The problem of findingneighbor optimal designs for a general correlation structure is studied. This paper gives optimality universal conditions for incomplete block designs when observations on the same block are modeled by an autoregressive process AR(m) of an arbitrary order m. It extends and generalizes existing results for models AR(1) and AR(2) as in such as those of Grondona and Cressie (1993) for AR(2) and those of Gill and Shukla (1985) and Kunert (1987) for AR(1).