For the third-order interaction subvector a single comparison depth is optimal, while D-optimal designs for the full parameter vector use two depths, explicitly proven for S=4 and numerically verified for full profiles with S=5 to 12.
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Optimal $2^K$ Paired Comparison Designs for Third-Order Interactions
For the third-order interaction subvector a single comparison depth is optimal, while D-optimal designs for the full parameter vector use two depths, explicitly proven for S=4 and numerically verified for full profiles with S=5 to 12.