Super‐simple resolvable balanced incomplete block designs with block size 4 and index 2

The necessary conditions for the existence of a super-simple resolvable balanced incomplete block design on v points with block size k = 4 and index λ = 2, are that v ≥ 16 and . These conditions are shown to be sufficient. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 341–356, 2007

[1]  Christopher A. Rodger,et al.  Linear spaces with many small lines , 1994, Discret. Math..

[2]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

[3]  Ruizhong Wei,et al.  Super-simple (ν, 5, 5) Designs , 2006, Des. Codes Cryptogr..

[4]  Hao Shen,et al.  Resolvable Maximum Packings with Quadruples , 2005, Des. Codes Cryptogr..

[5]  Douglas R. Stinson,et al.  Frames with Block Size Four , 1992, Canadian Journal of Mathematics.

[6]  Gennian Ge,et al.  Asymptotic results on the existence of 4‐RGDDs and uniform 5‐GDDs , 2005 .

[7]  Gennian Ge,et al.  Some New uniform frames with block size four and index one or three , 2004 .

[8]  Chen Kejun On the existence of super-simple (v,4,4)-BIBDs , 1996 .

[9]  Donald L. Kreher,et al.  Super-simple (v, 5, 2)-designs , 2004, Discret. Appl. Math..

[10]  Andries E. Brouwer Mutually orthogonal latin squares , 1978 .

[11]  Gennian Ge,et al.  Super‐simple resolvable balanced incomplete block designs with block size 4 and index 3 , 2004 .

[12]  Zhenfu Cao,et al.  Super-simple balanced incomplete block designs with block size 4 and index 6 , 2005 .

[13]  Vladimir S. Lebedev,et al.  On optimal superimposed codes , 2004 .

[14]  R. Julian R. Abel,et al.  Super-simple Steiner pentagon systems , 2008, Discret. Appl. Math..

[15]  Frank E. Bennett,et al.  Holey Steiner pentagon systems , 1999 .

[16]  Ronald C. Mullin,et al.  On the existence of frames , 1981, Discret. Math..

[17]  R. Julian R. Abel,et al.  Super‐simple holey Steiner pentagon systems and related designs , 2008 .

[18]  Christopher A. Rodger,et al.  Existence of certain skew room frames with application to weakly 3-chromatic linear spaces , 1994 .

[19]  K. Heinrich,et al.  Super-simple designs with v⩽32 , 2001 .

[20]  Iliya Bluskov,et al.  New upper bounds on the minimum size of covering designs , 1998 .

[21]  Peter Adams,et al.  On the existence of super-simple designs with block size 4 , 1995 .