Best Known (72, s)-Sequences in Base 32
(72, 119)-Sequence over F32 — Constructive and digital
Digital (72, 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
(72, 324)-Sequence over F32 — Digital
Digital (72, 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
(72, 2299)-Sequence in Base 32 — Upper bound on s
There is no (72, 2300)-sequence in base 32, because
- net from sequence [i] would yield (72, m, 2301)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (72, 4599, 2301)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324599, 2301, S32, 2, 4527), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 804851 184996 935587 060051 369114 981375 408264 314680 840819 125641 683750 258837 877319 096300 590810 578072 668968 973559 781023 576490 820400 545615 560510 200063 451653 384236 660913 729000 523187 453931 094549 643851 336757 650064 603957 198941 909117 871340 435615 087110 699132 992276 174631 537274 566036 218851 027616 334099 653921 201224 645731 252203 004110 510543 434963 167820 503358 839577 490852 506245 892586 072022 603114 581453 996383 295122 350531 059366 054168 372127 734221 399810 612691 680755 804589 942856 740699 396988 124542 540619 148142 721256 698629 484678 561159 211776 748497 371561 444108 784250 638219 724926 855142 198906 267129 759214 536818 160603 621411 347365 634361 801510 817717 153326 819286 431754 153121 911354 195899 851630 277627 050064 660319 336143 488037 693044 419263 790559 093419 011766 263228 251736 504541 125811 468769 220348 024736 616421 819668 306209 274325 041605 664910 879875 084543 037390 584270 724207 652238 738256 041649 749939 653283 139362 533257 720868 846902 357412 297940 863784 727114 534590 830080 908682 823031 716513 473659 789796 501876 975430 052055 969427 201445 775677 306796 926101 842770 876708 272348 563838 324501 800741 868324 077828 043566 705875 126883 212197 173854 746678 977632 587917 275840 012338 639695 701402 107079 294002 695494 330650 010921 164772 932743 304626 284910 692950 895021 967880 206919 200113 674177 120122 851910 834167 888727 828550 157871 404194 275308 290888 537601 095890 619334 777143 029236 555027 443486 577046 417588 775720 358203 868102 272892 556844 898916 478636 772497 785549 371360 422401 144112 850621 068764 135198 747521 671142 382237 905006 722618 003119 608016 992363 633125 521384 490191 656578 914949 427579 209581 470497 265377 463290 751065 634602 160275 585462 623885 263336 925911 526894 276323 314812 704085 129258 385679 234056 502471 520812 551379 794892 588330 470728 362257 847574 038386 341550 090180 675563 751823 996594 591509 855562 887581 038791 232492 502494 516026 473035 876688 784471 126306 211629 330422 598935 938060 361340 966113 468645 174386 022381 626802 821177 460258 972231 513479 999064 815034 839865 345095 361559 609713 092355 318966 648084 398648 866390 915774 299208 017257 033172 411080 741434 995310 359164 464693 990267 329783 705522 370079 580457 746306 443893 848545 668527 475890 755817 173369 330001 287141 018393 318809 363827 416751 630255 879481 009754 310414 614047 314136 247614 451004 851303 386153 579224 218826 575784 198934 783030 347615 544096 593390 925773 448732 210721 377660 141880 784555 551274 322222 162586 476731 264715 910992 946423 510351 722899 463948 113721 315133 510316 721590 385917 676173 044708 542292 947648 557554 109702 227967 841770 140724 412847 881600 907460 136279 568942 401968 497487 384023 980367 066590 812086 246083 757097 120974 523152 539211 761550 624549 203994 758109 349129 289801 308237 682049 301775 747832 895702 513143 184858 808402 721181 300881 015176 903048 040673 080740 448305 060415 540431 308464 503156 050182 901617 218807 127729 023338 857283 278598 368360 342994 422971 747690 142142 144986 295219 473526 705393 969283 892897 104106 372896 959597 623288 842356 638115 724242 790392 174035 450440 932541 888847 322595 292646 814560 719236 507302 947147 170294 655724 705046 668242 296174 430721 728772 011151 677988 331719 838068 268862 055414 651320 666541 575546 109582 268211 855473 631069 029341 789581 841529 837859 606218 467622 713533 480989 156605 418888 670326 190592 667315 457739 590381 449988 024971 324990 555529 858309 262560 738276 666973 535295 809131 518995 777708 230642 666983 798889 333646 902660 646544 465974 758914 180739 061092 200444 325195 093958 102916 586970 775239 197291 366148 582553 586383 690416 738685 169711 152369 297857 209326 469986 449478 217574 