Definitions.-An arrangement of v objects (called treatments) in b sets( Y* C: \. p( W2 n. A) A
(called blocks) will be called a pairwise balanced design of index unity and type + e# U) q4 L' e! I2 f, b% r9 V* H(v; ki, k2, .. ., ki) if each block contains either k1, k2, .. ., or km treatments which0 J6 z; y) h7 u# V) w9 d
are all distinct (k, < v, k, $ kj), and every pair of distinct treatments occurs exactly' M4 U4 y0 s6 U( `5 ~" ~
in one block of the design. If the number of blocks containing k, treatments is/ H; G% n) ]( e N. B- M8 P
b,, then clearly b = A bi, v(v-1) = i biki(k -1)。。。# b* M5 Y! y3 X1 y B& y