In this paper we present a method of constructing main-effect plans for symmetrical factorial experiments which can accommodate up to $\lbrack 2(s^n - 1)/(s - 1) - 1\rbrack$ factors, each at $s = p^m$ levels, where $p$ is a prime, with $2s^n$ treatment combinations. As main-effect plans are orthogonal arrays of strength two the method presented permits the construction of the orthogonal arrays $(2s^n, 2\lbrack s^n - 1\rbrack/\lbrack 2 - 1\rbrack - 1, s, 2)$
Some Main-Effect Plans and Orthogonal Arrays of Strength Two
Addelman, S., & Kempthorne, O. (1961). Some Main-Effect Plans and Orthogonal Arrays of Strength Two. Annals of Mathematical Statistics, 32(4), 1167-1176.