In search of 4-(12, 6, 4) designs: Part III

D. R. Breach, Anne Penfold Street
1993 The Australasian Journal of Combinatorics  
A 4- (12, 6, 4) design that is not also a 5-(12, 6, 1) design must have at least one pair of blocks with five points in common. It is shown that there are just nine non-isomorphic such designs; so, including the 5-(12, 6, 1) design, there are ten 4-(12, 6, 4) designs. These designs are characterised by the orders of their automorphism groups and they all contain a 4-(11, 5, 1) design.
dblp:journals/ajc/BreachS93 fatcat:t5nhq25wqbcuxc7sjptd22ki5i