References
- ADICEAM, F.—NESHARIM, E.—LUNNON, F.: On the t-adic Littlewood conjecture, Duke Math. J. 170 (2021), no. 10, 2371–2419.
- BECK, J.: A two-dimensional van Aardenne-Ehrenfest theorem in irregularities of distribution, Compositio Math. 72 (1989), no. 3, 269–339.
- BILYK, D.—LACEY, M.—VAGHARSHAKYAN, A.: On the small ball inequality in all dimensions, J. Funct. Anal. 254 (2008), no. 9, 2470–2502.
- CASSELS, J. W. S.: An Introduction to Diophantine Approximation. In: Facsimile reprint of the 1957 edition. Cambridge Tracts in Mathematics and Mathematical Physics, Vol. 45. Hafner Publishing Co., New York, 1972.
- DICK, J.—PILLICHSHAMMER, F.: Digital Nets and Sequences: Discrepancy Theory and Quasi–Monte Carlo Integration. Cambridge University Press, Cambridge, 2010.
- GARRETT, S.—ROBERTSON, S.: Counterexamples to the p(t)-adic Littlewood conjecture over small finite fields, Preprint, arXiv:2405.14454 [math. NT] (2024), https://doi.org/10.48550/arXiv.2405.14454.
- GÓMEZ-PÉREZ, D.—HOFER, R.—NIEDERREITER, H.: A general discrepancy bound for hybrid sequences nvolving Halton sequences, Unif. Distrib. Theory 8 (2013), no. 1, 31–45.
- HALTON, J.: On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals, Numer. Math. 2 (1960), 84–90.
- HOFER, R.: Halton-type sequences in rational bases in the ring of rational integers and in the ring of polynomials over a finite field, Math. Comput. Simulation 143 (2018), 78–88.
- HOFER, R.: Kronecker–Halton sequences in 𝔽p((X−1)), Finite Fields and Appl. 50 (2018), 154–177.
- KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences. In: Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1974.
- LACEY, M.—BILYK, D.: On the small ball inequality in three dimensions, Duke Math. J. 143 (2006), 81–115.
- LEVIN, MORDECHAY B.: On the lower bound of the discrepancy of Halton’s sequence I, I. C. R. Math. Acad. Sci. Paris 354 (2016), no. 5, 445–448.
- LEVIN, MORDECHAY B.: On the lower bound of the discrepancy of Halton’s sequence II, Eur. J. Math. 2 (2016), no. 3, 874-–885.
- LEVIN, MORDECHAY B.: On the lower bound of the discrepancy of (t, s) sequences: I, C. R. Math. Acad. Sci. Paris 354, (2016), no. 6, 562–565.
- LEVIN, MORDECHAY B.: On the lower bound of the discrepancy of (t, s) sequences: II, Online J. Anal. Comb. 12, (2017), Paper no. 3, 74 pp.
- LEVIN, MORDECHAY B.: On a bounded remainder set for a digital Kronecker sequence, J. Théor. Nombres Bordeaux 34 (2022), no. 1, 163–187.
- DE MATHAN, B.—TEULIÉ, O.: Problèmes diophantiens simultanés, Monatsh. Math. 143 (2004), 229–245.
- NIEDERREITER, H.: Random Number Generation and Quasi-Monte Carlo Methods. In: CBMS-NSF Regional Conference Series in Applied Mathematics Vol. 63, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.
- NIEDERREITER, H.: Recent constructions of low-discrepancy sequences, Math. Comput. Simulation 135 (2017), 18–27.
- ROBERTSON, S.: Combinatorics on number walls and the p(t)-adic Littlewood conjecture, DOI: 10.48550/arXiv.2307.00955 (2023).
- ROTH, K.: On irregularities of distribution, Mathematika 1 (1954), 73–79.
- SCHMIDT, WOLFGANG M.: Irregularities of distribution, VII, Acta Arith. 21 (1972), 45–50.
- SCHMIDT, WOLFGANG M.: Diophantine Approximation. In:Lecture Notes in Mathematics, Vol. 785, Springer-Verlag, Berlin, 1980.
- WEYL, H.: Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), no. 3, 313—52.