Best Known (66, ∞, s)-Nets in Base 32
(66, ∞, 120)-Net over F32 — Constructive and digital
Digital (66, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (66, 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
(66, ∞, 325)-Net over F32 — Digital
Digital (66, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (66, 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
(66, ∞, 2114)-Net in Base 32 — Upper bound on s
There is no (66, m, 2115)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (66, 4227, 2115)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324227, 2115, S32, 2, 4161), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 484468 946990 525286 549537 947553 573069 016608 960399 001302 988305 764782 354214 044509 817664 637714 805522 649239 046240 848606 224535 837616 030129 749415 092952 278802 467705 356806 107523 835680 624012 501981 366452 150295 771441 372598 765878 742675 467258 822371 887939 265304 287921 673091 405499 648989 366164 644248 716895 202256 754114 953067 183216 149074 042759 336002 752040 644848 635853 987957 290930 197109 730170 969586 848826 834583 807931 059276 321697 027035 484976 597185 999035 967716 284616 338781 720847 460037 767313 920709 903878 570554 334964 481003 478506 234202 329468 575867 698773 164167 434144 575537 452130 407920 987370 113658 876689 025308 986824 504276 395018 597003 640045 435993 239704 703238 332034 183145 049547 573645 093854 323343 554492 696077 218101 212776 804289 205215 156117 309508 227326 883517 258544 253369 891947 711359 867971 466629 130444 671297 380305 505015 114011 165932 160159 488852 245566 937464 314058 866402 110715 811568 523176 416573 408790 658282 052944 151737 517356 755212 474617 084817 104915 334867 378666 239753 546943 093165 901798 880763 522401 558327 520856 101435 098485 622846 848979 253551 364419 980035 850265 278639 864659 362486 782316 437600 825473 857469 735733 017386 287281 548769 129602 434692 435490 529536 988014 872967 062709 009805 426576 684089 449476 687798 976174 874667 358840 239486 897005 959300 067181 643482 419608 014599 006362 455579 979348 267895 450173 161914 700568 035561 913353 198463 253898 297191 877765 406705 143663 179330 412476 927424 737666 873081 767627 511434 418634 927868 176367 185436 301404 444393 012169 176607 423369 080798 074307 935262 151847 516937 278799 014497 172803 058667 567715 282378 196145 133849 928628 595651 557394 960034 194219 106765 012717 157539 310371 423024 853740 976639 132482 736988 113367 449461 515670 689296 227258 773558 293083 695844 286846 076683 750254 170674 344401 475924 906035 696316 403256 697897 002760 577566 240569 592987 745919 255858 341556 303891 744313 371088 451898 722082 263149 336024 170029 841331 431738 721693 949126 710363 429618 768947 659970 266225 124714 999733 113333 445547 478347 301663 339721 079388 255748 061269 327215 939000 669362 039491 633478 266659 036854 123358 640133 971385 595363 225937 333759 158796 175669 392181 386878 794970 572706 479789 584672 965503 167241 819454 326122 954727 533848 496181 596914 790308 039967 894004 346079 401356 731130 740818 991909 114167 013559 627141 297242 270108 916971 416769 742011 855319 625079 124079 196351 033522 742914 764645 027132 008257 337923 997115 151054 645377 322424 657543 023461 562425 571256 269276 574179 808253 494912 337655 342946 957331 822710 106011 639060 534193 007963 710204 943805 900688 050821 923874 630139 618498 113395 313539 335348 833036 824026 025705 285726 691048 231138 872777 635046 124822 193696 868792 720309 666989 736761 044497 663086 709527 714633 804564 524204 821536 084320 864187 879663 998372 029049 761378 922684 810221 281342 945298 582678 947735 609554 899811 345731 293798 196668 807402 987080 265554 150924 243187 275167 424893 156635 291253 397995 195462 829609 578253 309589 350969 612338 155641 518581 185345 807038 678439 335112 402581 994979 171735 581435 682467 132435 779887 883083 918908 858862 107113 429917 336195 851652 713283 179329 049084 242533 054166 788133 116567 827516 103192 266295 937580 591612 388534 389054 123230 466046 342022 495423 992026 