Best Known (63, ∞, s)-Nets in Base 32
(63, ∞, 120)-Net over F32 — Constructive and digital
Digital (63, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 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
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
(63, ∞, 325)-Net over F32 — Digital
Digital (63, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 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
- t-expansion [i] based on digital (44, 324)-sequence over F32, using
(63, ∞, 2020)-Net in Base 32 — Upper bound on s
There is no (63, m, 2021)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (63, 4039, 2021)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324039, 2021, S32, 2, 3976), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 85067 575142 913202 895219 026827 574709 768471 991769 367312 957276 438362 609759 196506 525789 010705 774509 712992 001230 646071 339742 916627 877972 314171 216687 830847 040099 868281 187675 860257 485936 888592 531475 930619 842602 622638 585321 758431 817271 605937 644782 438279 289430 044717 677822 011558 848739 785816 495855 027360 105387 848142 291482 556251 022209 321601 046135 208169 140592 372087 177819 538397 856148 801130 451487 974192 991171 906710 469567 166055 968394 051476 629189 648145 266060 974036 135091 101895 157958 948898 053139 818226 104113 802826 143887 090563 009517 682359 015610 400523 133839 328608 621137 063896 993920 499756 463535 118126 556388 582961 918621 437815 433879 844800 286554 318604 674903 725220 138418 505730 254972 811982 461035 028320 735239 219169 538779 512704 907049 592391 667793 293917 570413 388708 087576 631238 819204 242164 346248 890992 217235 493924 370675 465516 915019 914441 674946 445677 708152 159591 359451 138743 241683 894833 059879 018860 500478 020755 777985 585952 036896 915508 307915 206466 637343 276436 379739 666829 086989 119227 865638 067470 555991 407098 310370 943402 643233 819574 177341 840486 496506 469943 448187 908037 499912 068212 237826 211323 272085 648414 435506 428851 678326 899101 447290 505957 120467 253371 990556 281392 865863 038859 931131 317836 544438 421837 225770 747385 564502 039780 920897 635417 858102 388752 019851 319679 487315 635094 207426 758681 761753 083984 748171 148248 433723 323825 958335 995917 295440 340276 426462 513961 585413 765875 232725 959740 287764 423130 953859 991783 933814 314323 750579 820493 250233 579802 240353 389484 629226 009133 898578 774074 639789 885397 030030 486848 199040 778486 083626 881461 140889 100700 004522 875844 553630 029509 434819 103498 013825 212406 945727 572685 639692 065994 288961 799887 501360 505884 841655 025588 466507 678368 474712 671453 745965 271606 385966 258521 172530 736546 577826 818530 467699 274209 136009 335865 585130 194893 674667 870655 986571 396854 071433 465651 084952 784770 294315 868918 192511 003487 134692 801737 419437 369626 784221 091495 608749 612461 306783 277171 783224 816521 196108 517298 222405 802342 137432 157312 577521 312671 089165 292029 558645 427642 434243 828125 019622 971811 079482 721538 523037 459773 967847 382445 979444 874184 255852 073531 935569 536236 619731 377995 806863 648078 654807 022721 811798 299301 000158 674517 270199 136668 265290 163014 851997 763246 408281 918153 053471 683908 378634 499625 623231 396702 046647 870876 642708 927921 457808 940009 140440 829998 268404 032489 777401 909280 672089 126164 369715 060451 152085 185467 960733 870998 181937 782319 603213 211386 733868 118350 724331 732430 710321 137420 379446 434433 713296 001243 919977 108186 187468 663697 234226 454064 910106 773636 209597 297187 159346 633898 614483 557077 153500 059926 286171 088245 414325 574632 902004 612057 336728 363347 515894 110866 260344 106006 047495 643377 817147 416409 236098 823644 058994 374776 606926 532665 615699 647385 021472 364826 758914 677244 168675 712820 542051 406430 999196 051868 840321 940590 160146 661023 725696 982476 512109 787278 586612 177276 505190 863722 