This is a short note showing the existence of all twovariable designs in order 80 except possibly (13, 64) and (15, 62) which have not yet been construced. The designs are constructed using designs in order 8, 16, 20, and 40 and applying lemmas and theorems concerning orthogonal designs. Three-variable designs (a, b, n-a-b), which are useful in constructing Hadamard matrices, are also considered for n = 40 and 80.
Cooper, J and Seberry, J, A note on orthogonal designs in order eighty, Arts Combinatoria, vol. 1, 1976, 267-274.