Information on Result #1881306
There is no digital (53, 53+k, 1436)-net over F27 for arbitrarily large k, because logical equivalence would yield (53, m, 1436)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (53, 2869, 1436)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272869, 1436, S27, 2, 2816), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 129669 868475 026737 177148 232580 755366 245617 115156 004677 875561 733209 825430 652470 615989 664897 977244 272472 150955 990179 481075 994809 263140 175745 804526 400545 446802 733726 891194 430829 569800 936359 837328 788982 738214 529485 934513 743495 501150 147185 152190 253062 549781 601900 006663 863343 961492 812395 453300 098648 163233 938855 776852 016341 133793 279674 539218 265357 658806 709933 747542 195777 923267 511741 567138 217295 929038 094270 701290 083411 241417 052071 040921 426627 895207 399662 824750 389117 812146 756411 230577 697550 063908 643005 006314 328774 039243 553761 858739 651171 990999 107404 212171 822385 738052 117076 544081 142077 431272 157643 621681 876278 076930 832418 486892 437116 022757 439492 193862 555376 239187 511204 845091 566517 674601 687205 183320 992425 131851 320947 956371 835322 672743 290126 699335 426779 937387 105341 124216 420647 424691 121093 901103 083194 702925 371939 292682 788236 818972 787456 033972 517144 524879 314666 688060 668642 174378 789362 579698 987601 206613 476565 926366 283714 824325 620722 031412 848319 465912 624926 521380 088124 758456 828110 713355 142827 924276 188146 805758 858570 393640 874673 795108 224976 068737 732845 647758 276579 644668 671098 093019 051417 823711 271772 366081 741286 438443 485887 113967 067970 834603 881108 536690 008573 167689 571762 430698 313782 147685 701079 063048 692144 472943 590236 508033 341153 234548 523330 962114 047816 790333 879235 064877 952336 485569 734190 552455 694186 201100 722629 749203 127230 831350 201575 910793 964864 738381 490034 224660 451296 695777 489081 825049 602771 956436 483745 312799 829980 305644 908106 118925 420220 632823 292227 113618 390955 760186 799956 953607 897027 442822 426930 185542 327313 440702 680865 874537 577932 901974 889740 899376 149852 515979 237642 388417 397929 509792 719403 751680 730119 435556 295505 310451 842391 600097 762676 679416 797656 627044 421944 939922 971313 894797 271228 449310 257430 431399 519469 404899 595937 641589 080543 545650 727228 567281 718539 054304 346587 084524 043379 725030 727794 825101 585319 608428 986444 034306 556346 981588 274672 300534 979816 907159 999668 485152 271956 592839 234223 576377 628061 234627 431768 520526 576064 920201 107102 814389 908090 602582 079431 439206 505147 501670 552035 813708 276408 053030 785693 615986 741958 688178 078606 422844 519468 491155 410425 309314 751016 205288 212959 178656 215458 079523 588937 905943 155508 336721 688377 579550 519446 872360 603117 573696 008784 492211 771965 876166 283452 268161 408192 077513 550109 446771 890012 171646 971129 336029 183601 084329 997087 367945 777181 736165 016227 956455 619477 770813 251638 951748 048762 122218 792589 165563 628971 462678 845591 997222 897281 100785 458697 084579 921126 325943 219107 300016 771052 798183 980581 312311 702200 363588 473880 418082 633524 453357 216776 640979 405937 650406 306041 314720 680354 174968 204199 467985 212446 348269 105143 249966 910438 664235 415719 301253 472621 149947 021097 583674 420473 647239 418038 021123 753608 466650 465916 486218 380857 578665 095142 406502 787649 475819 095964 499682 486263 391452 756861 590192 129317 681079 517755 647985 715170 090012 212556 053207 477386 613317 893850 968926 271742 756927 174658 886047 659846 760290 314129 699765 570310 591039 051728 702360 545401 501418 503245 724718 770788 563566 341321 444580 746680 134913 339687 732054 229966 641628 918283 001423 003583 332765 874016 116115 335987 587604 518642 026614 083945 520722 716137 389796 214846 828909 364831 578768 165602 198757 479405 549128 873452 926148 581940 346813 294074 403770 202082 743166 130793 847080 936167 779382 706280 102548 871156 558888 674776 323787 460595 584259 631443 510063 282517 859290 271424 412279 507314 643215 043875 440944 484187 914237 639494 002819 239285 150938 765166 801451 426379 607851 381231 464622 789918 607889 362302 392923 107892 933972 554617 933443 268149 897421 887532 114222 984168 691175 983675 923185 015420 924601 839140 249037 288282 013981 087994 608443 490359 276743 581666 965034 993470 942659 690155 535313 882202 630316 203837 034898 620764 256526 919447 534743 312200 499363 060806 320333 257221 136684 996823 940297 697774 636345 537300 541566 209437 786188 665555 730963 968564 701368 941363 768413 934340 453054 798238 764652 358969 060126 157373 328819 611496 100473 242214 135651 022525 084550 268270 815902 080265 469022 945695 306942 060853 769401 193479 305919 159617 368766 015702 624481 654238 725395 876999 150901 832894 008480 763347 278352 503363 372973 710807 245639 358391 098445 030252 168867 648505 046218 088748 487491 046596 120821 249937 891074 959510 101848 740294 250480 251843 069572 238302 868864 643546 682876 229357 091855 881209 281861 297393 / 313 > 272869 [i]
- extracting embedded OOA [i] would yield OOA(272869, 1436, S27, 2, 2816), 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.