Information on Result #1858268
There is no (76, 2424)-sequence in base 32, because net from sequence would yield (76, m, 2425)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (76, 4847, 2425)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324847, 2425, S32, 2, 4771), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 354 589878 140450 988377 369588 359033 976785 085630 145553 878278 699721 204250 563345 316437 068206 819025 156237 087752 787706 576741 104924 157885 256701 174132 219906 221134 035608 587915 199153 367179 034603 374230 300145 996538 064290 815156 428512 941006 145099 743533 714271 605556 885043 393137 775730 608978 410046 108565 623758 595953 738188 537306 853012 547194 850783 032576 903685 324141 289674 580067 608756 616938 367763 265097 090544 593782 552113 638642 107098 520634 259091 874060 235338 202682 307844 014111 386334 888796 771329 464669 084377 506064 641992 835997 705769 151538 757131 461214 297481 894051 843340 321107 220862 635607 162777 076276 476061 230856 112832 956712 570242 164351 834787 201180 577504 333121 022369 729675 772021 515749 450244 209947 646220 438263 278256 892822 120990 334408 037042 518203 772829 727587 265188 023282 011515 609400 529901 995861 108709 103680 866553 497724 211650 945347 581907 566488 583929 016872 771799 466893 250504 910079 014325 737050 553574 085204 302956 503875 909895 645931 154546 694109 659562 443733 872414 796416 226701 139211 680152 971833 252559 151778 064407 776335 590153 808247 652205 670585 688039 273509 145036 532314 847679 026875 224504 916795 040197 135459 732890 692354 661113 852107 060396 212777 290436 463839 172761 075771 019992 291737 465658 979037 543603 154781 493548 939317 101668 119985 534731 442840 380253 721002 182001 297497 725979 946025 281152 827802 863435 722798 009599 827915 505321 491802 954018 577047 994309 420264 157340 806333 125660 482168 584490 912842 283225 585292 084416 237007 065272 418938 372311 954765 495362 532259 119820 387458 583207 973538 128526 589693 586008 834877 440656 984978 692163 124618 100342 792230 855561 989617 993761 189965 694719 541947 648429 654220 968026 163848 062044 029950 805333 032360 787519 951493 706909 016580 336026 231517 991167 212770 093117 864128 755726 037413 656057 148831 696536 974209 167658 024097 499383 357317 142978 720229 671945 735197 203165 608938 481284 483050 919166 081151 977073 422138 644340 523194 887643 611546 531843 174125 599851 837981 657609 476088 977254 133366 677086 102098 090194 780280 791092 709658 583407 558654 497861 387385 173829 153863 795325 960495 159042 261215 958991 072765 159992 483403 203243 725746 492522 997058 212064 441434 092446 290274 373705 179367 008046 784303 469085 738669 967869 873463 682084 999693 674322 423977 761204 095553 735909 923389 218750 013602 075244 173097 915873 700984 378573 918368 076613 893258 396144 158680 115706 844942 877206 661957 007958 165817 229168 037254 725413 575598 904176 019542 579899 462970 654176 704537 145464 600604 382908 092395 596596 206368 361562 680970 239009 773718 496881 340905 042960 313986 240288 602398 569097 304019 712830 067483 917416 542121 353924 730183 740972 784670 730486 175350 118811 490286 049913 982313 867616 279721 231506 245193 968629 182185 430621 948071 636095 581966 655892 149175 326728 570622 643269 623686 767367 551949 910930 346996 441048 921381 652945 897429 859386 138651 500774 783553 990732 596313 309341 337522 452031 529142 633408 950216 266709 543054 111752 502296 262173 312736 230591 948958 605848 768803 019020 109971 317291 270049 226277 513266 470470 298064 200717 401763 061517 838473 479167 825783 883220 702754 489725 277178 107928 713579 022458 406947 801955 932259 869072 365422 922549 468996 867391 720101 991779 028362 608254 461209 195465 514666 564797 046843 791405 021242 074482 809571 249875 844940 644632 523083 144606 825202 151395 508984 307229 070931 542935 873723 506100 827104 685421 763859 221931 829191 437005 360563 684504 235098 264748 504414 716723 879864 567029 344896 625747 901949 301829 926907 537406 010782 202213 759957 576979 626852 330845 808174 665655 281224 148035 015501 003012 245840 775243 167497 524906 968030 550621 961577 542062 830823 220420 310469 386427 831463 636080 045451 539766 113055 006447 891198 507921 147567 125864 001109 049135 347978 395109 396341 843398 411941 407452 853781 780260 761718 997724 344124 651118 820526 989961 660681 726356 778575 236502 856359 798382 787868 000521 344747 854479 234084 470873 969902 033555 993119 789496 100237 744161 926691 476613 579442 793130 334083 079498 222473 394592 634917 403100 466465 670761 617399 687125 570849 144361 451447 708154 688534 841458 650775 