A balanced 1-spread of PG(5,2) obtained via cyclic construction
data(spreadn6t2b)The spread is formatted as a 3-dimensional array, where the [i,j,k]-th element indicates whether or not the ith basic factor is present in the jth effect of the kth flat of the spread.
The spread consists of 21 subspaces \(f_1, f_2, ..., f_{21}\) given by \(f_1=(EF,BCD,BCDEF)\), \(f_2 = (A,ACF,CF)\), \(f_3 = (B,ABCDE,ACDE)\), \(f_4 = (DF,F,D)\), \(f_5=(E,BC,BCE)\), \(f_6=(ABC,ABEF,CEF)\), \(f_7=(AEF,ABDF,BDE)\), \(f_8=(AB,BDEF,ADEF)\), \(f_9=(BDF,ABCDEF,ACE)\), \(f_{10}=(DEF,BCF,BCDE)\), \(f_{11}=(ABCE,ACEF,BF)\), \(f_{12}=(BEF,AE,ABF)\), \(f_{13}=(ADF,AC,CDF)\), \(f_{14}=(ABCDF,ABE,CDEF)\), \(f_{15}=(AF,ACDF,CD)\), \(f_{16}=(C,AD,ACD)\), \(f_{17}=(ABDE,CE,ABCD)\), \(f_{18}=(ABDEF,CDE,ABCF)\), \(f_{19}=(ACDEF,BD,ABCEF)\), \(f_{20}=(BCEF,DE,BCDF)\), and \(f_{21}=(BE,ADE,ABD)\).
Spencer, N.A., Ranjan, P., and Mendivil, F., (2019), "Isomorphism Check for \(2^n\) Factorial Designs with Randomization Restrictions", Journal of Statistical Theory and Practice, 13(60),1-24 [https://doi.org/10.1007/s42519-019-0064-5]
checkSpreadIsomorphism for checking the isomorphism of balanced spreads.
checkStarIsomorphism for checking the isomorphism of balanced covering stars.