U-Type Designs via New Generalized Partially Balanced Incomplete Block Designs with <i>m</i> = 4, 5 and 7 Associated Classes

Abstract

The traditional combinatorial designs can be used as basic designs for constructing designs of computer experiments which have been used successfully till now in various domains such as engineering, pharmaceutical industry, etc. In this paper, a new series of generalized partially balanced incomplete blocks PBIB designs with m associated classes ( m = 4, 5 and 7) based on new generalized association schemes with number of treatments v arranged in w arrays of n rows and l columns ( w ≥ 2, n ≥ 2, l ≥ 2) is defined. Some construction methods of these new PBIB are given and their parameters are specified using the Combinatory Method ( s ). For n or l even and s divisor of n or l , the obtained PBIB designs are resolvable PBIB designs. So the Fang RBIBD method is applied to obtain a series of particular U -type designs U ( wnl ; ) ( r is the repetition number of each treatment in our resolvable PBIB design).