MOLS                package:crossdes                R Documentation

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_D_e_s_c_r_i_p_t_i_o_n:

     The function constructs sets of mutually othogonal latin squares
     (MOLS) using Galois fields. The construction works for prime
     powers only.

_U_s_a_g_e:

     MOLS(p, n, primpol = GF(p, n)[[2]][1, ])

_A_r_g_u_m_e_n_t_s:

       p: A prime number less than 100. 

       n: A positive integer.

 primpol: A primitive polynomial of the Galois Field GF(p^n).

_D_e_t_a_i_l_s:

     If trt = p^n is a prime power, then trt-1 latin squares of order
     trt  are constructed. The elements of the squares are numbered
     1,...,trt.  These squares are mutually orthogonal, i.e. if any two
     of them are superimposed, the resulting array will contain each
     ordered pair (i,j), i,j in {1,..., trt} exactly once. The squares
     are in standard order, i.e. the first row is always equal to
     (1,...,trt). A primitive polynomial may be constructed
     automatically using the internal function 'GF'.

_V_a_l_u_e:

     For trt = p^n, an array that contains trt-1 latin squares is
     returned.

_A_u_t_h_o_r(_s):

     Oliver Sailer sailer@statistik.uni-dortmund.de

_R_e_f_e_r_e_n_c_e_s:

     Cherowitzo, W.:
     http://www-math.cudenver.edu/~wcherowi/courses/finflds.html

     Street, A.P. and Street, D.J. (1987): Combinatorics of
     experimental design. Oxford University Press, Oxford.

_S_e_e _A_l_s_o:

     'des.MOLS'

_E_x_a_m_p_l_e_s:

     MOLS(7,1) # 6 mutually orthogonal latin squares of order 7
     MOLS(2,3) # 7 mutually orthogonal latin squares of order 8

