Best Known (59, s)-Sequences in Base 32
(59, 119)-Sequence over F32 — Constructive and digital
Digital (59, 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
(59, 324)-Sequence over F32 — Digital
Digital (59, 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
(59, 1895)-Sequence in Base 32 — Upper bound on s
There is no (59, 1896)-sequence in base 32, because
- net from sequence [i] would yield (59, m, 1897)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (59, 3791, 1897)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323791, 1897, S32, 2, 3732), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4628 479624 736397 642973 365423 779171 921126 260274 763538 921066 553408 870655 634163 235865 875098 689629 476191 270600 758789 391182 541004 658869 244670 940233 822263 627784 576226 639242 381300 038648 327739 702066 723989 147092 060839 776926 545040 132514 427007 436235 646959 215916 986962 569798 036229 269782 154189 582375 794546 677114 659062 065564 279812 310449 357481 212589 652218 971914 647199 146695 657250 666102 622928 610312 826328 372067 029157 633585 983736 095334 811825 430537 776644 851322 750099 695468 388276 333389 392514 047132 426263 817827 473861 819634 500123 572231 645828 804461 389880 309022 012817 699485 950196 791921 247027 311723 739428 802177 246995 152313 825398 256458 798900 341288 950760 546321 346245 094725 767779 041209 025053 771767 401348 022068 976385 379188 195055 234630 359136 984646 378635 900615 751634 242621 844422 404070 325499 446191 528810 748259 108916 718720 341679 661627 643691 964064 912867 988252 132876 189347 699508 817963 513928 628099 725441 241905 296789 844632 595707 881977 483301 886482 823200 850305 628810 823054 202331 170531 355117 819253 568273 015794 840544 302009 355596 437258 775873 277624 091450 459200 492868 507566 071288 474140 203868 960355 457096 479275 117984 080443 522083 021180 411489 577672 266357 329019 245825 190486 354785 868815 812048 730664 597386 577326 535291 024193 701373 735770 868101 122791 968417 545045 256218 645003 753421 788939 110843 362593 358206 151228 225712 863287 255228 242522 110206 635230 309925 409056 384929 126155 207223 363190 328362 052120 257945 964931 267135 269434 942968 627656 641349 658503 361692 263840 286606 825986 773904 569466 704397 309569 367051 094986 554256 647869 915911 665480 340774 895602 984835 055536 014415 095650 093242 695084 221566 804035 444902 767320 953805 801921 039674 960076 026231 764499 115964 286151 802310 818915 322582 895940 036153 813479 483075 213406 920930 541325 276700 387616 934460 247796 888649 454414 612780 323657 463885 829811 866033 708938 830154 723170 195718 400427 798974 244826 858992 755039 132442 334952 636920 704100 752161 608776 332827 925916 003191 956881 439799 820124 224700 095574 606988 577632 537957 272085 872196 176635 365668 831153 822891 972899 321124 858049 314044 938937 252990 069721 225683 977709 818449 492756 728587 128567 029572 811336 340356 254420 882973 371934 673307 514831 023481 570538 828589 822437 054710 639943 841807 768893 697891 077053 849719 413539 241100 523761 496999 855760 445427 578248 482675 735541 457254 371237 080878 484539 612324 919396 341700 234251 796849 036523 171088 522706 566486 205028 808506 835543 109090 459337 648161 492559 933923 425440 377836 702243 925329 545718 842010 474592 075435 394930 869129 536162 596089 310697 529515 139048 304489 138462 075897 916065 158664 417391 393289 605501 260565 599157 521306 682647 104798 734036 199790 577158 379743 781573 260643 053699 602968 974349 879835 994137 074319 215597 967897 015220 371468 443993 198401 507309 317351 037495 399581 454931 215527 343238 845585 669601 567161 556446 229947 000882 439153 582877 001487 855750 