Best Known (60, 60+∞, s)-Nets in Base 32
(60, 60+∞, 120)-Net over F32 — Constructive and digital
Digital (60, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (60, 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
(60, 60+∞, 325)-Net over F32 — Digital
Digital (60, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (60, 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
(60, 60+∞, 1927)-Net in Base 32 — Upper bound on s
There is no (60, m, 1928)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (60, 3853, 1928)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323853, 1928, S32, 2, 3793), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 792094 322132 681671 412546 259851 906707 124920 354535 191200 724175 854608 097624 843393 406940 936932 914784 870740 815089 777156 550093 709822 571508 856041 676693 132687 189625 669549 911777 518706 943934 590973 122432 792797 353036 773996 839727 551316 128980 896944 868498 314412 141591 517021 932201 810208 518690 132120 689116 167847 548469 886514 523771 519375 244738 713585 186107 438585 660142 830066 091742 250233 496946 412088 935811 761499 601510 758296 018455 075048 122918 801872 376032 324681 335030 574617 969156 684533 050334 188992 769725 248394 747521 112931 792512 282817 157012 365408 703858 597580 592553 129144 886673 126832 981218 602910 372941 023867 680621 264693 363880 261326 146128 699805 253600 789231 942328 498101 433312 008887 541279 458256 746943 129130 210491 256493 521324 651810 430999 787425 597226 354531 771923 545986 681225 297111 961568 877100 085104 011334 351162 579239 203419 519018 460386 062583 519443 761494 213414 703818 577958 071143 960446 727052 113865 099429 889906 297486 701010 213465 210370 028708 150301 314508 979392 903363 422210 267162 867536 584977 781719 881550 845699 886561 641681 318747 541174 085123 957130 454896 669669 337096 902538 647688 391076 284842 251439 257081 229580 509135 180779 554680 577624 627859 811456 741206 120251 173093 108928 050278 317470 099783 805123 880420 248824 605105 873819 953607 052538 409403 855476 262332 182457 313091 095599 489134 521938 464286 566744 490684 631909 964425 600266 294659 513439 593222 234775 702781 789814 167729 670440 649859 709098 580555 874703 271035 929399 507196 434759 516844 127367 361992 954605 683919 157398 578818 284060 560883 664510 685946 559920 751578 697137 893605 814393 749685 222847 842108 901670 953734 959184 374657 974425 722417 939826 918482 140055 207608 633581 806556 796774 375881 834653 276047 027857 847040 751362 629691 434021 151540 903859 036193 655059 871875 945593 076040 775860 242590 433312 607657 062802 133831 114930 837591 792060 036872 864154 464059 040695 518337 074288 008508 795808 693306 456104 139120 713825 242180 183748 271760 626280 750746 361187 521691 527235 710209 164804 636981 487494 526888 258263 256508 348734 711788 823766 802593 795771 511507 756578 594069 560449 283190 839815 249400 394519 569738 958055 909938 864817 365852 868925 749278 094882 811210 062187 132970 829534 099709 218734 982365 051977 180180 130579 384689 802806 008570 747098 031509 587246 905651 569135 124460 588003 387914 932128 726331 729541 595159 405641 668764 514884 502725 495646 693212 572794 813401 480562 812531 583929 817758 768431 547824 934693 864787 756084 440181 103955 909615 747275 055521 693009 626230 801744 375279 737947 770285 618236 651346 300607 141229 569778 702066 267541 747245 955984 301106 497671 762385 002670 776111 508196 311056 867793 532537 212793 482617 519141 115721 506166 186155 359668 684616 348257 160235 541124 079040 064462 209729 496835 878603 433209 711006 752968 943362 625307 354789 724466 700805 324474 313807 713971 625396 812057 422718 216934 620765 428750 247294 086493 693193 748851 412862 850534 456844 