A balanced 1-spread of PG(5,2) obtained via cyclic construction
data(spreadn6t2c)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 \(f_1=(F,ABCEF,ABCE)\), \(f_2 = (E,ABDF, ABDEF)\), \(f_3 = (D,ACF, ACDF)\), \(f_4 = (C,BF, BCF)\), \(f_5=(B,AE, ABE)\), \(f_6=(A,DEF, ADEF)\), \(f_7=(EF,CDE,CDF)\), \(f_8=(DE,BCD,BCE)\), \(f_9=(CD,ABC,ABD)\), \(f_{10}=(BC,ABEF,ACEF)\), \(f_{11}=(AB,ADF,BDF)\), \(f_{12}=(DF,BE,BDEF)\), \(f_{13}=(CE,AD,ACDE)\), \(f_{14}=(AC,BDE,ABCDE)\), \(f_{15}=(BEF,ACD,ABCDEF)\), \(f_{16}=(ADE,BCEF,ABCDF)\), \(f_{17}=(CDEF,ABDE,ABCF)\), \(f_{18}=(BCDE,ACDEF,ABF)\), \(f_{19}=(ACE,AF,CEF)\), \(f_{20}=(CF,BD,BCDF)\), and \(f_{21}=(ABCD,AEF,BCDEF)\).
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.