We investigate the relation between distributional chaos and minimal sets,and discuss how to obtain various distributionally scrambled sets by using least and simplest minimal sets.We show:i)an uncountable extremal distributionally scrambled set can appear in a system with just one simple minimal set:a periodic orbit with period 2;ii)an uncountable dense invariant distributionally scrambled set can occur in a system with just two minimal sets:a fixed point and an infinite minimal set;iii)infinitely many minimal sets are necessary to generate a uniform invariant distributionally scrambled set,and an uncountable dense extremal invariant distributionally scrambled set can be constructed by using just countably infinitely many periodic orbits.
