Information on Result #1854348
There is no (65, m, 1749)-net in base 27 for arbitrarily large m, because m-reduction would yield (65, 3495, 1749)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273495, 1749, S27, 2, 3430), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 143 982334 258727 969438 970720 342114 792506 836790 794705 733421 174665 060204 877720 523353 119767 905809 998480 637574 832413 358380 371847 210926 999617 376782 109107 423126 266752 252987 155955 412975 821136 911005 830906 914327 026547 885555 654265 935123 759233 586488 423946 128849 909986 688345 298035 000231 743336 778587 591999 065569 290530 955712 899339 997262 856303 898504 048561 484264 511572 057084 057041 871045 650777 146948 911051 010678 086108 576419 737852 586767 524424 825928 368878 921054 762874 025456 156705 626022 190389 538708 789265 600722 429672 171295 570837 471821 902980 781472 068696 115016 570682 099337 757156 296401 555624 081653 929975 319025 003554 855788 345842 160614 216124 265087 652823 195938 284272 021594 596301 472403 891624 660483 576436 834482 351107 962788 411819 216950 649641 279052 329225 411798 404011 949770 368467 732786 120022 397353 719156 598858 127508 356711 342616 685117 492656 615406 545304 034223 614583 241611 392405 514474 608328 228886 304550 126803 930706 204048 981341 526678 003657 933764 511035 060658 613003 274972 604747 077456 886853 951532 282370 962771 316548 754652 512062 396692 370138 268676 625571 829467 135825 467443 413407 637947 739693 197725 363091 826135 999752 686353 491071 771403 616156 223908 431139 809014 323468 152291 567619 720612 228392 350267 517140 024113 819748 241226 882059 254393 643918 502820 614971 275688 210194 524754 409297 002627 764496 887657 702099 617355 850428 849183 388632 958324 562367 190647 550078 120545 399776 474144 609389 352982 571128 388388 968124 478809 397993 862677 266354 819217 753501 757710 982974 596358 453181 962730 303585 942072 797176 843202 563536 595090 606594 666445 083291 154610 867268 723077 121052 350011 664169 968225 036706 784575 620913 450037 504313 148024 340748 232631 416515 904749 129791 951594 907904 903376 433285 356283 945646 596934 184493 533928 586232 980776 447317 666468 042290 250625 586395 775915 024397 614735 648089 770815 747659 174405 626848 815478 947994 722098 037100 973486 917408 242876 580574 918750 787511 532260 154760 640089 111057 112462 500843 001919 456152 298495 479873 479677 833572 791153 236030 231877 070230 826882 247286 753558 022990 725687 160742 281914 963663 103135 354629 903175 109472 766388 421828 838651 079949 923577 591202 773009 258675 479547 743097 615103 217755 361978 905969 304280 587682 562396 525382 345135 111204 467242 645749 444407 783019 838514 860261 501470 429360 045983 904887 820711 522340 524412 361280 017731 090381 263841 022642 112889 983164 668612 969550 498484 569315 468086 822259 289999 810144 530057 590927 763667 003536 238440 824844 574689 070142 198611 327760 744870 468998 857715 117558 706668 808628 735816 022297 064952 658034 658745 159447 091500 446366 391736 565497 549684 030942 816337 895165 956445 929606 348550 576079 847890 316415 234100 998689 093002 482439 238135 882025 112965 612693 659545 767906 920563 499394 415596 233691 884593 028817 166826 102708 409103 070659 515634 102930 412731 489846 723936 190398 426000 298565 274507 185435 641403 677634 983549 530313 605028 956451 143409 924389 542407 886517 041907 693123 560559 379466 402010 109530 390778 028829 949736 382007 605826 609730 775188 307617 701471 992302 667905 516091 711095 084223 533411 876112 737900 731488 451531 561120 199138 388109 891015 462813 035952 591422 293510 733528 387833 980529 457603 036753 413752 065828 303292 005276 452130 234481 170925 359988 515163 758237 933178 528171 877312 406940 783009 755947 688141 817593 113189 589068 102713 283642 063618 438483 357487 357395 974079 617293 489593 373193 112729 430367 068914 452750 046925 181754 388897 941707 985730 507611 278342 845872 913373 901185 218759 347899 579020 824429 544001 583998 421530 892305 697497 668669 468204 441470 508267 449203 216771 673009 671106 215267 138516 374066 765839 563107 108067 075161 252434 853059 182002 227013 866101 120639 531989 225443 053166 931362 108577 865704 460436 321278 115592 062902 204653 636245 871665 481219 961427 532339 430572 377337 216973 394537 529752 332028 508892 606965 315086 330785 020310 187993 604818 727659 586879 110741 213422 749660 911126 435705 640615 608134 068926 946690 407502 011470 725265 645188 288781 654743 972666 794440 347163 648451 484291 105884 065599 389180 471285 001872 883853 131028 377047 821163 562937 591249 890745 464313 674778 386294 848770 795146 702963 624312 129964 568593 094124 106324 829937 580425 581683 537257 525781 566289 489528 718695 786973 858212 304218 919791 226038 698468 174186 136800 955249 229820 181161 004063 325585 861975 993172 766909 229200 652037 513930 072001 779579 020221 698782 975096 169965 067973 521087 181355 332805 384453 548560 138730 500940 891912 774076 810799 397881 734215 286660 886851 921438 140365 036864 871286 668323 129503 443808 839057 525458 132834 863117 225495 384233 259102 687464 938935 613337 003621 515585 575948 246895 960997 411884 282992 360062 085486 388027 150325 428382 106125 683502 656120 860512 966369 737018 898680 114576 642352 536921 582772 258848 458608 211806 789347 947243 901899 843306 208465 249429 026412 104409 840319 791556 654148 826362 338874 246229 928652 396542 742726 830040 921657 439714 244080 296305 227066 752612 782154 097430 173932 168289 287982 483982 699028 588075 900901 747005 005286 586211 009025 149435 003040 444637 426651 979949 674650 086653 336731 901719 319377 140325 465222 443269 379153 972354 529402 007809 135193 445417 379781 006402 201298 374369 432546 933609 706585 745357 874420 008273 242917 671023 739254 997403 534494 841280 314516 667999 431526 459238 012692 893741 229178 968310 308526 506181 804860 758664 645925 695866 775967 007447 676533 060307 351377 274039 801638 545190 059159 028713 670798 696803 995757 443469 617647 247781 066397 421045 967005 258769 176284 877042 732769 / 3431 > 273495 [i]
Mode: Bound.
Optimality
Show details for fixed m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (65, 1748)-sequence in base 27 | [i] | Net from Sequence | |
| 2 | No (65, 65+k, 1749)-net in base 27 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (65, m, 1749)-net in base 27 with unbounded m | [i] | ||
| 4 | No digital (65, 65+k, 1749)-net over F27 for arbitrarily large k | [i] | ||
| 5 | No digital (65, m, 1749)-net over F27 with unbounded m | [i] | ||