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Euclidean $t$-designs, which are finite weighted subsets of Euclidean space, were defined by Neumaier-Seidel (1988). A tight $t$-design is defined as a $t$-design whose cardinality is equal to the kno...wn natural lower bound. In this paper, we give a new Euclidean tight 6-design in $mathbb{R}^{22}$. Furthermore, we also show its uniqueness up to similar transformation fixing the origin. This design has the structure of coherent configuration, which was defined by Higman, and is obtained from the properties of general permutation groups. We also show that the design is obtained by combining two orbits of McLaughlin simple group.続きを見る
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tight6N-AC