Best Known (74, ∞, s)-Nets in Base 32
(74, ∞, 120)-Net over F32 — Constructive and digital
Digital (74, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (74, 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
(74, ∞, 325)-Net over F32 — Digital
Digital (74, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (74, 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
(74, ∞, 2362)-Net in Base 32 — Upper bound on s
There is no (74, m, 2363)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (74, 4723, 2363)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324723, 2363, S32, 2, 4649), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 065289 355627 176825 481972 605755 793564 122295 877646 613157 671157 894937 283866 706077 827881 007602 731475 556741 624159 992071 058347 856263 705688 315287 790366 610553 159150 046659 525924 331426 018785 349061 063014 514225 814945 000621 007354 890537 352930 473879 730052 852383 856746 842903 564263 892804 565183 603166 223991 916267 712617 649542 928284 650123 058354 023692 738529 553945 872882 268054 754879 720259 974867 175538 329080 870558 991310 996909 346051 877957 122157 748056 347827 641749 285252 641361 150613 208447 360885 034834 710299 041861 722147 056795 033121 029438 610567 699941 799431 127304 430931 440065 885364 217933 564491 179542 239197 898873 090330 397327 669318 377545 693778 406223 448948 279946 920711 475068 060244 440036 244898 825686 101891 638071 396710 170892 908135 446403 618185 657055 242703 861160 494221 291794 798192 894774 360419 274095 266019 627226 880398 276394 581341 227980 975961 267522 466927 050155 139346 263477 717171 065858 430022 672662 583102 072811 230263 329463 837094 999411 883287 899522 647756 768801 355406 120230 305545 501037 856406 326897 225340 542806 644158 576936 317223 256260 578072 003154 124416 590433 348042 243415 658486 049185 741980 500352 018655 743212 779961 466930 481560 204983 875246 099194 743408 679519 658643 483471 968358 427077 083176 164939 978503 836675 189530 463378 172592 398375 992532 639557 825292 742229 945717 377541 830792 001310 991158 361982 826523 450954 447676 685809 684110 250664 956260 967184 647520 168645 148111 926276 667068 748095 529435 899623 143911 269996 029662 897020 929484 409565 481538 158723 694078 991946 951607 046014 384544 562781 874010 503999 805480 332841 927312 600468 812019 825546 163922 203756 323100 351678 320686 611865 335300 243192 685904 029217 840431 432672 121630 036401 184808 743491 420923 141458 606158 955074 078325 428015 576701 708284 322182 185159 556383 309058 417349 594587 757462 159614 261976 511026 705427 317239 744716 689009 455506 609332 470057 771611 008612 295007 038315 437295 086398 878425 345142 509722 040501 918884 984388 574529 797634 509669 791905 136842 519859 375236 828030 956015 903686 068580 212324 036757 253073 625019 660014 833293 644630 469334 755644 664972 843928 497106 457716 547810 591746 617172 296006 074104 930484 608735 880629 538454 569715 781820 210051 240176 165070 203151 023519 649713 358509 717123 461775 414327 083804 938804 891127 823245 821540 587306 060329 936571 203387 362877 525176 758058 506794 485773 780699 372930 204788 202156 766224 849860 027428 986277 323803 313626 744506 417562 569614 230778 207136 529274 236901 041269 311321 502764 548320 101276 730502 601014 679843 221662 412589 459739 049291 163031 595072 748764 447632 595253 367052 482035 648827 099258 597189 473679 398200 948688 554102 297588 453875 110715 112675 810112 233803 051840 007263 962965 441723 376754 538332 580361 231373 867318 430232 380262 628443 590778 057406 378116 190251 508837 743980 477230 803607 866730 499436 044818 816674 452898 324616 100670 764542 988069 137889 752021 129831 917182 216855 799931 178275 642243 818457 450479 513418 957345 428090 804498 444936 078798 953295 364008 443596 115273 138008 525504 528578 337130 206337 449920 814105 159630 084599 167315 057548 818873 003842 822944 361480 776544 042165 047205 748496 652416 583673 385129 395148 343237 950289 104977 114392 352061 053567 508638 936008 800871 521543 255663 523883 628671 547436 876255 857659 524594 184826 196938 242262 474014 145522 560968 225127 558015 157532 967363 619969 490219 975028 858246 884203 319935 092974 347041 559008 236709 257842 468850 519397 543039 171758 831402 224204 979106 364788 385044 394854 941527 240832 786677 969327 753431 894412 083894 883365 489442 115857 738631 795205 157072 417005 260844 877688 642695 476208 558154 519535 367213 521114 033896 321648 432704 262376 757571 