Information on Result #1881550
There is no digital (24, 24+k, 809)-net over F32 for arbitrarily large k, because logical equivalence would yield (24, m, 809)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (24, 1615, 809)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(321615, 809, S32, 2, 1591), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1916 892852 758759 406387 104160 013785 139237 109371 137514 553282 113433 366481 443553 619669 178962 857727 903367 068594 240544 828313 131276 336122 184663 252420 750733 341694 535725 610606 878305 154594 086740 089609 901820 530163 475368 335807 689586 404312 596031 675887 049458 429826 321567 025093 441621 971886 235307 571519 287842 771195 341450 063415 959918 242387 248408 826983 213744 583658 662119 923194 111680 336433 323763 513624 019448 719167 336378 842399 600074 359996 275495 929380 121957 992402 123996 001055 960657 083390 523039 853749 845471 861677 047634 211956 358899 003535 649976 467444 915006 487011 222458 029393 159895 109694 427231 495732 842112 257711 955382 828324 018281 098119 558166 217066 960748 062612 415210 761552 047491 108075 988395 919460 226703 012245 028712 024318 090981 522328 848633 481978 700430 900639 052383 356248 749929 032383 762018 511121 769449 598021 786911 047910 813404 145816 802406 611503 007393 126038 865218 522300 964366 371577 176298 033733 371820 443009 005804 054689 834543 611281 157138 183012 015359 668233 653789 074670 458196 108386 886382 835926 210542 400719 778372 711609 887715 611474 711582 251292 039979 157460 026722 889933 161581 251755 621767 364556 337649 714494 564359 545773 969039 702568 550712 762680 883646 655567 295508 304954 313917 322492 082827 369169 738831 603470 493607 319014 071307 808581 132136 458263 425582 558926 864333 169928 648054 416301 705306 877465 635264 446766 140886 348639 431268 637545 726282 668942 178963 315348 627712 961308 422190 779179 900813 791485 468762 140891 829568 109744 295338 047334 969835 097569 274903 597062 232642 028869 957928 097216 959304 047068 945341 786563 103037 373329 833575 665716 053806 939703 361716 121791 946817 557856 403302 752209 517708 862658 961634 147644 415160 268254 544497 150534 715493 264693 926857 677681 135521 495695 633018 391573 248130 125051 568690 243768 588020 047649 275056 799093 108822 787256 132423 820224 419573 010856 583777 206179 768932 842325 988311 462383 434409 499850 221478 570778 749995 956642 289131 814305 676260 246298 473409 922908 321074 909804 188900 617665 175820 337416 316110 295469 455059 466890 356755 074674 567102 561864 543658 314084 007715 180860 866471 883793 499517 526747 152135 619693 622224 984779 905216 045348 462104 219231 781389 098608 333603 801678 186721 789928 932484 939788 575816 851355 904794 566672 544401 664837 402691 398764 686106 162263 556446 241124 758989 842189 396912 192142 284547 919219 316814 539923 666482 911273 337374 051730 893683 206329 198553 764999 602612 338465 840837 834675 318391 318213 217923 153142 149894 605546 992766 060940 411661 468950 145781 315272 833004 203742 487680 551628 560569 981706 204707 809280 302625 748761 233058 291844 697095 457182 641950 339983 106162 717913 143973 990006 059073 273856 / 199 > 321615 [i]
- extracting embedded OOA [i] would yield OOA(321615, 809, S32, 2, 1591), 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.