Information on Result #1881586
There is no digital (42, 42+k, 1368)-net over F32 for arbitrarily large k, because logical equivalence would yield (42, m, 1368)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (42, 2733, 1368)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322733, 1368, S32, 2, 2691), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 645229 804959 680258 799435 592330 763280 475716 071385 686295 246934 415896 780969 910883 499440 558180 201823 971671 926951 627570 225220 652468 293253 699110 516047 454113 316519 468597 646904 811254 153865 267391 851402 233426 850958 602794 748365 902762 950784 960552 252218 963451 380826 361844 724682 203741 544663 129531 650960 962606 982233 296891 459993 956397 683956 811052 368823 601309 713440 503701 588896 256453 896673 230060 210241 394232 949696 854370 597581 676672 458394 956091 018448 197858 549915 273292 470859 591723 199700 761333 727036 919005 614055 750597 426390 593715 668105 404655 603223 524725 786541 118133 660294 316686 670282 010971 563711 607354 477349 234638 030852 024894 847039 077817 692123 346263 616173 546219 466202 822125 100748 797201 650009 618591 293287 823783 586672 693760 481123 583549 377149 626930 701508 837386 904424 380406 642484 884598 730493 560899 139465 555539 146640 968222 472265 677143 544623 616567 804163 634796 064148 778961 843680 139533 645256 974875 902655 547052 883299 560944 786461 560689 484036 311803 544487 089439 890335 190663 270743 569252 862482 620796 575706 416768 675989 853920 326888 419372 794858 708969 431872 867206 016272 269720 574214 559595 416035 730697 711902 158267 604848 200682 003542 161157 614852 670113 057977 884134 165977 388445 337970 306809 797120 033658 659633 771616 474881 884629 760948 609597 070443 200030 761588 267164 314129 749064 542649 654373 591191 561370 786355 124481 475613 521244 588386 007414 301256 691813 494766 969169 226840 383744 953327 921445 616835 182844 195529 987636 502329 256143 276570 398084 559504 615230 724897 017073 481642 953499 628941 711191 544244 808957 243913 260533 864081 775574 593298 344526 905827 311148 462999 106937 366793 841556 014263 307305 731530 601568 902325 607536 763634 083011 179021 555411 111649 206934 764654 972312 484837 994708 412073 908852 192634 681669 663599 501228 328770 478367 526846 095169 535224 519399 406813 043992 396753 266272 619028 246053 938455 143405 001159 829228 573795 288466 267205 606672 698508 461607 759125 851607 868195 739155 945296 879213 743796 593157 491647 057272 230264 021959 641097 428415 428674 516073 700004 516098 303042 954183 064132 279299 813427 027658 666432 536466 649771 614880 340934 808406 812550 936845 319053 241374 739597 239206 921835 483832 547186 089146 400626 493642 265762 942205 322784 427857 964176 776921 865443 975617 845427 292045 951295 035000 729766 700394 248776 916986 202731 100756 488715 954165 973111 250023 160892 503079 448214 944543 702432 283198 591389 736461 239181 260835 251549 631284 004879 587925 904120 335395 220803 271542 492657 945770 964537 515623 081905 904218 961905 445089 677842 663232 004704 417418 782652 331752 411988 549075 061174 742764 167325 925458 078192 610015 971065 647197 589855 138541 339598 856009 887131 123058 134937 966214 401378 260553 607603 747999 135112 233702 758494 370270 531695 869092 743634 749404 311765 427901 704077 070921 759171 333191 614920 096152 714149 452679 673280 206982 081876 389265 756348 989145 747663 570776 480091 997744 596658 828816 751878 911825 387591 869098 406407 243213 561272 420637 467071 603869 814179 806195 646475 432562 015237 005132 794841 449583 759631 178756 273393 602879 886222 985530 125078 409662 880629 056382 496263 819235 511457 042873 395336 446436 093094 786786 233955 304458 940535 599615 934527 647094 340971 619419 935406 780311 393754 879265 411022 958816 146751 771930 786236 274061 569431 463522 052517 167182 271335 530032 787171 402618 764309 494687 636996 057280 326414 617996 604438 443213 027875 598056 532458 586662 910806 701063 462057 175238 170148 402952 766952 476503 733180 411899 056544 244370 827404 632299 842810 233436 814395 179752 291442 504781 200874 356003 147752 398631 069399 751163 374628 676731 879629 906542 259691 314841 646712 989966 858324 981631 272272 461957 258047 873105 249654 247151 364126 995998 996022 598683 638976 708804 875733 773502 966526 144423 634527 604343 090127 111895 839930 931901 881215 348305 825336 474459 135043 471647 801172 898230 069922 974363 954199 116523 151655 029610 198934 462448 407676 097832 688309 092332 514479 138318 753802 350021 651000 150585 011193 466679 956461 448114 769070 320570 132438 990155 355156 846378 764485 656083 707373 339016 746644 926307 500310 393137 887871 780392 918589 258700 930300 364078 482780 432821 008032 311734 026713 258495 420763 504222 512830 698637 526548 435898 390998 571696 772238 124751 152662 003612 275828 294426 180117 221029 965847 747465 596851 367810 384969 390700 195553 371558 509214 733486 601322 911289 257551 076424 928062 082302 613540 944273 868087 314830 825247 407834 250014 955305 905860 457297 926320 604834 557406 572645 605005 955943 358769 835462 875409 605699 043328 / 673 > 322733 [i]
- extracting embedded OOA [i] would yield OOA(322733, 1368, S32, 2, 2691), 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.