Best Known (62, s)-Sequences in Base 32
(62, 119)-Sequence over F32 — Constructive and digital
Digital (62, 119)-sequence over F32, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
(62, 324)-Sequence over F32 — Digital
Digital (62, 324)-sequence over F32, using
- t-expansion [i] based on digital (44, 324)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 44 and N(F) ≥ 325, using
(62, 1988)-Sequence in Base 32 — Upper bound on s
There is no (62, 1989)-sequence in base 32, because
- net from sequence [i] would yield (62, m, 1990)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (62, 3977, 1990)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323977, 1990, S32, 2, 3915), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 272084 034035 589802 858395 799299 296030 561864 082251 221604 951460 132114 361399 019596 351882 208342 816032 500591 678505 455428 449857 533651 941626 671557 864348 590381 148999 290160 077289 163893 559477 883139 387516 842741 232408 185530 573890 072442 942533 808918 908978 455096 486229 305056 028083 804946 028965 250983 280677 055181 610183 813033 692449 528182 106548 298731 744593 426286 294792 881692 712055 699120 363500 448123 668931 816076 296217 173987 459820 264813 108940 986014 335455 867375 679955 781285 360671 711684 662099 180591 806771 828601 225634 857244 762159 988564 504124 387810 154011 554218 280454 425012 678826 213563 905894 229579 756490 732117 543365 628303 445806 457081 950430 010536 807866 564947 574662 152249 697775 717971 856890 575967 248928 838741 876968 178793 723454 561188 371491 555003 411684 569558 752860 073380 029412 384925 779512 279776 746866 063655 049316 533138 892632 681226 056216 773546 298272 482807 215260 381870 770438 900075 045402 779025 186068 582178 807593 367743 970855 234117 894585 009102 679633 932760 952737 724247 415206 100209 962614 841235 861695 089048 668929 886054 027780 677841 778643 135537 428652 857071 081799 032692 321658 057064 936722 202895 672060 840229 087704 744317 767964 051860 266690 363463 189084 171914 307359 035939 715009 698786 022815 128691 867026 028493 468975 890633 575914 790915 017633 728757 833578 548902 263606 781571 121050 567912 280882 385590 786379 157419 235757 449959 615368 501208 953105 048585 008356 651727 190454 466246 734355 116185 087031 731278 387436 033189 732134 121755 441427 259862 143032 465453 304458 041598 277614 680828 966847 980035 734969 907740 644480 115303 395035 167452 672687 709326 559061 483701 256910 461559 528987 943623 038578 444561 387964 600313 083563 835352 692793 062192 880042 245812 329084 456527 752005 597256 071711 925315 961701 355811 515819 241865 069285 099840 141748 255670 867912 275118 606238 611369 494226 668771 495501 460823 942452 058791 577766 590818 696539 341976 373030 429691 132225 607764 284080 057135 611018 567273 899864 178063 828841 676517 564939 196590 485393 363528 991153 564326 049363 959413 566605 592491 433157 653117 792464 580392 683609 485236 004831 766438 809615 833632 927486 029610 214603 965718 761666 606693 055885 119257 523344 689881 949633 404207 975375 106824 585175 640830 454507 153875 774963 826712 010724 493781 485397 963883 247442 742706 662629 187517 140906 315435 603116 338368 418050 444534 139271 206212 232283 100671 794126 192434 800116 867205 343509 971552 502342 873724 881684 257869 004336 921059 285136 214787 090050 472133 583399 765181 075516 535300 770260 808883 915293 668103 053703 659263 953935 966591 871459 440449 049820 352623 378693 285063 756882 938050 774465 795513 720791 279083 010871 188282 881775 321750 106697 989563 518666 950603 203843 305623 707754 498464 456947 345335 482862 769960 360939 371531 077538 386150 263726 403511 648237 946656 435122 845563 634460 875895 700384 898068 128049 777304 091326 832841 736231 301732 990164 210089 749397 084094 657934 416068 937021 721858 723150 218128 972549 880366 205776 646350 570121 595942 703068 589946 814369 962521 371545 311927 344527 