Nonreduced extended affine root systems of nullity 3

In 1985 K. Saito [S] introduced the concept of an extended affine root system (EARS). His study of these root systems was motivated by his interest in singularities. Later in [AABGP], this notion played an important role in the study of extended affine Lie algebras. Saito classified the EARS's of nullity ≤ 2 which have the further property that the quotient modulo a "marking" is reduced. In [AABGP], a construction was given of all EARS's, and this was used to give a classification of EARS's of reduced type. However, when the EARS was not reduced, the isomorphism problem for the construction is quite difficult and the classification was only done for EARS'S with nullity ≤ 2. The present paper extends this classification to nullity 3.