Information on Result #1854828
There is no (77, m, 2456)-net in base 32 for arbitrarily large m, because m-reduction would yield (77, 4909, 2456)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(324909, 2456, S32, 2, 4832), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 939254 140677 858183 887551 169585 373243 674618 122017 909242 009201 612298 362869 780952 352936 767822 148653 507233 354084 056045 137494 988921 720909 189442 175123 063718 264318 898632 219514 590585 448442 969654 188500 596799 402694 491600 480750 352409 916107 837420 897234 209149 281076 320843 857914 213634 731594 105642 937248 136945 950098 874548 073141 125251 220917 886297 480928 115514 694246 059333 135705 640500 969224 165218 857201 417973 294171 135263 176357 816693 944409 390269 028045 676055 062797 079521 004154 613101 570487 522531 206030 738287 404777 903041 527742 561249 028549 240909 667856 039533 425525 295423 619132 853202 321039 921036 923976 196602 874869 440392 659118 485055 107390 818450 626239 371834 729389 956710 627224 663750 151192 806479 560296 559880 170568 550744 789462 478945 017392 440020 736901 798516 786160 505796 563665 895305 905534 368176 342462 775731 230699 260912 920035 598464 611252 076660 091946 883459 661043 491894 467843 321665 253290 119873 309214 866210 876578 201487 052494 136705 983069 711902 324067 758457 920864 875527 426058 153174 188473 667893 392336 421102 949137 391496 364578 116036 517309 056046 325796 293846 404165 820900 160078 321763 235682 399198 083738 683879 086703 313015 751126 604457 936123 876505 249168 508736 456153 842901 421499 417708 149053 064776 030509 056139 281787 490064 885378 723935 307040 559069 513811 439485 917736 625285 713653 998612 200993 857829 801559 176657 423101 384330 933529 985404 552746 478052 602616 300040 238099 982918 834753 371947 630252 618314 559512 660002 373862 592492 352144 687345 552800 079694 034890 469433 387173 490466 363324 334864 460105 555322 788241 502136 784370 833520 326155 367366 196225 069183 349279 120306 891897 614950 557646 339205 238646 459450 961442 379239 493348 356245 414645 014949 182926 880085 381095 367270 830500 241449 414372 700346 767805 113321 491301 948008 900362 240212 336352 184527 232694 659683 226826 786841 203687 940744 663031 414789 274789 524001 521582 346615 299627 362885 880308 417759 988583 543766 108990 213025 222653 984385 848431 836414 313613 177194 569630 873977 776842 497185 900759 561967 865201 286868 203159 651480 117281 045380 306660 301272 054748 363937 460492 908847 907072 072277 040986 796224 398642 891777 200676 365798 122383 593896 568641 091145 679380 027193 696417 722386 007587 754851 044202 237564 602691 446765 453209 033024 763340 215503 535347 976387 332644 575652 979520 838609 914939 241944 692211 731162 965287 024382 497322 925516 779153 672424 520142 650095 080224 979668 957590 120490 448667 899028 672668 806699 050063 901865 928873 159286 875498 370223 868232 197090 730332 653086 434504 329176 957095 995144 546843 428130 251399 741354 184074 273254 233663 638783 478974 203137 146281 777941 114217 750674 471322 645097 911552 470615 119897 024763 772438 652581 917454 583644 223937 247021 980813 059501 130068 054569 580215 112029 267388 131546 425623 206733 995841 566230 873127 368806 354597 143859 118607 508734 180393 815413 257699 830794 262093 807622 457395 313421 210973 222795 886152 157520 149365 273905 656244 490287 287725 249114 004835 620548 744430 083400 489632 740740 923671 532055 327750 068485 236653 191180 269299 616257 306868 113592 183778 922042 231981 975784 029578 835518 079726 462760 397118 649212 778245 816583 517217 198390 497687 477267 904148 333587 094512 705985 006331 589493 069165 918447 553892 558634 535552 639404 692362 466632 554465 209937 150936 774284 197859 462446 332591 042133 157861 532846 423543 018938 146231 612484 382628 925275 601701 562242 653285 065773 595382 313497 933059 773581 773755 897240 541332 375488 061819 447769 567432 961939 053217 008830 365012 494595 293775 740371 162813 615890 254094 438332 796525 765225 648919 964447 149553 707551 188583 317336 775790 023597 902354 052016 417182 867747 788442 412703 039797 514684 708515 962936 858739 621372 125784 265200 255200 424746 772609 584349 984022 241477 196717 101256 049315 438594 499506 423309 498985 410713 348778 585980 613301 274681 649104 675726 886261 799438 235781 571613 530832 223326 616323 097611 434110 903906 560900 557062 965998 400487 281078 361932 245398 439406 048204 285574 241284 899905 003107 071963 580483 700963 337375 014012 601198 861334 860170 447168 152407 978882 265142 778861 948780 234992 193943 697485 002199 253516 593774 344138 628577 518673 