Information on Result #1882432
There is no digital (4, 4+k, 1286)-net over F256 for arbitrarily large k, because logical equivalence would yield (4, m, 1286)-net in base 256 for arbitrarily large m, but
- m-reduction [i] would yield (4, 1284, 1286)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2561284, 1286, S256, 1280), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 77514 941103 823062 629619 767295 783364 677367 914094 229688 383954 651776 941163 013206 432903 761584 170373 309652 249456 862584 961263 809088 100370 033465 217962 285963 676584 196574 067968 902830 763996 638853 683443 484938 159462 467698 531317 217291 843477 946793 180876 505596 053979 872609 737294 989238 778894 279316 795787 384184 889693 021643 344769 999264 496619 811373 534003 543332 237214 335024 886955 004043 376747 542438 654809 072389 352854 529120 273826 840918 129431 619787 958225 704007 079168 279522 142495 433918 113965 799166 168225 893996 617549 084848 737351 024063 569549 393631 318514 194047 229283 722177 032370 349741 321264 063766 434860 779792 525138 711852 131740 228456 007606 181841 312181 628880 803583 075081 037068 055773 753572 807876 059995 068054 651299 273549 551791 289839 012864 351289 668791 412890 390723 685386 674870 577843 716377 839133 240660 640736 000353 815146 553483 372792 924193 617278 727678 740250 001038 734414 288066 301379 339625 166786 921887 081457 198843 494800 524962 599047 964021 268177 231426 660639 694163 225704 092335 768069 604857 115202 716434 998617 843853 511544 744130 558004 029767 077695 858983 157839 641158 061056 554124 237807 578616 272821 280628 536144 593313 962034 200143 158934 581767 544951 725070 683147 747361 386253 764477 735787 014940 251543 419925 465368 995678 544000 323336 668724 038958 282894 308972 910805 899706 442421 939968 066309 058350 857649 846420 443146 471702 569305 590418 386281 874386 384975 886868 021090 568559 337297 929372 716751 766528 885227 536584 502530 928243 543773 868349 079761 380217 345717 479533 690572 516177 908340 690972 495358 391212 904262 998853 409244 654368 237029 892531 337723 095755 704798 716684 783450 314389 693661 668175 683507 523286 079089 013631 815682 362598 781035 439328 825643 927692 725752 499500 858615 116681 946940 136076 111507 223567 541998 822171 061978 897378 881880 389773 247989 280557 497147 150598 590422 540316 908162 993457 844798 211169 642154 524909 601948 987519 161308 018308 694475 163059 421718 657752 508454 992645 292708 626753 323573 346089 018286 440331 494273 193291 038984 662214 722006 521290 975670 530487 023146 170307 039618 529854 621483 114672 832852 422811 124143 575935 434955 909897 010190 789499 862534 833879 407559 792370 137520 609145 433124 856569 971993 897196 387453 105502 618013 109043 785677 398390 897201 628669 577664 514817 117390 196985 955321 216246 360326 938358 408949 092438 138642 762781 571524 106077 360424 116499 687850 616789 632087 443784 203951 906684 093758 454210 497558 689044 366872 096887 844492 010056 371037 383170 569400 272834 817450 598354 754242 763802 600005 091427 537118 497145 465432 092039 217615 038353 512109 530158 545735 786743 137924 610727 133719 020223 258084 666359 703744 191475 136317 849659 897998 042542 605117 970207 052882 115002 842381 101357 658912 377667 259180 030764 167277 658705 778719 710181 897499 804756 257735 912281 374824 941270 412678 110387 071126 947026 096865 320222 212919 668675 586254 333863 639976 828812 002478 876041 708058 681245 895437 371262 260632 856920 075323 439786 258559 310743 548128 956268 733514 934919 656211 221921 384464 094701 463103 381063 006003 903194 805719 362676 377509 971298 633880 111094 771930 294781 513141 307244 654441 281765 700135 533506 865014 103462 153795 181841 206777 562474 765648 753392 224161 885438 481829 852410 940922 585293 091857 098914 333325 529555 176712 983298 560367 812655 227233 040234 223489 292188 573956 059702 280536 168291 869118 440046 298278 200189 076193 120913 472602 652108 576996 196352 / 427 > 2561284 [i]
- extracting embedded OOA [i] would yield OA(2561284, 1286, S256, 1280), 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.