论文标题
通用$ P $ - ARY设计
Universal $p$-ary designs
论文作者
论文摘要
我们调查了$ p $ -ary $ t $ -Designs，它们同时设计了所有$ t $，我们称之为通用$ p $ -ary设计。由于戈登·詹姆斯（Gordon James），通过对称群体的代表理论，无效的通用设计被充分理解。我们研究了非零用设计，并确定存在这种设计的系数的必要条件。这使我们能够将所有通用设计分类为相似性。
We investigate $p$-ary $t$-designs which are simultaneously designs for all $t$, which we call universal $p$-ary designs. Null universal designs are well understood due to Gordon James via the representation theory of the symmetric group. We study non-null designs and determine necessary and sufficient conditions on the coefficients for such a design to exist. This allows us to classify all universal designs, up to similarity.
