The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 35, Number 1 (1964), 389-397.
Investigations in the Partially Balanced Incomplete Block (PBIB) designs having three or more associate classes have been limited to the works of Vartak , Raghavarao , Roy , Singh and Shukla  and Tharthare . In this article we study the combinatorial properties, construction and non-existence of the cubic designs exhibiting a three associate class association scheme. The method of construction, discussed in this article, gives a new way of arranging a $p^3$ factorial experiment in blocks of sizes different from $p$ and $p^2$.
Ann. Math. Statist., Volume 35, Number 1 (1964), 389-397.
First available in Project Euclid: 27 April 2007
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Raghavarao, D.; Chandrasekhararao, K. Cubic Designs. Ann. Math. Statist. 35 (1964), no. 1, 389--397. doi:10.1214/aoms/1177703762. https://projecteuclid.org/euclid.aoms/1177703762