113179 436796 065532 561760 752920 305441 954678 406892 837826 264151 666314 495287 850369 765909 432689 543847 719980 168316 182269 309567 256185 916747 784946 126862 458264 946911 523873 976548 925654 378312 945605 762301 486169 625947 245051 500236 590737 075203 607193 689225 886501 545468 771010 450112 513236 462937 625244 339734 346461 656714 085806 829716 518048 498830 428149 872063 299550 738087 519149 231528 928641 218437 670686 307915 467399 451582 619202 294163 065790 838767 560368 807566 163521 000135 376942 366281 448681 110521 001674 342401 751277 242071 975928 490522 031425 308236 636270 415082 842759 505017 703566 267813 692310 688375 640969 387695 177431 934437 908682 528453 468043 045254 366959 324558 061793 247685 325573 564450 697415 839199 165667 702028 470071 082312 358960 732646 821595 568976 582884 156420 215126 737950 381648 377716 918792 006689 641919 131404 977670 123906 921407 544354 992296 301937 002182 991540 758279 433657 139786 312212 845060 681561 223120 553493 777770 669805 159091 779108 472960 733024 483997 870068 883493 995292 906128 843728 743802 819050 666080 134468 084111 753260 708135 505131 886533 374641 260203 211502 779998 246874 529246 077975 066943 495449 520237 149165 331585 696621 483141 296765 991976 365242 411960 556378 598092 567234 364788 872493 668982 529559 338295 951753 936493 375957 281825 686339 346339 932089 925947 922905 786385 578125 583694 222917 521512 301897 195600 002356 559399 748448 373492 127737 166008 177160 905237 600259 942615 235699 152917 078112 963923 074584 711584 514089 614344 357927 856002 537629 706241 941656 930655 888193 864095 792591 667243 196171 870793 838982 056926 460136 811941 155869 570439 577012 478878 504574 828574 399526 153839 574304 426717 513146 366176 448527 547979 961568 383967 639476 137731 348402 329645 129044 613768 734693 864975 566984 739984 600274 112236 721067 573680 277943 076739 166180 577151 363201 144175 784281 603201 491776 265449 892528 726612 956084 734702 920252 052908 277696 762540 073293 495751 698458 252465 460865 127203 449408 238474 332579 853661 130289 317733 140877 977932 794793 891208 603907 698854 117232 513147 189804 795189 258544 711289 392221 210122 278618 091757 056758 489068 061901 994875 693019 142230 464245 870140 104630 596869 073610 647733 788517 124049 216147 301707 308165 468844 530130 475074 616706 122533 736255 724648 709253 384667 248688 338166 208029 874495 894878 150691 932897 858093 307737 434690 307012 017901 073518 836289 253885 666253 735245 651438 065893 721523 225167 305736 738940 380643 865417 867248 651886 671805 612459 740347 507451 712210 614157 674562 937710 168524 492472 399114 284183 636438 135466 464918 667708 647733 448204 205358 000799 239887 469863 318077 732529 229380 721312 303608 202992 046114 405580 497743 971353 277787 469298 154018 058637 848509 003179 375663 163878 129450 754130 493565 489100 281464 046747 470031 743152 916112 377111 932552 139766 958034 823555 563924 788252 791453 993732 483812 536232 672501 721447 693713 188479 802570 311692 546053 684398 299414 314573 011885 259416 158265 107656 042136 268280 573622 575125 236027 668784 156258 915728 546513 856158 159154 061269 718499 407108 714473 360196 580687 581158 675881 921466 237216 600382 022450 065695 133360 994629 604743 459125 074232 630096 508622 817959 588473 446613 909540 425916 506642 392101 953961 830627 710376 047250 893200 479452 109923 159128 202710 148321 547627 947253 299822 513071 006672 804384 932008 007354 219425 413986 803592 715800 460100 937390 700501 543338 376456 992060 715894 159559 873740 390822 373571 036137 505473 671695 104150 009876 865026 183898 404806 059811 040866 552504 816417 981644 257122 478529 274476 485566 773047 901920 592677 906569 912010 734764 849664 605347 482698 655353 291424 506313 758215 240488 405687 761486 584631 797142 566308 109170 153714 381170 621712 202628 354813 367006 733056 511726 383065 339103 880509 281962 078288 161943 546600 411703 864607 181709 241052 757537 098639 119250 228242 047988 451877 231055 131446 185139 827437 150468 557012 115433 174120 894921 981041 069407 735109 653782 440106 079120 457136 453684 085797 345396 338881 017670 726913 707010 603953 336128 579060 687746 345645 715225 760575 527029 228020 170752 / 283 > 324599 [i]
- extracting embedded OOA [i] would yield OOA(324599, 2301, S32, 2, 4527), but
- m-reduction [i] would yield (72, 4599, 2301)-net in base 32, but