Information on Result #1881320
There is no digital (60, 60+k, 1619)-net over F27 for arbitrarily large k, because logical equivalence would yield (60, m, 1619)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (60, 3235, 1619)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273235, 1619, S27, 2, 3175), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 52 386046 148079 643683 671577 877171 506037 366483 442942 164946 451317 542390 509999 252231 162294 570399 229058 023129 396454 703319 379711 037732 843095 635670 219981 699612 340508 047624 393059 478828 977067 386064 973488 534866 956330 647257 615806 466614 174584 614950 494220 212512 721085 903300 762472 422131 423529 273974 431131 265007 626854 322940 905689 881196 753259 989478 586468 420205 494280 751978 040712 219793 845209 784908 832527 979711 225689 763010 375246 966962 365703 051563 601447 295795 127163 305112 119535 627920 979371 291722 818935 265606 305964 433373 063220 909810 917297 521956 997166 107687 338861 387808 510587 915935 284578 022606 477266 316515 671477 213654 996495 042892 614047 983037 076638 516002 228070 598408 000259 580262 477146 046604 135609 427508 731145 977854 439107 400058 367805 822995 628223 815973 009239 270670 769932 125967 124310 106704 191785 167963 828094 802650 358364 730651 961027 000741 349356 185901 618499 826728 761261 099885 132617 519224 483506 315618 666364 567303 954050 603600 750845 770837 983589 261277 662824 429555 336689 217897 049498 852991 050597 254096 326792 289719 474665 670228 236642 469540 565851 592299 942079 415840 255183 216620 621872 793127 260214 660920 792159 908599 740422 681801 571525 066824 498844 337158 207189 920690 622721 417978 349858 365700 038764 977248 364901 789665 101570 162025 499639 900223 896923 970364 638661 449342 228442 061318 025052 951282 111876 565268 140722 734431 951938 166294 599336 185886 473985 974289 141934 312564 530698 210697 702861 947564 555451 103486 203715 901554 331788 813242 034053 581886 816542 668979 055816 305560 310325 581990 103454 237625 388966 065266 260316 124811 358739 706771 637040 285665 444177 258523 979150 682743 516443 794840 267273 421229 498098 988646 965225 761469 324943 920184 453363 704223 811317 115263 309207 670047 608380 409934 856142 670211 126496 741305 334318 720506 773373 124322 926175 039332 634546 114170 886550 630643 002098 309457 883561 664929 430220 481032 978478 706207 927267 824422 977491 822776 144695 987824 993736 606519 115007 062267 861719 528140 918029 841447 052940 058405 957775 241043 834578 260261 514627 687346 395400 616567 555657 273295 333310 863845 881403 044514 127019 380860 017201 121491 957218 077893 657553 941888 012702 320079 334399 307393 564965 473875 360797 919650 719979 274263 188387 494842 741548 570470 670716 562008 071104 834201 075860 094983 767837 588141 486905 796249 558171 582627 649578 136267 411129 812270 502931 100283 384640 140928 078651 516872 411157 780178 565499 727043 081594 923728 676098 716267 909844 955003 661225 417876 346216 956676 997773 102220 978227 373607 581386 861751 477429 373467 147540 513591 534927 796741 101374 129312 822811 476380 340966 632513 013260 050311 077216 411214 942226 172249 778563 534059 947553 269910 250228 315522 375504 776959 562610 304729 362614 831049 768523 256620 128630 164222 281896 337694 686016 274296 938710 050890 528163 406656 177249 249008 014515 778497 244050 989145 824717 293585 453403 573892 825996 360230 149061 100210 026430 452995 804811 466613 107492 660847 206832 461420 683159 274595 237344 293117 356385 892823 471411 703129 833599 150393 795965 153080 289630 644700 505059 079466 942118 726612 510529 528947 295935 852898 660053 738657 075846 304942 768839 885455 448216 806673 634700 608624 516873 360487 300383 695288 089116 221021 485464 640403 914705 744310 483531 590349 210050 057577 795310 322041 749632 466233 507373 517068 078115 889656 215038 659683 047744 995745 421350 515813 924380 241876 515925 809212 073295 418578 687276 593816 598154 470615 013075 630819 003586 624702 280816 256778 467097 213047 406811 832886 286704 024544 011796 409822 129973 682316 239638 474208 473846 502691 472268 904323 686965 488781 130722 874708 387461 708185 812326 097947 738992 077929 594521 082297 085935 083519 867612 855047 167542 737840 182105 688471 617383 164493 953547 107267 150090 545093 124114 439604 384386 452051 917972 399257 155237 412246 583443 151450 535137 477652 787504 312172 161896 474045 969196 693798 757001 081466 922492 034721 406205 925549 876799 590959 928005 100930 294726 536726 363424 045622 510905 463781 807072 877476 063332 381828 185839 611383 889588 891868 272543 440484 559095 016460 695574 887601 847484 678014 706880 353103 658729 733835 290034 295819 274677 754888 546146 620699 828293 923885 487570 018132 847899 161779 725010 212763 557764 253351 616722 200967 379045 217635 430160 377285 863024 579338 582689 029609 835599 634344 969396 297276 177501 686713 484876 234360 737501 790372 361619 125938 923027 598217 417525 505564 375696 238618 152561 094242 267236 378289 789826 921106 899636 015759 928280 429974 916495 856411 141493 199081 357625 150362 722416 601628 363551 047729 271613 403957 540871 121818 339362 174224 436144 660384 053176 811163 653748 868970 065381 998975 034838 492580 833937 052046 837100 003326 614000 381476 014694 992657 211451 320144 480603 198803 690734 139759 589529 586867 713312 303221 351923 772669 709767 872046 609066 621240 606426 911431 791413 043346 842574 329427 573279 771291 483894 482076 282814 575711 169700 592902 488195 980592 778337 436025 724853 778932 966502 560254 496782 563227 322041 760088 373677 111893 561065 692306 487004 076166 121788 090610 491725 468523 275449 141752 441041 644145 241533 519036 657839 466772 516624 972369 597587 / 1588 > 273235 [i]
- extracting embedded OOA [i] would yield OOA(273235, 1619, S27, 2, 3175), 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.