Information on Result #1879170
There is no digital (175, 175+k, 543)-net over F4 for arbitrarily large k, because logical equivalence would yield (175, m, 543)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (175, 2709, 543)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42709, 543, S4, 5, 2534), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 107 468903 715051 745571 359017 151594 382585 613404 416172 187660 583502 376468 400000 068603 086496 735666 760184 144313 373215 905581 108611 757530 055738 487581 610187 723442 410164 538067 507082 109992 839633 711502 733994 048356 499492 532449 321368 616131 375499 238566 543048 399055 872999 777622 756788 221165 898727 601289 488672 093249 582227 221520 063554 278556 640410 118873 462583 281589 180931 691005 865626 138984 954019 564833 608265 914830 340843 021179 386303 463118 029531 657555 642254 925215 163728 822947 975397 928604 044388 482624 423937 649717 162973 075541 189745 353485 806680 032747 723440 445009 088825 042811 543184 724181 643580 836953 434333 541066 086533 180988 393248 037594 701724 408608 717730 383195 894921 990076 357443 729311 310844 996491 390047 756830 179720 139661 621541 488665 652866 060358 592278 004117 534219 696865 348075 838023 587300 393228 831611 803387 487559 661524 744357 604455 412409 214803 002069 601971 224451 234176 186718 856303 754640 065667 419981 310645 945588 489420 381407 476288 362555 871534 943466 960550 615540 797894 891350 380915 778408 906759 578561 111229 093766 642767 120292 906631 950176 770536 917255 812734 431651 931689 932569 121836 324753 716937 984716 141426 640684 951888 349579 025191 683452 130283 564313 510938 594572 003332 450188 113608 151701 531067 478939 887556 319443 939008 720593 249958 253242 208325 459659 210442 245966 036105 669746 836452 510643 994753 981295 092024 516106 368967 873774 759883 347587 407691 654247 588185 077528 771275 310589 849059 515058 509522 553352 842315 116337 689488 370895 216441 212339 914356 478298 823549 699907 376248 950006 624242 565052 508790 274378 718914 563447 167137 837062 056252 796173 706250 786557 303324 695081 996012 824533 938367 474515 775114 925590 007505 550359 258242 524996 048234 821874 765405 733181 012140 096540 278773 356879 035002 131573 048508 153856 / 845 > 42709 [i]
- extracting embedded OOA [i] would yield OOA(42709, 543, S4, 5, 2534), 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.