320089 781488 336702 190465 545843 761396 093956 658901 875151 711709 671168 211347 093805 832405 305105 577255 818551 073054 486192 164285 932903 505817 765298 779067 648449 307776 992408 250651 045093 295840 219035 533413 080412 960257 541464 094919 199163 638099 443553 641123 369147 070496 301487 265019 628000 426509 477445 822311 800161 132743 831808 695144 191699 664901 675799 271239 839181 203131 731316 736482 686665 068669 994690 287704 659350 727833 131953 038249 210286 779897 502434 077287 340358 151668 092200 809052 350944 371919 559677 361870 527009 970162 212330 161912 976744 986973 111633 849157 175437 468547 810173 771303 795276 790844 082394 471480 239385 048096 422512 138490 812909 697223 744688 375437 460998 096074 009178 202412 574292 668202 215775 711492 891242 287585 742050 552045 232158 740113 782770 286431 909899 757618 555512 176670 469668 708403 939921 245834 874445 935718 252340 986812 513400 394316 129695 786085 362757 359539 694621 057945 641780 213736 761505 358901 576401 191378 836690 695053 952317 416735 070776 342104 701404 299461 362974 814672 689931 684534 554223 849800 383968 182007 548220 777993 071651 151004 295123 008428 825601 931445 619380 382394 914536 984773 821484 222327 602933 990230 981029 002653 155150 493415 984008 813845 143378 896615 681531 124058 595316 566485 796557 560980 515484 487901 614340 134740 304383 430185 997128 804445 728097 612697 437641 299886 291488 522867 852828 914018 134945 163539 075482 889772 405398 745696 764826 175333 577446 814223 033675 104034 721768 066217 108313 708113 079713 079532 793285 342069 306251 883315 496378 796167 259099 947816 570036 827537 704193 464114 284339 305000 449229 292382 576790 637249 264279 033136 774037 383061 552993 017639 922244 349101 783086 402430 586958 787472 287330 953395 536731 657247 390703 759540 823863 845883 587590 639001 969762 611569 751774 636731 185157 545337 061695 038440 289144 328512 074337 778215 018413 892389 236981 370916 760640 651308 049283 531000 985834 387824 305805 160432 427893 713218 912335 264431 100756 640460 428164 051687 190370 601988 163715 513925 944279 866334 275260 917198 519593 387291 473185 388369 664381 892804 236388 630530 698814 554256 635300 930440 578648 325449 695606 486882 063691 033698 002189 201772 896987 297511 056806 295314 536642 533635 772122 513377 933130 382376 448596 388734 634539 483506 936536 417582 241199 025186 189761 149942 594367 254708 136947 861360 462423 254480 352334 834637 032111 629975 416368 965374 116015 902371 005822 250452 196009 892829 944883 813698 636322 887253 098126 492035 559759 062938 187269 966266 857642 194694 572166 962543 449898 634396 463586 337212 462927 902537 911976 084690 157533 972209 050464 675735 601388 158267 633471 545869 287728 329419 166593 087042 680560 496435 717367 335444 178256 724993 127558 707557 401858 855917 025639 076688 610581 150231 898361 192504 290704 514769 460458 136010 430255 096859 134468 189159 285096 490281 359534 081968 400515 542568 534960 298062 988284 768643 919336 203326 816729 911363 514885 092326 338501 608821 519723 132274 855964 126784 884483 416136 783939 521037 128381 703603 517762 564470 967020 596253 844150 082571 636494 436140 675348 285165 022864 818925 037693 479185 705702 751519 693309 791896 988515 684755 812394 235299 666976 206483 203000 009075 943368 482601 860239 709718 338247 567654 887426 864120 640839 713730 807528 757623 441404 744454 077408 481208 166082 575236 834170 129205 983797 351908 936154 022646 383176 808948 019997 977381 674836 216443 236056 563712 / 3733 > 323791 [i]
- extracting embedded OOA [i] would yield OOA(323791, 1897, S32, 2, 3732), but
- m-reduction [i] would yield (59, 3791, 1897)-net in base 32, but