  We present exact diagonalization results on finite clusters of a $t$-$J$
model of spin-1/2 electrons with random all-to-all hopping and exchange
interactions. We argue that such random models capture qualitatively the strong
local correlations needed to describe the cuprates and related compounds, while
avoiding lattice space group symmetry breaking orders. The previously known
spin glass ordered phase in the insulator at doping $p=0$ extends to a metallic
spin glass phase up to a transition $p=p_c \approx 1/3$. The dynamic spin
susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models
near $p_c$. We also find signs of the phase transition in the entropy,
entanglement entropy and compressibility, all of which exhibit a maximum near
$p_c$. The electron energy distribution function in the metallic phase is
consistent with a disordered extension of the Luttinger-volume Fermi surface
for $p>p_c$, while this breaks down for $p<p_c$.
