This web page contains a table of values of S(n) where S(n) is the maximum number of ones that can be found in a symmetric (with respect to diagonal reflection) Golomb square. A Golomb square is a square Golomb Rectangle . Symmetric Golomb squares are easier to search for than general Golomb squares and are often as good. For more about this see my paper "Symmetric Golomb Squares" (IEEE Transactions on Information Theory, to appear).

Examples achieving these values can be found here .

n | S(n) | Number of Squares | Exhaustive Search Time |
---|---|---|---|

2 | 3 | 1 | .00 |

3 | 5 | 1 | .00 |

4 | 6 | 7 | .00 |

5 | 8 | 2 | .00 |

6 | 9 | 16 | .00 |

7 | 10 | 57 | .00 |

8 | 12 | 4 | .01 |

9 | 13 | 20 | .01 |

10 | 15 | 1 | .01 |

11 | 16 | 4 | .11 |

12 | 17 | 15 | .32 |

13 | 18 | 44 | 2.19 |

14 | 19 | 262 | 6.59 |

15 | 21 | 2 | 14.65 |

16 | 22 | 2 | 102.48 |

17 | 23 | 3 | 279.41 |

18 | 24 | 22 | 1967.53 |

19 | 25 | 59 | 5365.38 |

20 | 26 | 106 | 36796.94 |

21 | 27 | 254 | 96431.68 |

22 | 29 | 1 | 174610.01 |

**
[
IBM Research home page |
James B. Shearer's home page |
Up
]
[
IBM home page |
Order |
Search |
Contact IBM |
Legal
]
**