361222 857917 895817 741019 029930 357441 293983 540314 427855 829632 371579 559969 792679 543486 325965 517503 629215 460304 938157 510352 617440 847679 631575 918748 687893 366632 913924 739998 153790 585540 183413 658630 653442 972802 683602 182786 070285 130469 633030 734280 921070 941864 086809 939045 475629 741669 366523 061221 319964 010079 728831 261350 742542 734995 910019 774580 059467 423993 269309 684806 493161 204234 394788 127822 293883 080598 711865 990817 532206 497956 180783 036084 785398 742322 745395 053582 548635 290571 104713 218870 058615 231557 615444 050930 401913 441575 636710 403836 913398 517993 517676 399788 413412 977366 009001 250911 826372 497895 906551 547345 505736 271212 318574 910806 474496 071680 408674 708127 185821 046162 890191 255569 231518 910971 593350 070092 382310 079357 703210 414432 762421 093732 364723 477393 359056 409443 532175 291574 065546 079567 377651 828761 700436 984414 605610 969330 593159 736866 212382 792317 612233 439711 422244 627013 319387 319378 996445 821810 595434 894402 703609 224494 841981 790866 553614 885852 010273 868499 216957 739811 519911 580274 147307 488242 578088 730101 241307 005159 003645 482200 504143 933084 806757 489736 668311 681830 827644 544125 277132 707131 333326 717858 823189 667033 935379 064961 432728 404869 728790 756573 882315 034386 420582 939443 286714 240625 317716 350802 748464 343899 900313 676297 476887 886443 010277 418130 318614 333180 129826 048649 640695 330100 206872 528500 844820 882628 391074 236556 346049 458622 858827 567004 751883 356225 040006 587605 095856 581161 641451 252103 609284 542075 959728 806532 614888 567484 521747 479148 109342 683431 479708 908214 879012 847802 615847 478939 938066 223433 222174 417771 232246 163488 210804 883285 575675 324812 073021 903376 775302 907667 692736 386848 351087 597840 634869 456479 590017 876589 115706 930838 599214 329356 999778 010129 274303 965188 056022 259561 286199 367563 561294 702929 160251 809007 954908 561202 682067 016942 866010 297358 270926 741344 308341 204724 266266 288166 373160 182498 829804 803949 450679 534183 679035 107721 067230 812311 643941 021199 638789 881082 745646 002235 281688 816043 616851 558067 264927 929911 314762 727539 418261 119295 230914 026779 168377 270696 811891 438423 336082 891328 540987 818753 010662 863411 530796 154683 169980 499612 421201 392703 507942 983580 491556 441019 495062 758867 195378 319149 043663 917323 484273 021716 335112 009079 137247 622827 284320 969630 269365 538808 271740 781239 642117 088234 561139 559638 318621 143629 249737 700783 362778 377749 871647 293024 789325 198204 571935 416923 986710 382647 697207 343292 916985 666530 067840 044359 733861 395527 736014 502874 722819 030222 239164 349040 297859 747060 952996 675379 238355 507307 787025 348846 648542 311819 427759 001386 123590 136665 835021 523567 542520 868309 798323 481709 145839 097084 254197 336688 817451 361120 889288 701162 223288 848320 741303 624741 670198 230686 113813 329277 404187 165551 762230 336669 048321 468237 507334 827509 485173 733545 739626 382565 656630 832042 874161 914404 291889 989133 587760 919259 261265 725596 373332 621679 730095 028808 291577 062171 912844 922219 302633 356808 901867 614632 362876 544537 227313 032433 365741 314306 001516 539290 669918 432688 757461 975062 379208 445860 492498 257812 027617 771743 390549 748617 153405 395263 457959 667086 684659 837809 621075 066263 282335 833040 477617 474181 691337 402739 345048 959513 632368 220929 909904 947117 247023 816531 243378 146483 956694 447128 569691 478982 997556 831551 953448 260829 161617 164534 674729 244573 525336 707441 362029 851275 245006 170789 333358 597815 890679 357141 903729 866034 071103 098057 821864 546448 746600 123087 602983 165742 876382 254832 986644 517655 470371 647467 475845 388666 843856 192142 856318 547730 560716 926533 520696 856204 530112 581110 053185 645741 221126 144714 536340 071663 918690 146015 121174 327601 343002 081864 583190 792351 345561 111664 497594 727428 022662 869715 378501 313490 572007 482673 779861 328770 320408 487958 089857 009022 048881 822750 024891 562816 296868 557883 715103 169766 409139 962700 451518 353304 849898 195651 696904 600025 038848 / 4833 > 324909 [i]
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 (77, 2455)-sequence in base 32 | [i] | Net from Sequence | |
| 2 | No (77, 77+k, 2456)-net in base 32 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (77, m, 2456)-net in base 32 with unbounded m | [i] | ||
| 4 | No digital (77, 77+k, 2456)-net over F32 for arbitrarily large k | [i] | ||
| 5 | No digital (77, m, 2456)-net over F32 with unbounded m | [i] | ||