Information on Result #1881296
There is no digital (48, 48+k, 1306)-net over F27 for arbitrarily large k, because logical equivalence would yield (48, m, 1306)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (48, 2609, 1306)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272609, 1306, S27, 2, 2561), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 142283 720200 486529 537154 300426 902190 569254 569944 983250 878800 696722 672441 476615 393187 083824 165988 746982 937649 110930 284848 927303 283986 055938 220434 367441 906837 403697 932607 227619 542363 675995 913671 880603 085849 357185 670632 623973 155179 058335 950270 372000 535295 834652 465277 141299 131820 663293 272991 308835 883428 231485 742683 841569 399286 008668 602931 416385 645989 346972 668734 085241 710442 282382 932404 034518 595771 220185 007730 557770 958425 256848 574909 419338 089959 054563 144241 111390 224328 842569 013460 159463 370557 461017 615785 936835 369744 081553 259352 566568 207478 010254 836715 677564 306494 959163 496775 727036 982211 487024 989418 040898 612057 349464 280499 440459 487962 361190 170515 175591 857854 109176 939903 843074 873080 891951 703448 319165 196965 234932 218406 067413 783762 771282 403205 095576 527116 783429 497693 957638 008344 060436 568486 464299 962359 096544 566713 770138 407475 625330 020892 380504 903686 320781 860199 110712 158370 555593 761498 788028 473009 393597 895219 733597 746250 908495 356323 551439 977041 750295 317205 060499 555877 001052 803374 085256 062313 248129 862474 463400 314988 910725 929418 322918 161808 473937 010402 562839 732531 161245 997590 512711 112056 747170 378604 317725 952894 691498 355204 154489 614242 484341 006121 136151 618141 306521 897741 947182 257012 769751 326548 290764 970971 115449 798099 398964 441713 277877 556271 635666 652718 152795 738473 981146 217185 179486 306916 035920 567242 077350 628213 885705 835882 042007 755504 534546 210332 575120 038638 886284 106606 104335 989059 797790 576107 720192 878849 996566 604802 234969 727336 525092 038431 900570 044475 601979 045149 127882 810859 408754 535516 096054 082983 815600 382491 587814 605241 013625 920220 569438 806941 930011 887405 487524 031859 779681 716124 071138 565637 187530 954417 529921 863816 367123 086837 388652 431699 486362 692229 574017 191802 434926 359542 562999 408849 759409 170321 290820 579973 903454 154087 547639 330259 451743 423159 440675 553123 714716 967759 153578 856601 650735 571753 195815 802817 143282 518261 001081 456217 107321 043534 403534 602541 879182 723960 688071 494329 427421 247035 032466 213377 897113 530699 184119 114764 983549 487481 909687 986928 807592 853548 030604 291558 744658 667046 004735 450657 797290 287001 232750 690972 983959 236800 087195 526773 196703 200318 688314 039908 804274 486194 388802 550217 366228 723035 038778 065031 928270 188690 230510 802122 277175 554092 913445 682376 221387 980162 647485 278105 338680 986906 087996 572832 898191 166144 166585 384527 278508 556784 015137 342276 498197 922909 876601 773859 315523 599919 748719 475017 553972 022875 500114 534587 833041 470856 554121 019423 697627 545513 266001 949444 151634 263004 065934 533534 692225 331884 766418 858226 250989 542139 725724 230154 297472 902418 340970 787861 275258 453579 132921 650928 058683 264942 745199 774165 976615 168066 751268 864963 464437 019064 405608 400272 241135 029210 738803 324545 931169 501481 727314 268609 432593 904436 826001 917889 636471 748060 093153 898086 937855 630380 750945 692589 466243 883109 219407 264765 883927 510932 239342 191833 140663 206591 119355 244304 202462 256574 660333 330363 202270 994305 836699 472398 963341 251659 748090 647203 005736 872501 827582 369959 021119 522023 560926 792712 945434 441715 443560 887720 720764 634849 722334 264441 938317 697206 525852 769700 242186 371306 306215 567674 818782 348621 696919 329614 881458 335436 188870 052830 975530 927783 492707 949118 117559 399666 445071 035858 113829 161726 741478 114801 216888 330839 952082 753319 534074 183567 840329 086236 225551 536671 966960 041810 375522 712947 445458 487539 698396 363632 879407 965621 884264 872849 630575 561266 626622 414124 678988 884157 773827 847341 535204 924859 893484 211030 060327 434457 109103 918258 404330 764079 624784 521655 386763 968872 356210 706336 798244 082917 097906 643389 175273 180941 150258 476642 728479 695266 973350 048513 966491 370296 874365 909475 422449 920933 751757 664110 488944 924008 383961 135267 576703 301799 665252 339758 463646 365198 982349 405004 699102 302032 052599 809394 374947 378237 300786 509143 633431 245002 338294 316295 379422 781407 173858 408157 944540 356770 983095 747847 466974 708875 403096 424667 980097 / 427 > 272609 [i]
- extracting embedded OOA [i] would yield OOA(272609, 1306, S27, 2, 2561), 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.