222846 478322 922149 374833 675151 727750 695572 842986 720659 248993 847976 723456 227931 895214 488852 317844 775411 316668 094377 391583 639934 311493 110963 181230 123121 144523 713997 336941 921426 960776 466742 279797 999204 334200 367916 023269 378137 148306 352685 700484 358973 332838 357841 524495 853892 988378 174467 774776 782319 682999 897532 253800 704589 156880 315155 234125 758805 459493 369645 613170 639535 132304 170000 753787 479121 519289 510641 602337 338256 854067 644947 836394 073783 245908 053039 474628 870673 182782 432583 686429 508843 037930 814712 079119 910180 005317 335484 499467 861713 691213 703275 698236 440302 788353 465827 057910 590536 196475 121528 726983 215872 324795 445502 154023 373510 251942 442642 507498 297425 953523 987717 483358 758996 925332 324105 405827 337393 894096 986342 881441 816865 729465 977351 495945 139050 327223 006639 819781 432086 429796 033395 334481 414986 375464 295547 919873 697781 610008 688629 843311 344343 264272 772170 732767 346332 922178 399901 029251 242373 182906 005746 407316 285387 716138 590348 487500 480690 386354 512798 523939 193381 028433 881079 274066 354138 926904 092901 708456 288862 170079 252101 173475 909225 008130 256869 601010 003547 191390 566922 330597 288703 731454 079675 252748 862739 020324 299408 214835 352782 433265 002911 873350 550730 268405 171556 049162 477270 974139 690259 996574 905433 050578 012336 181887 905473 569339 791204 030380 099657 126399 648908 882107 733213 415115 208021 572216 247704 324336 335412 496647 389737 753173 454453 399934 423970 923394 146206 642543 579207 991739 238429 853369 374369 030433 749720 714607 821935 774170 837998 435175 184536 892211 664019 974407 123732 003164 987452 292585 021438 752921 711482 270525 221429 872930 127419 081625 879769 664285 676696 526533 154121 942645 418477 829945 159666 073708 360771 739209 158392 209677 204038 539885 831098 282271 307516 761421 958161 629775 147118 056827 522769 580197 468139 751071 540734 746013 234310 761155 168193 179196 275615 455177 705726 417815 938241 242455 567060 030928 516281 632412 174131 548407 431235 540855 301003 441707 429282 328358 218463 641788 547805 859546 310263 378729 192566 902655 731438 404587 885894 036894 419218 089097 173925 815872 887247 235854 374150 370895 442752 545551 336123 914242 906361 185981 354505 621770 007349 255595 699339 175495 618051 899667 338449 416366 142317 246734 593277 440477 487392 790574 942229 847646 910496 477169 715315 890248 443651 188456 982417 465675 667615 548445 381801 736809 693666 144759 271472 666187 673658 340824 833958 625567 437127 297801 659508 203795 987929 500332 674807 078424 347610 837938 581977 611876 312333 518364 254556 278957 021910 348342 163949 182036 074724 758951 631602 460729 807649 703392 679760 123866 095174 286157 201267 862697 288638 327814 712007 886113 319215 092285 750993 521067 573891 727352 375117 658972 295636 323303 006828 983814 219792 901091 825560 195292 630084 681390 402021 783797 405538 429784 856965 867964 903890 547338 149300 935639 983428 112137 756782 161415 657937 951596 361804 127600 524742 726353 133604 474522 425407 374217 302587 873914 198416 459833 158842 049235 912632 482477 510997 923177 771404 467424 570911 244035 121547 735785 611440 158707 431009 350152 607236 178776 395713 033680 679487 302668 973438 686854 726012 723542 980319 714083 524684 119842 429297 326426 352086 004293 815817 378437 014108 884517 272086 487148 932996 339152 271802 317156 429197 513035 828569 638458 970875 249208 538606 872655 004449 656268 947342 515623 051954 982894 573100 177708 811779 092511 901561 641114 335056 601097 139248 211427 289048 778342 098269 161761 298674 738726 372257 707397 308917 838145 406288 751912 450716 813922 553345 172817 887052 693504 / 979 > 323977 [i]
- extracting embedded OOA [i] would yield OOA(323977, 1990, S32, 2, 3915), but
- m-reduction [i] would yield (62, 3977, 1990)-net in base 32, but