Estimate of the lattice QED phase transition from hamiltonian strong coupling expansions

Hamiltonian strong coupling expansions are evaluated for lattice quantum electrodynamics in (3 + 1) dimensions using the linked cluster algorithm. Padé analysis of the chiral condensate series (to order g^-28) shows evidence for a possible continuous transition at 1 g²_c = 0.75 ± 0.03 when the bare fermion mass is zero. The transition is signalled by a vanishing chiral condensate with critical index 0.22 ± 0.02. A discontinuous phase transition is by no means ruled out by the calculation, in which case the value quoted above is an upper bound on 1 g²_c. Strong coupling expansions for the vacuum energy to order g^-28 and scalar photonball mass gap to order g^-16 are also given.