015 088264 047374 756122 255287 149933 518254 875127 893126 787997 521126 731003 856650 041409 349361 441699 347838 882126 504897 900307 834625 332551 536442 945572 628622 353981 087605 020168 066473 192237 440546 481284 991792 398344 480074 642760 617794 072148 026216 523503 744333 612469 645819 064305 395943 155249 272532 575360 393995 527811 960591 797492 924428 845153 716899 956428 032698 903838 292836 401901 677607 878174 633243 573858 483317 777161 536523 184330 818984 334023 271189 454071 640722 775917 091966 425847 016851 281566 895487 492902 959275 608017 234566 867965 631594 628384 386379 598845 353951 240052 808232 317550 225993 097735 060264 322385 576928 164942 841641 620332 467007 078364 120096 729510 021662 386505 936782 079483 707600 802636 642782 223350 762988 774538 358373 948153 668400 656188 692349 546785 230570 606678 817732 091664 260168 855795 468738 673585 034998 903945 367666 564060 591804 201368 019463 166656 709689 409026 671256 929623 749929 899356 553030 953030 678378 810530 221513 396894 883691 909065 176465 681249 652772 373992 048011 875334 049773 102471 385656 995578 233049 574207 632694 903387 706622 559830 220211 604475 740196 802485 735568 623975 799398 410375 902800 934894 035352 549361 903803 582427 205967 157457 305046 317907 506829 067264 851153 697915 007060 066989 663668 021491 271314 347241 313697 864934 506834 545867 608439 659656 338770 524794 907166 325258 386235 386373 996069 251488 685957 920240 304598 610574 101367 257017 963165 711358 946502 567746 687496 902649 028513 485988 335741 278760 784213 617032 489594 123753 607305 473962 813674 658544 394310 280334 301557 044203 773473 909615 192792 485254 266608 168471 751402 160744 126963 233059 307566 134873 200142 624649 151813 664209 974156 943970 462039 730629 743816 736755 067295 132010 801314 558666 728346 363838 941851 997736 367426 760642 371860 208318 356382 377747 199025 010137 250444 841430 860669 624775 791117 928845 947259 851777 823026 105097 848545 158546 748727 363681 300383 576132 768749 829190 519121 695071 937989 737831 083066 838915 352744 466211 797256 997257 374789 549413 184119 170539 457296 165088 274856 047127 101625 130744 677560 643608 163390 814138 362100 074612 840097 586485 180116 552979 577761 105983 434288 512515 900824 537470 690223 510951 978488 471136 011391 225463 587532 951823 698853 105945 589737 005342 088857 162828 194038 673045 455194 709588 769379 628699 768061 269854 718612 917131 642713 170086 479521 526171 745272 993230 763513 465304 221914 688790 954406 686141 406875 441083 735283 958031 628791 801616 640499 905859 586336 448256 541685 990240 449482 489911 029210 991008 210985 858007 733374 120774 586938 772900 335466 043972 673850 204889 863571 976281 577888 279229 992526 410027 972842 804089 911573 412930 450886 755878 190882 765875 644260 442105 880775 526110 925794 391412 219713 481235 772061 964980 249366 612241 612575 859554 508323 633344 174513 920182 869070 567929 521134 704121 290836 572435 386027 516544 364726 431991 055231 328834 228671 171044 695235 118059 083490 626631 805106 843294 018998 523597 839267 870026 571468 495592 291181 448637 993536 555759 315269 874226 451614 992873 619164 883964 191255 178921 448320 139563 441003 671133 618224 261402 553812 199597 395763 296673 074152 582761 058850 241282 206219 412536 014421 046118 964465 439830 074497 734476 784096 878694 421488 168413 453566 975025 223897 265263 313988 108293 503950 551122 068400 452550 092521 119478 790146 487846 490463 417433 591603 084318 859592 290804 345705 919334 216538 313312 815190 502324 132939 163027 880159 927827 147242 967501 272178 586854 632115 / 3331 > 493363 [i]
- extracting embedded OOA [i] would yield OOA(493363, 1683, S49, 2, 3330), but
- m-reduction [i] would yield (33, 3363, 1683)-net in base 49, but