BALANCED TERNARY DESIGNS WITH BLOCK SIZE 4

A balanced ternary design with block size four is a collection of multi-sets of size four, chosen from a v-set in such a way that each element of the v-set occurs 0, 1 or 2 times in each of the multi-sets (which are called blocks). Also each distinct pair of elements occurs lambda times (lambda is the index) and each element is repeated (that is, occurs twice) in rho2 blocks. (Here, a block such as {a,a,b,c}, written aabc for short, is said to contain six pairs: aa and bc once each, and ab and ac twice each.) In this paper we give necessary and sufficient conditions for the existence of a balanced ternary design with block size 4, any index lambda, and rho2 less-than-or-equal-to 6.