Some Theorems for Partially Balanced Designs
نویسندگان
چکیده
منابع مشابه
Some Pairwise Balanced Designs
A pairwise balanced design, B(K; v), is a block design on v points, with block sizes taken from K, and with every pair of points occurring in a unique block; for a fixed K, B(K) is the set of all v for which a B(K; v) exists. A set, S, is a PBD-basis for the set, T , if T = B(S). Let Na(m) = {n : n ≡ a mod m}, and N≥m = {n : n ≥ m}; with Q the corresponding restriction of N to prime powers. Thi...
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A balanced part ternary design (BPTD) is a balanced ternary design (BTD) with a specified number of blocks, say b2, each having repeated elements. We prove some necessary conditions on b2 and show the existence of some particular BPTDs. We also give constructions of infinite families of BPTDs with b1 = 0, including families of ternary t-designs with t ≥ 3.
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Some Balanced Bipartite Row-column Designs
A series of balanced bipartite row-column designs (BBPRC-designs) into sets of treatments with v1=4t+3 (test treatments) v2=2t+2 (control treatments) with varying replication has been obtained by supplementing a set of v2=2t+2 treatments in blank positions of non-orthogonal RC design of Agrawal (1966). Such designs find applications in agricultural and industrial experimentation where the inves...
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1954
ISSN: 0003-4851
DOI: 10.1214/aoms/1177728849