Designs from pairs of finite fields. A cyclic unital U(6) and other regular steiner 2-designs

Bagchi, Bhaskar ; Bagchi, Sunanda (1989) Designs from pairs of finite fields. A cyclic unital U(6) and other regular steiner 2-designs Journal of Combinatorial Theory, Series A, 52 (1). pp. 51-61. ISSN 0097-3165

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/009731...

Related URL: http://dx.doi.org/10.1016/0097-3165(89)90061-7

Abstract

A general construction for Steiner 2-designs with prime power block size (and with a point-regular automorphism group) is presented. Its success depends on number-theoretic restrictions on the parameters-these are completely analysed in case of block sizes k ≤11. The new designs constructed include infinitely many cyclic Steiner 2-designs with block size 7. Among them is a cyclic unital U(6), that is, an S(2, 6 + 1, 63 + 1). It is the first example of a unital with non-prime power parameter and the second example of a cyclic unital.

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