## The Annals of Mathematical Statistics

### Cubic Designs

#### Abstract

Investigations in the Partially Balanced Incomplete Block (PBIB) designs having three or more associate classes have been limited to the works of Vartak [14], Raghavarao [7], Roy [9], Singh and Shukla [12] and Tharthare [13]. 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 $p^2$.

#### Article information

Source
Ann. Math. Statist., Volume 35, Number 1 (1964), 389-397.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177703762

Digital Object Identifier
doi:10.1214/aoms/1177703762

Mathematical Reviews number (MathSciNet)
MR158494

Zentralblatt MATH identifier
0123.36603

JSTOR