Construction and cataloguing of nested partially balanced incomplete block designs

This article provides some new methods of construction of two and three associate class Nested Partially Balanced Incomplete Block (NPBIB) designs. The methods are based on Latin-square association scheme, rectangular association scheme and triangular association scheme. One method of constructing NPBIB designs has also been given by incorporating a set of new treatments in place of each treatment in a Nested Balanced Incomplete Block (NBIB) design. Exhaustive catalogues of NPBIB designs based on two and three class association schemes with v less than or equal to 30 and r less than or equal to 15 have also been prepared.