The structure of nilpotent symplectic algebras of maximal class has been studied in Sorkatti and Traustason (J Algebra 423:615–635, 2015). In this chapter, we focus on the dual subclass of algebras of minimal class. In particular, we show that symplectic alternating algebras of dimension up to 16 that are minimal, in the sense that they are of rank 2 with minimum nilpotency class, have a class that confirms a conjecture that has been raised in Sorkatti (Int J Algebra Comput 32:67–84, 2022).