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Realizations for direct constructions of resolvable Steiner 2‐designs with block size 5
Author(s) -
Leonard Philip A.
Publication year - 2000
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(2000)8:3<207::aid-jcd6>3.0.co;2-f
Subject(s) - mathematics , combinatorics , block (permutation group theory) , block size , order (exchange) , prime (order theory) , character (mathematics) , block design , discrete mathematics , combinatorial design , key (lock) , computer science , geometry , computer security , finance , economics
We consider direct constructions due to R. J. R. Abel and M. Greig, and to M. Buratti, for ({ν},5,1) balanced incomplete block designs. These designs are defined using the prime fields F p for certain primes p , are 1‐rotational over G ⊕ F p where G is a group of order 4, and are also resolvable under certain conditions. We introduce specifications to the constructions and, by means of character sum arguments, show that the constructions yield resolvable designs whenever p is sufficiently large. © 2000 John Wiley & Sons, Inc. J Combin Designs 8:207–217, 2000