Information on Result #1881272
There is no digital (36, 36+k, 992)-net over F27 for arbitrarily large k, because logical equivalence would yield (36, m, 992)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (36, 1981, 992)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(271981, 992, S27, 2, 1945), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 397678 540189 085274 088056 630147 586357 585346 597800 473620 379552 119687 951785 629661 202338 867462 709038 706134 623220 079433 174977 298552 939902 217385 466725 456402 567105 164537 470365 190741 285235 087585 197121 343278 704222 195487 180043 194805 657700 468282 024005 206569 979427 186264 291734 603855 445208 043780 583197 560060 310328 125169 598631 257997 328795 192143 458533 110434 147417 169426 237575 920206 013231 949722 299871 218600 201990 669681 365387 657891 965742 852303 098224 457690 731387 289921 411924 029149 745999 973665 516136 931917 038039 923064 326380 510712 966527 036347 904528 235705 107093 056918 371501 978674 332265 756348 409736 208796 991069 098008 233197 714005 134770 234388 648970 009035 106009 076178 151723 060493 931606 487321 428608 405532 607452 845051 176302 495168 282875 369377 486227 983943 203081 538390 926217 132372 804817 093411 742660 749985 533949 502607 816271 590678 213320 229015 685682 380793 159934 337076 596962 880631 267081 995107 189140 462567 341236 703637 717388 708808 565777 070942 009968 734446 550745 577572 650597 927027 859722 000860 053106 530213 932961 887653 059971 246058 899859 406966 809398 898272 452609 197752 379359 458206 440362 567388 883158 418854 024441 925812 555205 580012 594104 832586 223162 447869 318603 992366 341657 467877 791961 379549 291037 828213 264703 575853 094632 412454 982011 751971 602766 170987 880295 471847 129544 701502 433114 917900 755832 924569 219113 942797 008771 606310 191256 681537 266799 495908 624279 516449 076798 974397 614864 671612 730901 466755 736602 181834 207930 528370 653169 458072 798102 476176 123392 272155 173722 087678 396005 561636 969024 611282 194337 621132 167107 285911 494987 850230 886106 399171 460486 979541 368592 720349 563078 791064 131750 942799 212501 658921 186766 647434 552485 627427 000128 310422 254489 766085 525990 094654 690478 443886 429658 930706 456096 657702 722995 064773 592699 720906 033669 650482 276115 856705 735444 118087 796619 129493 503555 078469 799759 031652 085503 219149 773731 853651 120897 401319 593601 056492 840025 236092 040166 006296 428435 771643 870499 007554 600330 309066 723189 946354 281937 791322 161876 546678 709506 858410 839797 159449 872710 601039 337998 072599 055792 586609 096607 750962 399972 350757 184535 974469 274448 158892 170517 245744 471638 150988 860816 609697 450706 077200 400228 314598 238980 031483 511810 571703 113411 730107 138195 462250 767166 340261 135234 592778 278406 144668 178560 664221 583785 659524 179807 412739 255976 746504 970195 859708 035604 888343 259952 351292 263994 296411 442015 898085 208630 943227 222471 889178 777426 356433 882985 660535 943479 862239 301772 026798 734146 207651 132076 418961 096900 758571 447840 254002 865460 773786 971130 138765 627971 219124 906839 648072 482427 068345 815094 806442 101192 117255 425680 016888 090416 179303 770758 748838 505217 603311 293300 087427 038784 437945 756080 379047 644503 684250 420131 676121 055396 797544 479620 008763 761974 502352 129515 094874 384487 425506 519013 179633 089408 256293 497324 097391 250687 979997 995280 984642 905445 800849 302432 971667 884784 267251 416495 218384 489948 645525 396138 807239 696699 287765 623740 616767 030766 699404 570096 194986 970020 117293 055755 734237 330131 203373 / 973 > 271981 [i]
- extracting embedded OOA [i] would yield OOA(271981, 992, S27, 2, 1945), 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.