Information on Result #1871780
There is no (56, 56+k, 1515)-net in base 27 for arbitrarily large k, because logical equivalence would yield (56, m, 1515)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (56, 3027, 1515)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273027, 1515, S27, 2, 2971), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10193 585363 403232 514646 720775 059147 068261 076947 681705 343024 913051 108486 198361 409967 686952 638287 607907 518405 794131 142437 380911 817416 244470 005701 953840 717825 935846 184506 477196 910299 522241 944542 158428 126282 221278 806207 383988 259595 754258 750108 428184 364159 529170 675476 367719 318923 114250 521000 425796 427258 786051 229355 040933 796020 743337 472200 132002 962118 903784 598304 663974 494531 467264 917987 376174 154201 725140 476632 528683 889651 511174 356228 698400 125888 934387 406368 403034 676390 587486 030988 937120 827596 600913 308168 433845 179906 036284 101846 940301 509594 496183 421800 738334 372729 450700 279512 954413 623257 411218 636678 208830 326795 324351 751319 934479 009838 862372 460066 276301 220132 230914 999511 501391 604127 699751 702923 474848 440400 057071 382544 147432 526827 546044 823088 980863 580929 489529 835260 751167 251623 240764 423415 086117 443653 052005 941730 544983 296567 961489 536889 286171 408235 325676 377056 212925 213490 836268 590649 290331 307307 394658 610646 878652 991212 565700 550680 658017 407587 463937 191680 463749 451611 881259 510569 335032 419357 066463 804183 361938 649046 722747 228261 978194 479155 907198 723595 180653 574835 069892 828878 567870 929783 917697 530844 477601 772928 101307 866294 394299 274909 541755 643002 574541 367827 451640 192457 377754 245061 365359 885866 186119 576784 458130 682658 017848 756391 235311 154533 223466 720188 271731 261801 672199 413481 939349 294873 516194 032659 337255 857829 439192 027537 840362 567407 194413 656029 578459 381231 458321 051842 372552 501367 484270 646502 778129 409768 931024 339062 078955 570401 280731 553114 698840 046119 764631 416732 385502 999282 455320 311224 207637 688779 496802 101356 596808 083290 292039 153228 655007 905545 100528 003931 605870 211273 729452 292669 459086 234041 979095 402420 015913 913993 416439 587102 471858 695374 522680 792040 140204 968917 859991 754036 944912 025465 932556 122067 098552 586968 836074 024727 593708 953192 168313 037515 247211 844726 963945 250288 302387 294416 043526 289228 212178 992921 985278 606827 779196 407481 683628 447346 246303 053091 685059 931914 649713 671679 987051 043626 847715 934334 978557 342647 696384 692590 850177 721634 545830 565541 122237 413824 344362 473662 490135 883907 015536 183836 541523 908048 248448 573677 883117 975102 450261 922865 753320 047480 578992 522625 050309 929584 097053 116445 732469 725422 430440 641021 293652 530070 051922 597370 930330 881742 431031 652497 205110 701611 305504 024401 193062 411071 506826 567249 723402 107005 089706 163066 397380 065561 753878 421937 607826 286887 008445 597021 390360 812065 160174 582737 215382 862857 165071 143092 018405 115002 263133 506540 526153 555658 226529 806356 753072 580622 051923 101378 080514 077045 235376 125301 250953 511793 827689 763525 251005 824737 338445 518397 722056 299185 982373 760546 236103 687206 760310 524485 108701 241866 149799 866562 530940 850039 903965 067296 641881 752853 469486 953958 127048 481750 537657 661703 143638 920222 519514 261002 243820 771754 533660 211120 711708 761399 442230 379320 239059 367478 990626 540258 607364 209966 494977 081205 075895 687799 123206 749638 742858 015928 105066 138173 337189 892632 810952 363210 897130 796538 681338 683239 350174 615499 986705 041964 789690 815402 103776 329588 449225 449787 209653 710665 636709 314973 722697 688286 566647 367157 210181 203917 199497 755625 846135 664048 385048 882767 195699 453996 698810 346417 875740 221280 159165 204900 697372 705392 664316 119525 119055 867040 685369 684522 796698 785974 241638 616272 388533 836103 272293 853505 101088 807347 077851 176148 406250 071360 228010 629234 555291 190811 453847 366280 251214 175533 106574 696604 139155 486375 737642 550814 057682 795157 156577 177650 826965 886364 512040 397195 131947 076707 039407 988383 230276 042391 280433 652117 853722 315379 438923 816719 137851 453577 049790 144537 889322 646973 190550 661306 591436 208701 096410 731106 348030 643570 460098 716025 465306 306252 677592 927234 564483 913933 503837 145187 115666 083836 746621 124272 666314 488124 674892 281071 849474 635879 837826 230832 461480 135201 230767 356244 420399 054823 333595 253822 220039 428415 561913 401513 226314 515734 078575 606972 181612 502039 904782 995858 241722 012900 730287 205925 857271 391344 396905 583627 044133 800511 213454 965611 134256 253838 173810 330119 193061 228386 451153 552305 989385 654835 721145 951367 177693 469556 345230 456692 174981 178549 153156 659267 729445 867342 000772 654993 574849 206445 548117 369109 661577 912819 455613 062870 645506 592993 750928 728113 729828 720910 302861 300545 126743 784700 980558 659401 346133 891724 718497 168468 918265 469023 706097 845839 458795 623009 780763 515836 152316 425124 531800 819959 374170 978881 676790 379033 680452 605296 549999 886800 470731 830601 772471 719922 721948 842169 871298 054176 817824 227046 579665 239774 085270 071458 715228 986038 774882 676588 576205 045343 511989 / 1486 > 273027 [i]
- extracting embedded OOA [i] would yield OOA(273027, 1515, S27, 2, 2971), but
Mode: Bound.
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.