Best Known (79, 79+∞, s)-Nets in Base 32
(79, 79+∞, 120)-Net over F32 — Constructive and digital
Digital (79, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (79, 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
(79, 79+∞, 325)-Net over F32 — Digital
Digital (79, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (79, 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
(79, 79+∞, 2518)-Net in Base 32 — Upper bound on s
There is no (79, m, 2519)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (79, 5035, 2519)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(325035, 2519, S32, 2, 4956), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 15766 740101 257628 747614 404719 765386 122437 757799 700979 740145 838655 399720 421508 669846 699982 419080 934887 635631 275945 430353 860170 468539 306468 069508 786671 811009 892550 218075 396421 781176 578387 798738 357756 622508 174701 977488 323215 163203 142518 060212 608698 591437 623479 675574 408671 207350 495212 578411 748792 174744 226626 869996 400362 845926 752964 258644 937732 915484 352112 008174 457915 354235 617178 332937 009898 879517 945717 518741 068381 782460 723652 017097 774064 803329 984974 851827 832129 116228 806732 403789 621361 055211 339156 255400 724567 638533 549283 180211 237148 676502 704404 114866 999749 669675 732781 405030 938136 340684 195568 415030 957657 364259 947189 659376 775721 646371 517420 892516 705772 632779 584086 898263 196934 810769 504101 967527 629686 366394 407511 029031 810454 850665 060233 392947 447958 309772 736399 236614 173026 804776 519177 504200 460064 709157 327661 082679 254386 804195 587146 399563 663992 425244 416813 472284 568760 781503 661326 783508 051364 537868 457297 548010 094040 321450 718016 003353 988017 222798 084286 530381 034169 813099 143823 032289 656063 339401 025429 273113 080376 794595 686245 618749 523034 082829 941048 840234 815375 858102 389407 448116 075700 422387 039971 299582 182361 056198 296507 701854 484905 309445 078555 258266 107013 103249 896465 258283 857382 292400 706770 374826 259417 220221 682094 996753 367245 048569 294139 177644 382187 916243 316330 360414 113210 139253 780639 792973 210939 276395 690508 327068 632773 560370 007696 904166 166234 478718 002364 381131 425614 900586 848973 364036 445168 761033 394618 937129 660496 362592 342433 920556 077713 050942 518825 173769 014072 252042 831156 396899 333966 056625 656497 656327 489962 912970 703372 028447 917164 852482 574511 080238 535421 815476 034972 818963 729750 065638 704209 032798 663004 671271 078640 790579 958815 999971 146605 625742 070266 994790 155023 557945 934901 068067 854522 271673 271344 647942 448032 721781 654126 428426 519545 152109 422483 201827 648149 734378 140181 704440 928290 954015 329120 637057 500514 204606 541036 065671 734849 792676 794552 034849 676442 336720 393541 143879 180207 277819 216436 048746 415435 214032 664535 489387 387541 686357 556453 656420 779621 262848 483083 617292 143815 850756 529069 611381 087430 448919 443912 163690 092885 377068 343966 217484 478569 443351 767951 045026 099399 633190 495355 266368 271514 085536 386721 227992 365270 939450 019024 648353 776893 278965 100492 917470 549010 039859 360320 122670 848710 655080 569959 645067 100067 962937 654348 687122 824878 349146 004238 056068 162227 087105 296020 299986 682023 168910 956776 500374 323268 992534 397021 014880 487068 890314 844838 916882 162508 155601 527527 691596 486378 717858 637248 996390 880847 700615 458515 617919 711613 007866 405669 374796 088605 835262 222951 022083 606413 823621 876714 591365 442503 550257 355908 557199 829032 875214 832183 906778 585095 134130 910314 875652 617846 743658 715681 598462 640918 342906 146620 967179 602027 045146 671499 588032 997824 941577 676324 305879 092767 852519 892139 366152 511368 534691 791903 550266 264463 392203 801625 265367 985494 672478 387900 925444 843371 079742 016248 452534 252749 760622 617348 308142 035539 918455 619092 006472 803369 841637 169639 997580 980252 060960 339271 762292 493456 418780 976947 073384 608299 043843 362308 976450 498464 798321 153627 904415 124846 742213 063571 995337 650948 072498 061293 458808 638735 372744 889501 502784 134712 326114 433245 527737 983539 797511 779269 658485 025142 293450 205954 039553 378857 568546 612926 995243 946229 753909 110658 003674 718960 750660 861040 451290 594303 865934 452233 338659 729277 220197 166378 872549 746634 597337 336783 930366 042277 482138 118645 937006 156488 593664 957541 281686 039616 389120 483317 086002 127013 344360 517467 117578 426311 680332 222487 466899 538681 465202 402106 072538 020245 185550 233860 627608 203475 607748 019909 510003 045591 905566 518138 575667 036105 661723 198418 790170 044919 909070 818484 219424 427509 241975 669796 752117 166892 013660 