# Rank of 6x8 Binary Matrices Test

#### Test Purpose

The test evaluates the randomness of the 8-bit groups of 6 sequential random numbers of the integer output. The stable response is the rank of the binary matrix composed of the random numbers. The test checks all possible 8-bit groups: 0-7, 1-8, ...

# Count-the-1's Test (Stream of Bits)

#### Test Purpose

The test evaluates the randomness of the overlapping random five-letter words sequence. The five-letter words have the specified distribution of the probabilities of obtaining the specified letter. The test forms the random letters from the integer output of a BRNG. The test treats the integer output as a sequence of bits.

# Count-the-1's Test (Stream of Specific Bytes)

#### Test Purpose

The test evaluates the randomness of the overlapping random five-letter words sequence. The five-letter words have the specified distribution of the probabilities of obtaining the specified letter. The test forms the random letters from the integer output of a BRNG. The test selects only 8 sequential bits from each element, starting with a certain fixed bit s.

# Craps Test

#### Test Purpose

The test evaluates the randomness of the output sequence of random numbers of the uniform distribution that imitates the process of dice tossing when gambling Craps. The stable response is the number of tosses of the pair of dice necessary to complete the game and the frequency of wins in the game.

# Parking Lot Test

#### Test Purpose

The test evaluates the randomness of two-dimensional random points uniformly distributed in the square with a side of length 100. The stable response is the number of successfully ”parked” points from the 12,000 random two-dimensional points.

# 2D Self-Avoiding Random Walk Test

#### Test Purpose

The test evaluates the randomness of the output vector of the generator. The stable response is the frequency of achieving the upper side of the lattice by the point walking randomly along the sites.

# Basic Random Generator Properties and Testing Results

This section contains the empirical testing results for the VSL BRNGs described in the BRNG Tests Description section and other information on the properties of BRNGs and the rules of the output vector interpretation.

# MCG31m1

This is a 31-bit multiplicative congruential generator:

# R250

This is a generalized feedback shift register generator: