This investigation was originally motivated by the problem of determining the maximum number of variables which can be accommodated in a 2ᵥᵏ⁻ᵖ design in 256 runs and of constructing such a "saturated" design. This problem is solved through the application of an algorithm given by the authors in a previous paper (Draper and Mitchell (1967)) to the particular case $R = 5, q = k - p = 8$. To obtain the solution, the complete set of even 512-run designs of resolution 6 and the complete set of 256-run designs of resolution 5 are constructed. Tables are given which immediately provide generating relations for all of these designs, "optimally" blocked.
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Draper et al. (1968) studied this question.