908996 128490 873344 271079 953858 547510 167551 350123 308797 884747 057954 503605 942695 873186 186475 374809 337344 956620 684171 787531 120056 493489 913472 875292 593274 842949 545516 673649 653548 130722 037715 113055 223954 945547 753417 500142 631823 394796 364909 264237 425408 395021 593446 951179 424894 532830 289715 985526 610186 373223 584582 454860 544584 391193 823701 045697 022367 827448 780590 249636 183830 120232 224923 892559 218122 216720 619578 946531 296197 287853 785135 249848 084468 428811 240665 801465 186332 904241 215617 055554 541848 291566 379935 114782 405821 090760 389945 620569 172572 997532 025889 589358 426831 835330 596174 759891 361860 717522 570534 838934 242838 623482 284936 906309 103422 900929 833314 781551 774386 687727 844701 595207 961756 034301 841362 996932 099251 533572 628423 044478 465311 533717 155580 803786 044731 673281 951332 484934 325834 697639 881598 635278 882551 497012 879584 125476 838739 143288 682947 897823 362517 278041 990856 775108 241278 893419 558716 768926 604022 479276 992664 364697 761432 078365 720744 120927 275852 962967 613040 649670 937717 265119 327950 961670 584857 259267 340861 016859 548167 122761 218099 965661 479400 048638 231535 685104 791273 712853 784374 612536 569281 456521 951189 465486 498322 150708 726830 265699 303679 593966 770479 915823 596092 275537 822945 604983 154322 011558 589920 977989 516242 275182 378617 074912 854526 413925 466147 605116 553316 973086 897305 696106 734551 767364 693685 034604 786346 413460 022164 454932 713883 068687 646352 463047 119473 062300 811243 994859 010077 678411 487407 215809 882239 747790 030278 679378 798860 940816 018874 299051 700336 206289 349883 155322 477295 539381 745698 696252 220106 523389 422817 022266 606362 686385 712788 696801 726675 929164 825517 737460 769795 054564 868925 371192 521279 747109 319465 747516 259045 303404 596767 190731 582832 540927 024668 010142 681642 531599 559371 343640 454930 198261 752779 419118 615223 187682 760051 424645 020784 905305 678868 950801 746801 843515 639606 498781 374684 278264 188400 213455 151801 619868 195199 717529 143764 548491 511764 981532 278214 132412 897278 152885 448759 728910 393952 756412 679988 796427 717742 657055 645764 548972 541155 168520 740125 379234 559465 736363 518213 665183 367908 182597 863959 791715 041304 894284 223106 589870 171768 931910 075266 891951 056274 352924 279384 400924 280664 257739 281031 425454 313007 623227 537394 640306 966138 073879 659992 521853 858003 391749 291934 135710 587889 361399 185278 275251 142939 159112 780242 633800 429548 591570 745293 688115 892471 156238 725021 421874 835645 463916 870275 719914 027691 156691 247024 583662 733228 699100 794643 834192 797304 468528 918886 268453 209372 203337 479694 562972 899441 168089 371744 754096 695759 393811 504587 070029 387414 721331 270432 572552 707781 269092 426405 037239 729426 710012 007806 215298 619482 938406 053019 156442 923474 347902 260675 152033 334872 215872 778971 447341 668005 439881 570205 683503 292498 449781 491230 166830 562144 899593 505589 867666 072870 416677 316558 286672 167510 584847 881256 973584 241809 481251 329078 288134 185119 410263 092034 017257 229271 058473 301906 770362 163284 983088 893608 468391 422328 451367 662364 776202 189275 386991 753017 870838 830354 867937 928611 052238 044415 893288 824973 547631 960635 929223 099293 329649 737555 019273 392314 274242 552173 945792 830599 450829 125287 508044 678595 429950 255536 387072 820178 414292 894227 982939 318640 154269 190839 676107 340191 282696 560235 083723 205669 022633 868572 106993 753354 603832 082148 215632 786913 583600 396289 727676 821586 480213 807451 966456 736068 809185 523268 309773 327945 160330 291966 482812 146420 539038 253912 066344 121379 757418 787351 485387 413356 333156 561247 491026 521810 722847 035361 090912 869262 493648 683008 / 3977 > 324039 [i]
- extracting embedded OOA [i] would yield OOA(324039, 2021, S32, 2, 3976), but