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Here we show the source code and the output of the program used in the paper Classification of tight \(2s\)-designs with \(s \geq 2\).

## Mathematica code

We use Mathematica to prove three single variable real inequalities in Proposition 4.3, and calculate explicit upper bounds for \(v\) in Section 6 for each \(10 \leq s \leq 626\).

Source code

## C++ (MPI) code

We use C++ to search all integer triples \((s, x, y)\) in the region

- \(10 \leq s \leq 287\);
- \(1 \leq x \leq 15,000,000,000\);
- \(x + s + 2 \leq y \leq 2 x + 1\);

such that

- \(\alpha_{s, i} := {s \choose i} \frac{x^{\overline{i}}(x + 1)^{\overline{i}}}{y^{\overline{i}}}\) is an integer for each \(i \in \{1, 2, 3, 4, 5, 6\}\).

The Boost libraries are needed to compile the code. We use the 128 bits and 512 bits unsigned integer, and the timer.

MPI is used to make the program to run on multiple cores. Please compile the code using an MPI compatible compiler.

Source code

We run the program on a cluster using a total of 480 2.4GHz cores.

- There are \(125,095,478,214,252\) triples with integer \(\alpha_{s, 1}\).
- There are \(25,535,426\) triples with integer \(\alpha_{s, 1}\) and \(\alpha_{s, 2}\).
- There are \(2,742\) triples with integer \(\alpha_{s, 1}, \alpha_{s, 2}, \alpha_{s, 3}\).
- There are \(37\) triples with integer \(\alpha_{s, 1}, \dots, \alpha_{s, 4}\).
- There are \(9\) triples with integer \(\alpha_{s, 1}, \dots, \alpha_{s, 5}\).
- There are \(0\) triples with integer \(\alpha_{s, 1}, \dots, \alpha_{s, 6}\).

The raw output could be found below.

Output