Some new BIBDs with block size 7

For λ ≥ 3 the existence problem for(ν,7,λ) BIBDs has been completely solved, except when ν = 253. In this paper, 3 new direct (ν,7,λ) BIBD constructions are given for (ν,λ) = (259,1), (106,2), and (253,2). Some features of the known (175,7,1) BIBD are also discussed. Finally, a few (ν,7,1) BIBDs are obtained recursively. © 2000 John Wiley & Sons, Inc. J Combin Designs 8: 146–150, 2000