- 1.
**Random**. The generated sequence should have as much the appearance of randomness as is possible, and as many of the statistical properties as are required of it; e.g., independence, stationarity, distribution characteristics, &c. Since the generator will, in fact, be deterministic, it should be simple enough that its shortcomings are well-known. In the case of linear congruential sequences, for example, it is their periodicity and Marsaglia's complaint that*points lie mainly in the planes*.- 2.
**Repeatable**. Although we seek to model indeterminate effects, our schemes must not themselves involve indeterminacy. Reproducibility is of the essence in any scientific experiment.- 3.
**Portable**. In the case of integer sequences, we can insist on identity of results across platforms. For floating-point sequences this is impractical, but individual numbers should differ by no more than round-off dictates.- 4.
**Fast**. All the schemes I have in mind are now so fast that speed is no longer an issue. The only problem might be with real-time generators for VHF acoustic signals in laboratory work with rock samples.

11/18/1997