Best Known (81, ∞, s)-Nets in Base 32
(81, ∞, 120)-Net over F32 — Constructive and digital
Digital (81, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (81, 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
(81, ∞, 325)-Net over F32 — Digital
Digital (81, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (81, 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
(81, ∞, 2580)-Net in Base 32 — Upper bound on s
There is no (81, m, 2581)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (81, 5159, 2581)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(325159, 2581, S32, 2, 5078), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 67852 633093 902496 252241 191936 087461 150058 541640 917102 747837 121714 396179 532890 438263 565996 951888 829982 675793 078393 545980 263295 769804 614981 668224 491475 253135 834958 835130 059930 838665 089044 821048 431385 195712 273831 364028 041912 276198 726849 531642 538638 867861 899525 998161 969736 458857 474924 354775 844246 667783 457854 970224 086286 348962 204822 589568 579662 505098 908754 186663 514568 204533 026077 685889 649986 484397 890696 110579 742226 483114 332047 436250 241403 309664 108351 346885 162663 014202 193524 271114 474037 900262 478080 369351 850315 055443 244346 128620 370318 896593 592275 539075 539255 007235 811615 365665 286440 024229 332880 169314 584745 076110 796158 120551 077148 070589 560334 184510 676013 684386 361967 183509 472052 886764 766993 302215 397580 319720 603774 432375 201660 187657 108990 305471 733976 426606 981893 537000 433956 635221 669040 352524 946335 820040 385935 123056 882345 242669 463457 245901 319939 261979 541129 861907 348168 439936 572747 680356 537543 754210 206787 579637 225986 075187 679265 584142 891067 602329 391150 046678 836800 680107 290098 100286 649933 355797 621614 576530 782055 364535 895217 342061 638927 670785 564252 976847 002578 220910 993020 222020 576371 243035 098236 348011 118344 522028 575418 317579 858352 314164 669627 645378 423947 711254 780538 649726 741553 507800 473112 983164 577300 900885 174330 059760 025428 262903 749601 448160 218602 222719 212506 842307 304152 022286 974918 833029 915765 044250 620026 522032 608601 572852 649424 400860 464140 908952 701994 049685 924707 619845 864152 000886 770399 934187 111331 640466 415480 052453 356193 545190 928974 098910 852090 659378 093011 413023 441840 729093 792173 302009 467093 785819 738379 231267 029571 908953 310004 370436 863942 091336 425323 402263 415908 996951 715957 329648 816129 940544 168553 625306 483900 940500 031894 480582 780093 963180 668827 625265 604997 830192 590823 204565 499027 100489 094634 938184 257934 209688 770786 009924 191492 177267 463883 614590 063671 586109 328427 619492 590306 428833 932947 934369 388634 620310 889213 929229 813501 829787 234419 541839 971844 318199 567124 273837 794112 509896 257475 455916 383301 544402 110482 804896 544064 335749 492600 380562 969489 631228 743389 611395 165047 646953 831295 250978 399258 805334 335241 650980 118405 250832 927189 432575 804597 356090 328341 477021 608353 784324 767706 868594 524551 962686 440310 263219 310011 537069 079672 167508 887691 741525 980761 352619 339164 920682 137608 156165 672218 337215 403143 471082 236745 070750 559570 056685 058724 508531 450343 872596 512086 435819 686479 949887 105784 532601 247664 988915 132224 822117 594588 844921 461539 428472 074993 088115 280638 355388 970298 477057 678914 361942 328569 216459 521855 428780 810397 842685 197442 580538 341398 918760 908471 732871 404798 271803 920778 646741 287793 108698 894069 323594 433196 760444 159723 445971 650577 127474 771995 023124 165707 035641 529455 785758 066312 881206 019035 077821 147790 523621 154804 000202 474356 539145 730132 461231 679142 236914 175245 107263 242848 334374 114842 017864 846187 955016 419512 600239 135771 863715 869441 127425 818097 621107 781387 515131 801741 987661 811299 214213 537709 160145 421306 574838 902795 172667 097203 759297 138919 934716 186985 511439 025504 576132 202475 986569 800906 297380 121465 146877 488805 811986 016223 519296 725392 951132 895594 797606 105842 367727 947405 506004 179223 364084 479890 212708 541126 142721 012438 558845 600463 688564 812306 450529 609360 598869 984873 508348 760918 275712 983302 685579 242084 339538 033993 181677 785467 719744 771564 122694 434984 448002 786209 887218 805372 595655 752150 578930 871072 214149 330137 218443 666024 694505 952708 303954 678380 828929 301058 399945 964982 820237 996044 725727 067142 737211 452514 676176 209843 773880 403504 812614 709193 202991 468136 634252 927756 661949 069748 880292 713622 414548 583086 764242 094334 189785 403764 390584 562689 465533 897830 587057 622487 535295 888134 013215 304570 470199 549107 363680 076430 191574 903989 145050 928170 955594 253010 210859 645017 603915 986883 851980 962619 417504 718036 696141 275185 831392 016224 397373 