function tau = tau_sobol ( dim_num )

%*****************************************************************************80
%
%% TAU_SOBOL defines favorable starting seeds for Sobol sequences.
%
%  Discussion:
%
%    For spatial dimensions 1 through 13, this routine returns
%    a "favorable" value TAU by which an appropriate starting point
%    in the Sobol sequence can be determined.
%
%    These starting points have the form N = 2**K, where
%    for integration problems, it is desirable that
%      TAU + DIM_NUM - 1 <= K
%    while for optimization problems, it is desirable that
%      TAU < K.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    12 December 2009
%
%  Author:
%
%    Original FORTRAN77 version by Bennett Fox.
%    MATLAB version by John Burkardt.
%
%  Reference:
%
%    IA Antonov, VM Saleev,
%    USSR Computational Mathematics and Mathematical Physics,
%    Volume 19, 1980, pages 252 - 256.
%
%    Paul Bratley, Bennett Fox,
%    Algorithm 659:
%    Implementing Sobol's Quasirandom Sequence Generator,
%    ACM Transactions on Mathematical Software,
%    Volume 14, Number 1, pages 88-100, 1988.
%
%    Bennett Fox,
%    Algorithm 647:
%    Implementation and Relative Efficiency of Quasirandom
%    Sequence Generators,
%    ACM Transactions on Mathematical Software,
%    Volume 12, Number 4, pages 362-376, 1986.
%
%    Stephen Joe, Frances Kuo
%    Remark on Algorithm 659:
%    Implementing Sobol's Quasirandom Sequence Generator,
%    ACM Transactions on Mathematical Software,
%    Volume 29, Number 1, pages 49-57, March 2003.
%
%    Ilya Sobol,
%    USSR Computational Mathematics and Mathematical Physics,
%    Volume 16, pages 236-242, 1977.
%
%    Ilya Sobol, YL Levitan,
%    The Production of Points Uniformly Distributed in a Multidimensional
%    Cube (in Russian),
%    Preprint IPM Akad. Nauk SSSR,
%    Number 40, Moscow 1976.
%
%  Parameters:
%
%    Input, integer DIM_NUM, the spatial dimension.  Only values
%    of 1 through 13 will result in useful responses.
%
%    Output, integer TAU, the value TAU.
%
  dim_max = 13;

  tau_table = [  0,  0,  1,  3,  5, ...
                 8, 11, 15, 19, 23, ...
                27, 31, 35 ];

  if ( 1 <= dim_num && dim_num <= dim_max )
    tau = tau_table(dim_num);
  else
    tau = - 1;
  end

  return
end