740670 902897 023210 299515 475985 769578 635537 267984 988776 778654 967009 885418 715229 805122 335851 098216 561539 245854 273045 672708 085988 671059 984765 445964 643199 989943 090571 078973 552769 898204 450919 245007 415513 355690 452334 291207 398611 954878 467747 040009 904777 502464 467480 090449 993039 431838 472887 091341 813756 654551 358116 529315 193307 576224 532676 573584 757406 126625 683604 260895 476236 764089 921555 425334 429326 877503 880888 704721 052141 546560 931828 464320 594740 339304 985670 397768 243572 457579 650053 819397 809621 392001 686812 071098 139059 649649 436384 507887 167298 076555 916977 498000 912792 108349 260855 829347 130656 719552 133501 596688 207304 928438 865237 759703 495354 996494 245521 527945 995246 816313 872732 554790 105554 537376 153176 890731 710721 882235 195091 316777 732395 851619 063137 020077 356107 611443 343313 940799 865732 750557 301522 339531 381354 366807 160720 730203 227842 910183 120212 742249 203722 470975 681917 710098 467232 061814 217247 639895 469434 790305 452733 341027 913021 040872 540272 678837 008368 886567 908646 429959 666022 146812 075658 305377 019935 110021 267764 105094 709557 844811 992977 603258 350841 142168 013620 672571 689369 224355 047487 873180 605881 687060 789319 872490 574083 700448 626529 521368 538463 871106 809466 277525 474855 866329 300134 350350 498047 851699 328324 900543 506386 990999 422160 093376 533871 929021 716645 131202 761458 285482 575950 114258 350175 942331 325551 592167 162225 599094 956563 517491 662860 624893 065973 480938 898011 674470 650259 605005 822409 401752 943060 905487 466666 520042 848932 886750 297422 837514 201218 081741 414425 416460 852135 070285 567997 400260 834661 895594 102078 420994 104847 549570 955507 187241 266713 155482 843830 195931 237341 199123 476027 444480 833095 105886 728147 698350 025176 359099 599933 721584 613628 016955 842556 248958 546475 751225 779753 089220 973236 635673 893410 622763 088823 216034 078701 161822 357745 619048 051580 341049 538230 098343 410834 842451 101068 673332 260334 594947 124063 082827 409162 380520 238304 770565 655467 585780 385090 222620 898778 407950 222417 419661 827119 996164 843992 480129 536731 265187 515965 407685 464428 543389 639490 041089 606420 433283 912084 787728 478193 370346 228196 527324 661857 399042 882923 961691 759891 581628 158950 172348 774928 244200 109081 567525 102872 227053 258244 930053 630560 706908 372228 715983 938947 402309 061455 977325 851818 809262 359016 190336 975570 953207 671583 778843 203746 739580 102849 015448 773317 566866 503539 421879 203663 912223 278850 938485 622393 040745 250306 189361 902574 002679 583087 004685 803051 542994 306508 128145 747732 162850 967249 331243 258991 118068 422419 957030 588885 771805 859201 169220 471190 056444 567051 856039 407977 525356 775100 256703 629381 831980 138993 074762 126589 733105 331140 379089 656149 054153 088204 435535 111466 045339 652617 807683 806439 495549 217829 944017 760137 658950 931131 590751 108509 094453 021693 516426 975460 485365 409761 716176 329551 650334 275101 230072 931293 769958 496875 803343 204686 647104 933983 103027 156616 233577 253242 931714 411625 074045 919097 590390 728824 345299 584203 138380 326249 225515 505061 710765 134233 802665 850359 410761 627368 864819 795591 665093 959354 149662 005953 763702 302736 301411 051623 071902 015455 202110 641308 329779 018271 085743 664787 389520 423141 836469 377749 859506 085234 017306 971083 531606 674437 657689 984346 700364 859878 164838 773148 170490 048146 945856 908516 780054 201672 381587 022248 877355 906102 517492 080637 742783 107563 217905 173064 056832 / 1897 > 323853 [i]
- extracting embedded OOA [i] would yield OOA(323853, 1928, S32, 2, 3793), but