Best Known (82, 82+∞, s)-Nets in Base 32
(82, 82+∞, 120)-Net over F32 — Constructive and digital
Digital (82, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (82, 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
(82, 82+∞, 325)-Net over F32 — Digital
Digital (82, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (82, 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
(82, 82+∞, 2611)-Net in Base 32 — Upper bound on s
There is no (82, m, 2612)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (82, 5221, 2612)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(325221, 2612, S32, 2, 5139), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7 037676 438271 886823 092918 037618 802155 650818 743336 854856 523800 302289 223744 828314 361275 665598 655887 059146 241437 798282 490760 953133 149819 673159 012841 031399 593476 383739 929532 496314 269423 037192 809809 767934 087262 989494 238938 452979 666132 372163 482786 974826 509825 912240 725076 316774 978453 056371 590910 269617 496535 825435 557549 707843 676518 068217 083057 889442 299092 608342 503048 886765 271767 424449 639530 583374 410490 626969 104087 118283 026536 557143 159122 713259 206921 005316 729626 033592 557863 517579 999971 045350 489134 089203 554624 090035 258597 749124 067760 166782 493070 607531 345734 471161 488922 568942 969329 676296 197594 720493 918995 700740 855833 560861 816256 239868 830242 419063 388470 858122 455518 991788 127855 829138 441273 309956 314748 770621 289241 900837 236747 819190 057757 599465 745530 853123 322416 490166 824860 166987 960718 755882 496897 210679 121186 473506 640116 142359 196946 130358 514401 272913 227900 300001 379416 879595 605721 883670 492550 894516 780409 611325 521284 334767 499231 415815 555052 013499 478385 405662 851991 093408 780684 828334 851687 878666 139389 272693 349246 782885 437753 832766 462628 991627 890318 397044 563008 534210 860591 163235 944620 491455 320708 672788 492843 811921 030934 694146 902593 027355 550755 022901 663918 482282 097121 219026 259540 821428 023326 024947 191266 212058 903836 205841 486640 442308 116450 161489 065706 951292 957636 483349 578738 878859 340275 637551 816156 504939 815586 692686 901936 343126 975213 016359 392141 911413 568743 944324 269671 854760 850455 849419 473840 371306 535884 438322 026769 505967 154633 951459 008354 487016 866588 972256 773418 093627 832791 915873 880550 891881 174481 707113 187806 773546 173297 575456 475691 891219 153684 940128 058363 923792 958071 324930 182313 638895 696839 365167 282368 965138 851136 659721 976143 861723 068668 904269 183464 134778 897927 037725 540014 567630 601724 798926 302875 439729 014829 808041 685687 871349 212194 470405 362809 372710 938528 506942 035511 992692 541522 949676 334986 128441 967938 003810 847998 937096 522956 734854 001751 783353 912414 752231 055810 066211 952348 638865 905605 262882 638583 251472 193983 435720 369066 899141 025039 695332 932912 331869 922489 331259 678712 003579 673754 630596 803360 394804 556690 483075 656368 728562 772906 944515 147805 792138 477704 370548 830796 531788 123328 767372 894447 244158 153764 748562 088809 553343 962517 822567 102452 692569 221623 293384 891164 543626 295939 396490 706817 697881 746874 751885 287436 230653 039095 611136 592766 384712 087823 210686 167567 873199 197356 944468 687597 440752 822591 796968 984438 963504 794784 915599 734896 207261 991934 605844 516766 978578 048159 242420 852369 666220 165466 224951 427918 777857 297829 372446 198390 215504 783339 321048 607279 752083 119013 508848 098262 936026 253392 809541 373801 806409 374711 380966 047702 410250 449279 337780 754855 582053 453623 133156 420660 353275 872923 082791 294154 301348 796106 550507 181736 169645 404282 475687 466576 464940 903615 753599 586079 985464 933019 363440 929438 115700 384713 626979 504435 279682 086245 646799 554492 526216 406617 557574 347873 743372 387072 333096 527967 970876 695048 323629 167187 556586 314619 691413 364716 433705 914017 710667 458479 210398 039181 558438 135928 757859 803143 880986 686919 657165 963349 925973 987751 638923 360635 651950 419062 969761 558301 395928 957051 659928 863573 248424 699540 695047 115688 276622 758968 947583 309942 307410 260301 598428 946861 312597 678376 926179 071492 904998 022199 832717 391015 309302 058324 076533 565931 786254 834146 500566 097795 977234 296015 002366 164091 478151 694801 954455 681318 220864 512833 020718 886493 039337 352253 833508 153724 301117 261577 210567 592764 825331 453044 918468 987179 017722 014646 830444 195791 482272 994810 699644 803791 243121 132130 854617 609291 016237 921302 018394 017646 093813 982580 190611 443564 810979 489922 217799 952850 825818 838413 554861 941655 050167 817323 293403 527037 956399 187253 988886 198788 948049 100345 780090 220426 254099 713622 366110 146471 597301 429467 477707 537009 349386 837719 516931 662468 469704 232853 556293 842299 492367 608973 495828 785299 827376 967756 