273750 296475 245817 573200 682412 090802 414483 755099 402156 568636 062706 049872 988252 803241 073041 919996 947421 552426 711682 960313 119229 622716 769351 860397 208126 985516 933393 743765 450135 032588 469028 943074 613367 354351 486335 511631 082059 117270 785829 943727 344170 603065 246388 284868 830502 270269 570233 833213 981244 131911 273103 828726 247621 028362 066601 944401 071831 956944 487242 702452 945320 868719 157090 746151 399919 245083 797279 067475 920272 845742 560484 779001 072758 608070 801678 583656 349823 455280 378516 517508 355242 549141 629416 606971 227758 351065 130850 634092 630811 884005 672747 994026 902159 553084 069611 280889 963840 724444 114474 576971 605375 813817 808640 874037 603633 975870 898535 968359 193856 976595 019198 321464 679336 567691 429626 690445 039862 003517 701098 230587 117063 779576 483573 619314 271900 479703 793507 605487 240459 454237 423500 027977 791799 637401 621913 873682 678063 021034 591095 571737 210237 927282 660554 794996 760576 528248 826128 683513 366318 839027 361561 583698 524492 650180 600738 364867 518341 680136 522021 061982 079665 568838 736582 665096 522329 007552 968083 322361 033336 372026 047601 802097 085670 992497 716491 116132 986848 367405 748105 135179 621068 146799 325057 733658 449802 230518 238490 421832 130448 053222 992222 801946 305191 877851 957724 312430 119663 699777 360445 291991 202490 652712 920661 061473 648774 080783 377070 290115 023760 990922 626161 715716 883155 006885 440081 852516 296732 908266 813925 883035 513153 966412 137922 526577 974400 748305 111873 348042 562982 326964 046825 833620 707890 929456 088042 480203 426050 865591 596063 711958 692858 138217 045449 959298 449024 382936 376965 666198 078904 523258 647555 394540 114587 683303 059045 590601 184387 727076 691865 102743 679150 291251 703886 148615 490127 750346 973360 236937 146980 454749 560875 543758 368930 655929 427214 035882 143296 797329 966092 596658 940787 409240 134937 347065 277639 668910 435071 344980 464464 996709 967029 952176 649178 051731 538885 002105 074000 456143 871684 593949 038175 617338 623095 188598 123701 006927 179855 304638 801509 727020 036486 620603 911450 060214 375288 722189 334275 428797 077420 264027 345937 217752 116523 450110 475024 352398 373239 924900 351718 538259 861600 112553 602665 357066 503891 074410 462280 343339 674264 273633 830013 187215 982275 895613 707878 040052 952588 902937 144935 604806 411779 766649 753359 594413 482270 629921 751272 390157 158695 796499 795936 749210 262693 921778 367819 522171 780509 134892 235778 790861 630723 493477 656498 742173 556392 332046 507977 921163 919236 524643 928552 411348 744955 594017 647183 327452 458633 108455 292421 095922 888150 114291 023214 825369 243397 227464 134570 432697 041433 168143 342622 601574 654196 765970 501020 269258 237205 866214 141717 052241 890970 528578 662208 244688 325507 278930 117048 534105 133464 709110 710782 849574 092065 103073 981780 291311 809702 686024 923961 470915 058493 666137 798819 681178 278612 846530 620979 599473 831744 385831 478191 411056 809900 802055 792739 219951 637481 745654 798026 988664 395814 659922 361512 656268 913164 827336 455860 387621 349901 642497 076696 312659 993647 824286 169946 192858 157239 861106 688731 631576 056650 635723 596103 988115 619122 902663 478320 257436 851622 229598 978085 692879 537327 982597 350105 439143 990274 555602 086141 073302 695407 927389 595690 554664 381976 663725 252766 388281 095404 949849 615037 847706 886313 153485 613255 648496 722899 537244 108610 374070 133170 264029 735693 420088 132141 304944 469406 724376 052079 047771 079209 674068 722165 189196 119288 666763 714632 618581 679982 271155 424106 220730 890224 115016 640872 352868 416378 001105 921159 705373 287707 238396 939451 875536 464452 020776 417221 929768 314057 805184 140139 572273 505883 908466 938340 330750 454810 921162 026413 347349 083567 875730 409154 825765 381059 685425 459759 812196 920924 205977 781109 987471 554225 619808 526950 814517 153508 174822 706334 594253 228681 150112 048523 523243 573248 520502 957675 419368 366520 146022 074615 121622 084809 259897 864769 274675 986432 / 1193 > 324847 [i]
- extracting embedded OOA [i] would yield OOA(324847, 2425, S32, 2, 4771), but
Mode: Bound.
Optimality
Show details for fixed m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (76, 2424)-sequence in base 32 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (76, m, 2424)-net in base 32 with m > ∞ | [i] | ||
| 3 | No digital (76, 2424)-sequence over F32 (for arbitrarily large k) | [i] | ||
| 4 | No digital (76, m, 2424)-net over F32 with m > ∞ | [i] | ||