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Let $p$ be an odd prime. In this paper we provide a construction which givesfour non-Schurian association schemes for every $p\geq 5$ and two for $p=3$.This construction is explained using incidences between points and lines of abiaffine plane and we also provide a pure algebraic model for it with the aidof finite Heisenberg groups. The obtained results are discussed in a more wideframework.

Construction of infinite families of non-Schurian association schemes of  order $2p^2$, $p$ an odd prime, based on biaffine planes and Heisenberg  groups: research report and beyond