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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 uses sequences with zero non-periodic and periodic autocorrelation function to establish the asymptotic existence of many orthogonal designs with four variables. Bounds are also established for orthogonal designs of type (1, k) where k≤63 and (l) where l≤52.    It is shown that any 4 sequences with zero non-periodic auto-correlation function and 8k−1 entries +1 or −1 must have length at least 2k+1.

A note on asymptotic existence results for orthogonal designs