851226 767984 635169 246445 478775 611701 606136 994219 840271 835776 473529 959444 275118 982655 387309 720924 889392 510284 210268 843686 513494 588836 552971 672786 653171 014401 026701 722706 739417 480516 091954 118941 699854 827773 816880 408629 844253 160131 485096 132603 517399 586069 284750 748981 336116 992025 124670 850348 686747 541993 258251 564984 464647 883144 434662 339845 057179 265278 736155 654283 152768 313847 525969 428545 176324 607944 867130 648844 244101 437068 855293 072687 174273 254354 735003 580752 150094 372556 977429 632018 372859 442332 534166 764623 355982 476227 424027 402424 991574 770274 351505 551179 057939 805064 376832 169413 847035 572941 826441 997404 476881 389782 455496 084773 017789 406098 785835 655694 145361 724283 208625 698566 146984 114903 719645 660478 047873 313646 679792 328350 549125 050084 876983 634424 614020 498518 980020 510090 981608 096398 510065 192384 676845 267881 874696 632922 735329 216711 172920 606621 451407 961210 824858 021347 402387 395380 546731 644547 566768 581582 958670 984225 788053 717836 177915 997147 461778 135020 949843 419152 715649 872074 796905 325866 756784 816204 764524 992481 346512 698143 481085 175685 376667 400751 471061 938493 517758 703126 180867 856793 058846 086823 784822 236434 442448 220976 454581 770069 777703 738631 203698 467968 282829 877364 225922 038488 648702 779097 145265 431995 098613 147258 913890 806468 637803 968044 383860 403724 144502 927841 597442 857120 202553 894930 664616 927251 001015 403132 721688 280614 270158 258811 992525 074525 533891 962375 023723 124988 150381 670582 783040 151969 884148 821206 696045 457862 052535 859193 083945 668662 453026 202958 287321 764022 676572 695343 791790 007211 813457 649422 842652 714350 762992 949897 708042 190808 665379 632864 256764 790761 252182 366981 771843 201298 323179 345503 937625 056303 041372 087193 873625 902664 663229 590984 115357 039197 738281 734005 503792 300593 708619 165525 332534 723316 716263 639490 892761 104738 799806 239265 697589 244476 075624 705241 750594 386216 060505 758944 617791 011051 986053 062410 050272 174276 942182 651722 463144 108985 331537 503896 447909 174221 270951 604601 970898 378487 323568 663819 148847 572273 531274 517994 224818 033563 320403 688545 490670 653338 112507 682690 320208 441322 058351 249323 346299 707799 919918 251851 291464 174715 328722 298735 332287 145130 326309 951629 978995 198172 318849 869812 893456 990664 996200 976581 990765 089665 944716 770484 717173 129694 743765 940019 509366 373014 159376 713116 082827 028446 531016 243276 366966 581402 085767 028520 127791 201979 908930 103450 857644 138202 674611 867794 634634 110938 440380 740233 253175 604936 991546 348826 709707 756895 981494 483013 792284 034996 625841 349511 330004 321640 404070 401512 281100 641015 306499 999331 866683 935701 891018 922008 028287 557735 939358 737649 194276 295888 484781 061813 973456 567692 059419 594993 973502 171777 786933 840395 000717 290777 138202 278966 235634 778817 527289 936674 044651 812859 902647 908886 785364 988764 641537 541393 311038 163705 296019 300235 864662 719729 049359 838958 075533 327586 855872 358677 062835 705157 421286 529237 537010 100020 536680 456567 928004 504602 827992 238691 405209 921362 258928 398179 209882 679619 724272 357668 606375 960451 267671 557810 943784 562137 083425 336534 989175 198255 841487 057898 392678 450794 232898 429382 290336 375812 226806 546444 927743 649684 774921 341698 225320 497016 730879 297334 532486 948194 168729 599204 252308 385809 392831 212731 257586 437084 877830 680641 486250 218980 855721 038706 109261 520008 903380 997980 069485 276707 074690 428990 245589 388087 378701 432363 176507 254403 713590 113554 862370 224348 716942 557682 964366 991638 476848 221928 466419 032287 855818 392869 421399 887332 827963 294356 400222 877725 738334 144612 638873 109447 613796 580730 575417 029625 901566 032314 559001 448616 359451 848530 727002 428638 359598 379238 190020 559941 049895 605875 451463 717207 718122 849808 364537 232028 189854 098795 347409 553905 701609 559599 096490 306381 777748 169631 166771 425532 109208 256359 411543 628715 250793 643425 520597 035049 300820 879549 158405 213085 962380 241153 220561 679777 487421 852338 403738 185149 326449 074307 564324 113916 040609 063878 161823 252004 344645 669388 216198 499522 238493 600299 034547 179930 427443 884413 820797 452288 / 15 > 324723 [i]
- extracting embedded OOA [i] would yield OOA(324723, 2363, S32, 2, 4649), but