1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
翁志文 (Dep. of A. Math., NCTU) Pooling design and its construction December 6, 2009 17 / 36
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
翁志文 (Dep. of A. Math., NCTU) Pooling design and its construction December 6, 2009 17 / 36
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
翁志文 (Dep. of A. Math., NCTU) Pooling design and its construction December 6, 2009 17 / 36
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
翁志文 (Dep. of A. Math., NCTU) Pooling design and its construction December 6, 2009 17 / 36
2009年數學學術研討會暨中華民國數學會年會
Affine plane and projective plane
1 In general for any positive integer r , prime power or not, we can define affine plane using the language of designs.
2 Aprojective plane of order r is a 2-(r2+ r + 1, r + 1, 1) design.
3 An affine plane of order r is a 2-(r2, r , 1) design.
4 It is known that there is a projective plane of order r if and only if there is an affine plane of order r .
5 The points and lines structure in Fq2 gives an affine plane of order q when q is a prime power.
6 The existence of finite projective planes of other orders is an open question.
7 The case r = 6 has been ruled out by Bruck-Ryser-Chowla theorem.
8 The next case r = 10 has been ruled out by massive computer calculations.
9 There is nothing more known, in particular r = 12 is still open.
2009年數學學術研討會暨中華民國數學會年會