Information on Result #1881596
There is no digital (47, 47+k, 1524)-net over F32 for arbitrarily large k, because logical equivalence would yield (47, m, 1524)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (47, 3045, 1524)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(323045, 1524, S32, 2, 2998), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 564 016684 985446 946608 374719 340389 213442 858502 175115 590360 698542 842490 666873 258335 311918 400373 907124 771352 792220 441485 142085 228650 452523 160458 612047 393482 904478 980691 375352 982656 796145 694002 015073 146503 206592 150007 779957 183399 688860 421823 750312 816308 970082 943427 190492 606057 639951 806618 444317 402701 799002 955877 620205 181501 405899 456687 104215 578502 187744 405486 938876 451306 172684 296418 704035 270300 222003 585749 203476 330582 085414 796015 550741 070631 578169 659437 373230 071170 913891 713039 088113 701098 138036 480207 803924 196675 463150 970855 969633 304749 673063 251835 927548 788088 658500 412922 003385 974169 496363 157352 458384 028953 922673 499542 680211 889657 439052 678411 124470 154958 531674 141873 638453 962888 941405 395054 803424 201406 872253 968044 612378 841968 658796 614354 688590 493094 341189 747389 134823 075685 515441 888455 687211 881857 625949 225010 110180 269584 541659 803581 149946 779225 755596 958901 215159 731967 712475 884844 580612 632262 496764 022769 396850 965576 422931 946378 213309 723459 823922 733949 658450 928814 610782 958715 772010 112669 860104 408941 533099 351094 254861 007549 091397 595404 350859 772585 210831 164023 406814 086446 814142 931712 447985 043955 798213 470783 327067 371640 954316 369985 796843 099023 719933 997129 195999 988851 769035 042738 385403 881554 993131 762264 371083 066777 014697 872494 260670 561369 379332 731214 073462 341379 929283 648479 024904 724820 938214 117832 437159 970909 481373 554451 083940 581056 962369 574495 373022 869278 190356 959477 520184 060563 264111 255803 758785 053791 865085 583680 579645 541323 962362 265441 271114 412850 549931 028813 375701 306664 666282 847881 407281 704759 183172 180015 580662 261002 064544 562056 810440 795379 735191 317348 242628 045835 433828 869320 258189 883559 437490 491984 177575 589950 908541 462941 268468 400272 645922 534422 893313 325751 431632 181633 625221 653380 646029 359296 819089 403004 290554 296112 486537 237679 116805 507239 313763 281336 989089 314020 772615 444578 519467 311536 868896 697915 068254 268284 531443 380239 972079 583952 234309 232884 132909 312777 832816 594014 684913 831556 554095 217794 287480 173723 064318 698979 212050 093701 512223 829552 023918 678350 457011 653750 316419 142965 690578 092134 210400 640192 348654 545201 718944 898175 376164 374580 381199 709288 642675 822635 908950 805802 689456 327711 957501 602839 938745 120314 795083 811968 563489 919744 698707 281097 685502 846108 852436 990713 942134 539014 856660 153528 291459 029708 217724 744402 922462 850830 601950 617534 279175 033221 924719 019248 192817 302157 878880 153719 921043 269003 331098 192794 117145 921094 737793 530562 052293 509085 296123 159826 972641 357344 357364 569139 662310 141354 471312 680019 294969 580201 425628 751873 628614 879053 148208 602764 927478 833199 717288 196611 534292 337491 770483 997863 045303 838987 959963 176972 590939 319495 532058 927496 042302 983294 129569 229691 303827 130857 787352 943920 577469 977698 910246 818797 437043 223252 792402 789234 859377 079823 138485 917403 324647 269052 888303 028041 598430 949201 464109 279595 142513 667918 904370 075918 552566 969085 560630 385266 895874 668979 383980 517966 545452 480938 252147 544777 503432 768373 744043 385521 349563 576549 771250 257574 190960 418031 022747 247620 885101 749256 267465 282380 220644 041233 472920 064231 964722 283341 641555 855480 140048 483639 617280 164305 929737 348207 971250 097029 649274 797572 639456 752536 990336 392672 450405 148912 896444 764292 931813 838314 050787 480567 261256 540052 670195 765165 661683 822272 707459 262100 607536 149487 599631 179754 311869 038397 313961 377934 410689 332277 228136 449447 781341 449612 152760 916556 489972 969051 264212 215854 418893 178255 967034 056494 736001 438955 621315 612927 519574 308484 329249 677180 185147 095379 901971 302021 422644 279088 297416 285795 887760 353050 248615 591546 386788 955632 773208 429078 804748 590194 627285 079071 791027 884112 788816 860125 033281 394748 772156 906023 037486 220869 206558 622748 656697 930333 774703 203008 615213 899909 125287 166066 065712 645115 639786 535990 142627 131781 924281 129714 864542 229681 575025 865588 275060 315387 978114 432963 593216 120814 704221 361241 623551 435822 347088 926575 980469 112882 630759 407712 164925 823272 220104 937287 802903 102024 333083 339700 819921 145317 170360 108190 055810 771708 955651 322834 659316 082023 465340 385428 133847 940552 370965 378692 549487 149634 287493 785905 885562 349642 497361 684581 721806 169139 841830 160012 847264 999328 901861 795433 563445 056670 034375 952150 237921 851895 854893 946559 208361 072293 054548 501769 772125 038073 817522 922097 085613 804786 304466 818898 512246 106079 229979 481304 560398 326931 936779 038825 921260 679708 711692 078737 770825 514717 500977 917264 640745 851874 780090 139220 907052 114432 812934 453564 432980 611658 635184 248747 554032 941102 937272 367701 070192 269699 285609 192695 014111 882553 866787 854252 841409 006732 259813 704250 283876 776868 663168 008355 444549 591765 062582 529720 384202 472816 776597 174744 052288 812219 121256 078941 008940 819755 040554 505924 121292 318604 895597 068598 734000 954439 155872 247048 040147 519999 367371 289299 779584 / 2999 > 323045 [i]
- extracting embedded OOA [i] would yield OOA(323045, 1524, S32, 2, 2998), 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.