Information on Result #1882436
There is no digital (6, 6+k, 1800)-net over F256 for arbitrarily large k, because logical equivalence would yield (6, m, 1800)-net in base 256 for arbitrarily large m, but
- m-reduction [i] would yield (6, 1798, 1800)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2561798, 1800, S256, 1792), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 21 222062 196582 820197 131768 655290 048887 649635 447262 440905 706214 957965 258381 638619 949545 929412 122411 873735 237726 334252 637966 363748 976320 112036 597240 635669 835359 720199 324379 465817 307266 109959 475652 795509 492837 178197 311331 718490 411991 699166 713235 761742 173746 557288 254919 706559 533828 792455 558834 451847 881093 333132 055034 343901 373071 454895 379479 226123 671167 216864 379140 786771 786364 793818 873335 927528 304255 490619 095831 751569 619023 863815 544451 298854 403887 402075 014673 661571 286158 916555 654109 826815 206223 574318 755331 140067 560151 236133 269121 732031 776453 971714 471407 691693 384987 409424 140694 361655 420213 182077 966948 088616 763713 177206 155857 138735 048579 846190 294044 490540 831713 169759 916586 355727 149633 588678 214591 717308 646221 939057 123967 788439 084272 986253 541641 841333 348363 421511 332707 026562 377381 732969 159364 195852 331791 320378 833694 849841 760235 863400 596693 313520 753996 984267 846789 007082 658982 206567 690444 272808 620071 241256 555679 051682 798892 168911 939390 346614 108797 017346 517439 069883 573659 106918 015492 800529 645688 691582 238499 863446 230610 138866 093554 900906 892976 849604 775053 518321 244496 573237 499752 145780 319360 950661 829988 696224 338485 684012 196314 220662 268828 780627 511619 435895 248531 950847 855997 072523 492172 130182 329968 651032 368712 034184 413816 383674 966724 470218 092627 177783 791725 198048 380757 542932 058934 301514 935711 929561 409553 768903 108191 672767 575077 207910 347157 982254 070592 318124 635391 917760 578166 902867 820553 711739 323590 595994 037750 993096 829508 521058 122632 306613 643543 414324 095071 425688 250344 024845 318253 706419 655551 882329 859468 242639 790119 912940 765528 711025 478851 453444 094793 082773 853787 638292 792650 961153 058726 865067 345987 231846 224852 915136 055812 545277 729327 867011 475369 414854 586126 590051 576784 262861 267433 117561 437219 662099 900865 324256 811619 668763 522699 279008 296979 761998 012428 872596 147617 981702 695659 630099 706402 516989 180575 063762 271511 740794 755123 948649 510775 864101 574978 515380 796331 054734 490142 430113 314102 179674 590916 820278 118574 573619 050086 606975 174276 074749 370521 408717 669024 757732 208938 120931 921897 638540 899319 874391 215917 024802 674573 012822 611701 327026 019390 801993 873623 564750 823108 387013 639684 018572 119292 049134 785705 304476 035672 205449 473857 716926 985183 106997 096466 908935 982508 341337 428708 346308 839569 120667 293601 795580 583752 529939 118488 695862 769608 451839 906506 004156 911410 891348 728689 580441 983402 656429 068474 433129 288942 553456 450839 813362 054392 301172 961933 379888 812839 805327 133557 754224 410668 922466 602643 777246 618576 081482 644671 381329 268477 917791 316012 577196 846960 100909 439097 812243 483213 169153 957968 770513 063947 171487 903983 751457 424430 278430 737554 577768 928423 286627 031876 543109 948629 018773 229883 789264 061095 771852 910746 290279 343833 059409 169759 141710 031528 797473 189328 599982 039093 715496 370723 967005 277896 258081 274535 798151 842838 112772 641832 988026 127880 522120 407998 254293 609925 453042 060992 597342 477209 794462 636568 801960 375723 385660 270480 135864 689006 162829 536775 283009 564591 667051 862768 871098 909666 781164 176738 499667 318299 363699 604197 227293 098179 930726 782044 418064 104140 785999 169029 406417 287833 455818 713833 520757 993770 014240 161045 904947 183079 532929 656990 236038 060484 206065 163992 267876 704835 409696 589367 336841 999326 511480 852485 972981 867172 840512 594451 848314 491153 590313 466173 240148 225554 514492 903588 243711 994220 518025 575876 700501 865948 560233 770928 283182 565071 349581 881134 971297 265881 421950 832910 544214 563332 507039 672125 503353 221107 623362 561121 502369 750678 115852 847310 714466 430667 785637 735664 190116 303989 711990 737582 415178 901276 839946 106307 843143 021466 989586 468819 748245 887754 526827 999606 747979 340503 997332 435491 163597 049982 302994 809599 680354 620594 034655 125344 636892 638379 616335 746763 058993 751819 762113 018409 085260 207181 948923 047584 938246 274669 830106 815069 132262 226179 494207 030846 900993 120255 075910 282304 522411 162407 734823 237912 484551 311882 000811 696137 492304 088227 584313 377194 953687 261546 497655 948294 542718 039424 323720 201913 935946 894109 442402 775296 714774 225153 659006 730145 720306 866239 286457 632736 992350 962427 651771 393897 786291 805646 380911 510953 015404 993453 187390 057909 234687 886515 838036 551881 949314 744708 018710 164156 277428 998807 667582 262282 536576 325551 119498 531010 883294 559551 898174 181447 746583 710306 819069 347125 530317 285860 663231 714845 007689 079118 913909 909382 693458 342209 438622 835907 182056 653468 401149 978102 738987 500668 503541 325676 176465 813660 800272 871097 906957 798914 878070 336435 660516 313115 779318 313904 911179 938103 043905 353740 937926 279168 / 1793 > 2561798 [i]
- extracting embedded OOA [i] would yield OA(2561798, 1800, S256, 1792), 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.