Characterizations of Regularity for certain $Q$-Polynomial Association Schemes
Keywords: $Q$-polynomial association scheme, linked systems of symmetric designs, real mutually unbiased bases, quadruple regularity
AbstractIt was shown that linked systems of symmetric designs with $a_1^*=0$ and mutually unbiased bases (MUBs) are triply regular association schemes. In this paper, we characterize triple regularity of linked systems of symmetric designs by its Krein number. And we prove that a maximal set of MUBs carries a quadruply regular association scheme and characterize the quadruple regularity of MUBs by its parameter.