Best Known (80, 80+∞, s)-Nets in Base 32
(80, 80+∞, 120)-Net over F32 — Constructive and digital
Digital (80, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (80, 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
(80, 80+∞, 325)-Net over F32 — Digital
Digital (80, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (80, 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
(80, 80+∞, 2549)-Net in Base 32 — Upper bound on s
There is no (80, m, 2550)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (80, 5097, 2550)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(325097, 2550, S32, 2, 5017), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 258019 911122 910395 739860 719801 189378 013957 624478 793026 076673 864688 429830 681250 434671 956575 403426 022444 365348 969762 010389 316613 140232 630025 360319 266011 789620 513044 457616 895462 651608 438789 496861 154534 675403 391240 251740 519601 529987 996599 054500 036127 633370 914445 392051 486779 583788 613595 018594 650833 888964 646961 889215 616263 898997 479868 601924 827411 891314 187313 372202 827694 566533 323846 930725 975758 369696 923530 779857 987039 478073 053741 730032 570358 511684 075295 706975 970687 367629 286223 123448 153371 784093 184565 157638 868094 866286 291624 929318 067712 180715 931834 396670 711218 371176 719834 112381 672558 644573 367661 862624 861643 952710 648639 325155 207191 044512 737453 538884 886440 961036 771422 430380 263622 361334 765019 503450 045241 866543 801399 939081 570773 379437 502917 007865 080030 652775 910641 328985 630635 135366 160548 194985 924632 272723 492774 536442 367006 281735 806912 244424 793272 126825 941129 014826 335724 583498 364446 723592 864961 698683 657533 144072 265152 822818 933414 435662 277192 037403 574382 854556 413571 967096 132660 932809 774699 775904 699933 178989 111979 943256 941458 571605 917931 098538 891203 207470 677756 575246 959479 189378 308741 394618 434524 305655 704519 417505 186239 857264 707374 900897 169294 938019 897368 115519 904455 099533 392639 370079 085041 176670 000739 902712 608959 323855 090305 510803 893083 714903 583429 535682 195408 956092 062960 358901 630673 201832 114086 374770 577365 916087 809274 456985 203307 004648 352117 896239 038125 396077 118826 734944 828971 592351 309528 539522 878185 685839 435569 413502 216997 560661 061142 181803 988373 967490 825215 338665 848277 548168 341337 814913 522027 756204 416565 438252 825491 411440 646144 291950 651773 233097 134773 278805 599557 858433 835638 418927 445976 383357 210374 400821 522533 717078 675709 971445 656505 226323 727523 307519 102816 703270 347123 703295 178825 442599 785399 028215 621920 806605 294785 567604 845607 197169 852225 663159 137339 948117 716479 753565 179592 980571 318188 080829 201840 864486 521845 565778 563254 034158 578178 374701 774575 235014 119391 964585 642343 000391 812289 629541 490779 577625 297706 803011 586225 079293 526210 474067 190379 350191 618080 548155 864152 675754 963914 733046 320173 636495 819403 098269 909215 216969 664542 039631 895870 651959 541860 721314 757440 414067 618792 437439 382443 787247 210713 026264 455212 936518 915007 920644 142216 669234 666808 386169 876423 467872 397923 806139 386006 946061 270160 763295 551567 014367 909329 373647 084905 552535 278724 493635 954445 837132 895316 169537 761917 550450 458455 248527 898354 575944 878121 386501 542415 839248 083055 636740 174005 607491 164504 903110 956451 451229 552880 658709 958528 018869 365756 310864 712555 060395 884042 253067 127370 420218 568864 590841 222333 416076 458052 728662 751540 229886 413548 476567 729231 775951 112935 848824 251045 745687 979285 061523 034171 887078 466814 248966 916368 340271 002287 490014 754247 235736 355765 220800 240078 593164 986697 448675 209737 009137 815456 350994 381035 870888 758824 401222 327282 129628 782123 698961 101883 651178 651384 139528 937801 429791 752096 512203 150799 917912 330539 382208 178922 593211 083560 915626 150807 713399 526331 033547 335310 067913 174076 506925 715139 892313 522246 915660 587432 055151 635692 906123 909057 781082 501328 171759 802355 440821 081531 700484 115008 793639 767050 872560 097022 556486 704264 623665 178787 160864 578304 343822 031936 891683 114331 402909 461524 297404 454032 976417 755408 718276 932818 389207 924224 560565 385482 294251 233810 133741 907431 963838 156064 364487 521591 219845 498235 844901 326906 794770 124402 404393 312212 363973 812686 155852 799213 038981 009608 261284 158382 328733 444614 297022 205611 588262 220985 264375 635995 008054 637012 972183 607472 536377 046843 671746 585097 954807 761526 551025 045646 589004 514788 877361 635974 323361 706826 047996 195121 850969 790429 004801 810544 461167 179211 039016 673741 477645 057572 445904 489617 850834 303140 888349 546854 975461 164476 632803 782517 128382 443407 