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For prime powers $q$ and $q+\varepsilon$ where $\varepsilon\in\{1,2\}$, anaffine resolvable design from $\mathbb{F}_q$ and Latin squares from$\mathbb{F}_{q+\varepsilon}$ 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 associationschemes, and determine their eigenmatrices.

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