We establish that the necessary conditions for the existence of Bhaskar Rao designs of block size five are: (i)λ(v-1)≡0 (mod 4) (ii)λv(v-1)≡0 (mod 40) (iii)2 λ. We show these conditions are sufficient: for λ=4 if v>215, with 10 smaller possible exceptions and one definite exception at v=5; for λ=10 if v>445, with 11 smaller possible exceptions, and one definite exception at v=5; and for λ=20, with the possible exception of v=32; we also give a few results for other values of λ. © 2002 Elsevier Science B.V. All rights reserved.
Chaudhry, G. R., Greig, M., & Seberry, J. (2002). On the (v,5,λ)-family of Bhaskar Rao designs. Journal of Statistical Planning and Inference, 106(1–2), 303–327. https://doi.org/10.1016/S0378-3758(02)00220-3