Information on Result #1881606
There is no digital (52, 52+k, 1679)-net over F32 for arbitrarily large k, because logical equivalence would yield (52, m, 1679)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (52, 3355, 1679)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323355, 1679, S32, 2, 3303), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 664159 570167 990287 294279 765860 264114 746474 733700 582067 768130 210531 296433 175022 933008 890993 282677 078711 306557 991737 390512 434533 291126 854680 640596 484947 277056 742776 731682 086664 501827 903330 214680 244846 945210 985272 445672 625823 966340 441922 088004 496186 167708 966130 081846 133782 268858 949671 378974 448828 753441 661246 581219 262053 740849 390952 262816 513528 571666 347473 490489 747992 195725 073562 809623 142670 729767 102584 630317 413587 302544 091253 963194 197623 336735 571893 782967 913109 345051 009419 409612 136087 696891 988889 693142 448161 552843 407715 128410 743415 359199 600807 573696 163924 949026 933738 188490 956873 843279 302826 098516 651920 834161 869005 615322 993404 947074 823915 245426 200833 547797 163974 507590 820315 088890 707620 420642 145679 929219 672806 740461 921013 819876 432251 141279 419743 619610 550446 850282 715043 956575 870405 922093 169439 867287 479525 276721 856190 245879 802613 115673 295116 650479 959045 875594 482933 386831 316852 611008 881743 949234 425964 254136 002315 968206 544095 523942 114756 495667 475890 450455 713116 111601 381058 556329 027846 773238 801424 592741 262166 298893 251771 648230 678306 911951 542385 438790 238190 351038 469086 926957 931398 564202 461627 871128 404765 743541 750901 458283 830461 563626 499916 770761 086633 864753 137295 229666 846305 940995 320513 807245 936990 766769 108809 405382 646996 164649 623372 547688 377934 791353 004004 264106 178278 874954 242204 433052 099882 883383 066315 749594 822223 535423 370788 747543 929214 901629 356977 146811 591605 668336 504298 207441 419566 683901 521624 381154 515345 016628 152444 892177 792687 575627 940026 355955 328178 363904 483991 176009 004676 366870 116828 229066 975909 395622 115740 600090 192178 622205 138877 651537 664797 037687 495932 789236 837597 671594 680552 760189 376819 393863 949060 858224 665328 154704 207660 720166 738252 659380 293424 434491 408387 389048 137614 392214 617747 572193 323183 697250 183571 623512 608576 269607 917768 387302 458290 034956 510745 110895 937670 183318 833606 506808 066045 111925 969782 220665 065021 427428 163123 064453 590843 100996 007722 328596 208909 428128 566024 301797 358692 599831 290810 564175 092062 365489 248460 658019 721636 762751 787423 622559 533064 846587 290516 714318 547747 719586 341659 145559 832586 926639 164902 260723 165058 792594 206406 131000 604524 400813 667164 205782 597229 737482 963851 432692 084829 853379 328850 619584 778651 374955 163021 351738 356855 282154 978077 534917 721970 354441 566354 181819 551959 272828 563891 625144 525003 739579 683408 939227 423320 193078 924355 224191 865914 783074 678083 295292 044903 551021 526289 336201 167652 805314 973548 722924 857492 668815 101367 017444 301928 422807 945575 451339 488337 250071 982958 421285 620715 308193 994570 131719 747362 239824 332698 667372 975902 486933 587504 019030 707432 611658 649470 414246 486835 569727 000384 340425 461068 738637 636932 070577 562983 840627 954699 700980 316806 854296 269432 397906 822987 515194 997482 053968 451847 890598 865645 590165 631257 320325 046358 702685 616059 319311 855245 566868 877136 934578 186099 020988 009441 264443 006476 357842 399493 143419 955013 243989 142866 910802 953723 571565 088051 369757 150715 616942 274803 185393 239363 212391 361777 424119 918741 371615 525685 238054 242602 935590 445568 801634 327805 883040 380509 837427 298280 930808 514536 731030 499958 922582 465313 762632 179862 757255 488882 727560 672009 103097 133879 089384 453034 884792 807770 739536 927929 788343 330448 798304 883442 851526 567264 586524 464989 258570 174226 398497 334914 185346 537245 995763 347075 339731 238248 456484 527629 617964 846730 434024 063803 308315 611583 427834 097546 180773 385268 834200 278177 634073 111059 287233 459311 136137 278828 972401 319279 746865 045188 070667 295045 770856 020100 448678 154527 665596 148149 540071 778014 151946 231322 940597 440789 075603 733530 236648 676225 473180 030612 712331 437412 206561 635307 606642 485365 673161 268613 749569 526384 309445 646943 853841 348738 511287 042288 138684 410745 953020 155100 580719 672812 836854 081256 492238 116207 646447 607634 147199 394925 431032 465174 233681 540772 635196 255172 706054 892297 000020 328801 850339 011410 445254 142839 566919 683541 524911 500242 211192 175796 890516 170165 200760 593984 589603 686798 116949 720956 468677 386856 850969 017420 464672 809073 809631 678431 572744 414099 500728 797056 330002 201855 324815 700446 771169 424146 390322 629335 204946 758611 695779 298147 964496 435336 633306 782690 185932 130120 398968 357499 211424 975387 386003 269751 930873 430807 678061 714568 670603 778778 758191 156649 561349 714847 029198 056042 134018 926801 351493 728311 943816 659673 307139 898679 690118 032565 396616 762236 153663 865213 636239 077570 762183 219543 188106 318016 864153 576265 985428 872256 665975 123140 571344 398759 056121 112229 698544 637792 379902 605459 359205 039989 334202 479697 502152 954242 813133 166529 123072 792319 374782 300008 471203 210974 608397 615144 404333 237434 467634 699020 216121 781252 784734 070880 841627 395929 347984 232195 347282 513368 711121 900219 073510 226746 712374 811495 322030 788573 176598 236617 377218 832779 109129 914054 446116 642752 118316 798439 477896 369934 546310 838981 759217 359547 129887 499152 351872 218245 699142 687823 174265 940697 401586 389000 017814 603052 998810 648517 113767 605671 924130 905096 048094 302687 791264 171998 611527 401093 234226 625707 115443 433758 491597 288970 079995 711805 098837 882367 376132 355256 865616 747140 910721 813829 402708 278654 544544 682072 188238 016921 616437 726443 519273 284804 200633 553686 972368 224006 944419 894014 985857 664501 361565 896481 424863 117626 979721 476408 936754 167178 754485 141776 029988 331870 962545 166429 192192 / 413 > 323355 [i]
- extracting embedded OOA [i] would yield OOA(323355, 1679, S32, 2, 3303), but
Mode: Bound (linear).
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.