  We examine the large systole problem, which concerns compact hyperbolic
Riemannian surfaces whose systole, the length of the shortest noncontractible
loops, grows logarithmically in genus. The generalization of a construction of
Buser and Sarnak by Katz, Schaps, and Vishne, which uses principal "congruence"
subgroups of a fixed cocompact arithmetic Fuchsian, achieves the current
maximum known growth constant of \gamma = 4/3. We prove that this is the best
possible value of \gamma for this construction using arithmetic Fuchsians in
the congruence case. The final section compares the large systole problem with
the analogous large girth problem for regular graphs.
