Information on Result #1881582
There is no digital (40, 40+k, 1306)-net over F32 for arbitrarily large k, because logical equivalence would yield (40, m, 1306)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (40, 2609, 1306)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322609, 1306, S32, 2, 2569), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 248705 806266 659173 228113 109014 648753 854391 361556 000271 935882 515396 308549 315697 101514 487050 240047 317995 675994 147218 003961 007040 944172 955292 700954 327068 942447 499348 747097 227657 942066 479255 873774 440584 735943 210143 278064 019045 266869 846193 346625 642130 755269 524350 123734 297202 897110 886851 535236 928372 202813 761069 005902 983392 611737 022182 730828 695062 612847 264625 786010 688559 195293 136432 099083 603370 141608 437981 060234 634937 871301 414273 058481 765870 679410 533460 952063 959386 968252 180599 828144 442252 246662 165344 862550 630089 446733 972761 192917 683115 473244 033801 630545 921635 656857 913519 767015 702357 774546 441248 979842 466783 057490 001861 471725 783794 862082 609488 999415 423978 997154 930578 915463 664516 477750 389741 302899 881347 537199 856729 447600 684757 848356 274874 158383 648104 431615 442569 974511 686905 950241 299442 912605 615120 389349 342475 705279 645683 504779 484781 280106 124154 229660 426623 778905 742225 505205 418312 699581 301648 480930 819982 469688 232876 782127 403521 413754 775741 513617 154864 182579 137872 749800 971012 714572 041188 330542 662809 729011 066075 469488 688401 548692 613543 179150 427089 215092 740675 091874 981688 449719 463967 323244 840808 126360 103762 863620 584968 112251 659430 966855 509313 476073 961784 956029 676026 782429 194234 832867 540657 253030 363149 412157 801491 675703 083506 902528 331760 774960 089836 539049 971918 418682 352879 981433 503715 164576 483474 530541 452947 608470 903474 817172 924441 798480 951899 290588 200611 170796 051992 554125 599768 173240 141015 060690 819238 587998 634157 422872 490753 866865 153183 368476 673191 342597 094943 564826 973985 674228 346400 861280 037842 703661 030151 734902 990030 562613 474510 779588 412922 299635 359799 789575 284724 328002 649509 833308 631721 626356 676603 708085 447865 745351 933047 013869 712231 159833 933970 388876 892039 818871 743819 706814 017179 277474 116441 729737 545331 240604 176743 733134 809981 050051 886639 678504 929402 075895 115675 888970 837451 904702 448858 143917 825795 273199 019661 758468 222101 507482 239194 343971 351655 689859 757465 029437 793154 601469 791505 651264 694409 575167 992352 081991 871829 080209 656796 884462 465500 072709 811499 959619 761062 879346 273601 149317 515913 829222 462531 105071 821977 550994 040303 747077 368331 987743 399470 220113 928656 546918 729392 518876 259405 389689 331122 276244 074966 091319 289412 749718 193481 934132 793739 388888 116941 922422 746924 778565 541873 918833 706158 260553 913813 146246 983062 749253 129380 352258 148250 267998 228566 119917 028216 438516 365471 295962 090261 962751 349777 957526 380777 440421 437767 482631 277296 657565 898845 258839 929239 250347 919125 115408 384877 491537 166910 811401 399663 144221 736367 359698 985127 484436 546484 152861 665874 824637 285920 576383 703310 498532 113256 777415 745252 145475 082180 107981 886968 695456 856511 657835 338018 995622 365862 425298 746225 552426 940269 912477 978638 075171 650110 694981 126407 370100 918911 045210 569753 557663 696411 189550 355003 199644 197876 945655 765687 461748 623614 611490 711241 833555 985983 351529 786412 905528 525540 421152 399441 549375 719928 859725 658241 267052 426080 952330 093912 282103 573519 654215 851825 671490 985142 553583 936644 741884 536163 371248 992993 808707 029180 068661 480550 949599 492410 357305 862232 523566 170924 071541 217455 505959 906664 710461 432893 070946 680936 145780 524080 559421 815409 956176 773541 675695 047747 904651 519851 986152 554684 815069 720651 979142 767695 077369 792844 184009 355186 083999 371804 203722 497190 412296 289472 446248 888915 246227 658508 388970 130527 998815 138924 643961 735047 894829 092275 922457 301091 473461 541366 195917 614318 108305 591794 556602 096423 084504 103553 536635 747400 261885 428873 383421 493911 699925 764065 670039 815502 311594 686653 297980 598135 207736 761009 313060 646546 166417 053395 323662 884595 711983 805540 983524 963682 711045 932179 098817 227426 029276 132048 972496 041276 206522 070654 578754 108651 755405 576005 808890 394724 230794 317299 984036 850211 676697 872845 366865 783986 546304 514947 135358 003762 181347 458919 365908 462925 513346 050153 343111 530915 406857 804364 374345 094219 505491 366139 210074 021226 261552 677113 062830 160572 717009 231415 041730 419135 638091 978374 069334 034872 758641 700955 844386 790863 572882 162019 660766 288304 271326 565299 136145 877277 186097 943356 505323 307661 112704 238800 450529 263616 / 257 > 322609 [i]
- extracting embedded OOA [i] would yield OOA(322609, 1306, S32, 2, 2569), 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.