ON DERIVATION OF INITIAL BLOCKS OF B.I.B. DESIGNS WITH MORE THAN ONE INITIAL BLOCK

A good amount of work has been done on the construction of balanced incomplete block (B.I.B.) designs by Bose (1939, 1942), Sprott (1954, 1956), Rao (1961), Takeuchi (1962) and others. Sprott (1954, 1956) obtained several series of B.I.B. designs through difference sets. The main purpose of the present investigation is to provide two methods of construction of B.I.B. designs obtainable through more than one initial block. The first method derives initial blocks of a series of designs from some specified blocks of a B.I.B. design obtainable by developing one or more initial blocks. The second method attempts to obtain one of the initial blocks (the basic initial block) through the different powers of an element of a finite field; then an appropriate method for generating the other initial blocks from it is discussed. A table showing the basic initial block for different designs has been presented. By these methods several solutions of some B.I.B. designs could be obtained from different initial blocks. An examination was therefore made to see if these designs were all isomorphic.