// 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"

	maxPartsCount             = 10000
	maxPartSize               = 1024 * 1024 * 1024 * 5
	minPartSize               = 1024 * 1024 * 128 // chosen by us to be optimal for HDDs
)

// optimalPartInfo - calculate the optimal part info for a given
// object size.
//
// NOTE: Assumption here is that for any object to be uploaded to any S3 compatible
// object storage it will have the following parameters as constants.

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;
  }

			Optional:    true,
			Type:        "duration",
		},
		config.HelpKV{
			Key:         apiListQuorum,
			Description: `set the acceptable quorum expected for list operations e.g. "optimal", "reduced", "disk", "strict", "auto"` + defaultHelpPostfix(apiListQuorum),
			Optional:    true,
			Type:        "string",
		},
		config.HelpKV{
			Key:         apiReplicationPriority,

Example: Limit a MinIO cluster to accept at max 1600 simultaneous S3 API requests across all nodes of the cluster.

```sh
export MINIO_API_REQUESTS_MAX=1600

# 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      |

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;
  }

---

Für dieses Beispiel verwenden wir jedoch ein sehr einfaches HTML-Dokument mit etwas JavaScript, alles in einem langen String.

Das ist natürlich nicht optimal und man würde das nicht in der Produktion machen.

In der Produktion hätten Sie eine der oben genannten Optionen.