Construction of new symmetric designs with parameters (66,26,10)

It is known that there exists only one (Tran van Trung's) design for (66,26,10) up to now. In this article we consider designs for (66,26,10) with the Frobenius group F₃₉ and we prove that there exist (up to isomorphism) exactly 18 such designs. © 1995 John Wiley & Sons, Inc. We characterize the proper t-wise balanced designs t?(v,K,1) for t ? 3, λ = 1 and v ? 16 with at least two block sizes. While we do not examine extensions of S(3,4,16)'s, we do determine all other possible extensions of S(3,K,v)'s for v ? 16. One very interesting extension is an S(4, {5,6}, 17) design. © 1995 John Wiley & Sons, Inc.