MinT - Information on Result #599790

Information on Result #599790

There is no digital (7, 49, 66)-net over F₇, because extracting embedded orthogonal array would yield linear OA(7⁴⁹, 66, F₇, 42) (dual of [66, 17, 43]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(7⁴⁸, 52, F₇, 42) (dual of [52, 4, 43]-code), but
  - residual code [i] would yield linear OA(7⁶, 9, F₇, 6) (dual of [9, 3, 7]-code or 9-arc in PG(5,7)), but
    - bound for MDS codes [i]
2. OA(7¹⁷, 66, S₇, 14), but
  - discarding factors would yield OA(7¹⁷, 65, S₇, 14), but
    - the linear programming bound shows that MÂ â‰¥ 64 199960 422464 012484 678956 / 260754 952177 > 7¹⁷ [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.