MinT - Information on Result #598928

Information on Result #598928

There is no digital (6, 21, 26)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3²¹, 26, F₃, 15) (dual of [26, 5, 16]-code), but

constructionÂ Y1 [i] would yield
1. OA(3²⁰, 23, S₃, 15), but
  - the (dual) Plotkin bound shows that MÂ â‰¥ 31381 059609 / 8 > 3²⁰ [i]
2. linear OA(3⁵, 26, F₃, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,3)), but
  - discarding factors / shortening the dual code would yield linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), but
    - 20 is the largest size of a cap in PG(4,Â 3) [i]

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.