LatNet Builder Manual  2.0.1-11
Software Package for Constructing Highly Uniform Point Sets
Bibliography
[1]

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

[2]

H. Cohen, editor. A Course in Computational Number Theory. Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1993.

[3]

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.

[4]

R. Cools, F. Y. Kuo, and D. Nuyens. Constructing embedded lattice rules for multivariate integration. SIAM Journal on Scientific Computing, 28(16):2162–2188, 2006.

[5]

J. Dick and M. Matsumoto. On the fast computation of the weight enumerator polynomial and the $t$ value of digital nets over finite Abelian groups. SIAM Journal on Discrete Mathematics, 27(3):1335–1359, 2013.

[6]

J. Dick and F. Pillichshammer. Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration. Cambridge University Press, Cambridge, U.K., 2010.

[7]

J. Dick, F. Pillichshammer, and B. J. Waterhouse. The construction of good extensible rank-1 lattices. Mathematics of Computation, 77(264):2345–2373, 2008.

[8]

Josef Dick, Peter Kritzer, Gunther Leobacher, and Friedrich Pillichshammer. A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Journal of Computational and Applied Mathematics, 276:1 – 15, 2015.

[9]

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

[10]

Takashi Goda. Good interlaced polynomial lattice rules for numerical integration in weighted walsh spaces. 285, 06 2013.

[11]

F. J. Hickernell and H. Niederreiter. The existence of good extensible rank-1 lattices. Journal of Complexity, 19(3):286–300, 2003.

[12]

F. J. Hickernell, H. S. Hong, P. L'Ecuyer, and C. Lemieux. Extensible lattice sequences for quasi-Monte Carlo quadrature. SIAM Journal on Scientific Computing, 22(3):1117–1138, 2001.

[13]

F. J. Hickernell. A generalized discrepancy and quadrature error bound. Mathematics of Computation, 67(221):299–322, 1998.

[14]

S. Joe and F. Y. Kuo. Constructing Sobol sequences with better two-dimensional projections. SIAM Journal on Scientific Computing, 30(5):2635–2654, 2008.

[15]

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

[16]

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.

[17]

P. L'Ecuyer and C. Lemieux. Variance reduction via lattice rules. Management Science, 46(9):1214–1235, 2000.

[18]

P. L'Ecuyer and D. Munger. Algorithm 958: Lattice builder: A general software tool for constructing rank-1 lattice rules. ACM Trans. on Mathematical Software, 42(2):Article 15, 2016.

[19]

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

[20]

P. L'Ecuyer. Random number generation. In J. E. Gentle, W. Haerdle, and Y. Mori, editors, Handbook of Computational Statistics, pages 35–70. Springer-Verlag, Berlin, 2004. Chapter II.2.

[21]

C. Lemieux and P. L'Ecuyer. Randomized polynomial lattice rules for multivariate integration and simulation. SIAM Journal on Scientific Computing, 24(5):1768–1789, 2003.

[22]

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

[23]

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.

[24]

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

[25]

H. Niederreiter. The existence of good extensible polynomial lattice rules. Monatshefte für Mathematik, 139:297–307, 2003.

[26]

Dirk Nuyens. The construction of good lattice rules and polynomial lattice rules. In Peter Kritzer, Harald Niederreiter, Friedrich Pillichshammer, and Arne Winterhof, editors, Uniform Distribution and Quasi-Monte Carlo Methods: Discrepancy, Integration and Applications, pages 223–255. De Gruyter, 2014.

[27]

W. Ch. Schmid. The exact quality parameter of nets derived from Sobol' and Niederreiter sequences. Recent Advances in Numerical Methods and Applications, pages 287–295, 1999.

[28]

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.

[29]

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.

[30]

V. Sinescu and P. L'Ecuyer. Existence and contruction of shifted lattice rules with an arbitrary number of points and bounded worst-case error for general weights. Journal of Complexity, 27(5):449–465, 2011.

[31]

V. Sinescu and P. L'Ecuyer. Variance bounds and existence results for randomly shifted lattice rules. Journal of Computational and Applied Mathematics, 236:3296–3307, 2012.

[32]

I. H. Sloan and S. Joe. Lattice Methods for Multiple Integration. Clarendon Press, Oxford, 1994.

[33]

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