A computer generation of all pairs of mutually orthogonal Latin squares of order ten and dimension 35 or less is undertaken. All such pairs are successfully generated up to main class equivalence. No pairs of mutually orthogonal Latin squares of order ten exist for dimension 33. Six dimension 34 pairs, which are counterexamples to a conjecture by Moorehouse, are found. Eighty-five pairs can be formed with dimension 35. None of the pairs can be extended to a triple. If a triple of mutually orthogonal Latin squares exists for order ten, the pairs of Latin squares in the triple must be of dimension 36 or 37.

正交主效應計畫(Orthogonal main-effect plans)因可無相關地估計主效應，故常被應用於一般工業上作為篩選因子之用。然而，實驗通常費時耗財。因此，如何設計一個較經濟且有效的計劃是很重要的。回顧過去相關的研究，Jacroux (1992)提供了最小正交主效應計劃的充份條件及正交主效應計畫之最少實驗次數表(Jacroux 1992)，張純明(1998)針對此表提出修正與補充。在此，我們再次的補足此表。 正交主效應計畫中，如有重複實驗點，則純誤差可被估計，且據此檢定模型之適合度。Jacroux (1993)及張純明(1998)皆曾提出具最多部份重複之正交主效應計畫(Partially replicated orthogonal main-effect plans)。在此，我們討論所有三因子部份重複正交主效應計畫中，可能重複之最大次數，且具體提出建構此最大部份重複之最小正交主效應計畫之方法。 / Orthogonal main-effect plans (OMEP's), being able to estimate the main effects without correlation, are often employed in industrial situations for screening purpose. But experiments are expensive and time consuming. When an economical and efficient design is desired, a minimal orthogonal main-effect plans is a good choice. Jacroux (1992) derived a sufficient condition for OEMP's to have minimal number of runs and provided a table of minimal OMEP run numbers. Chang (1998) corrected and supplemented the table. In this paper, we try to improve the table to its perfection. A minimal OMEP with replicated runs is appreciated even more since then the pure error can be estimated and the goodness-of-fit of the model can be tested. Jacroux (1993) and Chang (1998) gave some partially replicated orthogonal main-effect plans (PROMEP's) with maximal number of replicated points. Here, we discuss minimal PROMEP's with 3 factors in detail. Methods of constructing minimal PROMEP's with replicated runs are provided, and the number of replicated runs are maximal for most cases.