Commutative association schemes obtained from twin prime powers, Fermat primes, Mersenne primes

Abstract: For prime powers $q$ and $q+\varepsilon$ where $\varepsilon\in{1,2}$, an affine resolvable design from $\mathbb{F}<em>q$ and Latin squares from $\mathbb{F}</em>{q+\varepsilon}$ yield a set of symmetric designs if $\varepsilon=2$ and a set of symmetric group divisible designs if $\varepsilon=1$. We show that these designs derive commutative association schemes, and determine their eigenmatrices.