The Existence of FGDRP(3,g^u)’s - Yan, Jie; Wang, Chengmin (The Electronic Journal of Combinatorics, 2009)
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 of A can be arranged into a gu/3× gu array. This array has the properties: (1) the main diagonal consists of u empty subarrays of sizes g/3× g; (2) the blocks in each column form a partial parallel class partitioning X G for some GG, while the blocks in each row contain every element of X G 3 times and no element of G for some GG. The obvious necessary conditions for the existence of an FGDRP(3,g^u) are u≥ 5 and g0 (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)}.