MinT - Information on Result #599708

Information on Result #599708

There is no digital (4, 19, 42)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5¹⁹, 42, F₅, 15) (dual of [42, 23, 16]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(5¹⁸, 23, F₅, 15) (dual of [23, 5, 16]-code), but
  - residual code [i] would yield OA(5³, 7, S₅, 3), but
    - bound for OAs with index unity [i]
2. OA(5²³, 42, S₅, 19), but
  - discarding factors would yield OA(5²³, 41, S₅, 19), but
    - the linear programming bound shows that MÂ â‰¥ 1431 381081 044673 919677 734375 / 117616 346784 > 5²³ [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

The following results depend on this result:

	Result		This result only	Method
1	No digital (4, 20, 42)-net over F₅	[i]		m-Reduction
2	No digital (4, 21, 42)-net over F₅	[i]
3	No digital (4, 22, 42)-net over F₅	[i]