Families of ternary \((t,m,s)\)-nets related to BCH-codes (Q5939035)

The most powerful current methods of constructing low-discrepancy point sets for quasi-Monte Carlo applications employ the theory of \((t,m,s)\)-nets. (For a recent survey on \((t,m,s)\)-nets see \textit{H. Niederreiter} [Niederreiter, Harald (ed.) et al., Monte Carlo and quasi-Monte Carlo methods 1998. Proceedings of a conference held at the Claremont Graduate Univ., Claremont, CA, USA, June 22-26, 1998. Berlin: Springer, 70-85 (2000; Zbl 0941.65003)].) In the paper under review two new ternary families of digital \((t,m,s)\)-nets with the following parameters are constructed: \((t,m,s)=(4r-4,4r,(3^{2r}+1)/2)\), \(r\geq 2\), \((t,m,s)=(2r-4,2r,(3^r-1)/2)\), \(r\geq 3\), \(r\) odd. The construction is based on a link between BCH-codes and \((t,m,s)\)-nets exhibited by the authors [Lect. Notes Stat. 127, 221-231 (1997; Zbl 0974.94027)].