Information on Result #1881318
There is no digital (59, 59+k, 1593)-net over F27 for arbitrarily large k, because logical equivalence would yield (59, m, 1593)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (59, 3183, 1593)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273183, 1593, S27, 2, 3124), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 78268 830819 704416 044951 660633 798075 841777 822540 095325 628462 193302 644081 759217 040955 211522 853013 290684 038477 307591 343701 374995 022220 051386 455130 871205 872452 315672 351942 413766 437318 801384 213722 710110 318823 814448 689713 587346 609356 106689 502062 998968 349711 480661 193443 727271 274481 721344 724449 985407 745604 904463 918375 356122 160865 257502 205332 107082 521044 343066 453204 348946 545100 449265 204872 739824 459795 687144 818190 268003 081915 984526 684062 354046 254284 730676 215691 783862 887799 005295 150699 078444 422006 619296 824753 493797 323768 687520 379941 432860 695676 264934 986587 646375 558538 507591 896826 133313 233059 460945 818896 364550 176342 823240 052908 674427 978726 548143 648640 718535 355270 473389 371080 379651 945678 459954 052334 287666 835275 086043 378710 049731 401029 595646 519284 921549 048973 087437 166633 390404 278903 416274 136438 013868 050072 923539 557635 231271 763950 736681 949578 944632 672081 089194 961350 676530 482612 740480 296501 195029 623061 861891 473219 256591 981133 802247 193376 275433 377992 036664 848106 028086 556454 929395 967561 040535 839162 641230 105254 008510 764300 586004 010516 262630 752541 698272 855317 364858 537915 189724 884104 551341 166662 962836 290833 937889 091010 257039 976264 124986 374082 658547 991235 767083 823866 598356 050775 359025 212774 874088 875991 284522 000132 532914 754515 577526 811175 549825 096869 314830 026811 430071 901575 191608 530676 371085 121668 092113 013688 224000 083816 090812 656940 962568 998544 309350 664143 776647 800078 330584 380868 208105 767112 970821 875134 837099 563157 024372 126640 359933 387594 404528 764101 174433 292093 578128 910040 092159 755219 666217 389251 723317 951723 323517 074772 818448 394568 151557 541852 402227 318972 149754 336202 524133 576483 554780 621686 985817 431699 107673 733908 730007 184504 024945 870733 122718 577873 859439 203050 446749 833901 421621 354259 476027 455696 684640 531006 860516 921678 006099 584547 493261 887578 021695 075387 601864 106875 980167 191315 085453 161405 327782 056989 618799 880640 581841 418657 074232 837109 539082 717668 725860 897808 396636 279980 750898 375880 841030 362313 300648 397592 430681 389788 243383 598836 497999 628224 609618 697612 035056 277914 013219 351780 657672 641095 031817 000062 320568 669666 018688 067361 698846 066120 693005 375695 762340 610784 776737 609749 088014 995979 172795 947571 187103 247856 045638 144726 993897 594244 922383 656388 088427 503214 728005 232658 439894 967496 208438 017203 760549 661695 738718 992104 160665 044809 463306 111837 635070 252603 654709 210163 317292 147917 231894 543156 748983 201724 537602 063722 401256 002628 313825 022820 064156 441547 565492 215112 527750 461839 054502 766203 723630 110938 537361 360463 332407 876959 929640 527801 893991 897977 886224 123157 439666 911822 318689 783733 771577 128394 007099 776790 457035 853352 392601 926258 909365 030284 146739 220049 254303 643467 827462 427756 006014 887414 238181 640221 441382 953514 819962 860498 247961 955993 191278 419932 728082 261807 078095 125919 508905 536407 223560 095454 932016 156290 383787 216924 331413 297350 570552 883571 538344 751216 572444 158003 728566 851263 276504 238983 006992 680623 473093 833491 203997 539663 329883 352311 975488 678668 991045 661094 563837 867620 280727 054998 019756 850991 704528 229743 357632 481836 100737 493079 304669 396441 239237 438608 170856 712743 648774 567876 103212 156752 465176 154222 096862 619445 658111 712361 602956 210160 620407 057099 696390 141492 824153 785975 800907 404225 983530 254963 272410 978162 172304 060019 466970 237597 914533 107066 161316 317889 166421 275844 222885 310132 481229 174043 492409 378315 447584 972619 152875 166085 928385 967899 839834 608069 336447 557996 947957 036973 090998 068797 696406 194187 199348 744078 585298 156829 871122 967314 875121 643234 897751 586882 526623 860420 068820 344585 845924 134170 364527 244540 350512 728819 844040 987458 997974 265388 658547 802261 281410 394898 279824 960830 857640 601556 287272 097845 987678 380953 044690 373922 157352 223244 313849 352146 864285 578485 754468 561437 006497 518835 406811 443253 168906 590148 203820 223147 483014 565649 112823 941238 140614 848430 083999 887521 079681 850703 568780 445886 343675 001848 376868 174555 824965 753643 823451 091320 255275 074404 510963 691075 407273 589346 517723 742295 357628 472105 719921 544621 256821 717184 489492 547699 008348 101552 892419 849043 666415 327614 184199 648870 176329 449592 742691 958534 556676 489920 141469 955585 207823 916885 467935 700069 694609 500113 955150 799065 551230 728676 212683 065340 308922 292251 071839 054349 736441 023245 080040 717425 979314 769797 004348 641206 212320 306688 707337 028538 102069 627268 208457 576703 639848 994455 398204 813390 883506 586365 920322 205421 062792 908542 935768 568636 591138 723802 078171 706194 043486 147515 705946 945789 582944 764637 910949 306241 130993 952871 229036 029827 546998 304911 096894 538061 958674 946793 801929 768376 777336 846056 026684 100499 481055 879665 292293 422531 362765 825714 640617 747194 636682 000102 861880 406861 035176 328719 204511 150051 744308 817295 674886 722470 192060 812376 447569 454476 024943 175505 755588 300507 / 625 > 273183 [i]
- extracting embedded OOA [i] would yield OOA(273183, 1593, S27, 2, 3124), 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.