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In this paper, we investigate the existence of large
sets of 3-designs of prime sizes with prescribed automorphism
groups $\PSL(2,q)$ and $\PGL(2,q)$ for $q<60$. We also construct
some new interesting large sets by the use of the computer
program DISCRETA. The results obtained through these direct
methods along with known recursive constructions are combined to prove
more extensive theorems on the existence of large sets.
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