Enumeration of t-Designs Through Intersection Matrices

Classification of designs with nontrivial automorphism groups

“…There are several common algorithmic approaches, which are used to search for configurations with particular properties and clever computational techniques play a central role in this area. In the case of t-designs, classification has been done for few classes, see for example [1,2,3,4,5,6,10,11,12,16].…”

“…A good example of this is [19], where to prove the nonexistence of 4-ð12; 6; 6Þ designs, the authors made use of the classification of the smaller 3-ð10; 4; 3Þ and 4-ð11; 5; 3Þ simple designs. For examples of complete classification achieved through extension, the reader is referred to [4,6,12].…”