MinT - Information on Result #599785

Information on Result #599785

There is no digital (6, 9, 483576)-net over F₇, because extracting embedded orthogonal array would yield linear OA(7⁹, 483576, F₇, 3) (dual of [483576, 483567, 4]-code or 483576-cap in PG(8,7)), but

removing affine subspaces [i] would yield
1. linear OA(7⁶, 1659, F₇, 3) (dual of [1659, 1653, 4]-code or 1659-cap in PG(5,7)), but
  - 1 times Hill recurrence [i] would yield linear OA(7⁵, 239, F₇, 3) (dual of [239, 234, 4]-code or 239-cap in PG(4,7)), but
    - a result by Edel, Storme, and Sziklai [i]
2. 9735-cap in AG(6,7), but
  - 2 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7), but
    - embedding in projective space [i] would yield linear OA(7⁵, 239, F₇, 3) (dual of [239, 234, 4]-code or 239-cap in PG(4,7)) (see above)
3. 62933-cap in AG(7,7), but
  - 3 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7) (see above)
4. 409252-cap in AG(8,7), but
  - 4 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7) (see above)

Mode: Bound (linear).

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.