AI 中文总结
本文提出从ARSRGD设计及广义哈达玛矩阵构造成对可加BIB设计的新方法，结合广义哈达玛矩阵的已知结果得到含此前未知参数集的新无穷系列成对可加BIB设计。
AI 中文摘要
成对可加平衡不完全区组（BIB）设计的集合的存在性，即成对可加BIB设计，已在文献中通过直接构造和递归构造进行研究。本文提出一种从仿射可解半正则可分组（ARSRGD）设计构造此类设计的新方法。由于许多已知的ARSRGD设计由广义哈达玛矩阵得到，我们也描述了从广义哈达玛矩阵构造成对可加BIB设计的对应方法。结合该构造与广义哈达玛矩阵的已知存在性结果，我们得到了若干新的成对可加BIB设计无穷系列，包括参数集存在性此前未知的设计。
英文摘要
The existence of sets of balanced incomplete block (BIB) designs with pairwise additivity, called pairwise additive BIB designs, has been studied through direct and recursive constructions in the literature. This paper presents a new method of constructing such designs from affine resolvable semi-regular group divisible (ARSRGD) designs. Since many known ARSRGD designs are obtained from generalized Hadamard matrices, we also describe the corresponding construction of pairwise additive BIB designs from generalized Hadamard matrices. Using the construction together with known existence results for generalized Hadamard matrices, we obtain several new infinite series of pairwise additive BIB designs, including designs with parameter sets whose existence was previously unknown.
