Quasi-Random Monte Carlo means deterministic sequences or points. They are usually chosen because they have a lower discrepancy than "randomly" chosen points. Paskov and Papageorgiou [#!kn:PakovPapageorgiouCUCS1996!#] review the history of applying Quasi-Random Monte Carlo (QRMC) to high-dimensional problems in finance. The text by Niederreiter [#!kn:Niederreiter1992!#] is one of the classic texts on QRMC and is the basis of most of the theorems presented later.
Some recent applications of QRMC have been made by Boyle, Broadie and Glasserman [#!kn:BoyleBroadieGlassermanJEDC1997!#] and Boyle and Tan [#!kn:BoyleTanJEDC2000!#].