Information on Result #1877389
There is no digital (27, m, 2296)-net over F81 with m > ∞, because logical equivalence would yield (27, 2296)-sequence in base 81, but
- net from sequence [i] would yield (27, m, 2297)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (27, 2295, 2297)-net in base 81, but
- extracting embedded OOA [i] would yield OA(812295, 2297, S81, 2268), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2208 011562 418339 492393 286906 212471 670359 514780 783529 649597 268467 540147 231794 937501 691455 471605 977518 520633 098155 309480 222614 604910 859835 521274 337713 972046 676959 542092 670251 387926 386718 113923 498352 587036 736053 524410 144298 760004 004973 608333 894800 056301 539396 826081 498487 790778 413188 216623 576525 915116 430294 840276 269300 324752 807984 592267 900826 121157 505061 902988 414869 742940 105533 639606 032790 138308 671674 725343 844116 456998 456402 487617 317546 302686 313773 395896 399060 442516 364000 539832 396651 920056 408446 391598 445393 339757 552299 478363 187324 973213 625952 892204 973810 211131 486172 266036 737210 937184 366772 325747 386672 023731 453844 631296 781736 407611 770137 211224 665854 337852 122142 353019 790475 789499 427417 062416 900709 906825 917123 903656 279646 263897 165848 773325 756671 734667 764630 915926 649195 999387 606626 777492 094510 079064 545353 469160 034645 533207 419386 370653 112037 700143 003193 432642 454801 842155 349905 701206 050105 369089 178448 043530 453216 813459 911913 493713 877281 991067 151380 590508 738860 709952 925226 990209 243142 183326 680367 518381 918208 349609 277577 946613 018978 024322 932869 255303 309871 715652 167668 226375 033379 643842 046811 038489 008854 355126 408191 371142 017371 489416 306096 850160 759939 587950 976974 027864 830410 480133 447522 191961 205058 295632 159312 256818 850162 587859 002701 552822 313743 852408 155105 332237 965026 029154 644621 948644 092320 132737 001824 380855 717726 790774 457225 618329 606493 650424 520556 410662 252572 786440 617407 833663 502726 962978 918094 541807 914544 478635 067016 408047 675301 113848 919375 300983 639603 091689 771205 821045 456626 731709 260083 318556 514927 874864 022036 938206 967496 215733 182581 650809 752918 046262 911203 839941 083057 720882 914627 897683 192797 710879 747619 226245 991849 840557 308767 907687 548887 586912 736382 867797 874951 155210 257985 270358 300098 386498 549669 994729 205872 726188 734101 335455 324593 821193 996858 707600 284027 847055 739263 568198 690771 669528 771874 561277 295334 621275 455703 861071 239491 581043 961466 421522 286789 137369 310534 508175 091957 069613 110056 551159 279696 667633 549996 532700 446880 288215 206988 477678 064907 218093 883267 285473 097754 299226 395967 932926 258694 411445 740245 574045 068282 514788 980990 599299 617455 855571 360174 208481 196438 737888 057884 419647 909958 844947 632631 690546 103136 864134 218785 249100 039997 748787 866646 803321 099587 450532 050534 714619 217714 349951 934994 244262 458040 146807 788396 943200 930661 071369 717853 182633 241754 419361 574679 599304 072373 806410 150328 400293 618770 900376 272129 917903 391013 018324 245828 272395 857099 000853 262583 727319 625688 838870 905946 032333 173526 521178 075270 787798 070345 343481 076490 098290 767583 575784 489583 737276 538001 600563 900826 826036 511157 941493 887851 254240 594992 111585 770362 709032 723435 227457 490654 458383 029279 789494 135935 668433 212483 761499 272184 518188 464691 682978 800160 654431 478714 620864 927928 557203 615286 788816 801217 115369 225439 439439 473090 189992 321363 145073 577552 871269 188092 501587 843232 580210 337782 294033 608325 997809 210723 622183 014724 819651 033417 765357 287339 348438 915046 858704 069853 443287 567748 989059 447087 977951 585579 937431 820806 569554 458998 992825 023022 198866 355013 838993 877464 593003 136388 282183 120810 856796 482619 891168 484338 022959 918744 456936 243159 261319 489998 607892 333317 497875 307836 201991 523048 406563 298589 094532 095663 894422 510152 372892 641280 982593 910271 850346 444401 779200 801815 654790 594670 748711 469682 938261 918869 712338 540301 818623 958219 432243 799334 740865 956499 899768 925379 092972 353325 859728 566828 683575 964685 118782 735926 427953 828845 862975 257382 724423 755159 004428 545510 512545 661067 654619 628166 567506 688204 740922 971239 311396 458210 239302 435963 834239 123727 291596 906118 235989 999556 813000 281689 900922 731202 943146 071294 807024 006899 662783 729735 304137 430277 153720 834554 797764 501900 154545 185414 183567 712741 927778 876290 152979 056513 917022 227780 918060 009363 205376 030646 670082 258388 052648 872033 694971 259266 971084 050555 897123 005417 300723 927532 319771 203275 323426 525602 806474 020726 696299 198397 738854 519076 633241 144475 774445 826936 054272 453346 649481 923230 278049 997616 047895 573906 638502 418120 548330 359128 641431 436826 326717 009146 184847 493960 196334 961034 110037 934469 998926 854289 852714 137276 903137 355169 268350 251899 072477 608011 719523 573555 079893 068884 554284 852579 478760 831468 804607 590191 133775 354283 355295 646843 783170 901412 440262 728170 719037 305106 453709 475050 561133 993574 431947 675946 815594 201688 509009 981991 983725 313307 296288 968727 126677 601983 042824 495497 848569 184818 825904 012174 534001 555910 632494 674409 462435 325716 394497 453699 986888 771762 433865 254542 989626 420949 846149 396751 249865 220385 856043 725718 524106 062749 / 2269 > 812295 [i]
- extracting embedded OOA [i] would yield OA(812295, 2297, S81, 2268), but
- m-reduction [i] would yield (27, 2295, 2297)-net in base 81, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.