Best Known (73, ∞, s)-Nets in Base 32
(73, ∞, 120)-Net over F32 — Constructive and digital
Digital (73, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (73, 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
(73, ∞, 325)-Net over F32 — Digital
Digital (73, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (73, 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
(73, ∞, 2331)-Net in Base 32 — Upper bound on s
There is no (73, m, 2332)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (73, 4661, 2332)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324661, 2332, S32, 2, 4588), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12256 886752 407655 449078 498158 933208 757803 970032 920549 943262 614629 874368 091839 308474 129620 351646 294688 887684 784310 332197 780580 048271 057690 053922 042336 648823 196121 717159 889653 799615 711416 427591 974666 425511 718880 473196 754633 218092 947147 664513 785436 013035 605903 938832 916953 247895 122733 593197 615801 158643 203041 040322 194201 893097 355728 547184 946734 167016 293192 448863 040392 652016 357674 694134 266931 072940 730896 229891 411213 391437 289185 264831 388726 549526 144898 242244 242517 260647 894063 341999 366621 201097 258458 240661 899458 641891 351569 868300 383394 661362 750080 213051 484658 391094 323008 702242 993636 352226 252777 033982 722920 211233 998738 125776 485180 588922 440968 285365 201618 430548 196187 317963 671634 341609 001563 762041 019167 566728 487810 113169 830832 509165 617161 176588 466336 709809 262290 331169 832688 702762 515114 141618 202858 480795 455220 875767 699423 061514 340078 997699 769621 469670 248748 531752 881432 164972 215777 975281 813269 274908 138127 641918 540395 558499 675964 433336 531745 645127 855558 206076 676052 412635 748562 424439 558841 186669 677220 228410 959813 014509 489879 823358 951199 541315 340330 924789 566543 419409 871116 400565 471013 401549 704043 923272 827392 544210 371174 341065 789355 128067 547074 329301 002191 249323 460131 361774 516615 668942 721896 738738 979760 764272 336479 761483 699142 057771 611433 301781 271284 052233 774538 616408 971651 268614 933396 350725 899049 685811 564760 181845 612926 344728 640660 840092 175604 737902 640207 877609 237739 138151 414672 821144 363625 238929 481740 644847 997212 791408 253598 140874 038551 199863 632603 329725 130793 627155 308845 782417 430228 537845 948569 811685 642229 785048 151110 095820 554500 772229 622752 861064 217541 978087 173492 445368 285910 589473 250328 912637 483637 901516 509547 889023 900705 910766 816135 661747 428998 152901 539271 199206 162994 144303 323683 394737 068118 102880 585675 328324 688953 373766 208881 309549 332314 760027 014372 177446 282124 572319 698960 738849 770825 958647 635330 637897 201078 819647 847395 257016 010918 826467 518942 981665 412430 486637 560449 285973 892055 376466 984142 426780 304566 756824 237940 881893 919333 684052 316467 099170 843913 461264 040937 805956 316563 764158 918617 408736 032975 844989 641450 127266 202207 617113 593737 164556 326310 534245 468045 837343 060256 482540 204616 887909 200069 875592 376344 068397 030288 442362 107136 708005 459912 553468 418202 163426 556888 677436 655934 475010 025844 816840 170966 763413 866509 993657 692348 968512 894438 014787 368987 678613 702240 921204 021902 579318 731071 028571 897483 978993 472434 524161 039614 596998 692800 541682 927432 587601 007529 739031 423051 856097 018503 589236 357611 379067 842102 628166 133701 823709 171585 451403 915754 467464 143541 509222 804265 843709 595515 007851 227958 704367 473127 898189 045894 073464 278922 260504 711095 701734 278060 252336 896382 966458 475392 137070 060780 097215 519395 989724 949934 122119 972967 210346 070353 542827 969318 211203 512227 582319 321376 691482 443860 328785 854565 532028 735048 901852 585853 548957 314707 545014 287262 957594 709949 942857 764160 299583 441594 974110 305523 314189 130443 652192 656173 829251 786098 269751 381416 423548 641115 313544 914264 653083 202035 441736 806413 817616 270041 990942 513725 161191 894609 119369 100042 413543 056722 986794 271814 237783 222653 347273 932143 087653 324482 429782 248944 792247 228414 090177 764113 944641 487930 324212 299872 115893 652862 756953 030591 419149 743875 460235 873723 169970 157542 462471 032464 736122 797731 744042 307053 919630 054587 504963 261710 621996 758526 965417 417938 632158 317328 302416 677683 892932 168846 033246 901161 