Information on Result #1875887
There is no digital (28, m, 455)-net over F16 with m > ∞, because logical equivalence would yield (28, 455)-sequence in base 16, but
- net from sequence [i] would yield (28, m, 456)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (28, 909, 456)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(16909, 456, S16, 2, 881), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22451 440363 053231 383669 217875 033798 612730 636067 918224 120498 807982 490038 457328 283272 928474 756818 445384 754163 373604 419861 448857 152157 843420 979416 174623 038689 189128 936902 675306 452706 913729 864014 791855 425455 638257 807852 734269 477162 932142 245436 557088 418856 396038 595519 367638 646087 265264 864046 182437 848444 453045 271289 799372 923560 762193 811193 246046 012221 076574 396869 583529 684731 336796 054306 315497 913928 545114 146489 744791 648641 483473 350231 377766 473626 556653 243544 821608 581607 009928 991722 354364 363401 388323 473365 858151 851354 255891 610751 282642 798872 566049 030772 860137 096374 054855 966141 742714 464139 774349 683150 807834 235060 628494 380324 131216 312699 443680 368322 734953 351574 297733 502316 467003 521747 124421 067807 430473 654763 819562 508615 345248 108816 604043 339354 567647 479306 399324 206387 700502 303711 355383 216240 657416 105202 370691 896389 549085 960740 114246 752605 130168 479185 893270 856330 137375 775887 420802 129188 455912 126102 289997 973774 771887 899140 757592 453539 377450 077526 912960 480993 428249 158561 954769 921682 631339 115803 493942 941502 642519 209725 657009 576961 155101 667739 367695 022405 891742 557202 947451 915902 751649 634245 935104 / 49 > 16909 [i]
- extracting embedded OOA [i] would yield OOA(16909, 456, S16, 2, 881), but
- m-reduction [i] would yield (28, 909, 456)-net in base 16, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.