Information on Result #1881584
There is no digital (41, 41+k, 1337)-net over F32 for arbitrarily large k, because logical equivalence would yield (41, m, 1337)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (41, 2671, 1337)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(322671, 1337, S32, 2, 2630), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5130 173788 737183 961317 210416 737438 733512 847654 659936 315000 937560 768391 908061 532376 321383 141075 735080 365299 335425 480382 939915 093655 073650 277082 470917 578445 698303 927747 942920 239216 759540 932783 281814 767232 583623 928991 693248 156702 641360 168374 603507 360576 492731 215627 594536 246622 135107 816766 700084 358661 977241 610784 856334 455292 332306 451130 487297 019270 345706 802595 481517 959072 472586 773559 650014 812762 637154 904015 916222 959930 707347 634568 330530 635266 937368 737121 778873 193784 170694 183537 047292 572943 346224 115296 943163 623491 423818 897842 194842 528733 360082 403432 068803 146325 312957 950534 060188 650182 360471 145645 946235 797093 789917 479985 837114 030626 141291 478393 663376 310963 063460 956595 203683 954772 356321 986776 535065 021503 861425 704617 885001 536911 116243 823359 745821 417579 229028 325867 700686 448888 615163 939351 525686 156682 676444 999890 437261 147243 933642 694404 041433 319511 084237 428168 214875 040099 552484 993669 703411 268316 219906 036307 852877 165591 763378 244090 113870 762541 686963 738302 777384 951978 871235 300256 665670 549211 735539 178197 467568 673844 743816 126475 906689 336031 242226 063945 283215 214763 189475 131738 311302 236538 710709 149879 221173 091596 870289 206764 313607 882210 458294 355423 622417 556786 721248 083454 236361 313310 221470 918223 909027 348341 024789 027023 731702 357026 632928 955004 950709 410532 589635 647838 278425 175822 368323 599308 808005 995198 755107 367269 762862 391376 359729 609438 522713 052558 265907 314530 801736 218688 572699 727167 701367 732764 651464 097426 621167 272819 088043 877167 107725 692948 031674 152805 304212 531651 520267 566555 548938 069562 992936 919839 503208 576396 843767 665776 474800 181887 567684 049844 825458 596447 508699 576197 424641 886024 474272 810768 474703 274454 635648 277350 122420 032127 901318 777945 952422 059535 454910 506970 603122 161945 758281 495564 219971 519004 464025 885814 129819 864834 533574 751451 175404 744232 250144 567843 595005 506801 510233 834041 059924 428188 667834 568416 559212 366275 731376 982970 641453 615786 881551 562401 407321 078521 995403 309064 897315 698446 974357 602739 243242 848516 745528 409408 834134 944098 905195 879755 388649 964969 756516 920504 646926 358241 260619 713578 654634 923979 146931 369237 488110 715378 585737 011969 955989 636317 467971 511973 759770 512739 427582 917434 514325 523344 363246 436295 919034 499994 664684 984550 449331 525291 101225 136234 642835 193527 216073 828973 626679 197907 329033 228013 746856 125501 306320 139792 566693 640355 751396 822407 098586 202603 496672 934552 926591 909958 598435 351187 566178 664582 436845 842946 640037 941414 667462 286437 295512 251637 245737 594364 676017 738705 424653 710319 035578 130702 838802 266430 117256 689527 665625 690749 655270 992887 484328 952356 172482 731371 293880 554735 147610 995211 566727 215695 245050 117220 861172 321726 265702 754852 588801 452749 017237 303377 153019 196906 772776 088352 587721 408476 944107 179043 669044 660439 541830 091507 000073 614970 162437 700523 615374 710212 174636 892256 327691 101219 559527 953655 274153 799167 399022 353845 404766 576082 644874 886763 404646 053019 060264 354184 402025 945150 518299 492323 199714 638619 222928 861797 297285 264403 613423 874687 107244 133349 640578 287476 999931 898992 550804 323102 703589 840697 039582 091293 220517 042346 127265 509186 364123 545622 558035 890682 823463 622173 602187 825520 133680 689446 850438 175084 778143 392089 676779 452412 947744 263212 576735 612721 058551 148973 252425 682424 803684 822202 297268 141999 568890 725110 998373 408563 415268 324369 657438 017076 587601 318671 472245 143320 347253 028642 946010 362494 261437 622364 077909 693538 703550 761981 287915 974894 789431 030081 613044 202120 127799 852809 148553 618393 875604 768648 229870 224085 208892 761664 961131 050006 741435 374125 674167 976784 144927 938914 520670 927217 774639 380303 289832 931042 609303 483371 580327 554134 307730 871159 569917 791912 914798 759664 884869 197660 891838 935996 986865 398434 933426 305987 475858 558511 737365 112060 821637 077419 953492 244948 162740 911117 057054 657730 781347 137121 439116 663328 403619 047610 207339 497977 636232 831848 536806 464085 440089 366513 111737 032246 290172 158979 306607 315696 412140 774603 666721 780807 336872 217626 904883 551591 043768 158631 406949 110075 704115 190874 730177 422208 818624 019438 243047 511164 725955 819505 574740 800033 636987 557760 104560 438612 075070 244542 862577 176458 021448 532133 927059 722204 298359 036814 225364 368946 273307 353744 932864 / 2631 > 322671 [i]
- extracting embedded OOA [i] would yield OOA(322671, 1337, S32, 2, 2630), 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.