Best Known (43, 43+∞, s)-Nets in Base 32
(43, 43+∞, 120)-Net over F32 — Constructive and digital
Digital (43, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 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
(43, 43+∞, 308)-Net over F32 — Digital
Digital (43, m, 308)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 307)-sequence over F32, using
- t-expansion [i] based on digital (41, 307)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 41 and N(F) ≥ 308, using
- t-expansion [i] based on digital (41, 307)-sequence over F32, using
(43, 43+∞, 1398)-Net in Base 32 — Upper bound on s
There is no (43, m, 1399)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (43, 2795, 1399)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322795, 1399, S32, 2, 2752), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 21820 195384 721958 627116 460087 713504 317647 564409 981791 458696 349029 884585 601257 351833 928863 400240 707075 950053 092841 857074 723926 777642 523695 602734 988277 326390 453172 222784 404848 674074 932565 459473 655351 298414 987273 111593 028900 350677 990738 933923 134125 375309 570380 317674 395926 812963 809029 867734 645182 635994 914594 106156 289320 148250 356818 579399 490223 459341 617241 627590 895190 638801 453721 318986 937974 793759 745902 635027 854579 598133 239203 195200 665837 967829 039730 536243 491263 863943 266502 415967 022899 502986 880146 996970 638597 116879 939537 266356 837059 994587 811653 561246 254662 621483 146334 391100 717731 789788 618690 163225 202223 895428 428129 053566 154955 655587 215115 254227 072480 924254 361054 642037 895140 357991 675252 625534 133510 807960 906943 391067 130601 388863 909408 215795 303176 924002 807259 950425 891794 105410 135427 074454 797800 715013 221541 556526 648685 792011 741186 131009 665521 829912 139195 707771 758233 977608 109178 179266 821562 200076 842406 311175 778073 921243 992538 925912 003669 217498 913070 158723 355068 985623 450355 738110 577305 954863 233463 858523 986602 898429 202972 953002 699122 914495 709371 882879 006944 605338 377625 140397 247235 990856 715444 728166 960476 571481 682278 378896 648164 410983 591578 297767 580632 362289 442509 858063 836135 900327 982042 260532 338054 870316 844182 231695 045962 968843 859696 680373 710901 288423 634616 158898 029000 848779 498279 011617 090353 769906 846321 205559 526152 731722 366690 947000 147005 680654 372690 898884 993018 159889 665326 138620 314417 390434 243730 609825 170598 381943 511553 159670 933145 670236 601890 109700 257356 837054 546322 141208 211375 745724 390210 500073 914222 311319 664331 025780 501653 026321 277642 758460 224699 682114 049315 258875 829925 639843 878590 109609 102003 734100 897256 175401 251778 444502 973104 460506 119941 331552 997508 239644 598629 603024 567072 602889 157240 423747 093627 449123 001541 319939 944464 223959 930127 179171 443515 834532 783110 966562 931709 207213 693955 615640 209321 456423 254708 675675 782109 838894 088333 246738 271920 753705 218328 415818 451813 624144 908017 744242 911698 125998 242012 942688 538029 046311 622051 749118 158540 440331 545380 975589 632755 934814 315017 432164 821404 447113 220154 545793 331093 871506 979781 269625 132339 209007 540860 087023 395500 112197 861241 210920 367019 007041 187774 032625 365210 797580 334577 165554 467206 492551 370977 676733 998085 681153 627685 189126 108914 702184 225785 855922 971036 377909 926861 354645 760038 269213 387102 275985 638839 925701 679205 494370 167575 976946 510408 082992 146095 268065 133645 759197 361258 784715 162371 343742 983360 989790 228100 963996 702808 871181 006954 558125 292507 711875 877015 828070 640139 667749 242232 077717 518703 868402 529575 220170 795538 451975 088406 695419 221468 044143 789367 011274 326678 661068 780235 189085 619716 873211 103656 114209 872682 292174 550325 432185 998968 802714 741574 629480 610071 001733 156726 436111 661823 435519 679740 180376 391066 094997 087498 831990 109186 873453 641157 101866 628502 027390 172516 790783 081260 546858 569939 886565 156236 797890 183248 730395 168172 626977 039812 769510 312002 731708 309089 866496 195948 680872 390650 145146 390461 833504 852626 540997 819041 802593 207595 989718 421656 698523 521976 440852 952444 479146 297273 852254 589458 846987 278478 942610 750212 648352 068838 144443 528716 475929 267657 300739 277649 959041 816953 148520 530323 906277 555987 166626 250260 532285 031629 443535 416302 486165 277281 362163 388871 992167 575717 138603 957092 767895 158801 716606 304939 927228 815021 126648 178922 821589 116302 372640 642599 403075 376900 757731 013680 402899 936911 703257 972033 142274 832575 192314 678028 918087 794479 144564 736674 740642 195700 413621 104027 132726 360102 381472 234090 651718 271775 916453 888378 064641 285814 747203 686908 179938 577952 718746 937647 605845 994024 375654 401308 748777 543082 833310 933042 289255 821788 367960 239872 684895 887204 732359 187053 372132 805838 928713 705374 331091 335690 626797 995177 180896 795608 942245 387818 526513 359974 455291 834185 148883 465474 943195 763119 402650 992476 198263 322718 647268 548498 085600 987305 273748 181272 544369 323484 046038 441391 628525 938506 240533 755330 378480 027405 708901 974916 872655 191880 012328 168824 233778 020611 518853 949516 905966 659660 920846 990682 411972 374814 680558 871585 099549 640029 180153 088168 271745 735309 700432 300863 679660 602484 963268 089258 838624 144366 491943 544069 593798 919910 131029 372587 368658 539366 065912 705938 075691 923486 373568 873108 252940 422856 491296 444478 731072 579157 133018 389295 821680 531641 779411 035952 047193 932428 368364 669574 738908 155732 276903 064245 127512 891870 306589 123450 765312 / 2753 > 322795 [i]
- extracting embedded OOA [i] would yield OOA(322795, 1399, S32, 2, 2752), but