Best Known (61, ∞, s)-Nets in Base 32
(61, ∞, 120)-Net over F32 — Constructive and digital
Digital (61, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (61, 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
(61, ∞, 325)-Net over F32 — Digital
Digital (61, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (61, 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
(61, ∞, 1958)-Net in Base 32 — Upper bound on s
There is no (61, m, 1959)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (61, 3915, 1959)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323915, 1959, S32, 2, 3854), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1322 993194 549495 723124 903386 946016 569780 304921 511602 017457 022676 632665 648330 965855 427164 779330 057132 850982 163364 702594 891495 330113 854629 453694 010787 037488 968043 918631 600998 855142 890532 587724 467544 648903 343466 720350 261273 309557 317729 240328 127237 465522 073021 138669 899655 997704 112728 784857 202661 537362 682732 570249 542246 191019 282548 598917 404824 876407 879347 439733 633296 352974 070953 566278 046993 598534 983106 709780 971108 175703 808423 868395 319717 753388 638738 080421 175867 121207 841618 725310 430579 423220 571703 044954 230258 087153 726723 570332 107506 920434 092171 164713 467318 539112 884921 935138 746954 729083 743196 278808 161617 050299 281674 775282 388181 379993 950473 675976 397994 270813 690803 247155 265450 558206 659892 403152 380715 355750 301495 395715 039391 635300 928055 486598 099617 768783 634391 509303 239953 631870 925615 756060 180961 095191 468895 552682 433386 116446 238638 028746 190851 154165 779881 705112 218740 500119 381692 506034 103024 153894 833240 010603 597528 863034 127973 370962 149260 411312 268439 739189 855312 888934 218128 230927 649923 533476 866247 700934 257592 206082 050548 262259 368855 015566 717804 507690 628841 384704 333491 395506 010638 902473 301869 675896 458272 028034 902249 356769 596409 365847 165703 004752 378449 580653 523613 463520 571531 416717 860286 149130 732083 837078 703888 529437 615110 107939 772665 144615 084261 594313 841628 571142 606702 732844 188895 236430 227323 544916 013884 538417 692799 121155 635555 716272 944527 531031 406444 367257 788325 435510 198512 031212 010794 429166 826269 895572 168795 703982 005890 686996 201172 755142 692524 311000 494101 947890 327108 838900 392257 682843 031146 696134 027356 852801 897760 071443 201244 056184 965784 273133 538010 332926 698460 498158 311635 029000 337327 715027 924199 393710 733456 283373 888623 101235 582956 010419 860010 314284 064262 215996 602162 403931 202609 162918 153785 900441 622877 108623 466242 848359 560060 858974 584087 690855 565295 260865 025649 815419 017136 164043 502522 203534 271752 999317 435781 918810 736547 151127 407442 544446 355671 804407 848050 725956 363957 207369 447966 420488 223613 122117 026912 713052 015761 788259 898940 097436 114717 545378 668788 916880 711583 971338 509846 862321 988773 571976 129581 072524 711481 474443 637042 560195 013696 832991 867031 319666 239539 044193 436341 809379 102521 857485 847634 585610 976635 672703 769199 835300 079279 299867 311199 081903 559778 050412 396845 744273 242385 135967 253011 691656 491274 016493 969829 564975 126569 568461 031184 719477 946161 579233 706702 990877 570906 619425 253762 621494 313618 848860 759563 453546 135892 346196 532720 664275 798253 344495 159129 179846 588673 090109 905983 558592 177250 354349 877810 299776 034108 347490 886186 149428 310983 269021 542010 122500 758688 444456 274240 362183 851780 221658 737790 845143 586760 032002 747145 901766 188196 362768 068462 645336 100602 570184 433469 005330 841284 768751 582583 363644 479796 374227 915473 448729 197622 814637 020264 630128 662986 122830 320685 259493 391463 007549 