311802 997390 465368 371282 813280 251203 964672 151824 086592 819110 157891 106473 461238 466023 373108 187899 102840 489884 074638 234973 671466 684845 743937 674167 525324 708059 512837 134606 454980 353851 365099 419533 297712 210018 403671 063614 351702 192825 693274 627283 743409 117139 614317 590793 083673 241550 844597 083318 509024 683763 029541 645135 242797 093860 192517 604923 433013 932784 866314 682584 480895 639415 409296 756766 037891 785718 167032 331578 890451 115732 688259 297661 011661 579642 705282 808537 800324 542123 157107 088083 936000 016690 856779 226405 023519 873321 251880 937409 794220 062071 987784 480906 161442 082630 809420 785521 460217 774088 860412 986955 168657 418645 589580 222773 992723 845904 951347 576533 406683 422612 392652 158225 878235 714857 510378 856929 954279 241722 469310 766437 629268 222375 293370 346350 120545 049557 836684 337232 585321 232535 406659 458669 268699 243884 408082 664764 583723 559815 557917 044528 281909 793915 771395 720466 214299 967423 293327 152512 427891 662896 154700 651551 491887 280525 383091 620879 263614 146954 583302 903074 845306 134277 821325 635017 413655 151500 398105 158254 778470 887778 480408 085561 587666 404484 085660 193733 723138 354246 308442 645645 198624 579387 147978 371935 908221 032108 971268 079750 906738 023769 765155 729174 841612 589868 691684 553077 644081 326636 822562 732893 142271 313091 996489 166071 866657 785797 679974 820908 077201 103091 018002 562212 912248 438208 510057 844846 221374 475273 471272 321233 876206 801412 830012 479806 825116 766949 733740 696180 284377 794345 625792 063430 877497 670304 475742 068260 628000 071580 782544 552369 691922 208194 668147 495785 226162 459668 472938 977613 753584 297982 298231 599412 180544 846256 385534 557275 564207 540419 614258 912646 585325 525302 181933 081439 668426 919988 502893 995119 572531 577109 933386 124362 443877 457761 019450 645343 845533 461964 486087 918653 186480 007078 082668 471739 256301 429235 607885 045525 858188 340680 026284 937644 464086 178128 675371 983536 599541 567313 371059 185229 573209 957986 834211 454465 555840 539930 192350 620337 451081 296262 110928 623607 010290 192857 958200 618786 698745 234564 762725 228148 279706 294473 068414 053735 201682 723935 929465 821014 265875 643015 194612 591145 026663 046853 196593 244260 556686 713785 765160 957406 996050 250632 273800 060599 179826 206745 799047 074060 486946 172317 220720 672123 094337 841366 586780 935918 452347 484071 036935 822218 466248 250400 839873 753456 892031 377919 989675 930383 414215 306239 123072 687189 412953 188813 965799 943434 711845 958173 934046 508441 387574 174532 275571 514580 155632 449124 889519 000586 551956 029559 144363 957437 111148 899250 151695 794526 189775 999650 973190 777555 821391 405256 966947 144355 924960 087311 818344 262460 430023 117836 170635 517034 462453 701325 088204 811047 320596 857339 323017 761815 757553 698035 934137 049423 826863 644954 168355 721968 260266 947974 492820 684101 325965 154959 327227 172543 849777 107364 821070 427608 117521 612392 120948 780569 503393 935691 353159 150295 294854 637244 896674 700936 534720 414313 545613 504585 788636 633706 627667 311437 098480 162932 753815 532443 097727 595011 732822 805941 383867 754460 244754 518795 381285 024879 192921 301120 899922 559473 897008 497511 802291 103775 500973 894206 775565 029475 978236 720191 209657 831961 166585 036341 335021 590102 299338 672769 208643 715720 150720 408687 645404 019518 774285 833464 863820 650792 879413 869501 393442 438096 893610 839850 099214 524356 936393 046424 991871 762374 041857 878289 069859 687677 796634 464844 878859 565958 914606 009053 932058 073765 912989 976037 822187 282379 597503 274379 413128 943154 855895 880187 593431 945765 806514 674849 600539 660765 134313 226209 121583 148469 812413 450424 672189 480961 663061 218332 058852 329087 106237 634768 897501 576530 893708 644542 864269 041212 885918 859418 957714 586866 360226 440941 179090 517584 811902 018052 356081 074480 089166 594296 737146 257168 532832 835996 957622 817780 177729 890364 708851 270797 269810 079863 125578 276172 597857 601484 519010 078256 324961 335113 095800 957413 318454 137265 371271 402525 781473 639271 745882 528497 599317 063246 654618 412842 923679 465783 394030 817920 334226 775990 116442 417410 401230 259945 996288 / 353 > 324661 [i]
- extracting embedded OOA [i] would yield OOA(324661, 2332, S32, 2, 4588), but