Book spreads in

An ( n , q , r , s ) book is a collection of r -subspaces in P G ( n , q ) called pages, which cover the whole projective space and intersect in a common s -subspace called the spine such that any point outside the spine is in exactly one page. An ( n , q , r , s ) book t -spread is a t -spread in P G ( n , q ) for which there exists an ( n , q , r , s ) book, such that the points of each page of this book and hence the points of the spine are partitioned by t -subspaces of the t -spread. mence by showing that an ( n , q , r , s ) book t -spread exists if and only if the following three conditions hold: (i)  ( r − s ) | ( n − s ) , (ii)  ( t + 1 ) | ( s + 1 ) , (iii)  ( t + 1 ) | ( r + 1 ) . In general the number of different kinds of ( n , q , r , s ) book t -spreads is a tiny proportion of the number of different kinds of t -spreads in P G ( n , q ) . rest of this paper we present computer-aided classification results for certain types of ( 7 , 2 , 5 , 3 ) book 1-spreads.