TITLE: What are the major open problems in design theory nowaday?
QUESTION [12 upvotes]: I gather that the question whether the Bruck-Chowla-Ryser condition was sufficient used to top the list, but now that that's settled - what is considered the most interesting open question?

REPLY [5 votes]: Personally, I am most interested in design theory with an "asymptotic flavor", and I think there are (edit: were, pre-Keevash) some very interesting open questions in this direction.
To cut to the chase, I think asymptotic design theory today is effectively searching for a constructive proof of Gustavsson's Theorem:  All "admissible" graphs $G$ which are sufficiently large and dense (i.e. $\delta(G) \gtrapprox (1-\epsilon(k)) v$) can be edge-decomposed into cliques of size $k$.
There are loads of spin-off questions, such as completion of sparse partial latin squares, construction of optimal packings and coverings, or imposing extra structure on the graph decompositions.
(edit: I do agree that the Hadamard conjecture is bigger, for sure.)