Some constructions for 1-rotational BIBD's with block size 5

A bstract. We give miscellaneous constructions for I-rotational (4q+l,5,?\)-BIBD's, being q an odd prime power, investigating their possible resolvability whenever q (mod 10). Concerning Steiner 2-designs, the strongest result that we obtain, is the explicit construction of a I-rotational (4q+l,5,1)-BIBD (with a multiplier of order 5) for each prime q == 1 (mod 30) such that (11 + 5-[5) /2 is not a cube (mod q). As a particular consequence of our constructions, we get new (125,5,1) and new (156,6,1) BIBD's. The only ones with these parameters previously known were those obtainable from the 3-dimensional affine and projective geometries over Z 5'