Best Known (65, 65+∞, s)-Nets in Base 32
(65, 65+∞, 120)-Net over F32 — Constructive and digital
Digital (65, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (65, 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
(65, 65+∞, 325)-Net over F32 — Digital
Digital (65, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (65, 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
(65, 65+∞, 2082)-Net in Base 32 — Upper bound on s
There is no (65, m, 2083)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (65, 4163, 2083)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324163, 2083, S32, 2, 4098), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 364570 076804 626144 892568 717580 995139 705208 575524 842938 720966 097313 091762 681318 261411 727366 442364 710695 578067 526160 960303 873291 728821 314710 291723 012189 362705 917576 352082 250580 059554 507322 049449 882167 547257 703034 117408 799102 258331 174240 572443 101987 860203 647649 000214 539289 942640 503914 479029 355428 221666 310960 029067 528927 651392 762547 246351 890876 409175 124919 164577 300355 535278 866482 555649 386175 136949 262623 239026 336822 772679 894428 735676 319088 718320 670961 631569 111062 222352 541315 562206 933307 964444 866219 504880 151284 761613 138120 304522 043955 973409 553318 246915 375350 811458 981494 228861 026584 609135 493285 419763 796641 666001 987725 989612 624698 602942 845737 096483 229625 413258 990432 095244 196276 838543 634537 681767 180302 333819 244906 605013 502566 284445 706127 585832 336709 139552 938420 635028 928009 486179 622510 994418 734875 622366 778096 594750 318714 822132 987670 638538 553348 484291 833397 195603 935079 434951 133673 416922 390096 879613 485465 350675 526645 309560 649746 553083 109846 401582 254549 827446 353459 415505 339607 334812 690981 901667 075917 549581 664624 806165 788170 988892 703338 255088 499764 430792 844189 422399 854143 991799 950279 136730 251911 472677 913730 838992 321003 753250 726831 973566 932238 146971 556076 211475 644099 118200 259720 506107 481370 436027 830354 101238 318141 406606 315412 077726 651939 666904 027675 422643 388125 681918 456618 983886 570048 316528 533574 672721 844402 014898 223903 720671 276806 434731 354259 272026 033829 501455 972524 907137 629332 161126 615020 368691 093940 285293 790036 833226 138708 048665 553488 073434 140388 489992 838421 357160 213182 054440 902231 127725 044011 096943 183026 722107 641737 273150 291689 246754 547887 456196 007992 293857 188978 090024 857108 907564 644944 418821 169412 995059 942857 216008 484565 073528 506710 243531 205599 256948 960718 657929 789588 966264 181338 740255 415285 202493 981248 798635 614447 043375 531205 075032 093369 377096 905810 649778 306883 378919 967480 265567 653959 550963 628732 365390 296413 934927 487767 159323 846663 576168 052510 731901 919008 984824 254270 860343 526161 825869 885102 313181 304947 322782 967695 695515 742656 138739 599780 699842 414606 713275 133539 637437 105270 203451 993074 029964 144094 929366 824543 956376 288517 026453 687876 340395 716795 370157 752244 010086 330796 618680 838528 833657 958763 410386 097258 858417 335950 633024 311104 404361 379603 284052 943460 776631 792885 354537 167591 819405 802975 315216 496193 700501 355431 745766 889221 944792 451006 244845 740656 408198 967005 968942 576846 979611 087619 735331 633749 145744 374149 423167 553858 878571 691917 215002 499713 849227 888304 165862 556317 573852 279227 180953 535729 584834 436913 000743 100946 694450 897225 749381 605858 381482 934658 886008 270477 957952 509181 912340 987429 253768 575748 826462 608561 854189 561234 534920 843512 233107 403988 906518 277747 951999 366661 934149 560001 299110 297982 656447 788155 813017 571653 678129 285492 953602 214899 602090 832664 960622 583215 353792 633280 076620 458889 895301 851777 621125 415039 228419 610344 323022 972195 676263 398130 350817 869539 005102 537285 679775 026299 281201 671344 552594 875991 386245 887401 063930 831395 046526 645694 288489 266534 308670 