Balanced ternary designs with block size three

Abstract

A balanced ternary design (BTD) is a balanced design on V elements with constant block size in which each element may occur 0, 1 or 2 times in each block. The condition V≡0 (mod 3) is shown to be both necessary and sufficient for the existence of a BTD on V elements with block size 3 and index 2 in which each element is repeated in exactly one block and each element occurs in a constant number of blocks.