347647 094281 128648 604417 907392 844921 545061 092800 495622 204266 006009 042305 287058 043955 018475 997616 801892 504613 931952 157435 897811 427249 635904 306314 500414 606777 700012 554321 465763 135692 042335 125276 078009 280657 109414 564453 435472 757434 277565 831981 068623 347845 245126 708181 749930 035011 521537 818621 327576 970163 708737 796367 864823 848659 078538 453979 259555 858292 221092 724145 505005 734899 256075 366868 463373 119636 860743 478680 927198 895467 173400 165840 153079 122757 937561 704175 644282 129363 988275 887359 191346 996419 719970 612702 836195 523095 524391 244962 956954 545334 920250 981302 842684 591018 269723 630016 635894 374890 132999 965332 207626 419344 017665 641379 543042 155545 518222 522288 927682 640010 879402 539835 262482 553186 529480 899724 075739 815954 991994 996872 473157 969738 065555 882058 589990 560283 072965 690013 263966 901045 057537 013085 397897 933367 258992 701010 153575 236778 619346 733275 819911 630529 601210 787996 700519 933544 600838 189652 830587 621630 560070 406396 074076 564169 073033 836366 768311 564325 828759 219483 958777 914628 704717 429788 955553 950787 239209 721135 008210 192745 135209 750035 147354 938503 805178 218484 534265 039251 327725 255188 639777 982460 409169 492480 731661 946677 047729 307609 635560 330969 472700 003194 318437 956407 199644 385757 327488 767520 129953 297755 399119 433549 272072 938111 407287 896568 381501 278066 987089 851312 682462 656087 373249 374411 181956 697212 071034 415328 679868 318332 259538 776792 471388 320260 240976 263456 631926 663442 537514 170089 671847 406949 601103 270385 260064 690023 590614 346297 209523 624911 512845 345541 179165 452314 194501 408607 020814 934286 393549 093500 719438 415129 173314 964179 144335 273235 486704 638314 740088 627133 254861 158547 175080 134642 369235 111506 760186 520678 068425 372701 274712 159991 505619 325755 624838 535442 552995 029153 358602 593648 207092 407928 862978 524991 023325 012270 214523 987976 226897 735722 104798 748212 297815 668741 999778 375431 182248 889862 779941 044290 134152 684890 822957 625468 203279 075215 386441 669034 536813 842181 313559 432432 591936 396431 932043 467765 595330 866314 835680 166771 586526 812263 144933 124302 655321 592680 985596 817845 630519 815670 167167 841520 518197 844238 886347 659023 984712 205481 546080 297331 313124 550727 598870 175341 275167 437877 475287 399015 278258 061637 861992 350531 325840 430215 317713 990597 263456 947267 566900 504260 169690 351137 480597 754461 206329 584904 640651 880018 104457 560234 562314 090707 994727 248292 221742 909787 360511 170523 345229 182104 357392 148383 167402 485207 342253 276553 931554 240060 586397 677471 131511 484042 365339 548975 629625 341580 543593 382119 760034 248387 338257 062439 529407 170497 428935 825896 709427 757078 182648 885116 488266 475087 265990 991254 717302 877037 470778 299219 162004 536430 264579 464300 457013 426378 758391 088765 357120 923839 528913 992193 253448 859656 392030 497689 511077 551170 342094 032424 435518 613343 439392 481254 681476 315987 043948 583127 029332 180316 468146 276912 578980 921761 698154 982961 675796 121923 936655 386800 401168 810939 178023 179805 674891 090210 834977 528458 434202 503594 614922 909654 365085 634646 738529 259063 289851 994981 009808 436662 627645 849848 229551 284312 925559 060688 385301 973830 723102 660016 320103 714856 728200 624560 784361 370409 572385 407340 749193 107907 665279 628860 903610 833568 595543 544181 571566 751843 058599 730694 570460 279664 951135 740762 047678 208377 212887 718993 438265 858647 495166 581297 677451 236293 022635 599046 256514 922521 586762 609300 107313 058601 425398 363695 468646 944781 449145 521259 757575 295698 490843 988264 944606 369817 103926 169531 852770 705861 566309 718882 240551 292281 508489 018685 936837 565962 062290 274712 669346 256751 018781 999663 910591 764748 286688 153486 567792 294942 921166 568200 657826 809868 361888 357108 349182 159183 892174 976015 192636 053820 112411 129983 988966 419609 425500 642966 826862 972844 340570 849120 854249 121033 988808 348384 963048 505666 383486 456225 741216 042344 770785 802114 897309 534675 262589 869437 556233 861242 557917 680983 137652 371491 023199 764882 992603 992280 041131 988267 993166 664747 918337 271122 074322 816757 352483 623019 271248 199088 845641 844947 840931 870794 591919 704880 436399 589752 283800 856970 164199 853100 681314 121369 437438 063790 938934 896238 917717 317485 463200 503328 399765 792125 306512 258712 285408 908187 840477 881717 516854 581040 810704 575798 278856 248124 264291 975737 005904 699386 194367 542249 913030 453468 442555 812867 723897 415486 606228 775225 795405 397617 369119 981568 / 193 > 325097 [i]
- extracting embedded OOA [i] would yield OOA(325097, 2550, S32, 2, 5017), but