572814 535705 021391 440066 434934 856586 193159 985043 504057 442611 652142 883673 082012 097691 275262 106209 814121 799104 298984 646161 197582 669820 611225 049086 667730 332727 641524 324198 402541 126476 437698 363623 888452 189826 319921 569745 977601 861621 953554 109436 943236 768652 436184 402132 173449 997030 204584 285002 118139 173333 792575 470185 534628 696566 380688 378471 127653 682512 821975 764664 975628 334905 830698 151991 638456 685321 777020 592833 591269 562262 124865 212654 214624 923374 980007 269477 144920 672631 382860 082120 256580 052048 216845 359576 631306 308644 235973 300645 698080 783288 855423 462710 277970 348358 088076 478729 138253 949293 969956 022469 348796 223135 894965 867786 733789 057580 390497 962343 050614 250090 614054 322118 941182 206363 807415 930845 877502 007646 516869 606348 064008 158407 932986 891743 720311 499505 121619 403494 217245 548958 785576 345899 732312 100530 456242 054821 517140 580234 971997 293427 350434 978614 702135 483270 786353 694606 034984 405099 822942 930202 356175 144447 880277 481073 283107 896624 472173 942054 223047 552505 267250 426454 991079 116539 568511 974977 019783 997979 880782 230335 861887 308389 787466 642875 863122 308381 890259 499774 775268 203787 748200 519708 082278 987776 384150 023285 091756 385634 418825 561467 654775 264561 190394 736069 644856 326004 410218 285388 614224 058156 204103 613641 017488 544665 135916 259531 225212 513871 187154 205325 564375 962962 207199 823869 372200 742764 170744 369601 209459 516633 256325 183097 484339 481219 616984 561941 059646 537178 860752 942503 013110 594570 986841 146375 969165 928490 684328 918062 895437 602451 596949 142941 091662 794504 660123 539664 289214 418914 386961 970999 656924 020083 162357 969770 809905 861940 344174 885119 895933 739557 144132 288102 606820 457494 827320 085172 288087 178937 843308 436173 320467 808588 027001 319152 230591 232587 522257 662834 866300 374887 915291 788401 273757 396565 622751 343174 255883 752404 825738 964084 945441 509070 469650 231352 645772 039217 327398 835284 113312 981824 029629 213958 633586 580975 300537 010867 233396 650774 980081 132710 258272 892549 214780 329242 321836 485053 635431 871666 798502 223220 233950 850238 757855 851503 461678 637786 068918 337567 215755 738722 816477 758820 658503 957833 358025 820204 600418 881518 145652 711598 157393 126713 135095 779769 012289 803643 895187 708702 598684 092513 566092 628896 037267 234365 156011 705736 568140 327442 886974 513031 165907 906121 403025 129734 535894 278242 460595 652338 058829 135281 393226 409431 651736 099122 972911 287015 732966 513321 240834 147077 697764 141078 338586 697372 502741 114988 600737 101034 098028 615326 232218 786806 452631 554392 028405 985053 570073 649794 129859 525040 286308 243843 030613 444597 495445 936123 314928 570503 235928 495879 247322 536162 126740 560269 613258 527817 073627 635211 112426 934687 938647 664926 965721 018277 840327 656305 936113 517797 920640 397231 429266 475261 234584 804346 132112 438186 794685 764560 242994 015820 518665 483523 756233 707931 738717 016043 690678 345597 640885 649576 072659 030246 474812 048260 417078 798351 924865 670942 517564 895500 085654 154114 579062 018269 062193 312516 282441 560138 903615 069926 425417 562080 015950 285012 692019 897955 497396 560232 413560 395988 821884 338851 463201 460983 604601 847224 785151 901420 749933 351751 461245 160187 059488 953032 288044 935905 892689 802626 565571 642400 803110 190764 980032 462619 530617 271233 215748 981210 600291 733633 592158 257978 754341 080547 971009 782286 623453 037904 235497 557205 823512 051895 260425 643792 769334 397745 499747 026980 770553 521566 915128 007224 664890 950122 163723 327382 799709 868679 713636 285213 321546 617267 316446 847463 806074 164731 087321 537505 418382 683265 495968 135296 269396 805259 766794 029442 458941 665358 556863 032363 097734 368900 716824 115907 773824 206035 682970 206070 765460 127744 / 2081 > 324227 [i]
- extracting embedded OOA [i] would yield OOA(324227, 2115, S32, 2, 4161), but