: In this thesis, a type="#_x0000_t75" is considered. Each block consists of h consecutive complete blocks and, at the end, an incomplete block of size k-hv. For suitable number of blocks, a universally optimal design is found for a first-order stationary autoregressive process with positive correlations. Optimal generalized binary designs and balanced block designs are also considered. This thesis shows that when we have independent observation, extended complete block designs and generalized binary designs are universally optimal. A negative dependence parameter, and some other dependence structures, are also considered.