本計畫旨在探討同時比較v個試驗處理(Test treatment)與一個對照處理(Control treatment)在集區設計(Block design)之架構下,尋找最適設計(Optimal design)之問題。在本計畫中我們導出一個不等式,並利用此一不等式找出.PHI.-最適集區設計之充分條件,由於問題本身之複雜性以及時間之緊迫性,報告中之定理3.10尚有一小部分未臻完善,我們將繼續完成定理3.10之證明。若定理3.10可被完全證出,則許多用以前方法所無法證明其為最適設計之集區設計,其最適性便可證出。 The problem of finding optimal designs for comparing a control simultaneously with v test treatments in the block design setting is studied. A useful inequality for proving optimality is derived. Conditions under which a design is .PHI.-optimal are found under the assumption that Theorem 3.10 is proved completely. These conditions, if the aforementioned theorem is proved completely, generalize previous known results and lead to designs whose optimality cannot be proven using existing methods. We will keep working on the proof of Theorem 3.10, and believe that it can be done in the nearest future.