The Existence of FGDRP(3, g~u)'s

摘要

By an FGDRP(3, g~u),we mean a uniform frame(X, g,A)of block size 3, index 2 and type g~u,where the blocks ofAcan be arranged into a gu/3 xguarray. Thisarray has the properties: (1) the main diagonal consists of u empty subarrays ofsizes g/3 x g; (2) the blocks in each column form a partial parallel class partitioningX G for some G E g, while the blocks in each row contain every element of X G 3 times and no element of G for some G E G. The obvious necessary conditionsfor the existence of an FGDRP(3,gu) are u ≥ 5 and g 0 (mod 3). In this paper,we show that these conditions are also sufficient with the possible exceptions of(g,u) ∈ {(6,15), (9, 18), (9, 28), (9, 34), (30,15)}.