Combinatorial methods in the construction of point sets with uniformity properties

Mathematical and Computer Modelling

Volumn 23, Issue 8-9, 1996, Pages 1-8

  Mullen, G L ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

(t, m, s) nets; Hypercubes; Latin squares

Indexed keywords

EID: 0039860064     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/0895-7177(96)00035-0     Document Type: Article

References (20)

1. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104, 273-337 (1987).
2. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Math., Vol. 63, SIAM, Philadelphia, PA, (1992).
3. H. Niederreiter, Low-discrepancy and low-dispersion sequences, J. Number Thy. 30, 51-70 (1988).
4. T. Hansen, G.L. Mullen and H. Niederreiter, Good parameters for a class of node sets in quasi-Monte Carlo integration, Math. Computation 61, 225-234 (1993).
5. G. Larcher, A. Lauss, H. Niederreiter and W.Ch. Schmid, Optimal polynomials for (t, m, s)-nets and numerical integration of multivariate Walsh series, SIAM J. Numer. Analysis (to appear).
6. J. Dénes and A.D. Keedwell, Latin Squares and Their Applications, Academic Press, New York, (1974).
7. J. Dénes and A.D. Keedwell, Latin Squares, Annals of Discrete Math., Vol. 46, North-Holland, Amsterdam, (1991).
8. G.L. Mullen and G. Whittle, Point sets with uniformity properties and orthogonal hypercubes, Monatsh. Math. 113, 265-273 (1992).
9. H. Niederreiter, Orthogonal arrays and other combinatorial aspects in the theory of uniform point distributions in unit cubes, Discrete Math. 106/107, 361-367 (1992).
10. G.L. Mullen, Polynomial representation of complete sets of mutually orthogonal frequency squares of prime power order, Discrete Math. 69, 79-84 (1988).
11. C.F. Laywine, G.L. Mullen and G. Whittle, D-dimensional hypercubes and the Euler and MacNeish conjectures, Monatsh. Math. 119, 223-238 (1995).
12. C.R. Rao, Hypercubes of strength "d" leading to confounded designs in factorial experiments, Bull. Calcutta Math. Soc. 38, 67-78 (1946).
13. H. Niederreiter, A combinatorial problem for vector spaces over finite fields, Discrete Math. 96, 221-228 (1991).
14. A.E. Brouwer and T. Verhoeff, An updated table of minimum-distance bounds for binary linear codes, IEEE Trans. Infor. Thy. IT-39, 662-677 (1993).
15. S.W. Golomb and E.C. Posner, Rook domains, Latin squares, affine planes, and error-distributing codes, IEEE Trans. Infor. Thy. IT-10, 196-208 (1964).
16. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, (1977).
17. S.S. Shrikhande, A note on mutually orthogonal Latin squares, Sankhyā, Ser. A 23, 115-116 (1961).
18. R.H. Bruck, Finite nets, II. Uniqueness and embedding, Pacific J. Math. 13, 421-457 (1963).
19. A.E. Brouwer, Recursive constructions of mutually orthogonal Latin squares, In Latin Squares, Annals of Discrete Math., Volume 46, (Edited by J. Dénes and A. D. Keedwell), pp. 149-168, North-Holland, Amsterdam, (1991).
20. B. Smetaniuk, A new construction on Latin squares I. A proof of the Evans conjecture, Ars Combinatoria 11, 155-172 (1981).