Information on Result #1881338
There is no digital (69, 69+k, 1854)-net over F27 for arbitrarily large k, because logical equivalence would yield (69, m, 1854)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (69, 3705, 1854)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273705, 1854, S27, 2, 3636), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 658 872534 390462 329401 659384 788227 621007 241018 843879 987469 898038 733014 101410 050803 139178 854932 943282 855101 928821 400075 555332 465380 436729 705742 114078 436580 146303 270972 156389 590927 565032 393198 147437 527109 295069 426866 039281 309453 208509 337677 834265 084735 128558 133107 375640 049938 911935 946894 033515 858568 850052 438926 544757 420880 297612 957562 395315 122363 539317 079961 035323 318740 513552 050031 060363 452755 485273 246268 090190 969694 943142 097739 246491 624776 239428 679129 581122 422387 143914 725694 522824 354476 399711 239638 958099 063427 000086 273494 382434 701654 900280 103445 603694 322896 303246 811172 005628 703839 569971 549830 537020 712634 542315 165879 326276 866327 554840 503224 462219 376004 993835 884171 342270 943901 232451 771224 316974 159936 632395 529511 755884 221392 404218 276713 939462 315163 198726 052301 280207 533508 205659 011606 268563 789615 908274 902022 083382 419481 911735 026331 534576 487966 841420 116918 189381 679511 623533 374781 535612 216319 637740 636060 261558 774093 419724 903658 782601 875621 683749 507871 747550 373588 584566 277774 372578 486619 845874 015243 498869 952467 787827 099231 825167 220938 340721 345807 506157 913866 781628 807133 143468 836869 833673 471954 753532 743352 134532 286613 749107 904266 976194 761749 954006 897882 855183 440525 329414 767099 717095 216430 034307 800420 329224 579364 652939 225015 218245 191156 854646 498173 411051 207507 301573 089848 256742 474072 159158 172684 867667 923880 366230 671250 176277 487769 887851 243271 377189 979543 150738 343310 730562 866905 703533 354131 910064 460586 781324 226610 821377 083665 069364 234299 277860 436244 503586 119947 278244 746586 923613 081953 100676 396437 941637 786575 747920 786560 506625 684094 009272 881640 123156 299677 164093 292832 453641 676033 836922 826641 598057 295353 832457 529769 124554 533052 126303 354909 459093 797213 833497 402633 295178 128699 483092 818271 152530 670464 063566 042652 854909 807274 922633 875130 199413 768823 769652 622798 829623 142678 064730 067387 478643 331530 650747 457868 552984 003102 675959 483857 500213 882879 092673 956834 102940 182479 452467 042128 824989 661782 515561 547387 071361 219374 129269 570730 810023 403186 538133 758000 297222 765459 559069 495696 779927 532433 326684 231711 466215 107810 920084 324098 602574 771914 950491 133447 271623 422005 248751 502268 944694 458742 268702 879284 064958 062260 571009 245246 500730 565972 474460 430291 671853 481003 868216 895840 762239 901069 883667 967637 730393 008044 226465 051047 053306 391729 102124 652067 660405 086267 837390 830960 756493 430453 287918 942117 876767 919287 706017 105405 074531 953121 873492 710538 926721 806431 628954 348934 930593 732951 363292 158799 426700 952566 568784 201137 540076 973192 226419 256753 405164 788180 878661 425546 646275 125803 910066 338450 717132 237790 821189 835470 376396 380081 634655 286474 154447 816759 480899 395972 728127 113167 278192 888281 131779 253622 301161 852357 109950 483607 396196 892415 623419 386116 809184 339054 619197 796439 625371 756330 586251 538161 494040 957074 210737 613008 457738 707828 253644 229633 207630 641698 120695 181727 841500 123651 094260 629193 339323 999107 869988 079433 283753 838175 380840 644243 739355 769430 466931 381318 816102 727002 651103 737970 657448 793697 434574 360452 120651 926178 057648 294930 169872 709082 590568 686301 855253 432154 225241 496431 422831 302709 272670 457079 798129 972963 296875 897187 698091 694910 113037 676578 733927 053661 752610 222048 086366 119461 493959 631109 836842 804451 627803 005040 548734 894314 428886 084314 943569 655044 722109 099991 970874 792361 558573 894078 690028 187332 751817 141978 331612 053097 743923 326556 316725 397372 495910 312856 008850 619899 906509 456726 866488 098012 584110 053044 744076 704475 878600 373180 220022 514671 364909 941028 482056 414678 000404 787507 681980 500962 477616 350636 747107 378231 921178 656863 226372 521327 393409 273569 278049 727442 387983 492690 617479 880254 196469 362142 096903 951607 651657 253857 217029 305806 753342 298172 669216 420391 825539 927043 158266 791996 590317 573797 747078 759494 842513 707155 550143 495983 081612 636379 894648 099584 267935 978048 297372 152682 560505 419929 209966 837847 056744 614993 382677 764995 328248 652268 343295 839351 353982 082817 421737 895932 699223 000724 575529 022748 090355 485874 051517 860626 649283 482164 851737 482008 889925 944851 074103 624566 818817 527974 148709 417220 968046 077948 609374 240818 665463 091790 601866 167680 865656 741778 737012 805231 822635 537545 996071 728381 181961 097202 090807 891607 631741 502534 440614 965505 708861 925283 573025 935544 926915 316661 847156 054048 752472 096509 050867 779619 779036 375050 324980 785774 492519 814919 414232 039494 793964 793586 834908 257019 152432 487747 376306 032099 647862 725742 847353 630708 769777 131633 726833 083234 052700 876693 973494 796624 893077 169334 969849 630512 707846 693880 809513 528042 189600 370889 569757 341022 846443 935731 753016 890654 423977 979392 654913 685771 687708 763279 073913 896367 596821 701512 892955 560179 016348 540668 952182 019949 539429 053450 503137 407951 030704 541214 735707 238506 807222 300865 364960 303283 306959 940386 441516 530150 397871 141373 039843 934848 615341 342362 022442 642043 055093 077281 269859 101300 379193 436371 473522 654474 874972 792147 374145 772242 044443 165233 464384 354408 215491 952133 961691 099824 553577 719268 721886 660051 253245 293174 621460 077628 799662 349861 291388 495889 214669 282842 527165 287135 767576 359025 030834 331607 349125 796068 285523 605155 153448 192515 248256 438733 946374 169124 911791 801347 801378 921257 876044 396691 420273 398482 542195 680078 277721 318442 635153 580022 671717 510010 542198 602551 214448 260052 989465 830761 702787 432968 536396 570755 390871 842817 242306 041243 927767 487252 713912 470353 857117 242352 181408 565321 281596 260314 889612 606124 013007 162890 182578 947830 163702 302400 406786 806036 762665 790127 043013 613639 172933 062334 057090 497689 918347 254854 504540 712690 948817 / 3637 > 273705 [i]
- extracting embedded OOA [i] would yield OOA(273705, 1854, S27, 2, 3636), 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.