The purpose of this paper is to demonstrate the existence via construction of a complete set of mutually orthogonal $F$-squares of order $n = 4t, t$ a positive integer, with two distinct symbols. The proof assumes that all Hadamard matrices of order $4t$ exist; they are known to exist for all $1 \leqq t \leqq 50$ and for 2$^p$. Two methods of construction, that is, Hadamard matrix theory and factorial design theory, are given; the methods are related, but the approaches differ.
"On the Existence and Construction of a Complete Set of Orthogonal $F(4t; 2t, 2t)$-Squares Design." Ann. Statist. 5 (3) 561 - 564, May, 1977. https://doi.org/10.1214/aos/1176343856