MinT - Information on Result #526563

Information on Result #526563

There is no linear OA(4¹³, 1599358, F₄, 3) (dual of [1599358, 1599345, 4]-code or 1599358-cap in PG(12,4)), because removing affine subspaces would yield

linear OA(4⁷, 632, F₄, 3) (dual of [632, 625, 4]-code or 632-cap in PG(6,4)), but
- 2 times Hill recurrence [i] would yield linear OA(4⁵, 42, F₄, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,4)), but
  - 41 is the largest size of a cap in PG(4,Â 4) [i]
1752-cap in AG(7,4), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4), but
  - bound on the size of affine caps [i]
6329-cap in AG(8,4), but
- 4 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
23085-cap in AG(9,4), but
- 5 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
84865-cap in AG(10,4), but
- 6 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
314041-cap in AG(11,4), but
- 7 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)
1168660-cap in AG(12,4), but
- 8 times the recursive bound from Bierbrauer and Edel [i] would yield 41-cap in AG(4,4) (see above)

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.