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The group $PSL(2, q)$ is 3-homogeneous on the projective
line when q is a prime power congruent to 3 modula 4 and therefore
it can be used to construct 3-designs. In this paper, we determine
all 3-designs from $PSL(2, q)$ with block size not congruent to 0
and 1 modula $p$ where $q=p^n$.
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