746564 852455 412246 484412 727167 736561 761237 582510 715976 957665 544785 509332 372292 448909 072891 244961 257388 653471 369749 974453 605077 611113 553267 211314 117822 167877 615784 971677 306477 854126 294771 469762 838369 242111 294430 804185 655439 200390 724373 809968 375826 164314 331894 698901 896235 224940 994434 996448 985194 947614 804694 508745 574082 556274 573747 734808 604406 137421 412160 552790 417291 243793 821428 271555 578656 624215 348641 347636 758883 805834 631270 873164 940602 843165 567074 327944 824546 893989 885769 621182 936350 132352 362975 341024 114228 969156 904013 483765 658998 115589 136881 494752 944562 977064 581640 898967 653164 506425 803839 692435 475032 310778 166750 912872 245678 417146 674374 118903 527237 638771 023679 851502 601305 658090 491773 895653 472091 981079 029398 601070 096970 578105 656249 684432 754264 300997 397715 717954 527695 593306 874666 198188 492176 040867 664945 940043 854157 548813 371585 922622 320297 165266 754655 366230 463238 940675 871552 439112 544150 416558 042907 741779 531898 047359 490798 180006 613381 182564 116074 443849 822160 930543 036910 997568 891184 535868 407584 893751 647680 751210 133765 572494 995405 588916 139804 447763 281615 743474 560738 695999 509524 902975 729259 448883 976141 464404 163494 949404 613100 310205 111534 030159 899220 701712 786743 785552 898757 819166 740323 675418 339199 171994 603395 962410 008644 673879 799407 182857 372648 981668 992326 524209 763948 244193 744799 364168 028261 118163 798195 861087 568932 135424 365994 757932 952200 559949 822031 275250 068597 239654 595358 123097 122641 650082 984741 277790 954583 336110 268804 608981 206051 963255 892024 211387 963067 466219 488401 027217 260294 253251 985873 755671 333841 153700 573563 449874 429476 131529 605497 314628 666623 942592 113455 957354 346717 232666 128756 630517 586103 787767 691717 602457 243443 339090 840543 724138 574329 487216 377390 511969 015001 916905 236424 818723 193379 861542 110571 919931 003099 931465 848630 268587 914276 073271 697978 610696 131671 050785 679341 704461 248660 440852 131608 587681 926455 796344 293589 561250 597485 888222 266753 662352 905161 404038 150092 015840 963883 577044 290867 291207 516237 995428 473422 390663 843533 489161 960958 642523 914216 199280 136678 151805 968403 360036 810583 999856 836504 718590 477981 526004 478124 698149 628402 093692 992997 623413 735096 035453 210866 086104 510153 606706 812472 929517 435217 342847 150684 866044 538198 489444 025335 849610 699209 750800 635654 631011 047192 669800 424204 965886 999759 257523 748091 852280 787331 280913 087757 436186 863057 442882 435957 854682 462622 046249 712608 971240 302957 055521 960821 513774 867464 486398 822992 984440 930478 929271 770589 375708 231062 355357 065018 957780 869607 457506 775658 645507 090977 539588 916637 565666 317546 304573 751910 449563 043928 961623 828357 145408 786176 944084 536132 423090 820709 403645 836589 243672 627492 571901 120310 219662 663655 332662 901549 454728 003015 067420 053754 355239 710621 670199 806858 456701 145959 053344 378490 648104 499938 955505 639368 853735 550512 175938 643774 542452 039164 758977 273547 576400 310110 999196 171469 395960 436390 902057 459050 455650 649506 611265 919827 833109 161840 821814 859885 036224 221540 592189 200920 071189 752096 765145 402039 032241 202859 137880 667328 481179 897749 231334 625156 502347 136579 164610 953533 488268 025195 502288 219866 146691 965878 168477 005348 306870 805465 647515 116085 661656 166933 993160 247171 883340 957644 495290 145159 624888 975577 669600 964919 262546 742010 701283 567536 851442 988600 943550 823073 470429 594917 983309 446035 792851 186956 850117 279249 924304 689891 653639 700592 877613 530776 199139 587007 677423 661749 621752 033951 749489 488822 586541 406075 978936 319828 859997 836559 192192 726728 810397 105285 556428 813691 420699 271556 640282 771456 / 4099 > 324163 [i]
- extracting embedded OOA [i] would yield OOA(324163, 2083, S32, 2, 4098), but