Information on Result #1879160
There is no digital (170, 170+k, 528)-net over F4 for arbitrarily large k, because logical equivalence would yield (170, m, 528)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (170, 2634, 528)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42634, 528, S4, 5, 2464), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 227233 836758 559512 634815 543013 977176 554156 671712 485413 208845 070962 795582 983020 477321 205876 920084 623807 654382 652256 094169 842605 071596 692087 417017 194108 375450 977410 417844 407902 626240 530157 098722 902855 321370 613598 119575 501003 895648 050657 250341 464940 618345 361353 879017 826635 577915 906177 315563 545422 655437 402813 274462 419256 554583 650543 210680 992469 222209 499009 913917 177893 819094 706229 231876 445711 390851 437877 471751 449939 273257 994478 862366 965782 518170 698064 513712 130612 943950 896384 412346 469696 361748 861876 892082 489575 698861 965948 228840 351442 111912 687573 996181 709801 868670 830429 595268 008050 574788 370036 006018 305957 515635 951872 442265 606620 185144 313405 575410 142914 291390 194042 407916 117448 685694 188296 714342 421898 983970 958584 559039 612167 763904 150331 583692 898775 974583 872046 635331 031917 044696 492440 839253 220084 313228 740362 224242 847316 496248 051992 302814 845086 127868 834606 732776 550366 173559 626930 930099 087485 082988 740845 704479 537168 411911 310076 578407 731449 925694 961790 970043 064843 799941 672413 257902 203873 148519 639652 487435 480240 437473 376257 117948 160768 973877 762271 919996 044900 492315 460116 388802 465876 274212 854332 874236 990458 150552 886859 651109 215426 868379 446775 809276 574816 700935 176475 592972 917111 117615 124685 564753 880156 706343 714223 832433 563493 046357 442438 064067 773260 085099 138826 916485 991004 931959 530170 434449 582421 747258 954410 233046 015565 865308 787511 181812 682510 681839 069848 574126 170885 108614 244175 722784 053874 105007 691145 958375 738770 643217 060588 349940 764332 707822 873933 934078 180966 289971 330259 259071 301858 051446 473568 775481 507700 120215 414654 432749 422681 835531 954088 542412 962897 023240 534435 906612 887552 / 2465 > 42634 [i]
- extracting embedded OOA [i] would yield OOA(42634, 528, S4, 5, 2464), 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.