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trac #16604: OA(20,416)
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@nathanncohen
nathanncohen committed Jul 12, 2014
1 parent 326ece4 commit a621220
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61 changes: 60 additions & 1 deletion src/sage/combinat/designs/database.py
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Expand Up @@ -69,6 +69,7 @@
:func:`OA(12,298) <OA_12_298>`,
:func:`OA(12,342) <OA_12_342>`,
:func:`OA(20,352) <OA_20_352>`,
:func:`OA(20,416) <OA_20_416>`,
:func:`OA(12,474) <OA_12_474>`,
:func:`OA(9,514) <OA_9_514>`,
:func:`OA(11,640) <OA_11_640>`,
Expand Down Expand Up @@ -2892,6 +2893,63 @@ def OA_20_352():

return _helper_function_when_n_is_prime_times_power_of_2(20,352,zip(*A),Y)

def OA_20_416():
r"""
Returns an OA(20,416)
Published by Julian R. Abel in [AbelThesis]_.
.. SEEALSO::
:func:`sage.combinat.designs.orthogonal_arrays.OA_from_quasi_difference_matrix`
EXAMPLES::
sage: from sage.combinat.designs.designs_pyx import is_orthogonal_array
sage: from sage.combinat.designs.database import OA_20_416
sage: OA = OA_20_416() # not tested (~35s)
sage: print is_orthogonal_array(OA,20,416,2) # not tested
True
The design is available from the general constructor::
sage: designs.orthogonal_array(20,416,existence=True)
True
"""
Z = None
A=[
[(0,Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (0 , Z), (1 , Z), (4 , Z), (9 , Z), (3 , Z), (12, Z)],
[(0,Z), (1 , Z), (2 ,18), (3 , 2), (4 ,20), (5 ,22), (6 ,11), (7 ,19), (8 , 0), (9 ,26), (10, Z), (11, 5), (12,27), (1 ,17), (0 ,30), (1 ,22), (4 ,29), (9 , 6), (3 ,19)],
[(0,Z), (2 , 4), (4 ,21), (6 ,10), (8 ,24), (10,13), (12, 7), (1 ,11), (3 ,29), (5 ,12), (7 ,21), (9 , 2), (11,11), (4 , 5), (1 ,11), (0 ,23), (1 ,13), (4 , 6), (9 ,15)],
[(0,Z), (3 , 4), (6 ,17), (9 ,20), (12,26), (2 , 2), (5 ,12), (8 ,29), (11, 1), (1 , Z), (4 ,15), (7 ,16), (10,27), (9 , 2), (4 , 7), (1 , 5), (0 ,23), (1 ,24), (4 , 8)],
[(0,Z), (4 , 4), (8 ,29), (12, 8), (3 , 3), (7 , 8), (11, 2), (2 ,17), (6 , 4), (10, 2), (1 ,21), (5 ,29), (9 ,20), (3 , 2), (9 , 1), (4 ,14), (1 ,21), (0 ,24), (1 ,28)],
[(0,Z), (5 , 4), (10,22), (2 ,18), (7 , 6), (12, 2), (4 ,18), (9 ,27), (1 ,15), (6 , Z), (11,20), (3 ,15), (8 , 9), (12, 9), (3 , 3), (9 ,13), (4 , 4), (1 , 7), (0 ,14)],
[(0,Z), (6 , Z), (12,23), (5 ,13), (11,11), (4 ,10), (10, 0), (3 , 4), (9 ,16), (2 ,28), (8 ,27), (1 , 1), (7 ,23), (10,17), (12, 9), (3 ,20), (9 ,16), (4 ,17), (1 ,26)],
[(0,Z), (7 , Z), (1 , 3), (8 ,13), (2 , 8), (9 , 9), (3 , 0), (10,26), (4 , 5), (11, 6), (5 ,22), (12, 1), (6 ,17), (10,10), (10, 5), (12,15), (3 ,25), (9 , Z), (4 , 4)],
[(0,Z), (8 , 4), (3 ,10), (11, 3), (6 ,17), (1 ,21), (9 ,18), (4 , 5), (12,27), (7 ,20), (2 ,16), (10,25), (5 ,22), (12,21), (10,25), (10,12), (12,28), (3 ,19), (9 ,29)],
