A general method constructs t-designs from weighing matrices and association schemes, yielding 3-designs from conference matrices plus infinite families of PBIBDs with block size 4 and regular PBDs with blocks of size 3 or 4.
McKay, Combinatorial Data, http://users.cecs.anu.edu.au/~bdm/data/digraphs.html
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Constructions of $t$-designs from weighing matrices and association schemes
A general method constructs t-designs from weighing matrices and association schemes, yielding 3-designs from conference matrices plus infinite families of PBIBDs with block size 4 and regular PBDs with blocks of size 3 or 4.