For the notation and terminology used in this paper we refer the reader to Raghavarao (1971). The powerful method of constructing designs by the method differences is not so far used for $L_2(s)$ designs. The purpose of this note is to develop this method.
"Method of Differences in the Construction of $L_2(s)$ Designs." Ann. Statist. 1 (3) 591 - 592, May, 1973. https://doi.org/10.1214/aos/1176342431