It was shown in [11] that one can construct orthogonal arrays (λ 2³, k + 1, 2, 3) from arrays (λ 2², k, 2, 2) with the maximum number of constraints $k + 1$ provided that k is the maximum number of constraints for the arrays of strength two. This result is generalized here to construction of arrays (λ 2t + 1, k + 1, 2, t + 1) from arrays (λ 2ᵗ, k, 2, t). The structure of arrays (λ 2ᵗ, t + 1, 2, t) is analyzed and for λ = q2ⁿ, q odd, a method of extending any array (λ 2ᵗ, t + 1, 2, t) to $t + n + 1$ constraints is described. Orthogonal arrays (λ 2⁴, k, 2, 4) are discussed in detail for λ = 1 through λ = 5. The maximum value of k is established in each of these cases and arrays assuming these values are effectively constructed.
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Seiden et al. (1966) studied this question.