Information on Result #1881510
There is no digital (4, 4+k, 166)-net over F32 for arbitrarily large k, because logical equivalence would yield (4, m, 166)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (4, 164, 166)-net in base 32, but
- extracting embedded OOA [i] would yield OA(32164, 166, S32, 160), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1342 448621 178513 806457 130496 891008 054252 581523 695499 337317 567954 795831 125250 917382 469310 199960 529455 098251 226994 640611 878487 352847 987814 532833 360595 698339 669711 540983 186525 567293 756309 131827 130136 486250 385863 058475 434244 700315 824231 969943 145615 982592 / 161 > 32164 [i]
- extracting embedded OOA [i] would yield OA(32164, 166, S32, 160), 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.