Information on Result #1868572
There is no (154, 154+k, 165)-net in base 2 for arbitrarily large k, because logical equivalence would yield (154, m, 165)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (154, 1310, 165)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21310, 165, S2, 8, 1156), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 31 022999 506177 955228 138764 354540 542403 669572 956060 929994 800954 265780 833177 589174 652136 843253 713371 192217 833463 291758 872354 592043 694108 695447 245992 886331 651660 328668 467034 087066 103342 218502 114407 695930 674249 682074 369607 102426 380078 615856 848343 334833 591183 345207 485402 436403 921322 350330 574231 277610 235688 300767 315711 043284 626773 636665 555260 838860 692065 328072 447547 101447 187461 775204 606651 973670 797312 / 1157 > 21310 [i]
- extracting embedded OOA [i] would yield OOA(21310, 165, S2, 8, 1156), but
Mode: Bound.
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.