new OA for n=112,160,176,208,224,352,416,514,544,640,796,896

[nathanncohen]

As the title says.

Because this method also needs to shorten a matrix in the middle of OA_from_Vmt, it is split into QDM_from_Vmt and OA_from_quasi_difference_matrix (which was already called).

Nathann

Depends on #16582
Depends on #16797

CC: @videlec

Component: combinatorial designs

Author: Nathann Cohen

Branch/Commit: 24c4f7f

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/16604

[nathanncohen]

Branch: u/ncohen/16604

[sagetrac-git]

Commit: 00654fb

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

01689fd	trac #16582: MOLS: Table with n<600 and updated syntax
0c08a79	trac #16582: Merged with beta5
00654fb	trac #16604: new OA for n=112,160,224,514,796

[videlec]

comment:3

Hey Nathann,

In OA_14_124, it is not safe to ask for a finite field of size 2⁵ and hope that, by chance, its generator satisfies w^5 + w^2 + 1 = 0. You would rather give the constructor an explicit polynomial:

sage: R = PolynomialRing(GF(2),'x')
sage: x = R.gen()
sage: GF(2**5, 'w', modulus=x**5+x**2+1)
Finite Field in w of size 2^5

and I got a docbuild error

OSError: [combinat ] None:5: WARNING: citation not found: BvR514

Vincent

[nathanncohen]

comment:4

Yo !

In OA_14_124, it is not safe to ask for a finite field of size 2⁵ and hope that, by chance, its generator satisfies w^5 + w^2 + 1 = 0.

Yeah... And "by chance" it always works ?

Given that you are the one to complain about this, I will use the first's trick against you : conway=True :-P

and I got a docbuild error

OSError: [combinat ] None:5: WARNING: citation not found: BvR514

Ahahahah. I must have replaced 82 with 514 at some point :-D

I had also "made a small mistake" in the implementation. I had forgotten to set some flag from "False" to "True", which means that the new OA have a longer width. I didn't like to notice that I had implemented so many new OA and that they did not even reach the Handbook's bound.... Now all is good :-P

I also added an OA for 640, freshly debugged.

Nathann