Information on Result #1881552
There is no digital (25, 25+k, 840)-net over F32 for arbitrarily large k, because logical equivalence would yield (25, m, 840)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (25, 1677, 840)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(321677, 840, S32, 2, 1652), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 516588 054988 424733 827863 048063 052426 969891 173685 289503 099378 733874 443911 546255 701950 689531 154869 381518 545469 051220 747319 356668 758467 644707 102180 076127 385004 572209 229740 955636 447791 009583 028941 103121 709336 554039 092381 615042 957224 309501 595806 492424 067166 023448 154945 351052 756445 539029 646184 324592 451982 235454 452049 825756 826409 288303 349138 475814 121093 092704 346652 244817 108236 354058 173879 354970 988342 918354 589809 621675 715174 557796 593135 500608 170847 679247 391394 041195 081898 896346 917852 730817 103565 241892 416402 676449 526443 729001 054065 403430 041148 891179 265833 106046 514907 950175 594127 366894 167964 433962 272056 582351 876369 421404 694405 164199 504643 721183 028511 818447 316519 529252 819020 047073 450719 610174 547652 288001 221677 010919 935795 851788 337383 807904 242955 066742 169496 311745 638268 918588 339379 033886 730939 960708 397907 884993 610402 186904 976657 048104 902049 233535 459873 159356 219021 436910 002941 091032 512137 842709 663796 566669 574670 936758 582147 574552 748701 989230 848380 707246 271925 049921 601260 956694 473149 123611 420190 123520 673854 889834 257490 923003 743961 106905 970754 960749 768623 759738 203534 621958 330368 591135 034394 958482 849688 954931 997993 431210 723587 714809 904601 301490 089937 946154 216432 180685 570758 057676 191660 650817 740285 989710 144218 020676 657239 296354 995841 677570 057158 410291 809659 370570 315827 416348 629033 817283 250044 325176 805884 291034 548523 416737 634370 459132 783016 756606 581551 718038 790815 563025 587810 605298 738624 663210 838526 027530 286462 790782 133146 193098 108951 221404 738068 026502 764336 439380 002928 886197 690212 604217 946785 035025 431189 393225 794237 320975 633689 460073 919579 285584 841641 773845 122905 746969 713220 560262 200834 580024 023064 216833 790753 879894 500887 230797 094226 271253 167168 573197 763430 842554 702928 660172 036339 160507 363679 207140 801040 713373 019566 322132 557329 880900 403868 860623 219041 405152 005238 678974 164537 741556 584760 392317 015557 842873 025840 718031 037258 353469 267217 453000 760649 720547 034439 533383 818438 844307 540268 910434 670336 407706 907190 229268 502845 656040 590975 979271 303556 882191 753864 875184 137262 849959 938755 144656 561021 048580 857191 031620 493941 892568 956138 155742 257257 033080 160463 872475 588582 536730 248055 092233 002953 325633 782622 350111 048582 757934 919414 050315 115508 991057 403460 258036 328030 074824 744188 395282 433607 456274 452910 279662 705018 409270 345925 408153 260882 022420 839914 610144 522216 384652 792735 464812 878528 361386 881623 715937 552807 882785 939213 798302 752747 137692 135772 831671 194065 714329 688248 650459 032971 673123 923255 207692 556053 187258 796751 214455 021538 718810 212337 447564 828232 824335 679908 971719 002096 339566 740772 281670 221150 050452 137758 949376 / 551 > 321677 [i]
- extracting embedded OOA [i] would yield OOA(321677, 840, S32, 2, 1652), 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.