986086 304114 731019 381414 246947 823831 176930 451530 321527 814510 555319 217332 954201 542474 455417 334621 408148 227515 829635 103143 868190 958214 540471 278633 817397 860851 934259 903718 645474 989912 566688 024940 918508 592635 850033 764979 267544 734687 832359 794738 732297 790078 555704 292837 854284 865608 869919 383091 602003 205640 225295 819712 952511 040594 979450 724499 048191 259898 957157 894326 088956 245499 377914 658047 443783 779697 825028 474609 605293 316060 540030 858403 357520 205924 839640 171821 490687 637764 074004 458744 537735 605136 858506 029150 327339 880892 291255 293373 137003 847698 644544 676632 127318 918753 752510 333131 990796 380445 960642 539116 122665 137856 294275 029864 666214 871112 752021 885803 406888 353676 920255 364910 394923 958486 945871 298149 911919 162157 469004 641474 827513 635323 261464 009904 254075 970367 692139 553266 018314 115980 507588 563292 399328 008191 103766 355574 437839 301133 691490 610978 747349 439889 652153 651304 222053 468103 709220 659486 014133 362370 866449 686717 303952 778898 658950 248141 190634 318734 555146 800169 346751 413446 043162 027291 132079 979328 737089 520334 390122 071518 462034 162925 340654 139017 955013 467891 321045 283685 700153 842780 006643 667714 812691 296294 219366 643525 858589 768855 729540 975416 786306 975313 640948 511847 810605 763348 341871 518709 648023 088065 042944 058801 523536 252253 920987 804074 407512 370214 515906 875334 272477 937687 852321 877864 926010 122955 974032 337533 145709 435575 738703 341140 537751 455495 286571 715253 056309 741209 382817 884687 423535 901392 983465 364061 792730 132325 300830 668956 933376 985848 909186 820393 573610 197102 456833 450781 717198 007238 490570 393256 421406 816513 631711 110978 948102 056269 667593 812542 837491 733178 004320 041386 297710 204496 339488 311611 782707 332985 576788 802481 560891 237605 226679 975439 255764 410279 037865 864451 344352 232427 684568 606586 708907 215567 200300 924127 982986 037327 499843 567181 910802 521241 075193 270350 479763 526368 575432 573849 016943 338591 744009 609786 795843 985902 884747 455152 900144 656539 899730 308653 912074 804277 539393 535853 630499 496926 700230 021692 393095 559999 734541 895204 992685 863842 140698 579398 200086 031936 924580 335814 892526 640638 358873 396670 000619 698087 240164 760935 399282 507864 710983 788128 110480 311139 714821 349711 170260 910704 860996 219223 619482 043305 024732 536514 208186 708069 215299 860020 707227 523910 949174 027579 267408 311983 246407 476144 608591 847292 184417 406578 154054 137397 253046 847091 870821 969400 356683 365400 215369 629458 369228 515989 354647 039961 920358 352367 685368 253130 372489 511494 050189 187444 098116 963388 485796 552322 894678 638257 175640 453950 347835 510726 103272 264288 048306 920591 478605 908720 935731 601315 728556 997353 549162 826023 660036 756459 304550 855623 416522 566129 697740 936125 338664 845257 226294 063884 764637 302420 194119 871628 457965 820742 016687 089180 654263 354175 250659 690979 160183 393616 359479 956055 867613 099146 829665 023353 609509 896710 363088 508187 225595 574980 795313 031131 447021 454014 084323 722580 241177 744161 350809 623330 728185 169147 343712 794398 159031 936696 666138 153346 358046 716270 765944 486510 768918 975650 684855 917394 591376 782934 575274 127775 669040 668329 114376 797661 084814 503566 604284 184640 548861 357542 646975 916156 591104 366088 671448 981718 432644 338822 350693 400066 272868 803478 606039 303994 408151 756469 664549 176089 385719 979205 564895 067098 332295 163631 284434 005279 288933 370409 968237 621335 191746 418815 307093 599885 055371 512718 919288 350338 928294 101664 334536 625947 663815 893483 179613 111260 667817 194155 421990 079277 629605 972084 222985 638000 596146 346891 248837 048105 060453 098173 966213 536656 826757 490188 561535 697893 355918 407172 616217 521581 545398 306510 063230 672507 399197 007384 408232 467679 088436 481432 016771 064670 602086 964657 680995 671766 966336 156869 890967 180401 685782 277164 243668 758872 762488 045230 520919 329199 247563 996366 623037 813381 789091 942597 801338 899962 271308 811664 605936 645792 069457 646753 175926 838602 782359 838754 113046 468004 264360 952910 200145 769644 147952 187941 318035 533649 680581 041190 336533 673761 794155 226550 436230 949903 955858 417934 848796 818466 019049 778320 390842 077725 147919 541263 023646 587581 588175 333751 341962 119424 246904 969638 711805 779253 618798 108247 193085 558594 772059 484043 699719 523230 202940 712658 446102 401085 761918 357701 595469 653089 947151 149390 708529 794667 656792 315596 236462 640416 609024 571710 966625 631215 169699 093782 616436 830760 369949 913318 614388 675490 204338 277143 378398 334005 805056 / 5079 > 325159 [i]
- extracting embedded OOA [i] would yield OOA(325159, 2581, S32, 2, 5078), but