A hierarchy of complete orthogonal structures

Ars Combinatoria

Volumn 63, Issue , 2002, Pages 75-88

  Laywine, Charles F ^a   Mullen, Gary L ^b  

^a BROCK UNIVERSITY   (Canada)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142138271     PISSN: 03817032     EISSN: 28175204     Source Type: Journal    
DOI: None     Document Type: Article

References (30)

1. V.N. Bhat and S.S. Shrikhande, Non-isomorphic solutions of some balanced incomplete block designs, J. Combinatorial Thy. 9 (1970), 174-191.
2. R.C. Boss, On the application of the properties of Galois fields to the problem of construction of hyper-Graeco Latin squares, Sankhya 3 (1938), 323-338.
3. 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. Combinatorial Designs 7 (1999), 381-393.
4. A.S. Hedayat, D. Raghavarao and E. Seiden, Further contributions to the theory of F-sguares design, Ann. Statist. 3 (1975), 712-716.
5. A.S. Hedayat, N.J.A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications, Springer Series in Statistics, Springer-Verlag, New York, 1999.
6. P. Höhler, Eine Verallgemeinerung von orthogonalen lateinischen Quadraten auf höhere Dimensionen, Diss. Dokt. Eidgenöss, Techn. Hochschule Zürich, 1970.
7. M.E. Kimberley, On the construction of certain Hadamard designs, Math. Z. 119 (1971), 41-59.
8. K.M. Lawrence, A combinatorial characterization of (t, m, s)-nets in base b, J. Combinatorial Designs 4 (1996), 275-293.
9. K.M. Lawrence, A. Mahalanabis, G.L. Mullen, and W.C. Schmid, Construction of digital (t, m, s)-nets from linear codes, Finite Fields and Applications, Lect, Note Series of the London Math. Soc. (S.D. Cohen and H. Niederreiter, eds.), vol. 233, Camb. Univ. Press, 1996, pp. 189-208.
10. C.F. Laywine, A geometric construction for sets of mutually orthogonal frequency squares, Utilitas Math. 35 (1989), 95-102.
11. C.F. Laywine, Complete sets of orthogonal frequency squares and affine resolvable designs, Utilitas Math. 43 (1993), 161-170.
12. C.F. Laywine, On the dimension of affine designs and hypercubes, J. Combin. Designs 4 (1996), 235-246.
13. h-1) MOFS, J. Combin. Designs 7 (1999), 331-340.
14. C.F. Laywine and G.L. Mullen, Generalizations of Base's equivalence between complete sets of mutually orthogonal latin squares and affine planes, J. Combinatorial Thy., Ser. A 61 (1992), 13-35.
15. C.F. Laywine and G.L. Mullen, Mutually orthogonal frequency hypercubes and affine geometries, In: Coding Theory, Design Theory, Group Theory, (Eds. D. Jungnickel and S.A. Vanstone), John Wiley, 1993, 183-193.
16. C.F. Laywine, G.L. Mullen, and G. Whittle, D-dimensional hypercubes and the Euler and MacNeish conjectures, Monatsh. Math. 119 (1995), 223-238.
17. V. C. Mavron, On the structure of affine designs, Math. Z. 125 (1972), 298-316.
18. I.H. Morgan, Construction of complete sets of mutually equiorthogonal frequency hypercubes, Discrete Math. 186 (1998), 237-251.
19. G.L. Mullen, Polynomial representation of complete sets of mutually orthogonal frequency squares of prime power order, Discrete Math. 69 (1988), 79-84.
20. G.L. Mullen, A candidate for the "next Fermat problem", Math. Intelligencer 17 (1995), 18-21.
21. G.L. Mullen, Combinatorial methods in the construction of point sets with uniformity properties, Math. Comput. Modelling, 23 (1996), no. 8/9, pp. 1-8.
22. G.L. Mullen, A. Mahalanabis, and H. Niederreiter, Tables of (t,m,s)-net and (t,s)-sequence parameters, Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Lect. Notes in Statist. (H. Niederreiter and P.J.-S. Shiue, eds.), vol. 106, Springer, New York, 1995, pp. 58-86.
23. G.L. Mullen and W.C. Schmid, An equivalence between (t,m,s)-nets and strongly orthogonal hypercubes, J. Combinatorial Theory, Ser. A 76 (1996), 164-174.
24. G.L. Mullen and G. Whittle, Point sets with uniformity properties and orthogonal hypercubes, Monatsh. Math. 113 (1992), 265-273.
25. H. Niederreiter, Point sets and sequences with small discrepancy, Monatsh. Math. 104 (1987), 273-337.
26. H. Niederreiter, Random Number Generation and Quasi-Monte Carlo Methods, CBMS-NSF Regional Conference Series in Applied Math., vol. 63, SIAM, Philadelphia, 1992.
27. S.J. Schwager, W.T. Federer and B.L. Raktoe, Nonisomorphic complete sets of orthogonal F-squares and Hadamard matrices, Comm. Statist.-Theor. Meth. 13 (1984), 1391-1406.
28. S.S. Shrikhande, Affine resolvable balanced incomplete block designs: A survey, Aequationes Math. 14 (1976), 251-269.
29. S. J. Suchower, On the maximal number of mutually orthogonal F-hyperrectangles, Utilitas Math. 36 (1989), 77-82.
30. S. J. Suchower, Polynomial representations of complete sets of frequency hyperrectangles with prime power dimensions, J. Combin Theory Ser. A 62 (1993), 46-65.