MinT - Information on Result #599778

Information on Result #599778

There is no digital (4, 7, 11393)-net over F₇, because extracting embedded orthogonal array would yield linear OA(7⁷, 11393, F₇, 3) (dual of [11393, 11386, 4]-code or 11393-cap in PG(6,7)), 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)

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.