538637 167975 660032 306796 462794 506785 570102 700514 999871 409666 308996 120030 180372 744048 967733 338131 683836 592933 659505 409245 212816 049545 053722 879526 717785 653020 086437 790984 576072 343211 385626 795187 408467 264025 845183 819905 773016 774751 585013 521053 302371 878247 940420 964592 735244 480528 713726 262321 812250 430551 331311 553364 612135 428584 436380 163588 177682 838242 004310 163813 408329 331385 875874 110512 107163 301267 329064 729836 635165 389628 275878 036445 009773 510743 845211 025350 430061 874664 536935 600405 724448 194618 509945 645526 913111 667871 901279 771002 312101 184670 229203 366650 280771 984515 425816 974738 346967 910487 151988 751510 870189 650773 756361 716303 866496 693719 907870 173067 604776 759093 370768 514069 007033 249933 429813 012380 309166 208370 885284 554563 342868 496846 694422 168496 824229 147473 283163 820584 294308 665392 154265 607276 069844 032804 998224 976895 561828 806797 087897 516657 081429 824554 238348 319723 735199 089547 861933 556121 533721 131065 542826 304643 967174 998464 691411 446444 810968 418697 412027 689137 428361 508394 141993 825135 446393 252502 214053 996058 407870 793611 492907 009225 698340 336491 630972 876258 326950 987655 308507 559911 958190 485976 053984 587518 289053 010236 347993 691323 695781 944575 328217 555683 172489 213346 011098 296657 058815 492690 010752 931841 361918 651993 652174 027863 381451 356081 182529 177659 834612 826171 038304 566605 904117 132369 320401 597950 481738 727349 449086 925550 539261 809208 236966 406809 405710 404489 767195 327206 499830 215363 711024 915912 451099 727314 304738 978889 953302 363548 894157 161300 289889 954936 683069 087601 606613 231867 133636 828088 083621 233247 237358 170588 254455 964366 192114 206473 763448 862342 503121 863910 506597 975228 970153 141904 807631 865530 020186 049452 406471 157428 578493 637828 630089 332955 912096 154624 445984 310255 621687 400123 965003 791348 674683 420073 293277 767735 125526 516598 699492 703966 128972 734061 240413 435257 047761 486896 372420 171405 447183 988049 259721 430404 221557 022873 121272 959572 714550 424984 845254 831639 519587 964362 213762 867827 549963 984253 612706 654768 157872 761055 261772 932811 629617 417496 464133 914373 028117 580713 144706 748185 763761 919776 611105 501627 897585 374961 985986 245926 018961 783159 056888 787708 646487 727746 373183 204995 945328 207078 912821 174930 207382 855046 057665 754757 902794 991331 157970 180041 158043 370862 292196 878418 203040 178130 838066 550420 535777 384913 812232 235929 203925 610653 110740 119107 562082 394993 816854 989536 415949 369213 557261 671151 007650 953345 716167 571590 372515 428547 945344 974161 099606 669650 574449 050963 657450 112986 564327 294751 456927 347170 679838 188454 746150 911391 957790 870089 187473 257733 799591 688498 844410 727225 373639 716812 200624 585585 528830 183349 501834 872962 591911 150105 535359 690312 875937 298672 411856 494770 861698 150241 882135 154220 545485 820015 207152 793802 789515 683858 007495 100805 680375 776854 925284 546356 740896 505030 857308 529695 970443 384050 418824 785510 907464 083059 211529 422632 286661 648589 374108 186307 240279 509491 914494 865800 831497 595355 956548 773545 685547 437333 748695 448727 987667 239837 195332 908752 347363 214088 832151 411874 725086 614706 652453 994535 259651 565759 721558 243477 777137 586571 081008 397182 724873 980003 991825 382522 908434 553791 550971 447339 947422 310078 391166 725544 868247 671612 009789 839036 185619 616167 908811 757559 690685 562545 698259 181340 871791 100775 094636 536305 194942 444752 700085 050290 555588 209763 769924 382559 158013 435681 862686 839960 970388 864209 559902 150495 876914 399419 195395 921799 991176 766621 876178 200645 739771 294302 736230 074536 635439 042556 388839 949064 230762 267315 471457 346619 324216 270074 781796 829607 036887 603037 373776 971507 874167 342121 235520 437552 013988 299857 006682 758036 816514 449424 171393 238703 853970 141244 953422 840494 088356 486059 566491 507240 955216 936048 152441 057111 828306 588880 681638 280538 237286 295501 878833 927530 734154 648065 112721 203139 027042 603472 079073 165595 771006 742039 500197 646632 487902 381434 842687 852039 143231 604555 511368 979301 183495 759735 784374 882111 465615 727282 622095 980738 283915 986931 964746 524688 019626 411534 316121 379228 212952 425100 074059 138292 337644 147385 193916 935486 921207 234163 874220 199026 924160 070391 230019 183875 159300 735288 288195 018196 647244 478568 939362 976217 731873 308150 308039 554954 389217 597714 463345 808610 979843 771412 792844 164758 307525 468878 132591 198208 / 4957 > 325035 [i]
- extracting embedded OOA [i] would yield OOA(325035, 2519, S32, 2, 4956), but