Information on Result #1881852
There is no digital (24, 24+k, 1250)-net over F49 for arbitrarily large k, because logical equivalence would yield (24, m, 1250)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (24, 2497, 1250)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(492497, 1250, S49, 2, 2473), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 476441 557060 855730 205915 966525 979075 165984 646048 514641 025517 983496 294280 970364 440347 722825 125948 416988 659317 964922 760679 943300 079744 387082 994335 745458 537828 915586 721799 293175 207638 819806 414534 181294 961948 173353 737060 885908 957877 627053 344367 852949 928938 024390 852034 071002 979181 654673 221231 955777 729303 244536 904892 567550 236438 509009 052637 041840 087784 705479 944553 825031 311817 156376 899466 949217 821093 907087 974907 566119 218528 764205 152928 467350 006391 021890 808887 468205 647883 656937 223672 258834 161389 056190 285716 015440 472469 482456 303387 324246 189451 678360 669048 555434 672076 885256 728402 611143 114907 313982 291238 913644 853856 462592 999684 468295 874173 198012 755717 565419 227589 022724 045130 123689 645804 105885 278455 762026 842290 940526 389539 935609 752899 871006 981338 852291 375180 609174 886854 019514 693448 005467 259464 518569 218452 858424 820388 849993 136842 715373 709077 838226 176516 578767 667613 845497 335207 804620 760705 931693 402823 010311 619532 070483 855918 389960 803029 132054 532992 166686 178744 522354 731102 849677 485951 117927 593673 685792 488055 986607 271634 340020 666284 285876 411728 666671 883952 241539 223951 175538 153274 990441 098842 676668 301953 344638 220788 369068 016888 441101 751202 241204 712393 803432 691591 402354 490682 697432 094964 514048 756124 694901 494929 024383 971029 881310 508611 674873 790366 311777 992876 192407 165700 985122 197511 006142 714813 007050 120083 523441 834419 234033 009911 260552 572279 727687 343327 552955 681239 222886 215237 169601 258467 375348 117762 064684 853338 429009 306636 870633 832551 878864 341265 964354 446674 796172 816601 005365 188690 262353 040225 008566 049096 666998 904100 176765 650474 219592 639233 672314 223149 058429 309908 329927 504980 799242 079263 149638 693517 198632 976798 246434 960014 982799 786409 971243 622644 908009 909240 459069 856899 239949 729821 073582 216166 686357 411474 276737 168509 563956 558969 406631 284619 256408 191641 643067 391704 389859 220893 049745 629686 883084 328711 222001 614712 078853 298052 617359 665370 627734 546073 411760 907902 623674 633661 480556 099947 223471 628926 948622 663898 255137 466661 221040 848990 421052 924741 572890 417059 406064 262304 213564 937807 350365 242800 710615 084502 299702 113238 316769 058755 179869 948905 517792 749318 563997 249368 212525 873006 058723 926459 696519 879079 565532 029896 037816 872749 724733 389740 856077 376397 688346 712654 794755 663417 650870 250302 533434 387067 417984 783106 084702 443701 053032 649282 624264 876489 858649 505406 978473 782084 393044 149883 045133 688887 813866 299416 982090 637356 249820 353128 866100 882433 573728 503227 124840 628294 748314 287936 191162 134768 944318 189454 438789 311817 634567 933741 304770 116792 687470 411745 914247 252822 443257 518560 141099 543803 243610 066643 068871 929332 969378 192463 881100 058631 657397 647739 897357 109843 572394 117706 285329 180616 575406 399215 925932 824370 511889 968039 588725 385942 699757 498939 178486 847408 352585 851986 272867 540182 995414 935644 203530 854221 488850 849594 595979 732672 599037 415731 367334 923575 709066 222416 951168 398008 918740 475304 833413 298879 373753 760044 659834 023517 312326 933223 082594 103841 552981 114259 970393 105156 436224 252855 395016 231785 409528 437896 727135 540814 769983 464113 221385 641861 985251 308258 384526 101423 733964 348347 815261 522165 045367 501988 163300 218130 264345 361952 154630 701390 833768 294533 128107 704749 655143 452549 043444 650502 448261 115865 947322 343573 279073 075772 362927 379975 544621 198167 788999 707167 123720 944307 275483 988312 908236 398591 186548 868685 619101 455444 645460 125863 269748 278132 084074 409752 020974 552984 679786 724364 511889 039106 191094 634159 659222 993536 209736 099374 121986 491248 157487 601964 775066 488697 485711 618995 633847 657256 359843 756682 833696 061986 233649 279840 204158 165921 083610 435750 247445 419024 444363 497225 006584 081932 523329 683332 324013 620427 945356 106030 200177 525136 976741 343401 102948 198127 720441 083458 618173 443477 440392 220996 982461 753247 565019 826091 235020 712638 163149 996325 619217 408531 000722 339979 231236 195967 861204 705733 111725 944308 162014 915902 599852 300459 490989 153049 342021 364568 098979 190022 050360 233842 918173 080990 304577 802840 384395 015681 503206 325133 419959 388845 492779 618765 266370 151443 386039 704175 608714 953834 896797 260219 937285 864269 750593 456399 978421 872196 655438 998544 881646 487637 859452 678695 583721 350444 752960 414092 185329 428223 064579 059862 225192 331315 313915 138214 569810 224066 887142 956757 339259 836603 586898 434901 702970 320006 319366 307773 414704 913124 579061 673217 606735 698004 537254 681109 747568 120830 764210 036151 177193 260194 831984 516426 440436 031237 / 1237 > 492497 [i]
- extracting embedded OOA [i] would yield OOA(492497, 1250, S49, 2, 2473), 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.