On the construction of hypercubic design

Hypercubic design was introduced by Shah (1958) and Kusumoto(1965) in which the t=v^m treatments are represented by n-plets (x₁, x₂, ..., x_m),where 1≤ x₁, x₂, ..., x_m ≤v, and two treatments are said to be i-th associates if they differ in exactly i components. This paper deals with the construction of some hypercubic designs and gives their application to confounding plans for symmetrical factorial experiments. The proposed methods prove to be quite flexible in terms of choice of possible block sizes and are easy to use.