// n: expected insertions
  // b: m/n, bits per insertion
  // p: expected false positive probability
  //
  // 1) Optimal k = b * ln2
  // 2) p = (1 - e ^ (-kn/m))^k
  // 3) For optimal k: p = 2 ^ (-k) ~= 0.6185^b
  // 4) For optimal k: m = -nlnp / ((ln2) ^ 2)

  /**
   * Computes the optimal number of hash functions (k) for a given false positive probability (p).
   *

### Expanding existing distributed setup

MinIO supports expanding distributed erasure coded clusters by specifying new set of clusters on the command-line as shown below:

```sh

alias kv-pairify='yq ".configuration[]" | jq ".[]" | jq -r ".name + \"=\" + .value"'
```

Let's take for example a set of 12 compute nodes with an aggregate memory of _1.2TiB_, we need to do following settings for optimal results. Add the following optimal entries for _core-site.xml_ to configure _s3a_ with **MinIO**. Most important options here are

```
cat ${HADOOP_CONF_DIR}/core-site.xml | kv-pairify | grep "mapred"

final class SingletonImmutableSet<E> extends ImmutableSet<E> {
  // We deliberately avoid caching the asList and hashCode here, to ensure that with
  // compressed oops, a SingletonImmutableSet packs all the way down to the optimal 16 bytes.

  final transient E element;

  SingletonImmutableSet(E element) {
    this.element = Preconditions.checkNotNull(element);
  }

  @Override
  public int size() {
    return 1;
  }

# MinIO Server Limits Per Tenant

For optimal production setup MinIO recommends Linux kernel version 4.x and later.

## Erasure Code (Multiple Drives / Servers)

| Item                                                            | Specification |
|:----------------------------------------------------------------|:--------------|
| Maximum number of servers per cluster                           | no-limit      |

type endpointSet struct {
	argPatterns []ellipses.ArgPattern
	endpoints   []string   // Endpoints saved from previous GetEndpoints().
	setIndexes  [][]uint64 // All the sets.
}

// Supported set sizes this is used to find the optimal
// single set size.
var setSizes = []uint64{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

// getDivisibleSize - returns a greatest common divisor of
// all the ellipses sizes.

    tester.testAllPublicInstanceMethods(BloomFilter.create(Funnels.unencodedCharsFunnel(), 100));
    tester.testAllPublicStaticMethods(BloomFilter.class);
  }

  /** Tests that we never get an optimal hashes number of zero. */
  public void testOptimalHashes() {
    for (int n = 1; n < 1000; n++) {
      for (double p = 0.1; p > 1e-10; p /= 10) {

list_quorum                     (string)    set the acceptable quorum expected for list operations e.g. "optimal", "reduced", "disk", "strict", "auto" (default: 'strict')
replication_priority            (string)    set replication priority (default: 'auto')

    tester.testAllPublicInstanceMethods(BloomFilter.create(Funnels.unencodedCharsFunnel(), 100));
    tester.testAllPublicStaticMethods(BloomFilter.class);
  }

  /** Tests that we never get an optimal hashes number of zero. */
  public void testOptimalHashes() {
    for (int n = 1; n < 1000; n++) {
      for (double p = 0.1; p > 1e-10; p /= 10) {

Or you might have any other way to communicate with the WebSocket endpoint.

---

But for this example, we'll use a very simple HTML document with some JavaScript, all inside a long string.

This, of course, is not optimal and you wouldn't use it for production.

In production you would have one of the options above.

But it's the simplest way to focus on the server-side of WebSockets and have a working example: