Information on Result #1872430
There is no (23, 23+k, 1561)-net in base 64 for arbitrarily large k, because logical equivalence would yield (23, m, 1561)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (23, 1559, 1561)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641559, 1561, S64, 1536), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 109319 949786 027263 521965 179443 018573 921498 458442 963769 671471 609297 492966 495052 538751 914361 219642 800109 858431 022731 002922 805745 971310 378066 807783 737963 425499 172255 449565 500868 392161 439900 620610 028307 797117 472309 517834 753696 378407 445294 899583 659970 061064 069414 302932 991168 711096 933806 160489 614227 196893 222165 381816 727864 128792 207506 242438 839321 314872 387502 372633 392363 247906 035179 455183 817407 914840 001807 127054 495891 991932 122393 897257 636298 117592 556222 061106 152335 147556 629137 307230 122371 176983 325451 851220 695691 436474 374493 401546 515568 480158 378712 066607 559925 542480 378316 115112 700892 786785 813862 456680 135289 225537 385800 957915 537936 447084 446087 530179 010026 570085 172418 935152 724559 399809 362357 464734 765175 420677 766735 275795 735758 199878 716295 203837 064598 817059 007512 704714 726170 966593 054264 066176 834088 248583 527247 377787 945660 570561 770139 811656 064720 848078 912183 092367 048785 746303 222948 691506 258180 178585 789848 256842 390579 704911 210989 885630 020901 041941 012136 486999 521692 597539 636691 403943 362707 219481 619865 637713 592005 665777 653086 313456 218696 500398 473544 838962 666835 642799 290636 278150 160596 952123 031619 464159 507703 656838 721648 856817 821267 474378 741564 535384 074095 902986 289536 417126 489430 899870 877170 501774 316115 933801 156213 134986 830230 625969 783660 978101 054863 294052 249034 267487 551232 744854 760071 312496 198462 456260 373241 532989 435825 097735 726063 136391 064216 325590 561594 821914 242337 330550 244092 256058 939113 835750 776574 893729 049222 214996 840653 499717 579378 415348 044604 293475 150137 272281 102837 641506 709439 847532 903253 202833 893925 556400 415431 349168 271607 474418 882809 633423 811596 429261 654851 396672 349153 000206 420972 541516 044676 956223 977455 264465 251180 240856 890058 462440 248673 212632 658257 706845 238603 284074 821523 634225 763369 082106 985968 419690 741099 168625 316836 715011 787195 536267 214935 282356 940308 964459 921145 425496 057329 347136 535238 970866 095258 631563 943189 210718 789433 003150 351067 763894 619671 343165 137406 470102 536974 647398 217635 268229 272686 046349 958057 207218 631684 651570 021032 099731 217200 141594 850301 698185 750895 811650 391119 906103 026162 157795 272226 307565 985273 455661 910719 185080 920607 144879 765598 690969 097246 819568 064901 734126 302094 189771 821548 216283 405881 234588 846364 991100 876718 210385 829078 418969 779089 443678 652303 795254 761609 976784 630820 377134 257614 490870 851713 120452 951117 410850 211060 126423 252648 392545 797930 783460 175754 114860 998506 775686 841497 865871 842327 722940 727599 841948 779404 324146 930059 404162 842625 034179 700647 274277 982468 811112 348127 280972 762685 801529 745808 718477 542513 524167 689806 026027 925590 116725 483754 744178 091852 508584 514691 760567 135242 845712 141416 965742 449588 771795 299822 069917 610976 175478 931531 117249 379194 462187 476739 813234 099337 483297 460027 272584 556212 476509 292166 220919 002587 001016 510807 845806 969002 347488 196005 039530 350493 148506 343178 971603 435531 800400 578711 333772 685825 968439 995666 043361 421351 909635 018614 374400 / 1537 > 641559 [i]
- extracting embedded OOA [i] would yield OA(641559, 1561, S64, 1536), but
Mode: Bound.
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.