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README.md

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-## Lattice Generating Vectors
+# LDData: Low-Discrepancy Generating Vectors and Matrices
+
+A curated collection of **low-discrepancy point set parameters** including **lattice rules**, **digital nets**, **polynomial lattice rules**, **Sobol' nets**, and **RQMC randomizations**.  This dataset enables reproducible research and high-performance Quasi–Monte Carlo (QMC) and Randomized QMC (RQMC) simulation.
+
+The [LDData repository](https://github.com/QMCSoftware/LDData) provides **standard text-based formats** for specifying structures used in QMC point generation across arbitrarily high dimensions.
+
+---
+
+## Dataset Summary
+
+LDData is a dataset of structured parameter files defining:
+
+- Rank-1 **lattice rules**
+- Base-$b$ **digital nets**
+- **Polynomial lattice rules**
+- **Sobol' and Sobol–Joe-Kuo sequences**
+- Various **randomizations** (shift modulo 1, digital shifts, nested uniform
+  scrambles, left matrix scrambles)
+
+Each file type follows a simple textual standard to ensure:
+- Human readability  
+- Language-agnostic parsing  
+- Long-term reproducibility  
+- Extensibility to thousands of dimensions  
+
+The dataset is motivated by the need for **standardized, compact, transparent formats** in [our QMC research and software](https://github.com/QMCSoftware).
+
+---
+
+## Motivation
+
+Many QMC constructions appear across scattered software packages, papers, or custom formats. LDData brings these formats together into a **consistent, unified, machine-readable** repository for:
+
+- Researchers developing new QMC methods  
+- Practitioners needing high-dimensional low-discrepancy point sets  
+- Developers of simulation libraries such as SSJ, QMCPy, and LatNet Builder  
+
+This dataset is linked to the research works described in the Citation section below. **For detailed technical specifications and implementation details**, see
+[LD_DATA.md](LD_DATA.md)
+
+---
+
+## Supported Tasks and Applications
+
+### ✔️ Quasi-Monte Carlo (QMC)
+Generate deterministic point sets with excellent equidistribution.
+
+### ✔️ Randomized QMC (RQMC)
+Use the included randomizations for variance estimation:
+- Digital shifts  
+- Nested uniform scrambles  
+- Left-matrix scrambles  
+
+### ✔️ High-dimensional Integration and Simulation
+
+Used in:
+- Bayesian computation  
+- Option pricing
+- High-dimensional PDE solvers  
+- Uncertainty quantification  
+- Graphics and rendering research  
+- Machine learning sampling methods  
+
+### ✔️ Benchmarking
+Standard formats help evaluate new constructions against established ones.
+
+---
+
+## Features
+
+- Simple `.txt` formats with **one line per dimension**
+- Optional human-readable comments starting with `#`
+- No binary encoding or word-size assumptions
+- Supports extremely high dimensions (10,000+)
+- Extensible constructions (e.g., Sobol or embedded nets)
+- All formats interoperable with QMC software (SSJ, QMCPy, LatNet Builder)
+
+---
+
+## How to Use the Dataset
+
+### Load files directly from Hugging Face
+
+```python
+from datasets import load_dataset
+
+ds = load_dataset("QMCSoftware/LDData")
+```
+
+All data files are preserved in their directory structure and can be accessed
+using:
+
+```python
+ds["train"]  # or ds['default']
+```
+
+### Typical workflow
+
+1. Read a parameter file (e.g. `lattice_8d.txt`)
+2. Parse header (`# lattice`, dimensions, n, etc.)
+3. Parse one line per dimension for the generating vector or matrices
+4. Construct QMC point generator in your preferred library
+
+---
+
+## Dataset Structure
+
+The dataset includes multiple categories of files:
+
+### 🔹 `lattice`  
+Rank-1 lattice generating vectors:  
+- Header: `# lattice`  
+- Parameters:  
+  - Number of dimensions `s`  
+  - Number of points `n`  
+  - `s` lines of generating vector coefficients  
+
+---
+
+### 🔹 `dnet`  
+General digital nets in base `b`:  
+- Header: `# dnet`  
+- Parameters:  
+  - Base `b`  
+  - Dimensions `s`  
+  - Columns `k`  
+  - Rows `r`  
+- Then `s` lines representing generating matrices
+
+Efficient for high-dimensional digital nets.
