A survey on tight Euclidean t-designs and tight relative t-designs in certain association schemes
Eiichi Bannaĭ, Etsuko Bannai, Etsuko Bannai, Etsuko Bannai, Yan Mei Zhu · Proceedings of the Steklov Institute of Mathematics · 2015
It is known that there is a close analogy between the two relations “Euclidean t -designs vs. spherical t -designs” and “relative t -designs in binary Hamming association schemes vs. combinatorial t -designs.” We first look at this analogy and survey the known results, putting emphasis on the study of tight relative t -designs in certain Q -polynomial association schemes. We then specifically study tight relative 2-designs on two shells in binary Hamming association schemes H ( n , 2) and Johnson association schemes J ( v , k ). The purpose of this paper is to convince the reader that there is a rich theory even for these special cases and that the time is ripe to study tight relative t -designs more systematically for general Q -polynomial association schemes.