关于正交表最小长度的一个注记
A note on the minimum size of an orthogonal array
摘要：
一个基本的事实是k个因子的强度t的正交表的大小必须是某个数的倍数，比如L_t，它取决于因子的阶数。因此L_t是这些因子上强度为t的数组大小的下界，并且不大于完全析因设计的大小L_k。本文研究了数L_t之间的关系，特别是两个问题：对于什么t，L_t < L_k？当L_t = L_k时，完全析因设计是否是唯一具有该大小和强度t的数组？假设数组是混合级别的。我们将大小小于L_k的数组称为真分数。在我们的主要结果的指导下，我们构造了各种混合水平真分数的强度k-1，也满足一定的群论条件。
英文摘要：
It is an elementary fact that the size of an orthogonal array of strength t on k factors must be a multiple of a certain number, say L_t, that depends on the orders of the factors. Thus L_t is a lower bound on the size of arrays of strength t on those factors, and is no larger than L_k, the size of the complete factorial design. We investigate the relationship between the numbers L_t, and two questions in particular: For what t is L_t < L_k? And when L_t = L_k, is the complete factorial design the only array of that size and strength t? Arrays are assumed to be mixed-level. We refer to an array of size less than L_k as a proper fraction. Guided by our main result, we construct a variety of mixed-level proper fractions of strength k-1 that also satisfy a certain group-theoretic condition.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
