Relative t-designs in binary Hamming association schemes are equivalent to weighted regular t-wise balanced designs which are studied to some extent. In the paper, we extend the investigation to relative t-designs in nonbinary Hamming association schemes. Each nontrivial shell of a nonbinary Hamming association scheme is a symmetric association scheme which is called q-ary or nonbinary Johnson association scheme. Using the addition formula for Krawtchouk polynomials, we prove that the subset on each shell of a relative t-design in nonbinary Hamming association schemes supported by p shells is a weighted \(\mathcal T\)-design in nonbinary Johnson association scheme for \(\mathcal T=\{(k,h)\mid 0\le h\le k\le t+1-p\}\). We also give a combinatorial characterization of the subset of a relative t-design on each shell making use of regular semilattice. In addition, we obtain some lower bounds on the size as well as the degree of \(\mathcal T\)-designs in nonbinary Johnson association schemes.

二元汉明关联方案中的相对t设计等效于在一定程度上研究的加权规则t平衡设计。在本文中，我们将研究扩展到非二元汉明关联方案中的相关t设计。非二元汉明关联方案的每个非平凡壳都是对称关联方案，称为q 元或非二元约翰逊关联方案。使用 Krawtchouk 多项式的加法公式，我们证明了p壳支持的非二元汉明关联方案中相对t设计的每个壳上的子集是加权的\(\mathcal T\)- 在非二元约翰逊关联方案中设计\(\mathcal T=\{(k,h)\mid 0\le h\le k\le t+1-p\}\)。我们还使用正则半格给出了每个壳上相对t设计的子集的组合特征。此外，我们在非二元约翰逊关联方案中获得了一些尺寸的下限以及\(\mathcal T\) -设计的程度。