Information on Result #1880986
There is no digital (44, 44+k, 1110)-net over F25 for arbitrarily large k, because logical equivalence would yield (44, m, 1110)-net in base 25 for arbitrarily large m, but
- m-reduction [i] would yield (44, 2217, 1110)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(252217, 1110, S25, 2, 2173), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 351266 867314 131101 872698 397703 712773 914095 496840 845139 816340 084032 253057 567612 140629 439137 028269 467619 940687 801896 559635 761738 151273 063773 563776 498805 810800 420730 145336 778025 380518 328907 887057 102931 013076 629846 100214 397900 930867 617130 819775 707907 190070 785755 729425 202443 864599 089617 057440 164716 306448 387149 474429 383361 937156 239841 511594 827188 332961 555223 911400 329128 033907 474489 111406 112111 902501 577575 426326 832516 443664 898639 758559 321723 880556 710380 719651 382066 887226 214186 243488 815895 960142 391697 250796 157997 067915 625619 106958 651055 796969 303194 169607 211690 795058 463358 322341 193933 663171 401721 742122 896281 559507 951828 085209 928219 640585 658673 604866 540557 465376 120719 775174 350674 462033 340721 066189 400140 726975 124740 109023 858721 987780 982813 694790 595792 024040 660942 444969 038460 357096 991041 815858 759950 789469 988554 128134 126475 175652 074922 849997 286711 685843 086292 970312 024768 949263 432267 703197 115803 596349 837837 335262 387580 068828 591676 434517 277502 323055 321521 352081 613700 880376 782489 941854 707616 934128 572807 289406 757307 589183 051066 745278 528759 861237 455047 627826 160083 474583 546906 882576 065150 718818 761940 234006 429659 080514 458391 197782 877127 102323 148942 190777 904354 901353 967668 643248 065293 451759 785464 760644 461963 779659 594446 723094 999926 047547 751152 199958 555475 928756 330087 947655 533790 240123 775250 292769 047432 184271 958586 299037 598726 378170 205034 210590 152787 793218 359470 165884 532373 609304 190152 993369 214400 858602 716420 614760 990537 608277 910849 014531 487700 284202 325970 947979 965862 942145 031699 381898 240451 626964 270981 986680 421681 549506 839721 059373 793168 192463 660424 741260 830195 485338 031836 840693 054483 709143 696065 233488 613017 907899 469875 517704 348922 710399 093586 472930 305664 949360 449440 382335 015485 585953 021762 127231 183239 863252 231985 529776 336774 821712 191897 337189 062999 585286 248926 132406 913339 916456 795026 908763 470807 627622 793187 825157 217361 567167 160381 717458 935698 540601 205469 172242 615252 965971 788917 386762 696882 925508 251922 159858 585935 060663 528692 901828 593281 905936 101349 647445 103099 690358 142029 681727 413655 015619 088529 515535 337981 604122 669628 689349 269749 588814 062771 490753 967146 427918 995497 055092 861445 771837 128457 738518 615839 964629 469680 246296 754843 498936 569110 885503 956741 457783 446982 863798 504773 510138 627443 302359 970384 572319 236816 134986 715738 428335 743852 295467 737008 937624 833280 610795 359326 393284 148391 213326 547256 645051 917418 680166 560874 459336 371785 915963 702264 161949 751297 021436 174850 283736 030286 877836 363500 339819 885517 140340 739446 800213 144078 745408 887910 056569 824823 595728 518800 224801 551116 797294 384967 038252 248988 052940 275728 255271 548636 815470 720039 289460 864827 621293 579190 021986 180019 934417 520470 741241 758273 918090 141325 796720 196221 619327 353691 172613 605162 142587 381217 233263 117498 025815 078045 131880 695886 097546 025772 752171 106460 033614 066150 324295 237082 709063 506812 089232 518001 493169 666868 572883 140873 990310 051524 788809 052996 229623 758085 976240 165583 148984 212434 171908 280105 709950 275132 858051 863515 906176 796223 217908 939845 009065 928624 526155 721682 585688 608374 839108 023961 002539 154208 465297 258192 575626 362644 929801 106604 323620 851029 662153 355951 992110 648435 325612 713719 944935 064631 863497 197628 021240 234375 / 1087 > 252217 [i]
- extracting embedded OOA [i] would yield OOA(252217, 1110, S25, 2, 2173), 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.