[(0,Z), (9 , 4), (5 , 6), (1 ,16), (10, 4), (6 ,24), (2 ,14), (11,11), (7 , 2), (3 , 9), (12,30), (8 ,28), (4 , 2), (3 , 7), (12, 6), (10,17), (10, 2), (12,13), (3 ,26)],
[(0,Z), (10, 4), (7 ,11), (4 ,18), (1 ,23), (11,21), (8 ,28), (5 ,21), (2 ,29), (12,20), (9 , 0), (6 , 8), (3 , 6), (9 , 7), (3 ,12), (12, 5), (10, 1), (10,21), (12, 5)],
[(0,Z), (11, 4), (9 ,22), (7 ,11), (5 ,17), (3 , Z), (1 ,17), (12,25), (10,14), (8 ,18), (6 , 2), (4 ,17), (2 ,25), (4 ,29), (9 , 6), (3 , 2), (12, 8), (10,13), (10,14)],
[(0,Z), (12, Z), (11, 7), (10,26), (9 ,24), (8 , 4), (7 ,25), (6 , Z), (5 ,13), (4 , 9), (3 , 5), (2 ,19), (1 ,10), (1 ,26), (4 ,14), (9 , 7), (3 ,11), (12, 9), (10,20)],
[(0,Z), (5 , Z), (7 , 7), (6 ,27), (2 , 5), (8 , 1), (11,23), (11, Z), (8 ,23), (2 ,21), (6 ,20), (7 , 5), (5 , 6), (0 , 2), (2 ,12), (8 ,15), (5 ,22), (6 ,25), (11,10)],
[(0,Z), (6 , 4), (9 ,24), (9 ,18), (6 ,26), (0 ,26), (4 ,17), (5 ,24), (3 , 5), (11, 9), (3 ,15), (5 ,23), (4 ,22), (2 ,26), (0 , 8), (2 ,21), (8 ,25), (5 ,15), (6 , 8)],
[(0,Z), (7 , 4), (11,11), (12, 9), (10,10), (5 , 6), (10, 1), (12,24), (11, 6), (7 ,26), (0 , 8), (3 ,10), (3 ,29), (8 , 3), (2 ,24), (0 ,22), (2 ,13), (8 , 2), (5 , 0)],
[(0,Z), (8 , Z), (0 ,27), (2 , 0), (1 ,25), (10,21), (3 ,10), (6 ,20), (6 ,14), (3 , 1), (10, 3), (1 ,15), (2 ,14), (5 ,12), (8 ,11), (2 ,28), (0 ,15), (2 ,13), (8 ,22)],
[(0,Z), (9 , Z), (2 ,13), (5 ,11), (5 , 6), (2 ,24), (9 , 9), (0 ,14), (1 ,30), (12, 1), (7 ,15), (12,15), (1 , 5), (6 ,23), (5 , 9), (8 , 3), (2 ,27), (0 ,28), (2 ,12)],
[(0,Z), (10, Z), (4 ,18), (8 ,23), (9 ,27), (7 , 4), (2 , 2), (7 , Z), (9 ,10), (8 , 8), (4 , 0), (10,12), (0 ,21), (11,28), (6 ,15), (5 ,23), (8 , 5), (2 ,28), (0 , 7)],
[(0,Z), (11, Z), (6 , 7), (11,27), (0 , 0), (12,17), (8 ,11), (1 ,12), (4 ,22), (4 ,15), (1 ,16), (8 , 0), (12, 6), (7 ,16), (11,30), (6 ,21), (5 ,14), (8 ,17), (2 ,26)],
[(0,Z), (12, 4), (8 ,28), (1 ,22), (4 , 2), (4 ,15), (1 , 6), (8 ,12), (12,19), (0 ,21), (11, 2), (6 , 4), (11,19), (7 ,30), (7 ,11), (11,12), (6 ,20), (5 , 3), (8 , 7)],
[(0,Z), (0 , 4), (10,21), (4 , 4), (8 , 1), (9 , 6), (7 ,30), (2 , 4), (7 , 8), (9 ,30), (8 , 3), (4 ,22), (10, 3), (11,25), (7 , 1), (7 ,24), (11,20), (6 ,30), (5 , 4)],
[(0,Z), (1 , 4), (12,21), (7 , 3), (12, 2), (1 , 1), (0 , 6), (9 ,14), (2 ,19), (5 , 6), (5 ,12), (2 , 9), (9 , 9), (6 ,19), (11, Z), (7 , 4), (7 , 6), (11,29), (6 ,15)],
[(0,Z), (2 , Z), (1 ,22), (10, Z), (3 , 5), (6 ,30), (6 ,26), (3 , 1), (10,12), (1 ,16), (2 ,28), (0 ,20), (8 ,11), (5 ,29), (6 , 7), (11,21), (7 ,14), (7 , 8), (11,11)],
[(0,Z), (3 , Z), (3 , 4), (0 ,18), (7 , 2), (11,16), (12,28), (10, 4), (5 ,28), (10, 0), (12, 4), (11,10), (7 ,11), (8 ,17), (5 , 6), (6 ,16), (11, 4), (7 ,22), (7 ,28)],
[(0,Z), (4 , Z), (5 ,22), (3 ,18), (11, Z), (3 ,15), (5 , 1), (4 ,26), (0 ,10), (6 , 8), (9 , 9), (9 ,29), (6 , Z), (2 ,23), (8 ,28), (5 ,30), (6 , 8), (11,24), (7 ,16)]
]

