L. Afflerbach and H. Grothe. Calculation of Minkowski-reduced lattice bases. Computing, 35:269–276, 1985.

L. Afflerbach and H. Grothe. Calculation of Minkowski-reduced lattice bases. Computing, 35:269–276, 1985.

W. A. Beyer, R. B. Roof, and D. Williamson. The lattice structure of multiplicative congruential pseudo-random vectors. Mathematics of Computation, 25(114):345–363, 1971.

J. H. Conway and N. J. A. Sloane. Sphere Packings, Lattices and Groups. Grundlehren der Mathematischen Wissenschaften 290. Springer-Verlag, New York, 3rd edition, 1999.

R. Couture and P. L'Ecuyer. Orbits and lattices for linear random number generators with composite moduli. Mathematics of Computation, 65(213):189–201, 1996.

U. Dieter. How to calculate shortest vectors in a lattice. Mathematics of Computation, 29(131):827–833, 1975.

U. Fincke and M. Pohst. Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Mathematics of Computation, 44:463–471, 1985.

G. H. Golub and Ch. F. Van Loan. Matrix Computations. John Hopkins University Press, Baltimore, second edition, 1989.

H. Grothe. Matrixgeneratoren zur Erzeugung Gleichverteilter Pseudozufallsvektoren. Dissertation (thesis), Tech. Hochschule Darmstadt, Germany, 1988.

S. Joe and I. H. Sloan. On computing the lattice rule criterion R. Mathematics of Computation, 59:557–568, 1992.

D. E. Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley, Reading, MA, second edition, 1981.

D. E. Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley, Reading, MA, third edition, 1998.

P. L'Ecuyer and R. Couture. An implementation of the lattice and spectral tests for multiple recursive linear random number generators. INFORMS Journal on Computing, 9(2):206–217, 1997.

P. L'Ecuyer and D. Munger. On figures of merit for randomly-shifted lattice rules. In H. Wozniakowski and L. Plaskota, editors, Monte Carlo and Quasi-Monte Carlo Methods 2010, pages 133–159, Berlin, 2012. Springer-Verlag.

P. L'Ecuyer. Good parameters and implementations for combined multiple recursive random number generators. Operations Research, 47(1):159–164, 1999.

P. L'Ecuyer. Tables of maximally equidistributed combined LFSR generators. Mathematics of Computation, 68(225):261–269, 1999.

A. K. Lenstra, H. W. Lenstra, and L. Lovász. Factoring polynomials with rational coefficients. Math. Ann., 261:515–534, 1982.

G. Marsaglia. Random numbers fall mainly in the planes. Proceedings of the National Academy of Sciences of the United States of America, 60:25–28, 1968.

Phong Q. Nguyen. Hermite constants and lattice algorithms. In Phong Q. Nguyen and Brigitte Vallée, editors, The LLL Algorithm: Survey and Applications, pages 19–69. Springer Verlag, Berlin, Heidelberg, 2010.

H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods, volume 63 of SIAM CBMS-NSF Reg. Conf. Series in Applied Mathematics. SIAM, 1992.

M. Pohst. On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications. ACM SIGSAM Bulletin, 15:37–44, 1981.

C. P. Schnorr and M. Euchner. Lattice basis reduction: Improved practical algorithms and solving subset sum problems. In L. Budach, editor, Fundamentals of Computation Theory: 8th International Conference, pages 68–85, Berlin, Heidelberg, 1991. Springer-Verlag.

C. P. Schnorr. A hierarchy of polynomial time lattice basis reduction algorithms. Theoretical Computer Science, 53(2):201–224, 1987.

V. Sinescu and S. Joe. Good lattice rules with a composite number of points based on the product weighted star discrepancy. In A. Keller, S. Heinrich, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 645–658. Springer, 2008.

I. H. Sloan and S. Joe. Lattice methods for multiple integration. Oxford Science Publications. The Clarendon Press Oxford University Press, New York, 1994.