Unimbeddable nets of small deficiency

Aiden A. Bruen

Vol. 43 (1972), No. 1, 51–54

DOI: 10.2140/pjm.1972.43.51

Abstract

We construct some new geometrical examples of unimbeddable nets N of order p² with p an odd prime. The deficiency of N is p−j where either j = 0 or j = 1. In particular, the examples show that a bound of Bruck is best possible for nets of order 9,25. Our proof also shows that deriving a translation plane of order p² is equivalent to reversing a regulus in the corresponding spread.

Mathematical Subject Classification

Primary: 50D35

Milestones

Received: 26 July 1971

Revised: 17 November 1971

Published: 1 October 1972