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If one were to require quick and easy access to sizeable latin squares, room squares, Steiner systems, designs, balanced block designs... where to look, what software to use?

I'm interested in inequalities that guarantee the presence of cliques in incomplete block designs. Here's the set-up: I have an incidence structure $(V, B)$ which is an incomplete block design: $V$ is ...

Given $s>t\ge 2$, let $N(s,t)$ be the smallest integer $n>s$ such that there exists an “$(n;s;t;1)$-design” (i.e., a collection of $s$-subsets $e_1,\dots,e_m$ of $[n]:=\{1,\dots,n\}$, such that ...