+
+---
+
+### 🔹 `plattice`  
+Polynomial lattice rules:  
+- Compact format using integer-encoded polynomials  
+- Base `b`, dimension `s`, polynomial degree `k`, and generating polynomials
+
+---
+
+### 🔹 `sobol` and `soboljk`  
+Parameters for Sobol' sequences:  
+- `soboljk`: Joe & Kuo format with primitive polynomials and direction numbers  
+- `sobol`: Simplified direction-number only format  
+
+Used widely in QMC applications.
+
+---
+
+### 🔹 Randomization formats
+
+Includes:
+
+- `shiftmod1`: Shift modulo 1  
+- `dshift`: Digital shift in base `b`  
+- `nuscramble`: Nested uniform scramble  
+- `lmscramble`: Left matrix scramble  
+
+All formats are text-based and reproducible.
+
+---
+
+## Example: Parsing a Lattice Rule File
+
+Example file:
+
+```
+# lattice
+8
+65536
+1 
+19463
+17213
+5895
+14865
+31925
+30921
+26671
+```
+
+Python pseudo-code:
+
+```python
+with open("lattice_8d.txt") as f:
+    lines = [l for l in f.readlines() if not l.startswith("#")]
+
+s = int(lines[0])
+n = int(lines[1])
+a = [int(x) for x in lines[2:2+s]]
+```
+
+---
+
+## File Naming Recommendations
+
+To support discoverability and consistent tooling:
+
+- All files begin with their keyword (`lattice_`, `dnet_`, `sobol_`, etc.)
+- Headers contain:
+  - Construction method  
+  - Figure of merit (FOM)  
+  - Weights  
+  - Embedded range (if applicable)  
+- Comments allowed in headers only  
+
+---
+
+## References
+
+This dataset incorporates formats and ideas from foundational work in QMC:
+
+- Bratley & Fox (1988)  
+- Joe & Kuo (2008)  
+- L’Ecuyer (2016)  
+- Goda & Dick (2015)  
+- Nuyens (2020)  
+- And others listed in the detailed specification [LD_DATA.md](LD_DATA.md).
+
+---
+
+## Citation
+
+If you use LDData in academic work, please cite:
+
+```
+@article{sorokin.2025.ld_randomizations_ho_nets_fast_kernel_mats,
+  title               = {{QMCPy}: a {P}ython software for randomized low-discrepancy sequences, quasi-{M}onte {C}arlo, and fast kernel methods},
+  author              = {Aleksei G. Sorokin},
+  year                = {2025},
+  journal             = {ArXiv preprint},
+  volume              = {abs/2502.14256},
+  url                 = {https://arxiv.org/abs/2502.14256},
+}
+
+
+@inproceedings{choi.QMC_software,
+  title               = {Quasi-{M}onte {C}arlo software},
+  author              = {Choi, Sou-Cheng T. and Hickernell, Fred J. and Rathinavel, Jagadeeswaran and McCourt, Michael J. and Sorokin, Aleksei G.},
+  year                = {2022},
+  booktitle           = {{M}onte {C}arlo and Quasi-{M}onte {C}arlo Methods 2020},
+  publisher           = {Springer International Publishing},
+  address             = {Cham},
+  pages               = {23--47},
+  isbn                = {978-3-030-98319-2},
+  editor              = {Keller, Alexander},
+}
+```
+
+---
+
+## License
+
+Apache 2 License.  
+See [`LICENSE`](LICENSE.txt) file for details.
+
+---
+
+## Acknowledgements
+
+This dataset is developed and maintained by:
+
+- **QMCSoftware team**  
+- Contributors to QMCPy, SSJ, and LatNet Builder  
+- Community contributions from QMC & RQMC researchers
+
+Special thanks to researchers providing widely used generating vectors and direction numbers used throughout the scientific computing community.