Information on Result #1880940
There is no digital (21, 21+k, 555)-net over F25 for arbitrarily large k, because logical equivalence would yield (21, m, 555)-net in base 25 for arbitrarily large m, but
- m-reduction [i] would yield (21, 1107, 555)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251107, 555, S25, 2, 1086), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 454 875240 394158 557420 531935 976655 876909 944760 115909 236633 613613 651342 583733 700016 310700 801918 032292 538312 419153 866864 284573 864003 396817 518604 437033 328964 575360 697522 066566 062288 746137 200544 414624 084043 726423 720912 745677 410606 614609 680378 021700 582815 712988 793971 306062 402430 161879 123290 062514 543086 827855 146694 143400 838100 373101 261653 326532 039574 790660 312440 889392 949116 602782 555818 949715 364590 982961 805412 822886 468688 142573 164660 235620 890721 895620 020697 870022 861007 200244 988948 887508 683348 746075 028325 674437 857391 292196 309649 966800 757660 387062 349339 022586 424006 833706 026922 484667 258778 142648 554312 164599 316084 580063 542047 083611 756630 315721 616140 580184 740953 644024 097465 961480 777268 870306 219884 138542 838526 124858 407368 227796 510744 801522 810154 823958 591390 082256 087429 373995 490681 513106 813030 472102 827640 818625 653723 630436 760220 109403 433239 021582 153420 722612 985912 516365 493554 596308 666932 246887 019646 903217 839196 443396 099516 126871 576685 277367 906083 022398 376843 872975 971629 488325 122984 294393 883721 090282 539902 894768 633198 881058 082330 790464 555239 475358 877247 496041 402542 910491 920593 341581 873906 868996 116207 192235 148978 018215 093793 925404 580424 144581 967836 232472 234628 185781 556407 199002 411114 494934 899784 883064 491009 229489 447897 148000 105495 437171 613269 732374 395781 521239 133082 213110 583439 313213 707010 581557 754313 101790 115062 579803 185262 025724 919073 287246 750994 815665 267729 698782 942949 487063 245085 792651 365159 501231 049174 216371 340276 367687 746154 634607 903960 814882 468102 905870 347286 481246 161774 220977 372772 693381 303122 338310 540584 416230 558417 737483 978271 484375 / 1087 > 251107 [i]
- extracting embedded OOA [i] would yield OOA(251107, 555, S25, 2, 1086), 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.