Information on Result #1879146
There is no digital (163, 163+k, 507)-net over F4 for arbitrarily large k, because logical equivalence would yield (163, m, 507)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (163, 2529, 507)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42529, 507, S4, 5, 2366), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 15 470404 351066 670136 763990 887666 720043 251570 904749 891885 596128 756983 532208 008822 023415 588299 010940 717660 695245 780277 899063 318824 836340 406337 441372 487027 171849 642291 338795 926787 700465 103652 985285 018243 668112 457982 402212 161219 971733 277030 556021 372721 822411 622677 192323 063526 399228 535131 770554 724567 440347 326999 349901 192218 490773 657589 792450 402094 324697 880439 531916 785843 344172 395265 009593 794022 923862 346480 622717 658605 594000 379235 549248 831989 515610 404549 711071 380745 213116 979438 348344 505031 071243 443389 876706 558886 392576 498622 328547 196450 077282 267002 931889 721837 880593 102124 920561 928974 422255 455484 552972 660850 618274 899215 493909 803443 403466 468470 895807 076296 935880 302480 095579 607169 165339 692490 198918 075127 483323 302409 923450 222090 057625 968163 316546 357514 293105 870647 179607 418299 288307 256136 420060 229671 352213 264686 401945 730935 585452 204780 377409 830297 699293 868359 292771 615081 395567 800499 041465 843949 104908 438840 075702 307470 224244 611742 280633 220599 272188 721867 563793 535648 386095 745140 454421 849614 393373 108991 085202 541918 810093 038344 477518 416438 612696 177741 620463 695345 143129 866310 422960 820601 296049 792409 530530 780460 362666 214600 873327 705511 610299 650292 791715 179813 566457 486738 673555 619341 244020 012034 673539 992566 855993 373398 545872 332071 499829 333527 801642 948856 866218 566161 881594 027349 958628 653454 551747 540162 749301 895051 808355 148502 074358 888404 868984 349152 685009 024766 452286 237869 083649 893578 723054 310653 754598 586532 293519 611502 398608 595666 334392 313838 833234 533068 158351 426983 995786 047438 930574 573129 731347 311066 776821 446706 462720 / 263 > 42529 [i]
- extracting embedded OOA [i] would yield OOA(42529, 507, S4, 5, 2366), 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.