to the work of Plücker [@P1835], Kirkman [@K1847], Cayley [@C1850], and Steiner [@S1853] in the first half of the 19-th century. Today, the significance of Steiner systems extends well beyond combinatorics — they have found applications in many areas, including group theory, finite geometry, cryptography, and coding theory [@BJL; @CoDi07; @EtVa11]. For example, a finite projective plane of order $q$ can be characterized as a Steiner system $S(2,q{+}1,q^2{+}\,q\,{+}1)$, with lines as blocks. As another example, the Mathieu groups (which played an important role in the classification of finite simple groups) are most naturally understood as automorphism groups of certain Steiner systems.

A long-standing problem in design theory asks whether nontrivial (meaning $t < k < n$) Steiner systems with $t > 5$ exist. Keevash recently announced a resolution of this problem: his breakthrough paper [@Kee14] moreover shows that Steiner systems $S(t,k,n)$ exist for all $t < k$ and all sufficiently large integers $n$ that satisfy the necessary divisibility conditions. More recently another (simpler) proof was provided by Glock, Kühn, Lo, and Osthus [@GKLO16].

The classical theory of *q-analogs* of mathematical objects and functions has its beginnings in the work of Euler [@Euler; @KvA09]. In 1957, Tits [@Tits57] further suggested that 