A generalized Rao bound for ordered orthogonal arrays and (t, m, s)-nets

Canadian Mathematical Bulletin

Volumn 42, Issue 3, 1999, Pages 359-370

  Martin, W J ^a   Stinson, D R ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038853614     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-1999-042-x     Document Type: Article

References (13)

1. A. T. Clayman, K. M. Lawrence, G. L. Mullen, H. Niederreiter and N. J. A. Sloane, Updated tables of parameters of (T, M, S)-nets. J. Combin. Des., to appear (see also http://www.emba.uvm.edu/jcd/toappear.html).
2. Y. Edel and J. Bierbrauer, Construction of digital nets from BCH-codes. In: Monte Carlo and Quasi-Monte Carlo Methods 1996 (Salzburg), Lecture Notes in Statist. 127(1998), 221-231.
3. K. M. Lawrence, Combinatorial bounds and constructions in the theory of uniform point distributions in unit cubes, connections with orthogonal arrays and a poset generalization of a related problem in coding theory. PhD Thesis, University of Wisconsin-Madison, 1995.
4. _, A combinatorial characterization of (t, m, s)-nets in base b. J. Combin. Des. 4(1996), 275-293.
5. _, The orthogonal array bound for (t, m, s)-nets is not always attained. Preprint.
6. W. J. Martin and D. R. Stinson, Association schemes for ordered orthogonal arrays and (T, M, S)-nets. Canad. J. Math. (2) 51(1999), 326-346.
7. G. L. Mullen and W. Ch. Schmid, An equivalence between (T, M, S)-nets and strongly orthogonal hypercubes. J. Combin. Theory A 76(1996), 164-174.
8. G. L. Mullen and G. Whittle, Point sets with uniformity properties and orthogonal hypercubes. Monatsh. Math. 113(1992), 265-273.
9. H. Niederreiter, Point sets and sequences with small discrepancy. Monatsh. Math. 104(1987), 273-337.
10. C. R. Rao, Factorial experiments derivable from combinatorial arrangements of arrays. Suppl. J. Roy. Statist. Soc. 9(1947), 128-139.
11. W. Ch. Schmid, (T, M, S)-nets: digital constructions and combinatorial aspects. PhD Thesis, Universität Salzburg, 1995.
12. W. Ch. Schmid and R. Wolf, Bounds for digital nets and sequences. Acta Arith. 78(1997), 377-399.
13. M. Sobol', The distribution of points in a cube and the approximate evaluation of integrals. Ž. Vyčisl. Mat. i Mat. Fiz. 7(1967), 784-802. In Russian.