It turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a major open problem in algebraic computing complexity.Expand

We compute explicit polynomials having the sporadic Higman-Sims group HS and its automorphism group Aut(HS) as Galois groups over the rational function field Q(t).

We present all Belyi maps P^1(C) -> P^1(C) having almost simple primitive monodromy groups (not isomorphic to A_n or S_n) containing rigid and rational generating triples of degree between 50 and… Expand

We compute the genus 0 Belyi map for the sporadic Janko group J1 of degree 266 and describe the applied method. This yields explicit polynomials having J1 as a Galois group over K(t), [K:Q] = 7.

We describe the explicit computation of a family of 4-branch-point rational functions of degree 63 with monodromy group PSL(6,2). This, in particular, negatively answers a question by J. Konig… Expand

We use Müller and Nagy’s method of contradicting subsets to give a new proof for the non-existence of sharply 2-transitive subsets of the symplectic groups $$\mathrm {Sp}(2d,2)$$Sp(2d,2) in their… Expand