Information on Result #1879722
There is no digital (39, 39+k, 255)-net over F7 for arbitrarily large k, because logical equivalence would yield (39, m, 255)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (39, 761, 255)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7761, 255, S7, 3, 722), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3964 376987 249752 477912 340731 883215 219197 688410 830149 361975 494619 676989 743160 229115 792751 763269 783932 847454 500955 921474 954862 347746 364891 190225 813477 968068 020978 798180 108595 150141 608498 086057 023444 098746 188545 998876 932204 738911 254525 385345 553593 007196 768832 092309 282573 877158 770440 332947 631210 166742 331215 129177 800265 402290 929246 057411 407298 532692 772226 186417 941479 436422 080766 788888 752544 570391 831931 718685 437982 587566 249433 486684 926843 651710 223482 487764 336085 595772 182860 064999 346924 243761 621790 808800 448153 892313 012872 246160 593226 018971 124162 043157 274926 523927 891907 603407 464232 996954 416943 410731 986387 870214 033344 675793 175702 953141 566826 394107 / 241 > 7761 [i]
- extracting embedded OOA [i] would yield OOA(7761, 255, S7, 3, 722), 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.