Rudolf Schürer: MinT - A web database for querying optimal $(t,m,s)$-net parameters

An overwhelming variety of different constructions for $(t,m,s)$-nets and $(t,s)$-sequences are known today. An overview of important approaches can be found in [2]. Propagation rules which allow the construction of new nets based on existing ones, as well as connections to coding theory and algebraic geometry make it an even more difficult task to determine the best net available in a given setting. This problem led to the publication of tables of net parameters, with [1] and its predecessors being the best-known examples. However, parts of these tables had been outdated before the articles appeared in print. As a more flexible solution we present the web based database system MINT for querying best known $(t,m,s)$-net and $(t,s)$-sequence parameters. This new system provides a number hitherto unavailable services to the research community. Its advantages compared to any printed version of such tables include the possibility for fast and dynamic updates, distinction between digital and general constructions, different views on the data by appropriately choosing dependent and independent parameters, and last but not least its ease of use and its availability to everybody. We show examples of the usage of MINT, present its unique features, and discuss design and maintenance issues.

Bibliography

1

Andrew T. Clayman, K. Mark Lawrence, Gary L. Mullen, Harald Niederreiter, and N. J. A. Sloane.
Updated tables of parameters of $(t,m,s)$-nets.
J. Combin. Des., 7(5):381-393, 1999.

2

Harald Niederreiter.
Constructions of $(t,m,s)$-nets.
In Monte Carlo and quasi-Monte Carlo methods 1998 (Claremont, CA), pages 70-85. Springer, Berlin, 2000.

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