Information on Result #1870088
There is no (139, 139+k, 576)-net in base 5 for arbitrarily large k, because logical equivalence would yield (139, m, 576)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (139, 2299, 576)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52299, 576, S5, 4, 2160), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 205 662470 877861 848385 431169 237687 608825 052063 065450 449776 184273 342145 442327 324152 601083 922620 868608 459827 615161 152118 060470 134406 419941 845736 079932 364957 365424 473749 535499 146775 763889 415215 900134 056316 153278 108247 723564 000689 080743 824603 336774 265718 108030 489334 592520 620421 270993 397115 707863 705850 877102 156173 014962 656437 852814 382037 615416 288619 945401 962857 997812 580807 176077 855189 003303 783198 080393 586637 840266 861803 056389 836477 616610 549358 997177 779908 500726 759738 510592 868500 615471 867512 992659 617786 824518 126069 531162 800567 962458 881257 759726 530998 667366 135084 025030 040306 764434 909548 647669 243358 723681 270834 696945 424073 465218 025123 678267 418947 966999 332262 580053 352375 051049 378811 882051 650030 167727 125158 013921 877249 609414 095436 719384 618164 380611 899009 106833 246532 644925 885785 862166 416352 816579 881932 633940 213693 844124 921953 805004 471832 410399 989821 911140 041492 862993 979115 594836 848149 961575 392832 648188 756780 472058 381618 013593 856836 190787 232139 268917 650731 733936 113671 641272 434815 614788 435347 937003 544472 820465 931357 809536 921365 073983 611809 430019 141080 288651 771066 343930 160447 385293 229127 459083 371895 497868 206503 678209 861272 403526 005839 443061 804130 164024 048776 019613 144559 162977 796541 179007 128734 753617 435405 648250 553495 124579 365968 896543 698650 756753 832603 656312 838671 777516 412661 947220 268474 931104 489976 117914 431059 870696 101961 962279 393759 690970 201238 084983 761637 393416 254308 301858 419056 066550 722428 053560 246997 936360 989588 516983 713909 878047 934718 782647 524899 371351 930806 371638 196925 372271 264119 052848 198013 043265 222933 562888 481823 789040 770102 296859 693548 931273 177266 844387 478528 233259 567059 576511 383056 640625 / 2161 > 52299 [i]
- extracting embedded OOA [i] would yield OOA(52299, 576, S5, 4, 2160), 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.