ISSN:
1432-0622
Keywords:
Permutation group
;
Block-transitive design
;
Machine computation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
,
Technology
Notes:
Abstract The block-transitive point-imprimitive 2-(729,8,1) designs are classified. They all have full automorphism group of order 729.13 which is an extension of a groupN of order 729, acting regularly on points, by a group of order 13. There are, up to isomorphism, 27 designs withN elementary abelian, 13 designs withN=Z 9 3 and 427 designs withN the relatively free 3-generator, exponent 3, nilpotency class 2 group, a total of 467 designs. This classification completes the classification of block-transitive, point-imprimitive 2-(ν, k, 1) designs satisfying $$\upsilon = \left( {\left( {_2^k } \right) - 1} \right)^2$$ , which is the Delandtsheer-Doyen upper bound for the numberν of points of such designs. The only examples of block-transitive, point-imprimitive 2-(ν, k, 1) designs with $$\upsilon = \left( {\left( {_2^k } \right) - 1} \right)^2$$ are the 2-(729, 8, 1) designs constructed in this paper.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01189023
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