Construction Of S-level Designs With General Minimum Lower-order Confounding

One of the main tasks of the trial design is to find good designs and to analyze trial data effectively,so as to be able to estimate effects and possible models related to the effects in the trial.Therefore,in order to estimate the important parameters in the model,a good design should minimize the confounding between low-order effects.Some of the most popular criteria for choosing the best design are:Maximum Resolution(MR),Minimum low-order Aberration(MA),Clear Effect(CE),Maximum Estimation Capacity(MEC)and the General Minimum Lower-order Confounding(GMC).This paper mainly studies the construction of s-level designs under GMC criterion.GMC theory has developed rapidly in recent years,among which the second-level GMC designs research is relatively mature,while s-level relatively have few horizontal studies.Zhang and Mukerjee(2009)developed the GMC theory to s-level designs.Later,Li et al.(2020)studied s-level GMC designs via complementary sets,and tried to give the condition of s-level GMC designs with n=(N—sr)/(s-1)+t,0 ≤t ≤(sr-sr-1)/(s-1).However,there exist certain limitations to get optimal s-level designs.In this paper,we prove that a design D=Sqr∪T has GMC only if T has resolution IV,where Sqr=Hq\Hr(r<q),T C Hr and Hq is generated by q independent columns for q=n-m.Further,some new sn-m GMC designs are constructed when n=(sn-m-sr)/(s-1)+t,4 ≤t≤s2+1 through the method.