Group divisible designs with block size 4 where the group sizes are congruent to 2 mod 3

In this paper, we construct a number of 4-GDDs where the group sizes are all congruent to 2 (mod 3). We also show that 4-GDDs of type 2t8s exist for all but a finite number of feasible values of s and t. The largest unknown case has type 24818 and has 152 points. A number of 4-GDDs with at most 50 points are also constructed. These include one of type 4811101, the last feasible type of the form 4s1tn1 with at most 50 points for which no 4-GDD was known.