Information on Result #1881564
There is no digital (31, 31+k, 1026)-net over F32 for arbitrarily large k, because logical equivalence would yield (31, m, 1026)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (31, 2049, 1026)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322049, 1026, S32, 2, 2018), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 794 105559 719776 444999 331087 110207 426781 809940 036876 660048 497067 341909 551196 983793 695808 784918 958699 493430 578604 745281 768869 579866 594046 463628 844493 627960 259246 001716 384600 045535 679000 793507 209359 034666 872718 077008 136911 513542 996174 399731 346929 032908 546364 593422 268407 071538 117781 732933 280268 715495 824104 246490 141369 318089 278345 097670 367897 166506 720413 708832 585294 244013 934365 310895 163376 147748 343479 189101 695316 004961 494186 583478 453330 768152 001383 475556 457203 905334 345801 573107 470603 625097 349223 993821 871713 455081 957699 679307 319349 161835 499986 957158 962122 308587 566671 362876 397164 275661 600595 687934 330211 035985 190421 579809 857455 723769 416870 448186 759477 026098 688027 483094 433088 415455 345072 825504 191395 108719 829343 432892 771011 026853 658761 133834 325108 938738 849228 681667 956568 390134 621380 467050 072830 842962 609408 484776 007144 479091 676025 238976 561757 896780 853005 737197 359927 025798 036197 950853 583020 649481 782643 077471 939164 247955 936456 793002 498754 081924 844782 082252 935492 243880 767959 162765 588739 928163 064508 377061 052933 555145 504578 596069 818936 179731 766694 257116 796353 450535 287691 630610 800113 790109 234856 878384 740571 142380 102769 277439 690282 249044 946177 841740 828118 341930 642709 139321 654435 214054 343394 783696 813526 437521 698760 466035 128319 076860 192636 166057 200054 275979 034846 985241 959103 476831 922526 224288 668699 559060 998922 472096 141319 972865 113744 049242 166362 554031 125252 612449 079637 765122 941511 582839 182202 050162 439226 869121 843435 747831 447000 515635 486228 103933 903022 975491 215209 433858 574137 823547 732660 503553 493535 405350 786185 434792 327573 503507 254619 622592 429249 910481 848830 434684 287741 107395 393256 811689 121105 094902 997116 166594 664530 816528 835968 829571 425636 004924 313843 140458 811510 930449 314876 131660 757576 853901 181642 692836 808100 063143 303265 272511 831274 617650 914601 261535 336858 504670 930647 295824 343543 308688 594549 248746 576906 322355 984185 827082 210619 776774 534901 670864 038851 462151 256627 038003 296997 215439 007465 088983 439990 670095 125553 737706 774645 033300 730504 187461 453013 013277 830074 688155 270659 110230 020959 278030 572172 191803 492849 677950 636295 736021 810809 570720 698562 653656 457880 800276 052478 041655 240122 725608 488510 918172 022791 989163 327519 847443 883574 349029 782195 263804 399004 538342 995525 302255 178097 142813 284910 603422 965363 734941 452774 771550 452606 205000 188277 485980 537034 015172 331586 439704 431497 184933 934919 588273 114439 382654 242329 069424 822361 921353 161924 709409 236910 840174 345781 254319 472676 989829 592256 742836 867218 079144 346061 624909 060893 560264 230385 699935 515952 951521 641822 710740 318752 858931 515227 053629 612401 178335 550768 223416 061021 851238 160240 552420 816498 877810 290585 699690 745940 801144 844913 406784 128716 323855 734848 228909 540958 465185 884411 696006 039891 993155 428068 536411 863627 807634 063836 706651 047658 317180 517156 998178 880725 674595 792049 843297 465917 752163 220284 634448 302039 916566 706134 856668 710850 747008 142036 088949 108953 804934 953008 363377 015291 577297 656518 864322 989727 514924 559455 129318 175161 772581 955811 135738 449604 977611 287776 500337 310461 465677 455077 346496 337714 214646 357059 332371 022705 031502 253841 202186 957428 587799 961039 346323 092548 081512 759030 147307 095379 624703 973380 964556 753820 394327 113728 / 673 > 322049 [i]
- extracting embedded OOA [i] would yield OOA(322049, 1026, S32, 2, 2018), 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.