Information on Result #1879862
There is no digital (109, 109+k, 679)-net over F7 for arbitrarily large k, because logical equivalence would yield (109, m, 679)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (109, 2033, 679)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(72033, 679, S7, 3, 1924), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 34849 555708 563745 818987 824666 195749 397502 722634 753561 590171 507628 743541 373928 351056 404457 675268 686107 128099 001631 480375 964731 061196 442998 339063 387007 991979 056128 440177 114710 068120 813738 439206 737904 607662 526582 431528 245412 507128 682391 289041 906568 859545 637583 557446 713507 568216 032680 895166 349397 186134 157977 651231 420035 751035 648052 950028 130345 400530 235957 994627 558563 597609 859464 451841 810146 857156 423366 663857 151762 492747 566204 686177 325003 093794 408632 261262 323921 209793 916960 766073 824444 650789 757363 220744 632768 181869 042225 388127 676861 188434 225089 447873 980523 553212 187062 335058 459106 487417 429238 540589 842626 178877 365903 613671 985461 265673 515731 924099 514902 656458 696110 304070 336516 282290 942828 570435 844193 174508 923993 993729 699355 891154 884320 226235 842344 132925 349966 755812 425643 400714 319454 607925 237751 754841 553932 132641 188371 304482 340267 157365 530446 140690 285393 993550 143922 918224 713558 230463 850564 029650 551560 235272 678932 454595 058144 636162 561412 144216 707474 892077 875594 092542 429497 195445 644120 492603 097253 817719 257377 521621 338551 635101 961299 416871 206555 724329 607310 099607 799703 520117 264648 905256 003432 755776 686111 430819 400656 444197 029927 239658 358674 433360 523827 172571 846048 175393 243006 017939 116580 557403 088343 094037 911215 885334 625560 829055 017809 037231 642173 385823 408478 505792 965762 578989 336549 782124 063158 538398 558010 713892 977728 332997 435748 321778 244008 916631 966120 001803 266416 456955 446088 261425 393962 260170 226273 076301 364974 685042 617006 937233 467693 860567 152076 883437 549944 029215 168242 967413 985387 149761 438833 105038 933237 049841 428647 467180 636788 281789 040018 817638 590683 882228 032745 730819 703960 126708 818858 046125 086517 793887 453672 666241 852654 583454 840045 640893 688792 026086 267555 822255 550518 083911 341030 673075 613098 832156 894809 / 275 > 72033 [i]
- extracting embedded OOA [i] would yield OOA(72033, 679, S7, 3, 1924), 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.