Some asymptotic results for orthogonal designs: II

In a recent manuscript « Some asymptotic results for orthogonal designs » Peter Eades showed that for many types of orthogonal designs existence is established once the order is large enough. This paper examines 4-tuples (S1 S2, S3, S4) where Sl + S2 + S3 + S4 ~ 28 and establishes lower bounds for the existence of orthogonal designs of that type.