Best Known (56, 56+∞, s)-Nets in Base 32
(56, 56+∞, 120)-Net over F32 — Constructive and digital
Digital (56, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (56, 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
(56, 56+∞, 325)-Net over F32 — Digital
Digital (56, m, 325)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (56, 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
(56, 56+∞, 1803)-Net in Base 32 — Upper bound on s
There is no (56, m, 1804)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (56, 3605, 1804)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323605, 1804, S32, 2, 3549), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 52113 453851 767180 444829 043541 247845 319027 461943 057186 725435 947229 035153 578715 866988 511472 136460 564150 173917 013340 776057 489082 844360 062666 096034 740722 923289 549850 536715 326489 167951 961585 816482 422898 955475 041488 485592 898757 636222 040392 846267 267934 000193 805967 449830 776043 429853 789960 670770 511589 715584 414523 893322 919457 031826 219114 526468 879156 359415 837151 773359 732774 021330 076500 116661 663437 990834 248110 800194 269878 696525 410284 148108 656419 411789 985979 899918 643042 207047 799788 505049 021659 792566 337079 232743 910032 385257 329267 349892 728660 877931 639380 287310 338546 832105 554906 324419 860473 099575 169292 527172 401052 405101 518125 599631 497800 977561 159194 638110 978655 759229 905417 879204 640607 765309 457417 809715 878463 021178 285498 425419 227919 679718 557009 933076 691554 376945 488811 257200 225253 893046 326418 118372 758272 477948 671431 220646 887365 551192 390654 969532 065165 365214 171133 922736 600677 965607 800660 271556 739829 545772 909411 680086 086875 307415 371453 970548 472037 966847 220743 927162 109042 036639 397417 295818 761565 170520 231763 885246 408810 038843 247962 855044 716432 405505 855560 935639 437298 048575 624870 932570 605080 928973 662535 450001 382133 825297 200267 875632 785078 479364 613637 296372 491258 916393 238743 616337 557576 337910 740774 895425 924620 062788 287708 993981 943307 108911 208196 445207 977606 540669 303949 183892 013101 751082 075148 511605 957965 689458 152107 241976 851856 002446 047645 481526 633285 265294 505557 590052 823474 006507 620732 434155 749601 182336 786378 105660 091365 251730 797117 181961 374008 052239 684444 906574 447116 810391 398732 398919 342545 399047 788982 330881 368930 370497 207470 419833 493699 622252 798823 903841 225194 631870 263475 030836 258966 949576 436972 994958 610457 282054 180687 815907 278754 949456 647758 739973 040588 409537 688646 372790 727747 194195 017831 690143 350607 821108 500199 879108 107826 247496 024783 637595 646661 430676 243952 110563 502904 519931 419984 176025 931519 012705 947170 135952 628894 626836 845464 203774 434297 025056 048302 005865 302237 530886 736418 518683 524395 937243 680949 490147 682520 338274 968457 132095 064918 059737 926727 071583 800828 272064 209288 405554 583642 902080 083241 548017 574717 190000 278740 179589 243271 828002 571975 116017 176457 098622 532655 745273 538304 463158 015014 566124 521726 779500 560280 020557 874979 691816 107507 039631 078959 137509 245189 822907 275224 925034 521466 207263 965297 047796 956902 518047 797747 925916 888594 834707 108172 188372 004303 373203 661113 121970 380321 117437 919157 439151 447738 764512 144941 298005 669279 775517 108157 203113 895333 059100 605641 244654 944974 291987 609425 987156 782879 188365 699661 702539 460909 991127 391929 220659 787274 711477 613946 355925 478962 912745 391180 512318 270163 828417 924147 799368 313001 802379 771596 732643 147970 467483 533628 736719 777454 514030 712145 421961 225056 820294 744801 621386 694347 506759 706634 478698 950596 176645 942063 936407 688136 785846 769441 589202 624343 356740 876520 723184 500200 315428 712611 527065 135135 283458 617378 915170 755946 969890 686315 810281 919304 826365 443249 131780 466499 026666 055601 538736 929033 506377 805179 283579 036265 026924 235416 287830 570464 247099 447477 311912 057028 041406 654571 258229 334713 524580 788814 139471 451394 146132 728470 158534 943007 251367 226600 907009 575069 855717 556812 403993 199016 783731 369385 774075 161530 125481 232211 207734 469742 539253 892854 814094 276488 463221 512556 292207 664990 428994 425182 913661 540113 265012 323344 716825 709465 261133 717359 321718 955206 049511 111812 723702 145796 744964 072484 299049 937770 430132 479427 572502 822220 538394 833664 261258 272999 508997 380030 302295 827343 519267 274958 543817 713599 828899 353820 803648 541675 982621 437009 552203 172390 100400 411995 199028 280748 152157 642667 065126 221717 322735 342664 872461 567627 546296 660806 863383 608932 216115 801982 041679 556022 081734 853498 025184 842811 251496 363344 074492 059174 174712 854896 679739 643562 415616 607706 884261 015247 353488 479702 851258 168697 285911 490785 113813 973221 303157 786978 960804 727449 560798 156606 270176 563419 302726 625818 217556 898600 580900 454392 695065 352938 872698 631300 119846 568007 229192 467446 349799 850583 526101 528556 263096 237219 139544 203494 201702 177183 434681 202184 520301 355227 227516 685759 060655 729668 860717 584848 367090 784727 913041 476291 978742 550742 843590 153034 361903 477600 827914 006238 724789 032747 703028 185078 089002 267115 374183 653104 977946 419942 877665 059773 827353 090914 607738 469780 148661 123073 049454 256099 879560 180805 934552 572385 305633 019810 035478 828832 851316 195035 662688 730023 590364 638091 694817 338661 105461 247272 213530 921503 700128 783408 740955 324823 150844 714159 502698 885835 618511 131884 157395 194405 864238 355456 381220 362011 349606 420111 894616 635733 023805 136217 497821 691134 942579 922395 372977 926904 344674 900913 956967 706212 225690 727813 167029 372489 995981 370370 042449 675982 932021 195023 994515 230542 843282 331207 881471 420178 139910 317066 038099 842318 787942 958034 710503 075484 936011 425352 627471 983446 457330 626550 545282 598362 555997 690924 541287 557400 893209 437043 116764 178960 808251 282999 533953 200079 038225 256716 036426 840287 081526 137176 831896 398522 562876 429577 812935 576464 860354 727644 183407 772106 490687 865973 547466 924122 030119 273637 067914 710852 095159 675549 561762 855279 088102 153833 776795 997121 878316 876171 576390 187460 095037 087134 265549 247871 412869 001310 919149 848654 615433 831357 208503 029998 416602 897757 676917 979490 597943 515252 690575 932271 514800 117972 262054 882123 626479 681841 476682 248979 348611 236589 883152 115597 539698 766989 571081 519703 879430 019471 969083 974422 351030 572277 443360 904578 529015 070762 590814 343902 851385 642373 250628 527332 791426 212740 017778 054345 039741 061401 680801 197754 030266 537619 233455 728196 069961 445970 347677 547422 524826 649111 218061 872494 121678 175802 210384 441703 292401 008592 893989 601750 985409 921263 709956 401010 837609 090138 604134 465536 / 355 > 323605 [i]
- extracting embedded OOA [i] would yield OOA(323605, 1804, S32, 2, 3549), but