Information on Result #1880946
There is no digital (24, 24+k, 627)-net over F25 for arbitrarily large k, because logical equivalence would yield (24, m, 627)-net in base 25 for arbitrarily large m, but
- m-reduction [i] would yield (24, 1251, 627)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(251251, 627, S25, 2, 1227), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 216189 307154 663245 754260 854779 055633 385849 789209 935970 737891 076456 884115 406312 594802 231454 876666 111008 411814 816645 023555 795229 498144 538873 395693 407181 256325 779161 957123 238807 292834 164390 772550 596587 765619 197265 582300 775491 861400 145881 382723 573770 082210 122200 638267 027811 250527 253312 590701 488539 912132 146978 259930 096703 314482 588828 460781 058499 479613 507506 972053 244338 575928 906118 996043 842407 890131 430959 325317 156548 054599 763719 185128 021274 156981 630260 501020 949758 980781 164590 355166 464822 617810 205946 810505 312941 590207 615143 514351 785950 729939 706505 003245 634823 813704 371334 280249 251010 951709 402342 837018 253728 689933 096493 735879 734361 360973 770922 764782 225268 891106 470134 446269 990816 041130 097541 096002 407543 237189 289150 890047 545438 737860 524777 845724 099978 390413 298911 985412 338044 941692 424208 396059 459959 769215 061721 285644 942292 192014 624727 869515 514319 018801 191462 136068 702220 872404 654744 703724 477893 813217 320005 751309 447249 456265 588219 220247 434831 749665 121052 532247 810981 811887 094713 964667 457662 145161 517570 774496 728837 601759 380534 511996 886744 178514 722267 188195 980083 290948 203953 579393 901960 757532 724462 738420 428339 894431 560127 116713 889027 897426 573087 954794 515913 702476 016750 552073 580999 564022 908826 225994 875743 764240 697862 531228 295204 293740 039711 236889 941339 922542 759027 106735 290717 581877 926704 192283 577066 794978 372574 138151 399587 740133 333604 671182 661416 178706 185405 030635 232682 322717 795122 255378 708834 651261 419080 174498 910445 836436 655991 933603 232757 497888 877737 765484 159878 604874 833322 509086 047452 702033 556287 919287 054904 228523 394209 425996 165248 113546 642848 427575 188968 780546 994216 675563 331924 816755 077174 350259 318161 314974 065384 404449 698935 409501 648677 040765 624493 589351 709192 527730 876674 885720 382696 403947 035104 949059 292067 659043 823368 847370 147705 078125 / 307 > 251251 [i]
- extracting embedded OOA [i] would yield OOA(251251, 627, S25, 2, 1227), 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.