THE SPECTRUM OF PBD ((5, K-ASTERISK), UPSILON) FOR K = 9, 13

被引:0
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作者
HAMEL, AM
MILLS, WH
MULLIN, RC
REES, R
STINSON, DR
YIN, JX
机构
[1] UNIV WATERLOO,DEPT COMBINATOR & OPTIMIZAT,WATERLOO N2L 3G1,ONTARIO,CANADA
[2] INST DEF ANAL,PRINCETON,NJ 08540
[3] MEM UNIV NEWFOUNDLAND,ST JOHNS A1C 5S7,NEWFOUNDLAND,CANADA
[4] UNIV NEBRASKA,LINCOLN,NE 68588
[5] UNIV SUZHOU,DEPT MATH,SUZHOU 215006,PEOPLES R CHINA
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中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A pairwise balanced design (PBD) of index 1 is a pair (V, A) where V is a finite set of points and A is a set of subsets (called blocks) of V, each of cardinality at least two, such that every pair of distinct points of V is contained in exactly one block of A. We may further restrict this definition to allow precisely one block of a given size, and in this case the design is called a PBD ({K, k*}, v) where k is the unique block size, K is the set of other allowable block sizes, and v is the number of points in the design. It is shown here that a PBD ({5, 9*}, v) exists for all v = 9 or 17 mod 20, v greater-than-or-equal-to 37, with the possible exception of 49, and that a PBD ({5, 13*}, v) exists for all v = 13 mod 20, v greater-than-or-equal-to 53.
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页码:7 / 26
页数:20
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