Y = [None, 0, 1, 2, 18, 5, 11, 4, 13, 26, 25, 29, 24, 7, 20, 19, 9, 12, 15]

return _helper_function_when_n_is_prime_times_power_of_2(20,416,zip(*A),Y)

def OA_12_474():
r"""
Returns an OA(12,474)
Expand Down Expand Up @@ -3256,8 +3314,9 @@ def _helper_function_when_n_is_prime_times_power_of_2(k,n,A,Y):
298 : (12 , OA_12_298),
342 : (12 , OA_12_342),
352 : (20 , OA_20_352),
416 : (20 , OA_20_416),
474 : (12 , OA_12_474),
514 : (9 , OA_9_514),
514 : (9 , OA_9_514),
640 : (11 , OA_11_640),
796 : (10 , OA_10_796),
896 : (15 , OA_15_896),
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4 changes: 2 additions & 2 deletions src/sage/combinat/designs/latin_squares.py
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Expand Up @@ -43,7 +43,7 @@
340| 6 10 10 342 7 7 6 346 6 348 8 12 18 352 6 9 7 7 6 358
360| 7 360 6 7 7 7 6 366 15 15 7 15 7 372 7 15 7 13 7 378
380| 7 12 7 382 15 15 7 15 7 388 7 16 7 7 7 7 8 396 7 7
400| 15 400 7 15 11 8 7 15 7 408 7 13 8 12 10 9 15 15 7 418
400| 15 400 7 15 11 8 7 15 7 408 7 13 8 12 10 9 18 15 7 418
420| 7 420 7 15 7 16 6 7 7 7 6 430 15 432 6 15 6 18 7 438
440| 7 15 7 442 7 13 7 11 15 448 7 15 7 7 7 15 7 456 7 16
460| 7 460 7 462 15 15 7 466 8 8 7 15 7 15 10 18 7 15 6 478
Expand Down Expand Up @@ -81,7 +81,7 @@
340| -
360| - -
380| -
400| - -
400| -
420| -
440|
460|
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