Information on Result #1870162
There is no (25, 25+k, 170)-net in base 7 for arbitrarily large k, because logical equivalence would yield (25, m, 170)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (25, 506, 170)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7506, 170, S7, 3, 481), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12536 454905 070270 168217 475406 710220 135466 970684 438477 158451 870263 646849 295956 857283 038086 022573 434678 257137 365098 429542 396720 732948 068521 053094 178786 446153 885166 135883 141127 824934 031823 131545 401235 068739 977970 672111 682201 716692 716373 180581 818031 566168 920640 853926 587953 405903 919815 444199 279474 752622 278052 657924 455712 347233 588460 178819 035054 675875 554445 770687 092785 166569 043139 385208 971555 128696 221874 984421 945563 637039 707100 112349 / 241 > 7506 [i]
- extracting embedded OOA [i] would yield OOA(7506, 170, S7, 3, 481), 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.