953385 799742 689549 301146 272965 994796 182788 661758 708896 849362 873712 799267 924643 998199 684570 374442 591128 645947 817310 839185 196594 382220 928730 105507 921489 343020 897422 907632 873681 623851 438402 449558 234197 332770 995588 608520 840561 570036 225288 435871 194203 981275 643988 378477 129455 039703 845462 314083 403925 158205 008222 825726 966830 814513 604824 486293 023995 545243 992658 533260 388756 563689 424341 220547 070344 031382 929906 334195 089971 498150 868957 382664 553963 880798 762214 480366 477959 437069 760221 742611 706028 952397 801938 210465 952287 361493 394966 626990 526138 503332 003133 609921 013294 895466 238659 428816 163060 212294 840327 691671 730256 450095 166386 521322 090143 001504 593188 842544 580867 490193 478349 290987 798442 316634 843187 728071 723743 676911 375611 636478 700288 031611 475302 166377 466539 483432 804132 988458 707643 708620 593909 058442 252882 778437 936319 195527 809326 080059 868363 188252 746642 399661 923974 203362 879179 825060 199119 171430 491655 283504 550786 306851 873762 153415 873417 541821 389025 354867 743991 495403 103813 361073 753605 529159 007206 025426 683765 102119 776419 849699 663930 362872 586308 215736 610929 509158 383463 268995 205602 562383 144576 697830 831725 766911 117140 099380 316830 831566 406572 836739 633282 977324 749891 506231 775943 193945 137210 111367 756885 553107 471242 871506 455825 357830 072537 073547 414914 496061 932752 663264 626656 143839 776346 562088 589990 260402 693427 772228 512030 808283 910803 877961 678599 912284 674902 593982 326969 975358 086288 744833 891709 893861 713847 126705 975684 798176 025682 107131 122387 677503 012654 012909 774347 913923 450602 768807 283071 695228 610777 355280 922206 873089 838315 680747 172235 230807 849646 549456 409593 183588 043293 318661 966988 947007 608705 890991 375602 694058 186713 300139 338356 080881 757819 892086 605459 004363 853912 968419 423633 345230 092461 272223 183357 521967 651774 089783 745024 208840 233003 695642 638722 596013 185520 986938 108751 870361 942516 072297 984146 895331 204187 028963 239623 572297 724623 117819 502537 522068 833062 192026 092281 980043 448968 759220 817248 953009 238182 165563 045713 767538 746248 551041 006951 760096 350621 227754 162130 904688 051372 816315 179664 871606 372764 758997 773414 798374 480972 350219 832259 639361 225285 045556 278439 339383 548875 811955 366053 791298 099817 662476 889740 175516 942352 791790 229584 261253 117203 770635 965492 781822 821695 634098 401818 248215 585558 172440 802731 819418 806498 958862 873879 193844 823991 579349 046032 788709 554675 858933 509405 886189 721347 749865 150763 628351 177905 702471 641358 992853 977845 457953 463418 813240 345576 027165 556377 626198 009003 074735 061404 232574 607676 695983 204791 870102 241677 965068 863844 176823 372804 314151 184209 098662 056876 436938 049824 254103 730494 927518 039300 356631 929898 952512 236993 990275 992178 338026 178759 210176 121382 843823 994452 458140 254384 165137 936154 243894 193294 267203 536956 160133 708671 899794 654850 416680 206373 147276 986255 610998 640563 180392 202353 817378 019442 141929 076218 404109 885391 779921 438614 194180 377609 531671 455848 345986 701884 844603 776950 308298 030454 050603 035246 549244 578937 156535 133834 359239 422724 928818 850107 958053 909591 305053 781615 681738 127822 173149 920213 330119 352362 300472 589370 465096 125468 122075 841455 566650 858869 219663 784162 602477 925979 270039 333096 598209 573806 110139 556576 915121 745492 298919 469890 650998 294728 282658 706285 228807 530776 459498 744517 606911 307353 675100 989577 698514 201803 567972 981609 769509 196657 034795 452834 845174 881434 523029 003277 659837 123330 867557 219319 379391 346713 663955 597776 271304 116896 125256 418558 895458 373404 529728 427813 773991 914721 773723 363238 227068 933418 365477 634640 377590 893847 360454 860309 387655 700731 790936 207815 792875 827137 492712 742442 505771 216044 197107 426637 891597 187674 352167 990521 641883 677614 055873 720585 937179 067738 584416 963010 521626 202859 973914 164874 093931 311342 800768 038053 042286 098071 524471 676358 143744 146335 578821 379884 574455 935686 551089 563625 345740 531300 996799 652239 824142 291863 071219 917266 622558 587965 942136 696039 073350 685621 602827 394529 982188 265446 757006 142118 259161 217796 951430 187646 631820 295035 893781 886235 272124 839475 885024 346955 697530 960534 738591 476744 804013 148457 851834 176682 929036 427073 689867 669970 566032 411653 802387 999508 043810 473286 828440 726030 674179 286130 967869 891093 910298 141501 213231 702828 238415 730697 124199 859832 436078 905383 932650 249403 330546 214016 227542 356489 305410 487610 879099 175718 079750 334466 415505 007493 122547 709096 961435 017816 721423 315355 758862 247412 105216 / 257 > 325221 [i]
- extracting embedded OOA [i] would yield OOA(325221, 2612, S32, 2, 5139), but