Information on Result #1879234
There is no digital (207, 207+k, 639)-net over F4 for arbitrarily large k, because logical equivalence would yield (207, m, 639)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (207, 3189, 639)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43189, 639, S4, 5, 2982), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3022 687084 968248 951534 855064 403183 545059 021887 602408 156681 338615 278557 047462 162230 260402 885845 701582 149544 330061 002790 044385 074606 381967 352440 050251 353840 739601 295802 735762 863618 128262 663623 652907 288304 614669 311427 824286 380838 473718 448692 585777 296148 876131 827449 463860 469260 928396 454771 496997 608141 168079 092059 407844 994310 454854 225877 398565 988569 319553 772130 847282 400089 773964 555348 429205 599071 027086 008283 187959 854055 435199 487192 980596 343726 560498 356625 651928 604116 669518 345963 243830 752284 296109 617133 992639 806122 152647 971715 568971 068538 240923 971621 590901 838853 543200 442452 907891 697140 287106 112137 264994 496355 379409 974862 617347 463066 630322 072642 945002 202386 854774 130956 791362 366302 963183 761059 745083 471006 214638 820066 023330 877450 525607 442489 378933 239247 665526 183757 250504 237848 045148 794624 748789 274748 726412 146819 471991 516935 573586 253522 786273 444362 145051 816945 596414 031352 315492 064796 785918 740892 539125 688950 604673 937533 787469 922105 934676 735663 415457 690187 633502 245639 185845 765278 374466 981729 344621 756681 355950 373702 813662 891630 714295 219858 118179 266502 557758 957303 039043 095549 140919 206198 140072 169760 293100 400108 122556 958674 898344 065400 965602 511316 085307 438002 887020 902239 728217 252383 609261 237114 166287 692414 371193 020825 942941 314835 422021 721334 109393 310766 122437 101650 637258 189079 824389 502843 976726 748295 223491 073893 805639 291269 929861 703412 173567 440009 203385 251737 379506 296165 289529 129887 718048 611912 737736 314075 657694 428225 143930 458160 668763 754648 627835 164384 045791 506845 821872 403457 885851 091568 604279 456543 209142 382115 418306 208837 825983 156350 323163 664201 796620 708629 080548 022380 546309 265683 691915 937323 788445 837807 152824 916174 581921 086414 061670 758655 958439 620491 868316 211952 374172 832977 582772 499460 555160 679285 405833 605171 972084 837285 583403 815750 362086 814288 681164 552331 355166 633347 331135 401377 306543 800332 031135 862919 784873 789070 817101 691524 081210 604827 377157 561939 144594 646891 286498 232977 581013 427490 589734 732338 036736 / 2983 > 43189 [i]
- extracting embedded OOA [i] would yield OOA(43189, 639, S4, 5, 2982), 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.