097564 324069 184518 799726 727976 644003 375792 919453 568595 582945 311458 060137 272462 221498 843553 471236 395412 380228 237307 694033 780453 160272 164760 513635 515734 929493 191446 095040 665187 493849 687310 241029 355024 147190 410710 244067 870100 593168 485502 059808 493173 549010 435981 010599 631981 059574 808025 042305 308432 780081 858160 026539 962145 983381 826671 922364 927432 656699 097403 610169 806837 590425 728896 836305 374649 481326 593457 824468 550248 102327 156460 298850 514186 821306 373677 334220 641367 248771 521012 015232 292350 657521 514760 871401 072281 924838 906585 729165 084066 520796 922829 650008 281277 682734 663922 219159 577768 130388 551237 183478 191805 480026 726740 557282 358462 158507 363229 189478 252467 550214 289193 835380 307655 017218 899308 861611 615040 034627 371860 593186 785624 023264 002272 658365 461677 301290 637902 591281 485307 464539 720319 781085 915894 907084 121029 158770 666064 592225 378282 637925 941312 561807 035759 394186 496191 181380 880852 791344 524119 159133 860727 969860 589430 578887 963671 819808 970721 102691 045721 887045 523635 217467 525827 614173 472976 673983 138686 917580 262359 961585 881096 127014 084454 339496 954905 564018 465660 566782 080411 048327 905182 140046 839782 749178 195521 763980 608477 860665 266774 360058 332338 842438 205655 159089 683642 128519 621157 602995 831708 411803 975488 220814 223258 683972 833868 829350 690429 951078 603685 157269 730204 900367 873626 946730 480626 702047 458070 821414 234493 670884 034228 174239 036280 982253 632045 464821 168115 074907 503105 645315 170726 061185 714249 879548 759115 963528 221033 298435 145601 159822 240947 598229 771630 319565 711881 593630 663884 300424 072599 698802 726306 466035 431694 081014 431900 956635 720956 250120 959949 282654 634865 816968 860088 060454 018811 717511 729022 115372 364501 273135 029438 692045 512614 130173 394944 655962 639069 509796 657758 504267 749402 684880 049247 803258 734839 950613 494763 464323 734980 742050 954981 482145 899513 993791 330779 807929 507757 543555 931879 684782 378635 659059 482120 947382 025718 874592 421335 944391 105398 131709 856965 815695 282258 957916 209412 837272 245699 730392 632506 218158 519897 105374 000599 971367 539613 409668 229529 332452 715835 854719 420658 708937 479586 527342 349468 010379 423543 449594 939234 160860 092281 959064 201613 755701 745990 228388 396270 684433 178518 280623 494743 574834 107626 420404 892144 946117 117323 354590 676683 209960 206237 946548 521113 812652 600792 294432 541143 477914 543428 914123 323112 824620 997305 136399 346353 304268 276604 604764 622596 898987 082765 314735 374641 433961 992725 905012 683692 341243 033851 148616 087032 166223 961833 503767 703308 712746 510768 596627 532806 323743 269138 481955 210716 382172 954082 496846 727538 388145 266179 400082 841357 301058 834873 868522 107022 234821 996534 849349 071907 648170 238583 085792 676020 144906 305316 677542 479827 355163 924261 448567 925027 332662 179511 519259 071487 486590 219667 536668 177384 648005 942866 463722 512747 369330 399759 220947 663484 998966 643587 583248 950056 363299 390761 833337 030151 409491 704132 589161 877490 800311 224381 367257 300403 303543 374192 834948 471132 133518 498026 081191 701584 913707 589469 461545 594246 625401 328722 500172 606649 523307 052941 091329 505132 784920 648463 582595 543368 879201 045437 548946 665386 218264 594858 195966 889066 849491 316295 322507 473390 832472 782377 724775 424463 549077 115890 207633 968329 940039 462650 521817 388651 343462 494676 329233 407581 503508 670608 472692 463115 979368 519753 029853 692073 150559 475156 090982 072151 610109 470775 026944 835584 / 257 > 323915 [i]
- extracting embedded OOA [i] would yield OOA(323915, 1959, S32, 2, 3854), but