In this paper we present a method of constructing main-effect plans for symmetrical factorial experiments which can accommodate up to 2(sⁿ - 1)/(s - 1) - 1 factors, each at s = pᵐ levels, where p is a prime, with 2sⁿ treatment combinations. As main-effect plans are orthogonal arrays of strength two the method presented permits the construction of the orthogonal arrays (2sⁿ, 2 sⁿ - 1/ 2 - 1 - 1, s, 2).
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Addelman et al. (1961) studied this question.