In our recent paper Necessary and sufficient conditions for some two variable orthogonal designs in order 44, Koukouvinos, Mitrouli and Seberry leave 7 cases unresolved. Using a new algorithm given in our paper A new algorithm for computer searches for orthogonal designs by the present four authors we are able to finally resolve all these cases. This note records that the necessary conditions for the existence of two variable designs constructed using four circulant matrices are sufficient. In particular of 484 potential cases 404 cases have been found, 68 cases do not exist and 12 cases cannot be constructed using four circulant matrices.
This article was originally published as Georgiou, S, Koukouvinos, C, Mitrouli, M and Seberry, J, Necessary and sufficient conditions for two variable orthogonal designs ub irder 44: Addendum, Journal of Combinatorial Mathematics and Combinatorial Computing, 34, 2000, 59-64.